Mathematics (Linear) 1MA0 READING SCALES...Young Person’s RAILCARD off normal price Lisa uses her railcard to buy a ticket. She gets off the normal price of the ticket. The normal

Edexcel GCSE Mathematics (Linear) – 1MA0

READING SCALES

Materials required for examination Items included with question papers

Ruler graduated in centimetres and Nil

millimetres, protractor, compasses,

pen, HB pencil, eraser.

Tracing paper may be used.

Instructions

Use black ink or ball-point pen.

Fill in the boxes at the top of this page with your name, centre number and candidate number.

Answer all questions.

Answer the questions in the spaces provided – there may be more space than you need.

Calculators may be used.

Information

The marks for each question are shown in brackets – use this as a guide as to how much time to

spend on each question.

Questions labelled with an asterisk (*) are ones where the quality of your written communication

will be assessed – you should take particular care on these questions with your spelling, punctuation

and grammar, as well as the clarity of expression.

Advice

Read each question carefully before you start to answer it.

Keep an eye on the time.

Try to answer every question.

Check your answers if you have time at the end.

1.

(a) Write down the number marked with an arrow.

.................................

(1)

(b) Write down the number marked with an arrow.

.................................

(1)

(c) Find the number 430 on the number line.

Mark it with an arrow ( ↑ ).

(1)

(d) Find the number 3.7 on the number line.

Mark it with an arrow ( ↑ ).

(1)

(Total 4 marks)

20 30 40 50

2 3 4 5

200 300 400 500

2 3 4 5

2.


……………………..

(1)

(b) Write down the number marked with an arrow.

……………………..

(1)

(c) Find the number 48 on the number line

(Mark it with an arrow (↑).

(1)


Mark it with arrow (↑).

(1)

(Total 4 marks)

500 600 700

6 7 8

30 40 50

6 7 8

3.

(a) Write down the number marked by the arrow.

………………………

(1)

(b) Write down the number marked by the arrow.

………………………

(1)

(c) Find the number 460 on the number line.

Mark it with an arrow ( ).

(1)


Mark it with an arrow ( ).

(1)

(Total 4 marks)

0 10 20 30 40 50 60

0 1 2 3 4 5 6

0 100 200 300 400 500 600

0 1 2 3 4 5 6

4.

(a) Write down the temperature shown on the thermometer.

................... °C

(1)

The temperature falls by 8°C.

(b) Work out the new temperature.

................... °C

(1)

(Total 2 marks)

20

15

10

5

0

–5

–10

°C

5.

(a) Write down the number marked by the arrow.

………………...

(1)

(b) Find the number 530 on the number line.

Mark it with an arrow (↑).

(1)

(c) Put these numbers in order of size.

Start with the smallest.

52 31 1007 180

………………….………………...

(1)

(Total 3 marks)

6.


………………..

(1)

(b) Find the number 6.7 on the number line.

Mark it with an arrow ().

………………..

(1)

50 60 70 80 90

300 400 500 600 700 800

7.

(i) Write down the reading shown on the scale.

.......................... kg

(ii) Change 5.7 kg to grams.

.......................... g

(Total 2 marks)

8.

(a) Write down the time shown on the clock.

……………..

(1)

(b) Write down the reading shown by the arrow ().

…………………..

(1)

(Total 2 marks)

1211 1

10 2

9 3

8 4

7 56

0 10 20 30 40 50


NEGATIVE NUMBERS






Instructions






Information






Advice





1. Here is a map of the British Isles.

The temperatures in some places, one night last winter are shown on the map.

(a) (i) Write down the names of the two places that had the biggest difference in

temperature.

..........................................................................................................

(ii) Work out the difference in temperature between these two places.

............................°C

(3)

(b) Two pairs of places have a difference in temperature of 2 °C.

Write down the names of these places.

(i) ................................................ and ................................................

(ii) ................................................ and ................................................

(2)

(Total 5 marks)

2.

(a) Write down the temperature shown on the thermometer.

................... °C

(1)

The temperature falls by 8°C.

(b) Work out the new temperature.

................... °C

(1)

(Total 2 marks)

20

15

10

5

0

–5

–10

°C

3. Sally wrote down the temperature at different times on 1st January 2003.

Time Temperature

midnight – 6 °C

4 am –10 °C

8 am – 4 °C

noon 7 °C

3 pm 6 °C

7 pm –2 °C

(a) Write down

(i) the highest temperature,

.......................°C

(ii) the lowest temperature.

(2)

(b) Work out the difference in the temperature between

(i) 4 am and 8 am,

.......................°C

(ii) 3 pm and 7 pm.

.......................°C

(2)

At 11 pm that day the temperature had fallen by 5 °C from its value at 7 pm.

(c) Work out the temperature at 11 pm.

.......................°C

(1)

(Total 5 marks)

4. The table shows the temperature on the surface of each of five planets.

Planet Temperature

Venus 480 °C

Mars – 60 °C

Jupiter – 150 °C

Saturn – 180 °C

Uranus – 210 °C

(a) Work out the difference in temperature between Mars and Jupiter.

…………………°C

(1)

(b) Work out the difference in temperature between Venus and Mars.

…………………°C

(1)

(c) Which planet has a temperature 30 °C higher than the temperature on Saturn?

…………………….

(1)

The temperature on Pluto is 20 °C lower than the temperature on Uranus.

(d) Work out the temperature on Pluto.

…………………°C

(1)

(Total 4 marks)

5. The table shows temperatures at midnight and midday on one day in five cities.

City Midnight

temperature

Midday

temperature

Belfast −3 °C 4 °C

Cambridge −1 °C 4 °C

Edinburgh −7 °C −1 °C

Leeds −6 °C 3 °C

London −2 °C 6 °C

(a) Which city had the lowest midnight temperature?

........................................

(1)

(b) How many degrees higher was the midnight temperature in Cambridge than the

midnight temperature in Leeds?

........................ °C

(1)

(c) Which city had the greatest rise in temperature from midnight to midday?

........................................

(1)

(Total 3 marks)

6. The table shows the temperatures in four cities at noon one day.

Oslo −13°C

New York −5°C

Cape Town 9°C

London 2°C

(a) Write down the highest temperature.

...................... °C

(1)

(b) Work out the difference in temperature between Oslo and New York.

...................... °C

(1)

At 8 pm the temperature in London was 3°C lower than the temperature at noon.

(c) Work out the temperature in London at 8 pm.

...................... °C

(1)

(Total 3 marks)

7. The table shows the midday temperatures in 4 different cities on Monday.

City Midday temperature (°C)

Belfast 5

Cardiff –1

Glasgow –6

London –4

(a) Which city had the lowest temperature?

………………...

(1)

(b) Work out the difference between the temperature in Cardiff and the temperature in

Belfast.

………………... C

(1)

By Tuesday, the midday temperature in London had risen by 7 °C.

(c) Work out the midday temperature in London on Tuesday.

………………... C

(1)

(Total 3 marks)

8. The table shows the temperature in each of 6 cities on 1st January 2003.

City Temperature

Cairo 15 C

Copenhagen 1 C

Helsinki 9 C

Manchester 3 C

Moscow 14 C

Sydney 20 C

(a) Write down the name of the city which had the lowest temperature.

……………………………

(1)

(b) Work out the difference in temperature between Copenhagen and Cairo.

…………………………C

(1)

On 2nd January 2003, the temperature in Moscow had increased by 4 C.

(c) Work out the new temperature in Moscow.

…………………………C

(1)

(Total 3 marks)


FRACTIONS






Instructions






Information






Advice





1. A school has 1200 pupils.

575 of these pupils are girls.

of the girls like sport.

of the boys like sport.

Work out the total number of pupils in the school who like sport.

……………………………..

(Total 3 marks)

5

2

5

3

2. A train travels from London to Manchester.

It leaves London at 16 55

It arrives in Manchester at 19 45

(a) Work out the number of minutes this train takes to travel from London

to Manchester.

………………………

(3)

There are 800 people on the train at Manchester.

of these 800 people are children.

(b) (i) Work out of 800

………………………

of those 800 people are women.

(ii) Work out of 800

………………………

The rest of the 800 people are men.

(iii) Work out the number of men on the train.

………………………

(4)

320 of the 800 people are under 21 years old.

(c) Work out 320 out of 800 as a percentage.

………………………%

(2)

(Total 9 marks)

10

1

10

1

8

3

8

3

3. Danny shares a bag of 20 sweets with his friends.

He gives Mary of the sweets.

He gives Ann of the sweets.

He keeps the rest for himself.

How many sweets does Danny keep for himself?

………………………

(Total 3 marks)

4. A class has 29 students.

16 of the students are girls.

What fraction of the students are boys?

.........................

(Total 2 marks)

5

3

10

1

5. A box contains 200 tissues.

Toby takes of these tissues.

Work out how many tissues he takes.

.....................................

(Total 2 marks)

6.

Young Person’s RAILCARD

off normal price

Lisa uses her railcard to buy a ticket.

She gets off the normal price of the ticket.

The normal price of the ticket is £24.90

Work out how much Lisa pays for the ticket.

£ ..................................

(Total 3 marks)

5

3

200

3

1

3

1

7. There are 30 students in a class.

20 of these students are female.

Find the fraction of the class that is female.

Give your answer in its simplest form.

………………..

(Total 2 marks)

8. In a shop the normal price of a jacket is £60

The cost of the jacket in a sale is of the normal price.

(a) Work out of £60

£…………..

(2)

Darren has to travel mile to the shop.

(b) Write as a decimal.

………………

(2)

(Total 4 marks)

4

3

4

3

8

1

8

1

9. (a) Work out 4

1 of £24

..................................

(1)

(b) Work out 10% of 400 kg.

................................ kg

(1)

(Total 3 marks)

10. There are 24 men in a room.

2

1 of the men are wearing a red shirt.

3

1 of the men are wearing a green shirt.

The rest of the men are wearing a blue shirt.

Work out the number of men wearing a blue shirt.

.............................................

(Total 3 marks)


POWERS AND

SQUAREROOTS






Instructions






Information






Advice





1. Write down the value of

(i) 23

……………………………

(ii)

……………………………

(Total 2 marks)

2. (a) Work out the square of 3

.....................................

(1)

(b) Work out the value of 26

.....................................

(1)

(Total 2 marks)

81

3. (a) Work out the value of

(i) 42

...……………

(ii) 53

…...……………

(2)

(b) Write as a power of 10

10 × 10 × 10 × 10 × 10

…..……………

(1)

(Total 3 marks)

4. Find the value of

(i) the square root of 36

.............................

(ii) 5 × 102

.............................

(iii) 23

.............................

(Total 3 marks)

5. (a) Find the square of 6

...................................

(1)

(b) Find the square root of 225

...................................

(1)

(c) Find the value of 103

...................................

(1)

(Total 3 marks)


(i) 33

……………………………

(ii)

……………………………

(Total 2 marks)

7. (a) Work out the square of 8

.....................................

(1)

(b) Work out the value of 53

.....................................

(1)

(Total 2 marks)


(i) 72

...……………

(ii) 24

…...……………

(2)

(b) Write as a power of 10

10 × 10 × 10 × 10 × 10× 10 × 10

…..……………

(1)

(Total 3 marks)


(i) the square root of 25

.............................

(ii) 3 × 104

.............................

(iii) 43

.............................

(Total 3 marks)

10. (a) Find the square of 7

...................................

(1)

(b) Find the square root of 196

...................................

(1)

(c) Find the value of 105

...................................

(1)

(Total 3 marks)

WORK OUT THE FOLLOWING:

12

22

32

42

52

62

72

82

92

102

112

122

132

142

152


FRACTIONS,

DECIMALS AND

PERCENTAGES Materials required for examination Items included with question papers





Instructions






Information






Advice





1. (a) Write as a percentage.

…………………%

(1)

(b) Write 0.23 as a percentage.

…………………%

(1)

(c) Write 42% as a fraction.


…………………

(2)

(Total 4 marks)

2. (a) Write 0.15 as a percentage.

................................. %

(1)

(b) Write 35% as a fraction.


.................................

(2)

(Total 3 marks)

3. (a) Work out 50% of £60

£ ........................................

(1)

(b) Work out 25% of 20 metres.

........................................ metres

(1)

(Total 2 marks)

4

1

4. (a) Write as a decimal.

..................................

(1)

(b) Write as a percentage.

............................. %

(1)


..................................

(1)

(d) Work out of 50

..................................

(1)

(Total 4 marks)


…………………………… %

(1)


………………………… %

(1)

(Total 2 marks)

10

9

4

3

5

1

5

1

6. (a) (i) Write as a percentage.

.....................................%

(ii) Write 0.8 as a percentage.

.....................................%

(2)

(b) Write 76% as a decimal.

.....................................

(1)



.....................................

(2)

(Total 5 marks)


............................ %

(1)


............................ %

(1)

(c) Write 60% as a decimal.

................................

(1)

(Total 3 marks)


.............................. %

(1)


.............................. %

(1)


.................................

(1)

4

1

10

1

4

1

(d) Write 40 as a fraction of 140

Give your fraction in its simplest form.

..............................

(2)

(Total 5 marks)


……………………………%

(1)


……………………………%

(1)

(c) Write 30% as a fraction in its simplest form.

……………………………

(2)

(Total 4 marks)

10. (a) Write

(i) as a decimal,

………………………cm

(ii) as a percentage.

………………………cm

(Total 2 marks)


................................ %

(1)


................................ %

(1)

(c) Write 70% as a decimal.

................................

(1)

(Total 3 marks)

4

3

10

1

5

1


………………… %

(1)


………………… %

(1)

(Total 2 marks)

13. (a) Shade of this shape.

(1)

(b) Shade 0.25 of this shape.

(1)

-(c) Change 0.3 into a fraction.

.....................................

(1)

(d) Change 0.7 into a percentage.

................................... %

(1)

(e) Work out of £36

£ ...................................

(2)

(Total 6 marks)

10

3

4

3

4

3

14. (a) Write 92% as a decimal.

....................................

(1)

(b) Write 3% as a fraction.

....................................

(1)

(c) Work out 5% of 400 grams.

............................................ grams

(2)

(Total 4 marks)

15. Nassim buys petrol from his local garage.

On Monday, he filled up his tank.

On Tuesday, his tank was full.

(a) What fraction of the full tank of petrol had he used?

.....................................

(1)

(b) Write as a decimal.

.....................................

(1)

(c) Write as a percentage.

.....................................

(1)

(Total 3 marks)

4

3

4

3

4

3

16. A newspaper reporter did a survey.

He asked people what was their favourite leisure activity.

The table gives some information about the answers he got.

Favourite leisure activity Percentage

Home Improvements 22%

Shopping 14%

Gardening 9%

All others

(a) Complete the table.

(1)

(b) Write 9% as a decimal.

……………………….

(1)

400 people were asked in the survey.

(c) How many people said their favourite leisure activity was gardening?

……………………….

(2)

(Total 4 marks)


MONEY PROBLEMS






Instructions






Information






Advice





1. A packet of biscuits costs 56p.

A bottle of cola costs £1.14

Emma buys 4 packets of biscuits and one bottle of cola.

She pays with a £10 note.

Work out how much change she should get.

£ .............................

(Total 3 marks)

2. Farah buys

2 pens at 84p each

3 folders at £1.35 each

1 pencil case at £1.49


Work out how much change Farah should get from £10.

£ ……………………………

(Total 3 marks)

3. A badge costs 78p.

Sam has £5.

He buys as many badges as he can.

Work out the amount of change Sam should get from £5.

Give your answer in pence.

………………………….p

(Total 3 marks)

4. Complete this bill.

(Total 4 marks)

Michael’s Cycle Repairs

Description Number Cost of each item Total

Brake blocks 4 £4.12 £16.48

Brake cables 2 £5.68 £ ..........................

Pedals 2 £ .......................... £45.98

Labour charge 11

2 hours at £12.00 an hour

£ ..........................

Total£ ..........................

5.

Cinema tickets

Adult ticket: £8.65

Child ticket: £4.90

Senior ticket: £5.85

Tony buys one child ticket and one senior ticket.

(a) Work out the total cost.

£ ..................................

(1)

Stephanie buys adult tickets only.

The total cost is £60.55

(b) How many adult tickets does she buy?

........................

(2)

Kamala buys one adult ticket and two child tickets.


(c) How much change should she get?

£ ..................................

(3)

(Total 6 marks)

6. Kaysha has a part-time job.

She is paid £5.40 for each hour she works.

Last week Kaysha worked for 24 hours.

Work out Kaysha’s total pay for last week.

£ ....................................

(Total 3 marks)

7.

Joe’s Cafe

Prices

Cup of tea 70p

Cup of coffee 85p

Can of cola 75p

Roll £1.60

Sandwich £1.35

Jonathan buys a can of cola and a roll.


£ ………………...

(1)

Sachin buys a cup of tea, a cup of coffee and 2 sandwiches.

(b) Work out the total cost.

£ ………………...

(2)

Kim buys a can of cola, a cup of coffee and a sandwich.


(c) Work out how much change she should get.

£ ………………...

(3)

(Total 6 marks)


(Total 4 marks)

9. The cost of 20 litres of petrol is £18

Work out the cost of 1 litre of petrol.

………………………

(Total 3 marks)

Gary’sAutoRepairs

Description NumberCost of

each itemTotal

4

2

2

Spark plug

Wiper blade

Light bulb

£2.50

£1.50

£ ......

£10.00

£ ..............

£ 5.00

Labour charge 1½ hours at £ 16.00 an hour £ ..............

£ ..............Total cost

0000

0000

Petrol

10.

Pete’s Café

Price List

Cup of Tea 75p

Cup of Coffee 85p

Can of Cola 75p

Roll £1.70

Sandwich £1.35

Joe buys a can of cola and a roll.


£………………………

(1)

Susan buys two cups of tea and one sandwich,


£………………………

(2)

Kim buys a cup of coffee and a roll.



£………………………

(2)

(Total 5 marks)

11. Enzo makes pizzas.

One day he makes 36 pizzas.

He charges £2.45 for each pizza.

(a) Work out the total amount he charges for 36 pizzas.

£ ................................

(3)

Mario delivers pizzas.

He is paid 65p for each pizza he delivers.

One day he was paid £27.30 for delivering pizzas.

(b) How many pizzas did Mario deliver?

........................ pizzas

(3)

(Total 6 marks)


SHADING FRACTIONS

OF RECTANGLES






Instructions






Information






Advice





1.

(a) (i) What fraction of this shape is shaded? Write your fraction in its

simplest form.

..........................

(ii) Shade of this shape.

(3)

9 is the number that is half way between 6 and 12

6 .........9........ 12

(b) Work out the number that is half way between

(i) 20 ........................ 60

(ii) 100 000 ........................ 200 000

(iii) 6.5 ........................ 6.6

(iv) ........................

(4)

(Total 7 marks)

4

1

4

1

2

1

2. (a) Write down the fraction of this shape that is shaded.

Write your fraction in its simplest form.

.................................

(2)

(b) Shade of this shape.

(1)

(c) What fraction of the shape is shaded?

.................................

(2)

(Total 5 marks)

3

2

3. (a) Write down the fraction of this shape that is shaded.


..........................

(2)


(1)

(c) Write as a decimal.

...........................

(1)

(d) Write 0.39 as a fraction.

...........................

(1)

(Total 5 marks)

7

2

10

3

4. (a) What fraction of this shape is shaded?

..........................

(1)


(1)

(c) What fraction of this shape is shaded?

..........................

(1)

(Total 3 marks)

8

5

5. (a) Shade of this shape.

(1)

(b) Shade 0.25 of this shape.

(1)

(c)

What fraction of the shape is shaded?


……………………………

(1)

(d) What fraction of the shape is not shaded?

…………………………

(2)

(Total 5 marks)

4

3

6.

What fraction of the large triangle is shaded?


……………………….

(Total 2 marks)

7. Here are two fractions and

Explain which is the larger fraction.

You may use the grids to help with your explanation.

...........................................................................................................................

...........................................................................................................................

..........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(Total 3 marks)

5

4

4

3

8. Here are two fractions and .

Explain which is the larger fraction.

You may use the grids to help with your explanation.

...........................................................................................................................

...........................................................................................................................

..........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(Total 3 marks)

5

3

3

2


ADDITION AND

SUBTRACTION






Instructions






Information






Advice





1. There were 34 coins in a bag.

Jim took 15 coins out of the bag.

Rose put 17 coins into the bag.

How many coins are now in the bag?

...................................

(Total 2 marks)

2. 33 people were on a bus.

19 people got off.

15 people got on.

How many people are now on the bus?

…………………….

(Total 2 marks)

3.

Joe’s Cafe

Prices

Cup of tea 70p

Cup of coffee 85p

Can of cola 75p

Roll £1.60

Sandwich £1.35

Jonathan buys a can of cola and a roll.


£ ………………...

(1)

Sachin buys a cup of tea, a cup of coffee and 2 sandwiches.


£ ………………...

(2)

Kim buys a can of cola, a cup of coffee and a sandwich.


(c) Work out how much change she should get.

£ ………………...

(3)

(Total 6 marks)

4. Chris buys

1 map costing £4.50

1 whistle costing £1.35

2 bars of chocolate costing £0.55 each

He pays with a £10 note.

Work out how much change he should get.

£ .....................................

(Total 3 marks)

5. Susan is decorating her bedroom.

She buys

1 paint brush costing £2.46

1 paint roller costing £3.08

2 tins of paint costing £5.95 each


Work out how much change she should get.

£......................................

(Total 3 marks)

6. Rizwan buys

6 stamps at 25p each

2 packs of postcards at 89p per pack

1 pack of labels at £1.09

He pays with a £10 note.

Work out how much change Rizwan should get.

£ ............................................

(Total 3 marks)


(Total 4 marks)

Michael’s Cycle Repairs

Description Number Cost of each item Total

Brake blocks 4 £4.12 £16.48

Brake cables 2 £5.68 £ ..........................

Pedals 2 £ .......................... £45.98

Labour charge 11

2 hours at £12.00 an hour

£ ..........................

Total£ ..........................

8.

Cinema tickets

Adult ticket: £8.65

Child ticket: £4.90

Senior ticket: £5.85

Tony buys one child ticket and one senior ticket.


£ ..................................

(1)

Stephanie buys adult tickets only.

The total cost is £60.55

(b) How many adult tickets does she buy?

........................

(2)

Kamala buys one adult ticket and two child tickets.



£ ..................................

(3)

(Total 6 marks)

9. Farah buys

2 pens at 84p each

3 folders at £1.35 each

1 pencil case at £1.49


Work out how much change Farah should get from £10.

£ ……………………………

(Total 3 marks)

10. Mrs Adams bought cinema tickets for 4 adults and their children.

An adult ticket costs £5

A child ticket costs £4

Mrs Adams paid a total of £48

Work out the number of child tickets bought by Mrs Adams.

..........................

(Total 3 marks)

11. Work out

7.6 – 4.83

..........................

(Total 3 mark)

12. Christine buys

a calculator costing £5.95

a pencil case costing £1.62

a ruler costing 25p

two pens costing 48p each


(a) How much change should she get from her £10 note?

£........................

(3)

Christine needs 160 tiles for a room.

Tiles are sold in boxes.

There are 12 tiles in each box.

(b) Work out the least number of boxes of tiles that Christine needs.

................ boxes

(2)

Each box of tiles costs £12.20

(c) Work out the total cost of the boxes of tiles that Christine needs.

£........................

(2)

(Total 7 marks)


MULTIPLICATION

AND DIVISION Materials required for examination Items included with question papers





Instructions






Information






Advice





1. Work out 362 × 54

You must show all your working.

.....................................

(Total 3 marks)

2. Work out 736 × 24


.....................................

(Total 3 marks)

3. Richard paid 56p for 7 pencils.

The cost of each pencil was the same.

Work out the cost of 4 of these pencils.

......................... p

(Total 2 marks)

4. 487 is divided by 23

What is the remainder?


.........................

(Total 2 marks)

5. Work out 1572 ÷ 0.3


.........................

(Total 2 marks)

6. Work out 286 × 43

……………………..

(Total 3 marks)

7. Fatima bought 48 teddy bears at £9.55 each.

(a) Work out the total amount she paid.

£ .............................

(3)

Fatima sold all the teddy bears for a total of £696.

She sold each teddy bear for the same price.

(b) Work out the price at which Fatima sold each teddy bear.

£ .............................

(3)

(Total 6 marks)

8. Nick takes 26 boxes out of his van.

The weight of each box is 32.9 kg.

(a) Work out the total weight of the 26 boxes.

....................... kg

(3)

Then Nick fills the van with large wooden crates.

The weight of each crate is 69 kg.

The greatest weight the van can hold is 990 kg.

(b) Work out the greatest number of crates that the van can hold.

..........................

(4)

(Total 7 marks)

9. The cost of a calculator is £6.79

Work out the cost of 28 of these calculators.

£…………………….

(Total 3 marks)

10. Work out 3.15 × 24

........................................................

(Total 3 marks)

11. ‘Jet Tours’ has an aeroplane that will carry 27 passengers.

Each of the 27 passengers pays £55 to fly from Liverpool to Prague.

Work out the total amount that the passengers pay.

£ ……………………….

(Total 2 marks)

12.

Canal boat for

hire

£1785.00

for 14 days

What is the cost per day of hiring the canal boat?

£ .................................

(Total 3 marks)


TIME TABLES &

DISTANCE TABLES






Instructions






Information






Advice





1. Here is part of a railway timetable.

Manchester 07 53 09 17 10 35 11 17 13 30 14 36 16 26

Stockport 08 01 09 26 10 43 11 25 13 38 14 46 16 39

Macclesfield 08 23 09 38 10 58 11 38 13 52 14 58 17 03

Congleton 08 31 – – 11 49 – 15 07 17 10

Kidsgrove 08 37 – – – – – 17 16

Stoke-on-Trent 08 49 10 00 11 23 12 03 14 12 15 19 17 33

A train leaves Manchester at 10 35.

(a) At what time should this train arrive in Stoke-on-Trent?

.........................

(1)

Doris has to go to a meeting in Stoke-on-Trent.

She will catch the train in Stockport.

She needs to arrive in Stoke-on-Trent before 2 pm for her meeting.

(b) Write down the time of the latest train she can catch in Stockport.

.........................

(1)

(c) Work out how many minutes it should take the 14 36 train from Manchester to get

to Stoke-on-Trent.

............. minutes

(1)

The 14 36 train from Manchester to Stoke-on-Trent takes less time than the 16 26 train

from Manchester to Stoke-on-Trent.

(d) How many minutes less?

............. minutes

(2)

(5 marks)

2. Here is part of a train timetable for six trains from Birmingham to London.

Train A B C D E F

Birmingham 06 35 07 00 07 15 07 30 07 45 08 00

London 08 09 08 39 08 48 09 04 09 59 09 39

(a) Which train takes more than 2 hours to go from Birmingham to London?

.....................................

(1)

(b) Work out the number of minutes taken by train D to go from Birmingham to London.

....................... minutes

(2)

Paula has to go to a meeting in London.

She will catch one of the six trains from Birmingham.

She needs to arrive in London before 09 00

(c) Write down the latest train that she can catch.

.....................................

(1)

(4 marks)

3. The table shows part of a bus timetable from Shotton to Alton.

Shotton 07 30 08 00 09 00 10 00 11 00

Crook 07 45 08 15 09 15 10 15 11 15

Prudhoe 07 58 08 28 09 28 10 28 11 28

Hexham 08 15 08 45 09 45 10 45 11 45

Alton 08 30 09 00 10 00 11 00 12 00

A bus leaves Shotton at 07 30

(a) What time should it arrive at Alton?

.....................................

(1)

Another bus leaves Prudhoe at 08 28

(b) How many minutes should it take to get to Hexham?

........................................ minutes

(1)

Serena lives in Crook.

She has to be in Hexham by quarter past 11

(c) What is the time of the latest bus she can catch from Crook to arrive in Hexham by quarter past

11?

.....................................

(1)

(3 marks)

4. Here is part of a timetable for a bus.

Blunsdon 07 18 07 45 08 33

Cricklade 07 26 07 53 08 41

Latton 07 31 07 58 08 46

South Cerney 07 38 08 05 08 53

Siddington 07 47 08 14 09 02

Seven Springs 08 26 08 51 09 39

Cheltenham 08 50 09 12 10 00

A bus leaves Blunsdon at 07 45

(a) At what time should the bus arrive at Siddington?

.....................................

(1)

Peter arrives at the Latton bus stop at 08 35

He waits for the next bus to Seven Springs.

(b) (i) How many minutes should he wait?

........................ minutes

(ii) At what time should Peter arrive at Seven Springs?

.....................................

(2)

Marie gets the bus from Cricklade at 07 26

(c) How many minutes should this bus take to travel from Cricklade to Cheltenham?

........................ minutes

(2)

(5 marks)

5. The table shows part of a train timetable from Weymouth to London Waterloo.

Weymouth 0903 0920 1003 1020 1103

Poole 0940 1007 1040 1107 1140

Bournemouth 0953 1017 1054 1117 1154

Southampton 1026 1058 1128 1158 1228

Woking 1119 1219 1319

London Waterloo 1149 1220 1249 1320 1349

A train leaves Weymouth at 09 03

(a) At what time should it arrive at London Waterloo?

.....................................

(1)

Another train leaves Poole at 11 40

(b) How many minutes should it take to travel to Bournemouth?

....................... minutes

(1)

Sally lives in Weymouth.

She has a meeting in Southampton at 12 00

When Sally arrives at Southampton she takes 25 minutes to travel to her meeting.

(c) What is the time of the latest train she can take from Weymouth?

.....................................

(1)

(3 marks)

6. Here is part of a railway timetable.

Cambridge 08 25 08 45 08 54 09 26 09 50

Royston 08 46 08 59 09 15 09 43 10 04

Letchworth Garden City 09 00 09 09 09 29 09 54 10 14

Hitchin 09 04 09 33 09 58 - -

Stevenage 09 10 - 09 39 10 03 -

Finsbury Park 09 41 - 10 09 10 21 -

London 09 50 09 42 10 18 10 30 10 46

A train leaves Cambridge at 09 26

(a) At what time should this train arrive in London?

(1)

.............................................................

A different train leaves Cambridge at 09 50

(b) Work out how many minutes this train should take to get to London.

(1)

............................................................. minutes

Susan lives in Royston.

She has to be in Stevenage by 10 a.m.

(c) What is the time of the latest train she can catch from Royston to arrive in Stevenage by 10 a.m.?

(1)

.............................................................

(3 marks)

7. Here is part of a train timetable from Birmingham to Leicester.

Birmingham 06 23 06 53 07 23 07 53

Coleshill 06 35 07 05 07 35 08 05

Nuneaton 07 00 07 22 07 51 08 22

Hinckley 00 00 07 29 07 58 08 29

Leicester 07 17 07 48 08 17 08 48

A train leaves Birmingham at 06 53

(a) (i) What time should this train get to Hinckley?

..............................................

(ii) How many minutes should this train take to get to Hinckley?

.............................................. minutes

(2)

Silvia wants to catch a train in Nuneaton.

She needs to get to Leicester before 08 30

(b) Write down the time of the latest train Silvia can catch from Nuneaton.

..............................................

(1)

A train will leave Leicester at 07 27 for Stansted Airport.

The train should take 2 hours 28 minutes to go from Leicester to Stansted Airport.

(c) What time should the train get to Stansted Airport?

..............................................

(1)

(4 marks)

8. Here is part of a train timetable from Crewe to London.

Station Time of Leaving

Crewe 08 00

Wolverhampton 08 40

Birmingham 09 00

Coventry 09 30

Rugby 09 40

Milton Keynes 10 10

(a) At what time should the train leave Coventry?

.....................................

(1)

The train should arrive in London at 10 45

(b) How long should the train take to travel from Crewe to London?

.....................................

(2)

Verity arrived at Milton Keynes station at 09 53

(c) How many minutes should she have to wait before the 10 10 train leaves?

....................... minutes

(1)

Lisa uses her railcard to buy a ticket.

She gets off the normal price of the ticket.

The normal price of the ticket is £24.90

(d) Work out how much Lisa pays for the ticket.

£ ..................................

(3)

(7 marks)

3

1 Young Person’s RAILCARD

off normal price 3

1

9. The table shows the distances in kilometres between some cities in the USA.

Boston

1589 Chicago

4891 3366 Los Angeles

2474 2184 4373 Miami

342 1352 4539 2133 New York

5067 3493 667 4990 4826 San Francisco

(a) Write down the distance between Los Angeles and New York.

……………………….km

(1)

One of the cities in the table is 2184 km from Miami.

(b) Write down the name of this city.

……………………….

(1)

(c) Write down the name of the city which is furthest from San Francisco.

……………………….

(1)

(3 marks)

10. The table shows the distances in kilometres between 5 cities.

Hull

100 Leeds

162 73 Manchester

110 60 65 Sheffield

63 40 118 95 York

(a) Write down the distance between Hull and Manchester.

............................. km

(1)

(b) From the table, write down the name of the city which is

(i) nearest to Hull, .......................................................

(ii) 60 km from Sheffield. .......................................................

(2)

(3 marks)

11.

Reading

22 Slough

28 40 Guildford

30 22 47 Oxford

45 28 66 25 Buckingham

The table gives distances in miles by road between some towns.

(a) Write down the distance between Reading and Guildford.

........................... miles

(1)

Sophie drives from Slough to Guildford.

She then drives from Guildford to Reading.

Sophie then drives from Reading to Slough.

(b) Work out the total distance that she drives.

........................... miles

(2)

(3 marks)

12. The diagram shows the distances, in miles, between some service areas on the M1 motorway.

For example, the distance between Toddington and Watford Gap is 70 miles.

Complete the table.

Toddington

26 Scratchwood

70 Watford Gap

83 39 Woodall

111 28 Trowell

(3 marks)

Toddington Scratchwood Watford Gap Woodall Trowell

M1

26 44 39 28

13. The table shows the distances, in miles, between 4 cities.

London

74 Portsmouth

39 58 Reading

97 41 57 Salisbury

(a) Write down the distance between London and Salisbury.

...................................... miles

(1)

(b) Which two cities are the shortest distance apart?

........................................................ and ........................................................

(1)

Nassim drives from Portsmouth to Salisbury.

He then drives from Salisbury to Reading.

Finally he drives from Reading to Portsmouth.

(c) Work out the total distance Nassim drives.

...................................... miles

(3)

(5 marks)


TALLYS AND CHARTS






Instructions






Information

The marks for each question are shown in brackets – use this as a guide as to how much time to spend on

each question.

Questions labelled with an asterisk (*) are ones where the quality of your written communication will be

assessed – you should take particular care on these questions with your spelling, punctuation and grammar,

as well as the clarity of expression.

Advice





1. Jerry recorded the colour of each of the cars he saw one morning.

The bar chart shows this information.

(a) Write down the number of red cars.

............................................

(1)

(b) Which was the most popular colour of car?

............................................

(1)

(Total 2 marks)

2. José is in hospital.

Here is his temperature chart during one day.

(a) At what time was José’s temperature 39.0°C?

.....................................

(1)

(b) What can you say about José’s temperature from 6 am to 6 pm?

.....................................

(1)

(Total 2 marks)

12

10

8

6

4

2

0

white black red yellow

Colour

Numberof cars

6 7 8 9 10 11 12 1 2 3 4 5 6

36.0

36.5

37.0

37.5

38.0

38.5

39.0

39.5

40.0

40.5

Time pmam

3. Steve asked his friends to tell him their favourite colour.

Here are his results.

(a) Complete the bar chart to show his results.

(2)

(b) Which colour did most of his friends say?

....................................

(1)

(Total 3 marks)

Favourite colour Tally Frequency

Red 6

Blue 8

Green 5

Yellow 3

Frequency

Favourite colour

8

7

6

5

4

3

2

1

0 Red Blue Green Yellow

4. There are only red, yellow, orange and green sweets in a bag.

Peter recorded the colour of each sweet in the bag.

The bar chart shows some information about his results.

8 sweets were orange.

5 sweets were green.

(a) Complete the bar chart.

(2)

(b) Write down the number of red sweets.

..................................

(1)

(c) What colour sweet is the mode?

................................

(1)

(d) Work out the total number of sweets in the bag.

................................

(1)

(Total 5 marks)

Red Yellow Orange Green

2

4

6

8

10

12

14

Frequency

0

5. Lesley wrote down the colour of each car in the school car park.

The bar chart shows this information.

(a) Write down the number of blue cars.

..........................

(1)

(b) What colour were most cars?

..........................

(1)

(c) Work out the total number of cars.

..........................

(1)

(Total 3 marks)

16

14

12

10

8

6

4

2

0White Red Blue Silver Green

Colour

Nu

mb

er o

f ca

rs

6. Jessica asked some students to tell her their favourite pet.

She used the information to draw this bar chart.

(a) How many students said a rabbit?

...........................

(1)

(b) Which pet did most students say?

...........................

(1)

(c) Work out the number of students that Jessica asked.

...........................

(1)

(Total 3 marks)

12

11

Cat Dog Rabbit Hamster Goldfish

10

9

8

7

6

5

4

3

2

1

0

Favourite pet

Number

of students

7. This bar chart gives information about the numbers of rabbits, cats, dogs and lizards taken to a

vet on Monday.

(a) Write down the number of rabbits taken to the vet on Monday.

.....................

(1)

(b) Write down the number of dogs taken to the vet on Monday.

.....................

(1)

5 hamsters were also taken to the vet on Monday.

(c) Use this information to complete the bar chart.

(1)

(Total 3 marks)

0

2

4

6

8

10

Rabbits Cats Dogs Lizards Hamsters

Number

Animal

8. Ray and Clare are pupils at different schools.

They each did an investigation into their teachers’ favourite colours.

Here is Ray’s bar chart of his teachers’ favourite colours.

(a) Write down two things that are wrong with Ray’s bar chart.

..............................................................................................................................

..............................................................................................................................

(2)

Clare drew a bar chart of her teachers’ favourite colours.

Part of her bar chart is shown below.

4 teachers said that Yellow was their favourite colour.

2 teachers said that Green was their favourite colour.

(b) Complete Clare’s bar chart.

(2)

(c) Which colour was the mode for the teachers that Clare asked?

.....................................

(1)

(d) Work out the number of teachers Clare asked.

.....................................

(1)

5

4

3

2

0Red Blue Green

Colours

Frequency

6

5

4

3

2

1

0Red Blue Yellow Green

Colours

Frequency

(e) Write down the fraction of the number of teachers that Clare asked who said Red was their

favourite colour.

.....................................

(1)

(Total 7 marks)

9. Sophie asked the students in her class how they travelled to school.

The bar chart shows some information about the results, for everyone in Sophie’s class.

4 students travel to school by car.

7 students travel to school by bus.

(a) Complete Sophie’s bar chart.

(2)

(b) How many students in Sophie’s class cycle to school?

...................

(1)

(c) Which method of travelling to school is used by the greatest number of students in

Sophie’s class?

.................................

(1)

(d) Work out the total number of students Sophie asked.

...................

(1)

(Total 5 marks)

12

10

Frequency

8

6

4

2

0

Walk Cycle Car Bus

10. The bar chart shows some information about the midday temperature in Halifax on the

first day of some months last year.

Here are the midday temperatures on the first day of October, November and December.

October 12°C

November 8°C

December 6°C

(a) Complete the bar chart to show this information.

(2)

(b) Which two bars show the highest temperatures?

................................ and ................................

(1)

(c) Work out the range of the temperatures shown on the bar chart.

............................... °C

(1)

(d) Describe what happened to the temperatures on the bar chart between March

and July.

....................................................................................................................................

(1)

(Total 5 marks)

0

4

8

12

16

20

24

28

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Month

Midday

temperature

in °C

11. Six students each sat a history test and a geography test.

The marks of five of the students, in each of the tests, were used to draw the bar chart.

(a) How many marks did Ali get in his history test?

………………

(1)

(b) How many marks did Dennis get in his geography test?

………………

(1)

(c) One student got a lower mark in the history test than in the geography test.

Write down the name of this student.

………………

(1)

Fahad got 16 marks in the history test.

She got 11 marks in the geography test.

(d) Use this information to complete the bar chart.

(2)

(Total 5 marks)

20

18

16

14

12

10

8

6

4

2

0Ali Ben Cathy Dennis Erika Fahad

Mark

Key

History

Geography

12. Here is a bar chart showing the number of hours of TV that Helen and Robin

watched last week.

(a) Write down the number of hours of TV that Helen watched on Monday.

………………………hours

(1)

(b) On which day did Helen and Robin watch the same number of hours of TV?

………………………

(1)

(c) (i) Work out the total number of hours of TV that Robin watched on Friday and

Saturday.

………………………hours

(ii) Who watched the greater number of hours of TV on Friday and Saturday? Show

your working.

(3)

(Total 5 marks)

9

8

7

6

5

4

3

2

1

0

Number of hours Helen

Robin

Hours of TV watched last week

Sunday Monday Tuesday Wednesday Thursday Friday Saturday

Day

13. The graph shows the number of ice creams sold each day during one week

(a) How many more ice creams were sold on Tuesday than on Monday?

………………………ice creams

(1)

(b) Explain what might have happened on Monday.

.....................................................................................................................................

.....................................................................................................................................

(1)

(Total 2 marks)

Sun Mon Tue Wed Thu Fri Sat

Day

300

200

100

0

Number ofice creamssold

14. Daniel carried out a survey of his friends’ favourite flavour of crisps.


Plain Chicken Bovril Salt & Vinegar Plain

Salt & Vinegar Plain Chicken Plain Bovril

Plain Chicken Bovril Salt & Vinegar Bovril

Bovril Plain Plain Salt & Vinegar Plain

(a) Complete the table to show Daniel’s results.

Flavour of crisps Tally Frequency

Plain

Chicken

Bovril

Salt & Vinegar

(3)

(b) Write down the number of Daniel’s friends whose favourite flavour was Salt & Vinegar.

……………………..

(1)

(c) Which was the favourite flavour of most of Daniel’s friends?

……………………..

(1)

(Total 5 marks)


COORDINATES






Instructions






Information


each question.




Advice





1.

(a) Write down the coordinates of the point P.

(.......... , ..........)

(1)

(b) (i) On the grid, plot the point (0, 3).

Label the point Q.

(ii) On the grid, plot the point (–2, –3).

Label the point R.

(2)

(Total 3 marks)

4

3

2

1

–1

–2

–3

–4

4321–1–2–3–4 O x

y

×P

2.

(i) Write down the coordinates of point P.

(............. , ..............)

(ii) On the grid, plot the point (–3, –1).

Label this point with the letter Q.

(Total 2 marks)

x

y

–2–3–4 –1 1 2 3 4

4

3

2

1

–1

–2

–3

–4

O

P

3.

(a) (i) Write down the coordinates of the point A.

(............. , ..............)

(ii) Write down the coordinates of the point B.

(............. , ..............)

(2)

(b) (i) On the grid, plot the point (3, 2).

Label this point P.

(ii) On the grid, plot the point (–4, 3).

Label this point Q.

(2)

(Total 4 marks)

5

4

3

2

1

–1

–2

–3

–4

–5

–5 –4 –3 –2 –1 O 1 2 3 4 5

A

Bx

y

4.

(a) (i) Write down the coordinates of the point A.

(……………,………….)

(ii) Write down the coordinates of the point B.

(……………,………….)

(2)

(b) (i) On the grid, mark the point (6, 4) with the letter P.

(ii) On the grid, mark the point (3, 0) with the letter Q.

(2)

(Total 4 marks)

8

7

6

5

4

3

2

1

1 2 3 4 5 6 7 8 x

y

O

×

×A

B

5.

(a) Write down the coordinates of the point A.

(……….. , ………..)

(1)

(b) Write down the coordinates of the point B.

(……….. , ………..)

(1)

N is the point (–3, 2)

(c) On the grid, mark the point N with a cross (×). Label it N.

(1)

M is another point.

The x coordinate of M is the same as the x coordinate of N.

The y coordinate of M is the same as the y coordinate of B.

(d) Write down the coordinates of the point M.

(……….. , ………..)

(1)

(Total 4 marks)

4

y

A

B

O–5 –4 –3 –2 –1 1 2 3 4 5

3

2

1

–1

–2

–3

–4

–5

5

x

6.

(a) Write down the coordinates of the point

(i) A,

( ……... , …….. )

(ii) B.

( ……... , …….. )

(2)

(b) On the grid, mark with a cross (×) the midpoint of the line AB.

(1)

(Total 3 marks)

7.

Diagram NOT accurately drawn

P has coordinates (1, 2)

Q has coordinates (7, 10)

Find the coordinates of the mid-point of the line PQ.

(............ , ............)

(Total 2 marks)

x

y

4

3

2

1

4 53210

A

B

8.

(a) Write down the coordinates of the point P.

(............ , ............)

(1)

(b) On the grid, mark the point (–3, 1) with a cross (×).

Label the point Q.

(1)

(c) Write down the coordinates of the midpoint of the line PR.

(............ , ............)

(2)

(Total 4 marks)

9.


P has coordinates (1, 4)

R has coordinates (5, 0)

Find the coordinates of the mid-point of the line PR.

(................ , ................)

(Total 2 marks)

y

P

1 2 3 4 5 6 x –1

–2

R

–4

4

3

2

1

–1

–2

–3

–4

x

P

R

xO

y


ANGLES






Instructions






Information






Advice





1. The lines in the diagram are straight.

(a) Mark with arrows, (>>), a pair of parallel lines.

(1)

(b) Mark with the letter R, a right angle.

(1)

(c) What type of angle is shown by the letter

(i) x, .................................

(ii) y. .................................

(2)

(Total 4 marks)

x

y

2. The shape is made from a right-angled triangle, a parallelogram and a

quadrilateral.

(a) Mark with arrows (») a pair of parallel lines.

(1)

(b) Mark with the letter A an acute angle.

(1)

(c) Mark with the letter R a reflex angle.

(1)

(d) Measure the size of angle x.

………………………

(1)

(Total 4 marks)

x

3.

One of the four angles marked in the diagrams above is an obtuse angle.

(a) Write down the letter of the diagram in which the obtuse angle is

marked.

……………………….

(1)

(b) Work out the size of the angle marked x°.

……………………….

(2)

(Total 3 marks)

A B

C D

50°x°

Diagram accurately drawn

NOT

4. (a) Write down the special name for this type of angle.

.........................

(1)

(b) Write down the special name for this type of angle.

.........................

(1)

(c)

This diagram is wrong.

Explain why

..................................................................................................................

..................................................................................................................

.................................................................................................................

..................................................................................................................

(1)

(Total 3 marks)

120°

230°

Diagram Taccurately drawn

NO

5. Here is a diagram drawn on a square grid.

(a) Mark, with arrows (>>), a pair of parallel lines.

(1)

(b) Mark, with the letter A, an acute angle.

(1)

(c) Mark, with the letter O, an obtuse angle.

(1)

(Total 3 marks)

6. The diagram shows two sides of a rhombus drawn on a grid of centimetre

squares.

(a) (i) Measure the size of the angle between these two sides.

……………………°

(ii) What type of angle have you measured?

……………………

(2)

(b) Complete accurately the drawing of the rhombus.

(1)

(Total 3 marks)

7. The diagram shows an angle.

(a) Write down the special name for this type of angle.

……………………………

(1)

(b) Measure the size of the angle.

……………………………

(1)

(Total 2 marks)

8.

(a) Measure the size of the angle marked x.

..........................°

(1)

(b) What type of angle is shown by the letter y ?

.............................

(1)

(Total 2 marks)


CONGRUENT SHAPES






Instructions






Information






Advice





1.

(a) Write down the letter of an isosceles triangle.

.................................

(1)

(b) Write down the letters of two triangles which are congruent.

.................. and ..................

(1)

Triangle C is an enlargement of triangle G.

(c) Write down the scale factor of this enlargement.

.................................

(1)

(Total 3 marks)

A

D

C

E

G

B

F

2. Here are some triangles.

(a) Write down the letter of the triangle that is

(i) right-angled,

...................

(ii) isosceles.

...................

(2)

Two of the triangles are congruent.

(b) Write down the letters of these two triangles.

.................. and ...................

(1)

(Total 3 marks)

A

C

D

F

G E

B

3. Here are 8 shapes.

(a) Write down the letters of two different pairs of congruent shapes.

...................... and ......................

...................... and ......................

(2)

(b) On the grid, show how the shaded shape will tessellate.

You must draw at least 6 shapes.

(2)

(Total 4 marks)

A

D

G H

E F

B C

4. Here are 6 shapes drawn on a grid.

Two of these shapes are congruent.

(a) Write down the letters of these two shapes.

....................... and ........................

(1)

(b) On the grid below, draw a shape that is congruent to shape P.

(1)

(Total 2 marks)

CA

FED

B

P

5. These shapes have been drawn on a grid of centimetre squares.

(a) (i) Write down the letters of a pair of shapes that are congruent.

....................... and .......................

(ii) Write down the letters of a different pair of shapes that are similar.

....................... and .......................

(2)

(b) Find the perimeter of shape D.

....................... cm

(1)

(Total 3 marks)

6. Here are some rectangles on a grid of centimetre squares.

(a) Find the area of rectangle G.

...............................cm2

(1)

(b) Find the perimeter of rectangle B.

................................cm

(1)

Two of the rectangles are congruent.

(c) Write down the letters of these two rectangles.

..................... and .....................

(1)

Rectangle F is an enlargement of rectangle B.

(d) Write down the scale factor of the enlargement.

.....................................

(1)

(Total 4 marks)

7. Here are some triangles drawn on a square grid.

Two of the triangles are congruent.

(a) Write down the letters of these two triangles.

....................... and .......................

(1)

One of the triangles is an enlargement of another of the triangles.

(b) Write down the letters of these two triangles.

....................... and .......................

(1)

Two of the triangles each have one line of symmetry.

(c) Write down the letters of these two triangles.

....................... and .......................

(1)

(Total 3 marks)


SIMPLE PERIMETER,

AREA & VOLUME






Instructions






Information






Advice





1. A shaded shape is shown on the grid of centimetre squares.

(a) Work out the perimeter of the shaded shape.

.......................cm

(1)

(b) Work out the area of the shaded shape.

.....................cm2

(1)

(c) Reflect the shaded shape in the mirror line.

(2)

(4 marks)

2.

The shaded shape is drawn on a grid of centimetre squares.

(a) Find the perimeter of the shaded shape. ........................................ cm

(1)

(b) Find the area of the shaded shape. ....................................... cm2

(1)

(2 marks)

Mirrorline

3.

(a) (i) Find the area of the shaded shape. .................... cm2

(ii) Find the perimeter of the shaded shape. ..................... cm

(2)

Here is a solid prism made from centimetre cubes.

(b) Find the volume of the solid prism. .................... cm3

(2)

(4 marks)

4.

A shaded shape is shown on the grid of centimetre squares.

(a) Find the perimeter of the shaded shape. .......................cm

(1)

(b) Find the area of the shaded shape. ......................cm2

(1)

(2 marks)

1 cm

1 cm

1 cm3

5. A shaded shape has been drawn on a grid of centimetre squares.

(a) Find the perimeter of the shaded shape. .....................................cm

(1)

Another shaded shape has been drawn on a grid of centimetre squares.

(b) Find the area of the shaded shape. ..................................... cm2

(2)

(3 marks)

6. This shaded shape is drawn on a centimetre grid.

(a) Work out the perimeter of the shaded shape.

............................ cm

(1)


........................... cm2

(1)

(2 marks)

7.

The diagram shows a shaded shape drawn on a centimetre grid.

(a) Find the area of the shaded shape.

State the units of your answer. ……………………….

(2)

(b) Find the perimeter of the shaded shape. ……………………….cm

(1)

The diagram shows a prism made of centimetre cubes.

(c) Find the volume of the prism. ……………………….cm3

(2)

(5 marks)

8.

(a) Find the area of the shape. …...………. cm2

(1)

(b) Find the perimeter of the shape. …...……………

(2)

(3 marks)

= 1 cm2

9.

The diagram shows a shaded shape drawn on a centimetre grid.

(a) Work out the perimeter of the shaded shape. ............................... cm

(1)


State the units of your answer. ......................................

(2)

Here is a solid prism made of centimetre cubes.

(c) Find the volume of the solid prism. ........................................ cm3

(2)

(5 marks)

10. This shaded shape is drawn on a grid of centimetre squares.

(a) Find the perimeter of the shaded shape. ................................... cm

(1)

(b) Find the area of the shaded shape. ................................... cm2

(1)

(2 marks)

represents

1 cm 3

11. Here is a shaded shape on a centimetre grid.

(a) Find the area of the shaded shape. ................................. cm2

(1)

(b) Find the perimeter of the shaded shape. ................................ cm

(2)

Here is a solid prism made of centimetre cubes.

(c) Find the volume of the solid prism. ................................. cm3

(2)

(5 marks)

12. A shaded shape has been drawn on the centimetre grid.

(a) Find the perimeter of the shaded shape. .............................. cm

(1)

(b) Find the area of the shaded shape. ............................ cm2

(1)

(2 marks)

13. This shaded shape is drawn on a grid of centimetre squares.

(a) (i) Find the perimeter of the shaded shape.

............................... cm

(ii) Find the area of the shaded shape.

............................. cm2

(2)

This solid prism is made from centimetre cubes.

(b) Find the volume of the prism.

............................. cm3

(1)

(Total 3 marks)


METRIC & IMPERIAL

MEASURES






Instructions






Information






Advice





1. Complete this table.

Write a sensible unit for each measurement.

Metric Imperial

The height of a bus .......................................... feet

The distance between two

towns kilometres ...........................................

(2 marks)



Metric Imperial

The weight of a turkey …………………. pounds

The volume of water in a

swimming pool …………………. gallons

The width of this page centimetres ………………….

(3 marks)

3. Complete this table by writing a sensible unit for each measurement.

Metric Imperial

The height of a door ........................ feet

The weight of a man kilograms ........................

The volume of water

in a bucket ........................ gallons

(3 marks)

4. (a) Write down a sensible metric unit that can be used to measure

(i) the height of a tree,

....................................

(ii) the weight of a person.

....................................

(2)

(b) Change 2 centimetres to millimetres.

.................................. millimetres

(1)

(3 marks)

5. (a) Write down the name of a sensible metric unit that can be used to measure

(i) the weight of a grape,

.....................................

(ii) the diameter of a CD.

.....................................

(2)

(b) Change 7 kilometres to metres. ................................. m

(1)

(3 marks)

6. (a) Write down the name of the metric unit used to measure

(i) the weight of a man,

.....................................

(ii) the distance from New York to London.

.....................................

(2)

(b) Change 4 metres to centimetres.

..................................... cm

(1)

(c) Change 9000 millilitres to litres.

..................................... litres

(1)

(4 marks)

7. (a) (i) Change 5.6 metres to centimetres.

……………………………cm

(ii) Change 6700 millilitres to litres.

……………………………litres

(2)

(b) Write down the name of the metric unit which is usually used to measure the

weight of a person.

(1)

(3 marks)

8. (a) Write down a sensible metric unit that should be used to measure

(i) the height of a school hall,

...................................

(ii) the weight of a pencil.

...................................

(2)

(b) Write down a sensible imperial unit that should be used to measure the distance

between London and Manchester.

...................................

(1)

(3 marks)

9. (a) Write down a sensible metric unit for measuring

(i) the distance from London to Paris,

..................................

(ii) the amount of water in a swimming pool.

..................................

(2)

(b) (i) Change 5 centimetres to millimetres.

.................... mm

(ii) Change 4000 grams to kilograms.

.................... kg

(2)

(4 marks)

10. (a) Complete the table by writing a sensible metric unit on each dotted line.

The first one has been done for you.

The distance from London to

Birmingham

179 kilometres

The weight of a twenty pence coin 5 ……………………….

The height of the tallest living man 232 …………………….

The volume of lemonade in a glass 250 …………………….

(3)

(b) Change 5000 metres to kilometres.

…………………km

(1)

(4 marks)

11. (a) Complete this table.


Three have been done for you.

Metric Imperial

The length of your finger ......................... inches

The distance between America and England kilometres .........................

The amount of petrol in a petrol tank ......................... gallons

(3)

(b) Change 3 metres to centimetres.

............................... cm

(1)

(c) Shalim says 1.5 km is less than 1400 m.

Is he right?

Explain your answer.

......................................................................................................................................

......................................................................................................................................

(1)

(5 marks)

12. (a) Write down the name of a metric unit which is used to measure

(i) the distance from London to Brighton,

……………………………

(ii) the weight of a bar of soap.

……………………………

(2)

(b) (i) Change 240 millimetres to centimetres.

……………………………cm

(ii) Change 3.8 litres to millilitres.

……………………………ml

(2)

(4 marks)



Three have been done for you.

Metric Imperial

Distance from London to Cradiff km …………

Weight of a bag of potatoes ………… pounds

Volume of fuel in a car’s fuel tank ………… gallons

(3)

(b) Here is a picture of a woman opening a door that is 2 m high.

Estimate the height of the woman.

................................... m

(2)

(4 marks)

14. (a) Complete the table by writing a sensible metric unit for each measurement.


The length of the river Nile 6700 ............kilometres............

The height of the world’s tallest tree 110 .........................................

The weight of a chicken’s egg 70 .........................................

The amount of petrol in a full petrol tank of a car 40 .........................................

(3)

(b) Change 4 metres to centimetres. ............................. cm

(1)

(c) Change 1500 grams to kilograms. .............................. kg

(1)

(5 marks)

15. Write down a sensible metric unit for each measurement.

(i) The weight of a pair of sunglasses.

.....................................

(ii) The height of a house.

.....................................

(iii) The volume of toothpaste in a tube of toothpaste.

.....................................

(3 marks)



Metric Imperial

The weight of a bicycle ..................................

pounds

The volume of water in a watering can ..................................

pints

The length of this page centimetres ..................................

(3 marks)

17.

The diagram shows a man standing next to a lamppost.

The man is of normal height.

(a) Write down an estimate for the height, in metres, of the man.

.................................. m

(1)

(b) Estimate the height, in metres, of the lamppost.

.................................. m

(2)

(3 marks)



Metric Imperial

Diameter of a football ..............................

inches

Amount of fuel in a car fuel tank litres ..............................

(2)

(b) (i) Change 4 kg to grams.

.............................................. grams

(ii) Change 3500 ml to litres.

.............................................. litres

(2)

(4 marks)

19.

The diagram shows a building and a man.


The man and the building are drawn to the same scale.

(a) Write down an estimate for the height of the man.

.....................................

(1)

(b) Write down an estimate for the height of the building.

.....................................

(2)

(3 marks)



Metric Imperial

The weight of a chicken …………………. pounds


petrol tanker …………………. gallons

The length of a finger centimetres ………………….

(3 marks)

21.

The picture shows a man standing next to a flagpole.


The man and the flagpole are drawn to the same scale.

(a) Write down an estimate for the height, in metres, of the man.

................................ m

(1)

(b) Work out an estimate for the height, in metres, of the flagpole.

................................ m

(2)

(3 marks)

22. (a) Write down a sensible metric unit for measuring

(i) the distance from London to Birmingham,

..................................

(ii) the weight of a pencil.

..................................

(2)

(b) (i) Change 7 centimetres to millimetres.

........................... mm

(ii) Change 4500 grams to kilograms.

............................ kg

(2)

(4 marks)

23.

The diagram shows a man and a bus.

The man and the bus are drawn to the same scale.

The man is of average height.

(i) Write down an estimate for the height of the man.

.....................................

(ii) Find an estimate for the length of the bus.

.....................................

(4 marks)

24. (a) Write a sensible unit for each measurement.

Metric Imperial

The weight of a man …………………. pounds


bath …………………. gallons

The length of an arm centimetres ………………….

(3)

(b) Change 6.8 metres to centimetres. ............................. cm

(1)

(c) Change 7500 grams to kilograms. .............................. kg

(1)

(5 marks)

NOTES

DISTANCE

METRIC IMPERIAL

Kilometres km Miles

Metres m Yards

Centimetres cm Feet

Millimetres mm Inches

1 km = 1000m

1m = 100cm

1cm = 10mm

WEIGHT

METRIC IMPERIAL

Kilograms kg Ton

Grams g Stone

Milligrams mg Pounds

Ounces

1 kg = 1000g

1g = 1000g

CAPACITY / VOLUME

METRIC IMPERIAL

Litres l Gallons

Millilitres ml Pints

1 l = 1000ml


2D & 3D SHAPES






Instructions






Information






Advice





1. Write down the mathematical name for each of these three different 3-D shapes.

(i) .............................. (ii) .............................. (iii) ..................................

(3 marks)

2.

Here is a diagram of a cuboid.

Write down the number of

(i) faces ............................

(ii) edges ............................

(iii) vertices ............................

(3 marks)

3. Write down the mathematical name of each of these 3-D shapes.

(i) (ii)

(i) ....................................................... (ii) .......................................................

(2 marks)

(i) (ii) (iii)

4. The diagram shows some solid shapes and some mathematical names.

An arrow has been drawn from one solid shape to its mathematical name.

Draw an arrow from each of the other solid shapes to its mathematical name.

The cube has been done for you.

(3 marks)

5. Here is a diagram of a 3-D prism.

Write down the number of (i) faces, .....................................

(ii) edges, .....................................

(iii) vertices. .....................................

(3 marks)

pyramid

triangular prism

cube

cylinder

cuboid

6. The diagram shows a solid triangular prism.

Diagram NOT

accurately drawn

Write down

(i) the number of faces ..................

(ii) the number of edges ..................

(iii) the number of vertices ..................

(iv) On the grid below, draw a trapezium.

(4 marks)

7. Write down the name of each of these two 3-D shapes.

(2 marks)

(i) (ii)

(i) ........................................

(ii) ........................................

8. The diagrams show some solid shapes and their nets.

An arrow has been drawn from one solid shape to its net.

Draw an arrow from each of the other solid shapes to its net.

(3 marks)

9. On the grid, show how this shape tessellates.

You should draw at least 6 shapes.

(3 marks)

10. On the grid, show how this kite will tessellate.

You should draw at least 8 kites.

(3 marks)

11. Here are 5 solid shapes.

(a) Match each solid shape to its name.

One has been done for you.

(3)

(b) How many faces does the cuboid have?

.....................................

(1)

(4 marks)

12. The diagram shows some nets and some solid shapes.

An arrow has been drawn from one net to its solid shape.

Draw an arrow from each of the other nets to its solid shape.

(3 marks)


Mean, Median, Mode &

Range






Instructions






Information






Advice





1. Chloe made a list of her homework marks.

4 5 5 5 4 3 2 1 4 5

(a) Write down the mode of her homework marks.

…………………….

(1)

(b) Work out her mean homework mark.

…………………….

(2)

(Total 3 marks)

2. Peter rolled a 6-sided dice ten times.

Here are his scores.

3 2 4 6 3 3 4 2 5 4

(a) Work out the median of his scores.

.................................

(2)

(b) Work out the mean of his scores.

.................................

(2)

(c) Work out the range of his scores.

.................................

(1)

(Total 5 marks)

3. Here are the weights, in kg, of 8 people.

63 65 65 70 72 86 90 97

(a) Write down the mode of the 8 weights.

............................ kg

(1)

(b) Work out the range of the weights.

............................ kg

(2)

(Total 3 marks)

4. Here are the ages of 6 people.

5 18 10 14 22 12

(a) Work out the range of these ages.

.....................................

(1)

(b) Find the median age.

.....................................

(2)

(c) Work out the mean age.

.....................................

(2)

(Total 5 marks)

5. Here are the shoe sizes of 6 students.

2 10 7 6 10 9

(a) Work out the range of these shoe sizes.

.....................................

(1)

(b) Find the median shoe sizes.

.....................................

(2)

(c) Work out the mean shoe sizes.

.....................................

(2)

(Total 5 marks)

6. Jalin wrote down the ages, in years, of seven of his relatives.

45, 38, 43, 43, 39, 40, 39

(a) Find the median age.

.......................................

(1)

(b) Work out the range of the ages.

.......................................

(1)

(c) Work out the mean age.

.......................................

(2)

(Total 4 marks)

7. Mr Smith kept a record of the number of absences for each student in his

class for one term.


0 0 0 8 4 5 5 3 2 1

(a) Write down the mode.

………………...

(1)

(b) Work out the mean.

………………...

(2)

(Total 3 marks)

8. Here are 10 numbers.

3 2 5 4 2 4 6 2 1 2

(a) Find the mode of these numbers.

.......................................

(1)

(b) Find the median of these numbers.

.......................................

(2)

(c) Find the range of these numbers.

.......................................

(2)

(Total 5 mark)

9. Here are the test marks of 6 girls and 4 boys.

Girls: 5 3 10 2 7 3

Boys: 2 5 9 3

(a) Write down the mode of the 10 marks.

……………………………

(1)

(b) Work out the median mark of the boys.

……………………

(2)

(c) Work out the range of the girls’ marks.

……………………

(1)

(d) Work out the mean mark of all 10 students.

……………………

(2)

(Total 6 marks)

10. Here are ten numbers.

7 6 8 4 5 9 7 3 6 7

(a) Work out the range.

.....................................

(2)

(b) Work out the mean.

.....................................

(2)

(Total 4 marks)

11. Here are fifteen numbers.

10 12 13 15 15

17 19 20 20 20

21 25 25 25 25

(a) Find the mode.

..........................

(1)

(b) Find the median.

..........................

(1)

(c) Work out the range.

..........................

(2)

(Total 4 marks)

12. A rugby team played 7 games.

Here is the number of points they scored in each game.

3 5 8 9 12 12 16

(a) Find the median.

....................

(2)

The rugby team played another game.

They scored 11 points.

(b) Find the median number of points scored in these 8 games.

....................

(3)

(Total 5 marks)

13. Tom recorded the shoe size of five of his friends.


8 9 3 4 7

(a) Work out the median shoe size.

............................................

(2)

Another friend has a shoe size of 8

(b) Work out the median shoe size of all six friends of Tom.

............................................

(2)

(Total 4 marks)

14. The mean of eight numbers is 41

The mean of two of the numbers is 29

What is the mean of the other six numbers?

.................................

(Total 3 marks)


PICTOGRAMS






Instructions






Information






Advice





1. The pictogram shows the numbers of loaves of bread made by Miss Smith,

Mr Jones and

Mrs Gray.

Miss Smith

Mr Jones

Mrs Gray

Ms Shah

Mr Khan

represents 20 loaves of bread

(a) Write down the number of loaves of bread made by Mr Jones.

.....................

(1)

(b) Write down the number of loaves of bread made by Mrs Gray.

.....................

(1)

Ms Shah made 60 loaves of bread.

Mr Khan made 90 loaves of bread.

(c) Use this information to complete the pictogram.

(2)

(Total 4 marks)

2. The pictogram gives information about the number of goals scored in a local

football

league in each of 3 weeks.

First week

Second week

Third week

Fourth week

Fifth week

Key: represents 4 goals

(a) Find the number of goals scored in the first week.

………………...

(1)

(b) Find the number of goals scored in the third week.

………………...

(1)

8 goals were scored in the fourth week.

5 goals were scored in the fifth week.

(c) Complete the pictogram.

(2)

(Total 4 marks)

3. The pictogram shows the number of plates sold by a shop on Monday,

Tuesday, Wednesday and Thursday of one week.

(a) Work out the number of plates sold on Monday.

.....................................

(1)

(b) Work out the number of plates sold on Tuesday.

.....................................

(1)

The shop sold 40 plates on Friday.

The shop sold 25 plates on Saturday.


(2)

(Total 4 marks)

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

Key: represents 10 plates

4. The pictogram shows the number of books sold on Wednesday, Thursday

and Friday.

Wednesday

Thursday

Friday

Saturday

Key:

represents 8

books

(a) Write down the number of books sold on Wednesday.

............................

(1)

(b) Write down the number of books sold on Friday.

............................

(1)

20 books were sold on Saturday.


(1)

(Total 3 marks)

5. The pictogram shows the numbers of hours of sunshine on Monday,

Tuesday and Wednesday one week.

(a) Write down the number of hours of sunshine on

(i) Monday,

.......................... hours

(ii) Wednesday.

.......................... hours

(2)

On Thursday there were 4 hours of sunshine.

(b) Show this on the pictogram.

(1)

On Friday there were 7 hours of sunshine.

(c) Show this on the pictogram.

(1)

(Total 4 marks)

Monday

Tuesday

Wednesday

Thursday

Friday

Key: represents

2 hours

6. The pictogram shows the numbers of zips sold in a shop on Monday, on Tuesday

and on Wednesday.

(a) Write down the number of zips sold on Monday.

..........................................

(1)

(b) Write down the number of zips sold on Wednesday.

..........................................

(1)

9 zips were sold on Thursday.

(c) Complete the pictogram.

(1)

(3 marks)

7. The tally chart shows information about the numbers of text messages sent by

some students last week.

Name of student Tally Frequency

Anna 24

Bhavini 12

Cassie

David

(i) Complete the frequency column.

The pictogram shows the numbers of text messages sent by Anna and Cassie.

(ii) Complete the pictogram and the key.

(Total 5 marks)


CONVERSION

GRAPHS






Instructions






Information






Advice





1. The conversion graph can be used to change between pounds (£) and Euros (€).

(a) Use the graph to change 30 pounds to Euros.

€ ................

(1)

(b) Use the graph to change 16 Euros to pounds.

£ ................

(1)

(Total 2 marks)

0 10

10

20

20

30

30

40

40

50

Euros (€)

Pounds (£)

2. Here is a conversion graph between pounds (£) and Australian dollars.

(a) Change 20 Australian dollars to pounds.

£ .....................................

(1)

(b) Change £7 to Australian dollars.

..................................... Australian dollars

(1)

(c) Change £400 to Australian dollars.

..................................... Australian dollars

(2)

(Total 4 marks)

Australian

dollars

Pounds (£)

30

25

20

15

10

5

2 4 6 8 10 120

3. John cleans carpets of different areas.

He uses this graph to work out the cost of cleaning a carpet.

A carpet has an area of 30 m2.

(a) Use the graph to find the cost of cleaning this carpet.

£ ..................................

(1)

It costs £150 to clean another carpet.

(b) Use the graph to find the area of this carpet.

.............................. m2

(1)

A rectangular carpet has a length of 8.6 m.

It has a width of 5 m.

(c) Work out the cost of cleaning this carpet.

£ ..................................

(3)

(Total 5 marks)

200

150

100

50

O 10 20 30 40 50

Cost

(£)

Area (m )2

4.

This conversion graph can be used to change between metres and feet.

(a) Use the conversion graph to change 6 metres to feet.

..................................... feet

(1)

(b) Use the conversion graph to change 8 feet to metres.

..................................... metres

(1)

Robert jumps 4 metres.

James jumps 12 feet.

(c) (i) Who jumps furthest, Robert or James?

.....................................

(ii) How did you get your answer?

...............................................................................................................................

...............................................................................................................................

(2)

(Total 4 marks)

10

15

5

20

25

2 4 6 8O

feet

metres

5. This conversion graph can be used to change between litres and gallons.

(a) Use the graph to change 50 litres to gallons.

........................ gallons

(1)

(b) Use the graph to change 6 gallons to litres.

............................ litres

(1)

1 litre of petrol costs £1.15

(c) Work out the cost of 50 litres of petrol.

£ ..................................

(2)

(d) Work out an estimate for the cost of 1 gallon of petrol.

£ ..................................

(2)

(Total 6 marks)

6. The exchange rate to change pounds (£) into US dollars ($) is £1 = $1.50

(a) Use this exchange rate to complete the table below.

Pounds (£) 0 1 2 5 10 20 50 100

US dollars ($) 0 1.50 7.50 30 150

(2)

(b) On the grid, draw a conversion graph for converting between pounds and US dollars.

(2)

(c) Change $100 into pounds (£).

£ ..................................

(2)

(Total 6 marks)

7. You can use the graph to change between miles and kilometres.

Change 60 kilometres into miles.

.............................................. miles

(Total 3 marks)


FACTORS,

MULTIPLES PRIMES






Instructions






Information






Advice





1.

Using only the numbers in the cloud, write down

(i) all the multiples of 6, …………………………….

(ii) all the square numbers, …………………………….

(iii) all the factors of 12, …………………………….

(iv) all the cube numbers. …………………………….

(4 marks)

2. Here is a list of numbers.

2 5 7 8 9 12

Write down a number from the list which is

(i) a multiple of 6, .....................................

(ii) a factor of 15, .....................................

(iii) a square number. .....................................

(3 marks)


3 8 11 25 33 41

Write down a number from the list which is

(a) an even number, ..............................

(1)

(b) a square number, ..............................

(1)

(c) a multiple of 11 ..............................

(1)

(3 marks)

812

4

165

6

3

27

4.

From the numbers in the cloud, write down

(a) a square number,

..........................

(1)

(b) the square root of 16,

..........................

(1)

(c) the cube of 2,

..........................

(1)

(d) the prime number.

..........................

(1)

(4 marks)

5.

2 3 4 5 6 7 8

From the list of numbers, write down

(i) the square number,

.....................................

(ii) the cube number,

.....................................

(iii) the square root of 9.

.....................................

(3 marks)

32 16

2 4

8 6


17 24 25 26 35 43 44

From the numbers in the list, write down

(i) the odd number that is larger than 40,

..........................

(ii) the number that is a multiple of 7,

..........................

(iii) two numbers that have a difference of 20,

............., .............

(iv) the number that has the same value as 2 + 3 × 5

..........................

(4 marks)


8 15 23 27 32 33

From the numbers in the list, write down a number that is prime.

…………………………….

(1 marks)

8.

From the numbers in the rectangle,

(i) write down a multiple of 4, ........................

(ii) write down a factor of 21, ........................

(iii) write down a prime number. ........................

(3 marks)

18 42

9

3

12

6 81

11 30

18 42

9

3

12

6 81

11 30

9. Here is a list of eight numbers.

5 6 12 20 25 26 28 33

(a) From the list, write down

(i) a square number,

..........................

(ii) a number that is a multiple of 7,

..........................

(iii) two numbers that are factors of 40,

............ and ............

(iv) two numbers with a sum of 59.

............ and ............

(4)

(b) Tony says that “6 is a cube number because 23 = 6”.

Tony is wrong. Explain why.

......................................................................................................................................

(1)

(5 marks)

10.

8

9 10

12

30 3

5 20

Using only the numbers in the rectangle, write down

(i) an even number

..................

(ii) a multiple of 4

..................

(iii) a factor of 15

..................

(3 marks)

11.

factor multiple square square root half

(a) Use a word from the list above to complete the following sentence.

10 is a ......................................... of 5

(1)

(b) From the list below, write down the odd number.

10 15 18 20 24

………………...

(1)

(c) From the list below, write down the square number.

10 12 14 16 18 20

………………...

(1)

(3 marks)


2 4 5 6 7 8

From the list of numbers write down

(i) an odd number ............................

(ii) a square number ............................

(iii) a multiple of 3 ............................

(iv) a factor of 10 ............................

(4 marks)

13. Here is a list of 8 numbers.

4 7 10 16 18 20 21 32

From the numbers in the list write down a number that is

(i) an odd number ..................

(ii) a multiple of 5 ..................

(iii) a square number ..................

(iv) a factor of 42 ..................

(4 marks)

14. Here is a list of 8 numbers.

3 5 6 8 9 10 11 16

From the list, write down

(a) two odd numbers,

............ and .............

(1)

(b) two numbers with a sum of 15

............ and .............

(1)

(c) a factor of 12

...........................

(1)

(d) a multiple of 4

...........................

(1)

James says that 10 is a square number because 52 = 10

(e) James is wrong.

Explain why.

.....................................................................................................................................

.....................................................................................................................................

(1)

(5 marks)

15. (a) Here is a list of numbers.

3 5 7 8 9 10 12

From the list of numbers, write down

(i) a multiple of 6 .....................................

(ii) a factor of 14 .....................................

(iii) a square root of 25 .....................................

(3)

(b) Scott says

‘If you add two different square numbers, you will always get an even number.’

Show that Scott is wrong.

(2)

(5 marks)


2 5 8 10 13 14 16 18

(a) From the list, write down

(i) an odd number, ........................

(ii) the multiple of 6, ........................

(iii) the square number. ........................

(3)

Erin says that 8 is a prime number.

(b) Erin is wrong.

Explain why.

.....................................................................................................................................................

.....................................................................................................................................................

(1)

(4 marks)


POWERS, ROOTS &

BIDMAS






Instructions






Information






Advice





1. (a) Work out 4 × 3 + 2

.....................................

(1)

(b) Work out 20 − 12 ÷ 4

.....................................

(1)

(c) Work out (18 ÷ 3) + (20 ÷ 5)

.....................................

(1)

(d) Work out (3 + 5)2

.....................................

(1)

(4 marks)

2. Work out

(i) 3 × 3 – 5

....................................

(ii) 20 ÷ (12 – 2)

....................................

(iii) 7 + 8 ÷ 4

....................................

(3 marks)

3. Beth says 20 − 5 × 3 is 45

Pat says 20 − 5 × 3 is 5

(a) Who is right?

Give a reason for your answer.

....................................... is right

(2)

(b) Work out (12 + 9) ÷ 3

.....................................

(1)

(3 marks)


(i) the square of 6

.....................................

(ii) 24

.....................................

(2)

(b) Work out the value of

(i) −10 ÷ 5

.....................................

(ii) −3 × −4

.....................................

(2)

(4 marks)

5. (a) Work out 2 × (11 + 9)

..........................

(1)

(b) Work out 3 × 5 + 4

..........................

(1)

(c) Work out 20 – 5 × 3

..........................

(1)

(3 marks)

6. (a) Work out the value of (4 + 5) × 2 + 3

…………………

(1)

(b) Add brackets ( ) to make each statement correct.

You may use more than one pair of brackets in each statement.

(i) 4 + 5 × 2 + 3 = 29

(ii) 4 + 5 × 2 + 3 = 45

(2)

(3 marks)

7. (a) Work out the value of (2 + 3) × 4 + 5

…………………

(1)



(i) 2 + 3 × 4 + 5 = 29

(ii) 2 + 3 × 4 + 5 = 45

(2)

(3 marks)

8. Work out

(i) 2 × 3 + 4

…………………….

(ii) 3 + 5 × 2

…………………….

(ii) 16 ÷ (2 × 4)

…………………….

(3 marks)

9. (a) Work out

..........................

(1)

(b) Work out

33 × 10 – 6 × 5

..........................

(2)

(c) Work out

6 + 2 × (5 - 1)

..........................

(2)

(5 marks)

10. Frankie says that 15 − 3 × 2 = 24

Frankie is wrong.

Explain why.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

(3 marks)

6

38

11. (a) Work out 4 × 5 – 8

.....................................

(1)

(b) Work out 18 + 2 × 3

.....................................

(1)

(c) Work out 7 + 3 × 5

.....................................

(1)

(d) Work out 13 – 3 × 4 + 2

.....................................

(1)

(e) Work out (4 + 3) × 7

.....................................

(1)

(e) Work out 20 – (4 + 10)

.....................................

(1)

(6 marks)

12. (a) Write down the value of 81

..............................................

(1)

(b) Work out the value of 52 + 2

3

..............................................

(2)

(3 marks)

13. (a) Work out the value of (9 + 2) × 6 - 3

…………………

(1)



(i) 9 + 2 × 6 - 3 = 18

(ii) 9 + 2 × 6 - 3 = 15

(2)

(3 marks)


ORDERING

FRACTIONS,

DECIMALS &

PERCENTAGES Materials required for examination Items included with question papers





Instructions






Information






Advice





1.

Write these fractions in order of size.

Start with the smallest fraction.

..............................................................................

(Total 2 marks)

2. Write these numbers in order of size.

Start with the smallest number.

(i) 75, 56, 37, 9, 59

...........................................................................................

(ii) 0.56, 0.067, 0.6, 0.65, 0.605

...........................................................................................

(iii) 5, – 6, – 10, 2, – 4

...........................................................................................

(iv) , , ,

...........................................................................................

(Total 5 marks)

8

5

2

1

4

3

2

1

3

2

5

2

4

3



(i) 0.56, 0.067, 0.6, 0.65, 0.605

..................................................................................................

(ii) 5, – 6, – 10, 2, – 4

..................................................................................................

(iii) , , ,

..................................................................................................

(Total 4 marks)

4. Write these fractions in order of size.

Start with the smallest fraction.

……………………………

(Total 2 marks)

2

1

3

2

5

2

4

3

8

5

2

1

4

3

16

9



0.82 85

..............................................................................

(2)

(Total 2 marks)



(a) 76, 103, 13, 130, 67

………………………………………………………

(1)

(b) –3, 5, 0, –7, –1

………………………………………………………

(1)

(c) 70%, , 0.6,

………………………………………………………

(2)

(Total 4 marks)

5

4

3

2

8

7

4

3

3

2



0.4 35%

…………………………………………………………

(2)

(Total 3 marks)

8. Here are six numbers

75% 0.75 66 %

Two of the numbers are not equal to

Draw a circle around each of the two numbers.

(Total 2 marks)

15

7

7

3

10

8

12

9

3

2

8

6

4

3


BEST BUYS






Instructions






Information






Advice





1. Two shops, Food Mart and Jim’s Store, both sell Kreemy Yoghurts.

At which shop are Kreemy Yoghurts the better value for money?


.....................................

(3 marks)

2.

A pack of 9 toilet rolls costs £4.23

A pack of 4 toilet rolls costs £1.96

Which pack gives the better value for money?


............................................................

(3 marks)

*3. T-shirts normally cost £12 each.

Two shops have a special offer on these T-shirts.

Stephen wants to buy 30 T-shirts.

Work out at which shop, Stephen will get the better deal.

You must show clearly how you got your answer.

.....................................

(4 marks)

T-Shirts-R-Us

Special offer Pay for two T-shirts and get one free. Pay for five T-shirts and get three free

Budget Shirt Company

Special offer

1/3 off normal price

*4. Potatoes cost £9 for a 12.5 kg bag at a farm shop.

The same type of potatoes cost £1.83 for a 2.5 kg bag at a supermarket.

Where are the potatoes the better value, at the farm shop or at the supermarket?

You must show your working.

.....................................

(4 marks)

*5. Radox Handwash cost is on offer at Boots and Superdrug.

Boots 500ml bottles on offer at 3 for 2

Superdrug 300ml bottles on offer at buy one get one free

Where is the handwash better value, at Boots or Superdrug?


.....................................

(4 marks)

*6. Carrots cost £1 for a 1.2 kg bag at Tesco.

The same type of carrots cost 77 pence for a 700 g bag at ASDA.

Where are the Carrots better value.


.....................................

(4 marks)

*7. Diet Coke is on offer at Morrisons and Sainsburys.

Morrisons: 2 litre bottles on offer 3 for £4.50

Sainsburys: 24 cans x 330ml on offer for £8.85

.....................................

(4 marks)

8. Thomas wants to buy an iPod.

The iPod that Thomas wants is sold in two different shops.

Work out the difference in the cost of the iPod at the two shops..

£ ……………………

(5 marks)

Music City

£84 plus VAT

at 17½ %

Pod Direct

15% OFF usual price

of £120

*9. Railtickets and Cheaptrains are two websites selling train tickets.

Each of the websites adds a credit card charge and a booking fee to the ticket price.

Railtickets

Credit card charge: 2.25% of ticket price

Booking fee: 80 pence

Cheaptrains

Credit card charge: 1.5% of ticket price

Booking fee: £1.90

Nadia wants to buy a train ticket.

The ticket price is £60 on each website.

Nadia will pay by credit card.

Will it be cheaper for Nadia to buy the train ticket from Railtickets or from Cheaptrains?

.....................................

(4 marks)


FRACTIONS: ADDING,

SUBTRACTING,

MULTIPLYING AND

DIVIDING






Instructions






Information






Advice





1. Work out

....................

(Total 2 marks)

2. Work out

…………………….

(Total 2 marks)

3. Work out –

..........................

(Total 2 marks)

7

1

5

2

5

1

3

2

12

11

6

5

4. (a) Work out

....................................

(2)

(b) Work out

....................................

(1)

(Total 3 marks)

5. Work out the value of ×

Give your answer as a fraction in its simplest form.

……………

(Total 2 marks)

12

1

3

1

5

1

4

3

3

2

4

3

6. Work out 60 ×

……………………..

(Total 2 marks)

7. (a) Work out 1 –

....................................

(3)

(b) Work out 12

....................................

(3)

(Total 6 marks)

3

2

6

1

2

1

2

1

8

5

8. (a) Work out

………………………

(2)

(b) Work out 5 – 2

………………………

(3)

(Total 5 marks)

9. (a) Work out

.........................................

(2)

(b) Work out

.........................................

(3)

(Total 5 marks)

8

3

5

2

3

2

4

3

5

3

3

1

5

3

4

12

10. Work out

3 × 2

……………………………

(Total 3 marks)

11. (a) Work out 1 × 5

....................

(2)

(b) Work out 3 ÷ 2

....................

(2)

(Total 4 marks)

43

32

8

7

3

1

2

1

5

4



…………………….

(2)



…………………….

(3)

(Total 5 marks)

13. Work out 5 – 2

………………………

(Total 3 marks)

4

3×

3

2

4

32+

3

21

3

2

4

3

14. Work out

............................................

(Total 3 marks)

15. Work out

..........................................

(Total 3 marks)

5

21

2

14

4

31

5

23


RATIO






Instructions






Information






Advice





1. A piece of wood is of length 45 cm.

The length is divided in the ratio 7 : 2

Work out the length of each part.

...................... cm, ..................... cm

(3 marks)

2. Alex and Ben were given a total of £240

They shared the money in the ratio 5 : 7

Work out how much money Ben received.

£ .............................

(3 marks)

3. Ken and Susan share £20 in the ratio 1 : 3

Work out how much money each person gets.

Ken £ .....................

Susan £ ..................

(3 marks)

4. Melissa is 13 years old.

Becky is 12 years old.

Daniel is 10 years old.

Melissa, Becky and Daniel share £28 in the ratio of their ages.

Becky gives a third of her share to her mother.

How much should Becky now have?

£ ..................................

(Total 4 marks)

5. Amy, Beth and Colin share 36 sweets in the ratio 2 : 3 : 4

Work out the number of sweets that each of them receives.

Amy………….sweets

Beth………….sweets

Colin…………..sweets

(3 marks)

6. A shop sells CDs and DVDs.

In one week the number of CDs sold and the number of DVDs sold were in the ratio 3:5

The total number of CDs and DVDs sold in the week was 728

Work out the number of CDs sold.

.................................

(3 marks)

7. The ratio of girls to boys in a school is 2 : 3

(a) What fraction of these students are boys?

…………….

(2)

In Year 8 the ratio of girls to boys is 1 : 3

There are 300 students in Year 8.

(b) Work out the number of girls in Year 8.

………………

(3)

(5 marks)

8. Ann and Bob shared £240 in the ratio 3 : 5

Ann gave a half of her share to Colin.

Bob gave a tenth of his share to Colin.

What fraction of the £240 did Colin receive?

.....................................

(5 marks)

9. Peter won £75 as a prize.

He gave 4/5 of the prize money as a present to Roger and Bethan.

Roger and Bethan shared the present in the ratio 2:3

Work out how much they each got.

..................................

(4 marks)

10. Rosa prepares the ingredients for pizzas.

She uses cheese, topping and dough in the ratio 2 : 3 : 5

Rose uses 70 grams of dough.

Work out the number of grams of cheese and the number of grams of topping Rosa uses.

Cheese ......................... g

Topping ....................... g

(Total 3 marks)

11. 5 schools sent some students to a conference.

One of the schools sent both boys and girls.

This school sent 16 boys.

The ratio of the number of boys it sent to the number of girls it sent was 1 : 2

The other 4 schools sent only girls.

Each of the 5 schools sent the same number of students.

Work out the total number of students sent to the conference by these 5 schools.

....................................................................

( 4 marks)

12. Pat and Julie share some money in the ratio 2 : 5

Julie gets £45 more than Pat.

How much money did Pat get?

£..............................................

(4 marks)

13. Last year Kerry’s take home pay was £15 000

She spent 40% of her take home pay on rent.

She used the rest of her take home pay for living expenses, clothes and entertainment in the ratio 3 :

1 : 2

How much did Kerry spend on entertainment last year?

£.............................................................

(4 marks)

*14. Talil is going to make some concrete mix.

He needs to mix cement, sand and gravel in the ratio 1 : 3 : 5 by weight.

Talil wants to make 180 kg of concrete mix.

Talil has

15 kg of cement

85 kg of sand

100 kg of gravel

Does Talil have enough cement, sand and gravel to make the concrete mix?

(4 marks)

15. Jim has only 5p coins and 10p coins.

The ratio of the number of 5p coins to the number of 10p coins is 2 : 3

Work out the ratio of

the total value of the 5p coins : the total value of the 10p coins.


(4 marks)


PROPORTION






Instructions






Information






Advice





1. Here is a list of ingredients for making 10 Flapjacks.

Ingredients for 10 Flapjacks

80 g rolled oats

60 g butter

30 ml golden syrup

36 g light brown sugar

Work out the amount of each ingredient needed to make 15 Flapjacks.

..................... g rolled oats

..................... g butter

..................... ml golden syrup

..................... g light brown sugar

(Total 3 marks)

2. Fred has a recipe for 30 biscuits.

Here is a list of ingredients for 30 biscuits.

Self-raising flour : 230g

Butter : 150g

Caster sugar : 100g

Eggs : 2

Fred wants to make 45 biscuits.

(a) Complete his new list of ingredients for 45 biscuits.

Self-raising flour :…………………

Butter : …………………

Caster sugar : …………………

Eggs : …………………

(3)

Gill has only 1 kilogram of self-raising flour. She has plenty of the other ingredients.

(b) Work out the maximum number of biscuits that Gill could bake.

..............................................

(3)

(6 marks)

______________________________________________________________________________

3. Here are the ingredients needed to make 16 gingerbread men.

Ingredients

to make 16 gingerbread men

180 g flour

40 g ginger

110 g butter

30 g sugar

Hamish wants to make 24 gingerbread men.

Work out how much of each of the ingredients he needs.

..........................................................g flour

.......................................................g ginger

........................................................g butter

.........................................................g sugar

(3 marks)

______________________________________________________________________________

4. Here are the ingredients needed to make 12 shortcakes.

Shortcakes

Makes 12 shortcakes

50 g of sugar

200 g of butter

200 g of flour

10 ml of milk

Liz makes some shortcakes.

She uses 25 ml of milk.

(a) How many shortcakes does Liz make?

..............................................

(2)

Robert has 500 g of sugar

1000 g of butter

1000 g of flour

500 ml of milk

(b) Work out the greatest number of shortcakes Robert can make.

..............................................

(2)

(4 marks)

______________________________________________________________________________

5. Here is a list of ingredients for making 12 small cakes.

Joe is going to make 24 of the small cakes.

(a) Work out how much margarine he needs.

(2)

...................................................... g

Sharon is going to make 18 of the small cakes.

(b) Work out how much flour she needs.

(2)

...................................................... g

(Total for Question 4 = 4 marks)

*6. This is a list of ingredients for making a pear & almond crumble for 4 people.

Ingredients for 4 people:

80 g plain flour

60 g ground almonds

90 g soft brown sugar

60 g butter

4 ripe pears

Jessica wants to make a pear & almond crumble for 10 people.

Here is a list of the amount of each ingredient Jessica has in her cupboard.

250 g plain flour

100 g ground almonds

200g soft brown sugar

150 g butter

8 ripe pears

Work out which ingredients Jessica needs to buy more of.

You must show all of your working.

(4 marks)

______________________________________________________________________________

*7. 225 grams of flour are needed to make 9 cakes.

Marian wants to make 20 of these cakes.

She has 475 grams of flour.

Does Marian have enough flour to make 20 cakes?


(3 marks)

___________________________________________________________________________


USING A

CASLCULATOR






Instructions






Information






Advice





1. Use your calculator to work out

(2.3 + 1.8)2 × 1.07

Write down all the figures on your calculator display.

.....................................

(2 marks)

2. (a) Work out 51.62.3

85.36.42

Write down all the numbers on your calculator display.

.........................................................

(3 marks)


17.354.2

86.57.13


You must give your answer as a decimal.

................................................................

(2 marks)

4. Use a calculator to work out

48.02.6

4.20


Give your answer as a decimal.

......................................................................................

(2 marks)

______________________________________________________________________________

5. (a) Use your calculator to work out

36.28.5

5.21


.....................................

(2)

(b) Write down your answer to part (a) correct to 2 decimal places.

.....................................

(1)

(3 marks)

6. (a) Use your calculator to work out the value of 22 28.034.0

1236.45


(2)

...........................................................................

(b) Write your answer to part (a) correct to 3 significant figures.

(1)

...........................................................................

(3 marks)

7. (a) Use your calculator to work out 7.19.3

75.35.2 2



.............................................................

(3)

(b) Write your answer to part (a) correct to 2 decimal places.

.....................................

(1)

(4 marks)

8. (a) Use your calculator to work out 9.54.18

2.145.38

.



..............................................

(2)

(b) Write your answer to part (a) correct to 1 significant figure.

..............................................

(1)

(3 marks)

9. Use your calculator to work out the value of

(a) Write down all the figures on your calculator display.

..........................

(2)

(b) Write your answer to part (a) to an appropriate degree of accuracy.

..........................

(1)

(3 marks)

______________________________________________________________________________

10. Use your calculator to work out the value of


.....................................

(2)

(b) Write down your answer to part (a) correct to 3 significant figures.

.....................................

(1)

(3 marks)

___________________________________________________________________________

63.981.4

52.427.6

49.103.2

84.795.8

11. (a) Use your calculator to work out


......................................

(2)

(b) Write your answer to part (a) correct to 3 significant figures.

......................................

(1)

(3 marks)

___________________________________________________________________________

12. Calculate the value of 160tan

160tan



..........................................

(3 marks)

___________________________________________________________________________

5.17.2

6.22.19 2


034.0012.0

65tan170920


You must write your answer as a decimal.

.......................................................

(2)

(b) Give your answer to part (a) correct to 3 significant figures.

...........................................

(1)

(3 marks)


EXCHANGE RATES






Instructions






Information






Advice





1. Jamie goes on holiday to Florida.

The exchange rate is £1 = 1.70 dollars.

He changes £900 into dollars.

(a) How many dollars should he get?

................................. dollars

(2)

After his holiday Jamie changes 160 dollars back into pounds.

The exchange rate is still £1 = 1.70 dollars.

(b) How much money should he get?

Give your answer to the nearest penny.

£ .................................

(2)

(4 marks)

2. Tania went to Italy.

She changed £325 into euros (€).

The exchange rate was £1 = €1.68

(a) Change £325 into euros (€).

€ ..................................

(2)

When she came home she changed €117 into pounds.

The new exchange rate was £1 = €1.50

(b) Change €117 into pounds.

£ .................................

(2)

(4 marks)

3.

Menu

Hot dog

Chicken salad

Hamburger

Pizza

$5.10

$4.50

$3.80

$4.00

A British family are on holiday in San Francisco.

At a café they order 3 hot dogs and 1 chicken salad.

The exchange rate is £1 = $1.44

Work out their total bill in pounds (£).

£ ………………

(4 marks)

4. A student bought a pair of sunglasses in the USA.

He paid $35.50

In England, an identical pair of sunglasses costs £26.99


In which country were the sunglasses cheaper, and by how much?

Show all your working.

................................................................................................

(4 marks)

5. Hugh went on holiday to Italy.

While on holiday, he went shopping.

He bought a belt and a hat.

The belt cost 25 euros.

The hat cost 14 euros.

The exchange rate was £1 = 1.56 euros.

Work out the total cost of the belt and the hat.

Give the total cost in pounds.

£ ................................

(4 marks)

6. Linda is going on holiday to the Czech Republic.

She needs to change some money into koruna.

She can only change her money into 100 koruna notes.

Linda only wants to change up to £200 into koruna.

She wants as many 100 koruna notes as possible.

The exchange rate is £1 = 25.82 koruna.

How many 100 koruna notes should she get?

..............................................

(6 marks)

7. Tim is travelling home from holiday by plane.

He buys some food and drink on the plane.

Tim buys two cheese rolls, a coffee and an orange juice.

He pays part of the cost with a 10 euro note.

He pays the rest of the cost in pounds (£).

How much does Tim pay in pounds?

£ .......................................................................

(4 marks)

8. Esther went to France.

She changed £300 into Euros (€).


(a) How many Euros did she get?

€ ..................................

(2)

Esther went shopping in France.

She bought

2 necklaces for €2.60 each

1 hat for €6.40

1 bag for €9.80


(b) Work out her total bill in pounds (£).

£ ..................................

(4)

(6 marks)

9. Rosie and Jim are going on holiday to the USA.

Jim changes £350 into dollars ($).


(a) Work out how many dollars ($) Jim gets.

$ ..................................

(2)

In the USA Rosie sees some jeans costing $67

In London the same make of jeans costs £47.50

The exchange rate is still £1 = $1.34

(b) Work out the difference between the cost of the jeans in the USA and in London.

Give your answer in pounds (£).

£ ..................................

(3)

(5 marks)

10. The exchange rate in London is £1 = €1.14

The exchange rate in Paris is €1 = £0.86

Elaine wants to change some pounds into euros.

In which of these cities would Elaine get the most euros?

You must show all of your working.

.....................................

(4 marks)

11. Stephen imports cars from the USA. He sells them in the UK.

He has just bought a car in the USA costing $24 000.

It cost him £900 to import the car to the UK.


Stephen needs to make a profit of 20% on his total costs.

Work out the least amount that Stephen must sell the car for in the UK.

Give your answer in pounds.

£ …………………….

(4 marks)


ALGEBRA:

SUBSTITUTION






Instructions






Information






Advice





1. P = 3n

n = 6

(a) Work out the value of P.

P = ....................................

(1)

Q = 2c + d

c = 3

d = 2

(b) Work out the value of Q.

Q = ....................................

(2)

(Total 3 marks)

2. p = 5

r = 2

(a) Work out the value of

4p + 3r

..........................

(2)

n is an even number.

(b) What type of number is n + 1?

..........................

(1)

(Total 3 marks)

3. y = 5x – 3

Find the value of y when x = 9

y = ..............................

(2)

(Total 2 marks)

4. P = 4k – 10

k = 7

(a) Work out the value of k.

.....................................

(2)

y = 4n – 3d

n = 2

d = 5

(b) Work out the value of y.

.....................................

(2)

(Total 4 marks)

5. v = u + 10t

Work out the value of v when

u = 10 and t = 7

v = ………………………

(Total 2 marks)

6.

You can work out the amount of medicine, c ml, to give to a child by using the

formula

c =150

ma

m is the age of the child, in months.

a is an adult dose, in ml.

A child is 30 months old.

An adult’s dose is 40 ml.

Work out the amount of medicine you can give to the child.

.............................................. ml

(Total 2 marks)

7. V = 3b + 2b2

Find the value of V when b = 4

......................................................

(Total 2 marks)

8. (a) Work out the value of 3p + 4q when p = 5 and q = –2

………………………

(2)

(b) Given that y = 4x – 3, work out the value of x when y = 11

x = ………………………

(3)

(Total 5 marks)

9. Work out the value of 5x + 1 when x = –3

..........................

(2)

(Total 2 marks)

10. (a) Work out the value of 3x – 4y when x = 3 and y = 2

.......................

(2)

(b) Work out the value of when p = 2 and q = –7

.......................

(3)

(Total 5 marks)

4

)3–(qp

11. S = 2p + 3q

p = – 4

q = 5

(a) Work out the value of S.

S =………………………

(2)

T = 2m + 30

T = 40

(b) Work out the value of m.

m =………………………

(2)

(Total 4 marks)

12. A = 4bc

A = 100

b = 2

Work out the value of c.

c =………………………

(2)

(Total 2 marks)

13. (a) Work out the value of 2a + ay when a = 5 and y = –3

…………………….

(2)

(b) Work out the value of 5t2 – 7 when t = 4

…………………….

(3)

(Total 5 marks)

14.

A = 27

h = 4

Work out the value of x

x = ....................................

(Total 3 marks)

2

)10(

xhA

15. h = 5t2 + 2

(i) Work out the value of h when t = –2

.....................................

(3)

(ii) Work out a value of t when h = 47

.....................................

(3)

(Total 5 marks)

16. V = 3b + 2b2

Find the value of V when b = –4

(3)

......................................................

(Total 3 marks)


ANGLES:

PARALLEL LINES






Instructions






Information






Advice





1.

ABC and DEF are parallel lines.

BEG is a straight line.

Angle GEF = 47.

Work out the size of the angle marked x.

Give reasons for your answer.

..............................................

(3 marks)

______________________________________________________________________________

2.

DE is parallel to FG.

(i) Find the size of the angle marked y°.

..........................°

(1)

(ii) Give a reason for your answer.

...........................................................................................................................

...........................................................................................................................

(2)

(3 marks)


NOT

62° y°

64°

D E

F G

______________________________________________________________________________

3.

Diagram NOT

accurately drawn

AQB, CRD and PQRS are straight lines.

AB is parallel to CD.

Angle BQR = 113º.

(a) Work out the value of x.

x = ..............................

(b) Give reasons for your answer.

......................................................................................................................................................

......................................................................................................................................................

......................................................................................................................................................

(4 marks)

______________________________________________________________________________

4.

(a) i) Find the value of x.

.....................................

(1)

ii) Give reasons for your answer.

.....................................

(1)

(b) i) Find the value of y.

.....................................

(2)

ii) Give reasons for your answer.

.....................................

(2)

(6 marks)

*5.

ABCD is a parallelogram.

Angle ADB = 38.

Angle BEC = 41.

Angle DAB = 120.

Calculate the size of angle x.

You must give reasons for your answer.

(4 marks)

______________________________________________________________________________

*6.

CDEF is a straight line.

AB is parallel to CF.

DE = AE.


You must give reasons for your answer.

(4 marks)

______________________________________________________________________________

*7.

ABC and DEFG are parallel.

AEH and BFH are straight lines.

Work out the size of the angle marked x°.

.........................................................................°

(3 marks)


ANGLES






Instructions






Information






Advice





1.

PQ is a straight line.

(a) Work out the size of the angle marked x°.

..............................°

(1)

(b) (i) Work out the size of the angle marked y°.

..............................°

(ii) Give reasons for your answer.

...................................................................................................................

...................................................................................................................

(3)

(4 marks)

2.


Work out the size of the angle a.

........................................°

(2 marks)

x°

y°

126°

P Q

RDiagram accurately drawn

NOT

120º 140º

58º

a

3.


In the diagram, ABC is a triangle.

ACD is a straight line.

Angle CAB = 50°.

Angle ABC = 60°.


....................................°

(2 marks)

4.


PQR is an isosceles triangle.

PQ = PR.

Angle R = 23°.

Work out the value of x.

x = ...............................

(2 marks)

B

A C D

50º

60º

x

P

Q 23° R

x°

5.


ABC is a triangle.

Work out the size of the angle marked p.

p = .....................°

(2 marks)

6.


PQR is a straight line.

SQ = SR.

(i) Work out the size of the angle marked x°

..........................°

(ii) Give reasons for your answer.

...........................................................................................................................

...........................................................................................................................

(3 marks)

70°

50°

A

pB C

S

P Q R

xº 50º

7.


(a) Work out the value of x.

x = ………….

(1)

(b) Work out the value of y.

y = ………….

(2)

(3 marks)

8.

Triangle ABC is isosceles, with AC = BC.

Angle ACD = 620.

BCD is a straight line.

Work out the size of angle x.

x = ………………0

(2 marks)

xº43º

108º

yº

x 62°

A

B C D


NOT

9.


PQR is a straight line.

PQ = QS = QR.

Angle SPQ = 25°.

(a) (i) Write down the size of angle w.

......................................°

(ii) Work out the size of angle x.

......................................°

(2)

(b) Work out the size of angle y.

......................................°

(2)

(4 marks)

10.

Diagram NOT

accurately drawn


x = ………………...

(3 marks)

25º

w y

P Q R

S

x

11.

ABD is a triangle. ABC is a straight line.

Angle ABD = 70°.

AD = BD.

(a) (i) Work out the value of x.

x = ....................................


............................................................................................................................

(2)

(b) (i) Work out the value of y.

y = ....................................


...........................................................................................................................

...........................................................................................................................

(3)

(5 marks)

12.

Work out the value of a.

a = .............................

(3 marks)

D

y°

A B C

x°70°

a°

65°138°


NOT

Diagram NOT

accurately drawn

13.


In the diagram, ABC is a straight line and BD = CD.

(a) Work out the size of angle x.

....................................º

(2)

(b) Work out the size of angle y.

....................................º

(3)

(5 marks)


ANGLES: POLYGONS






Instructions






Information






Advice





1. Each exterior angle of a regular polygon is 30°.

Work out the number of sides of the polygon.

.....................................

(2 marks)

2.

Work out the size of an exterior angle of a regular pentagon.

..........................°

(2 marks)

3.

Calculate the size of the exterior angle of a regular hexagon.

..........................°

(2 marks)


NOT


NOT

4. The size of each exterior angle of a regular polygon is 40°.

Work out the number of sides of the regular polygon.

.....................................

(2 marks)

5. The size of each interior angle of a regular polygon is 156°.

Work out the number of sides of the polygon.

.....................................

(3 marks)

6. Here is a regular polygon with 9 sides.


Work out the size of an exterior angle.

……………………….°

(2 marks)

7.


(a) Work out the size of each interior angle of a regular octagon.

……………………………

(3)

The size of each exterior angle of a regular polygon is 300

(b) Work out the number of sides of the polygon.

……………………………

(2)

(5 marks)

8.


The diagram shows part of a regular 10-sided polygon.


....................°

(3 marks)

x

9.

The diagram shows a regular hexagon and a regular octagon.

Calculate the size of the angle marked x.


..............................................°

(4 marks)

______________________________________________________________________________

10.

The diagram shows a square and 4 regular pentagons.


.......................................... °

(4 marks)

______________________________________________________________________________

11.

Diagram NOT

accurately drawn

ABCDE and EHJKL are regular pentagons.

AEL is an equilateral triangle.

Work out the size of angle DEH.

......................................................

(4 marks)

12. The diagram shows part of a pattern made from tiles.

The pattern is made from two types of tiles, tile A and tile B.

Both tile A and tile B are regular polygons.

Work out the number of sides tile A has.

.................................................

(4 marks)

______________________________________________________________________________


AREA &

CIRCUMFERENCE OF

CIRCLES






Instructions






Information






Advice





1. Here are 5 diagrams and 5 labels.

In each diagram the centre of the circle is marked with a cross (×).

Match each diagram to its label.


(3 marks)

Diagram Label

Circle and

tangent

Circle and

radius

Circle and

chord

Circle and

sector

Circle and

diameter

2. Here are some diagrams relating to a circle.

Draw an arrow from each of the diagrams to its mathematical name.

The arrow showing an arc is drawn for you.

(3 marks)

Arc

Circle anddiameter

Circle andsector

Circle andtangent

Circle andsegment

3. The radius of a circle is 3.60 m.

Work out the area of the circle.

Give your answer correct to 3 significant figures.

…………….……………..

(3 marks)

4. The diameter of a wheel on Harry’s bicycle is 0.65 m.

Calculate the circumference of the wheel.

Give your answer correct to 2 decimal places.

.................................

(3 marks)

5.

The radius of a circle is 4 m.



..........................

(3 marks)

3.60 m

4 m

Diagram NOT

accurately drawn

Diagram NOT

accurately drawn

Diagram NOT

accurately drawn

6. A circle has a radius of 6.1 cm.

Work out the circumference of the circle.


...........................................

(3 marks)

7. The radius of a circle is 6.4 cm.

Work out the circumference of this circle.

Give your answer correct to 1 decimal place.

.......................

(3 marks)

8.

The radius of the circle is 9.7 cm.


Give your answer to 3 significant figures.

……………………………

(3 marks)

6.1 cm

6.4 cm

9.7 cm

Diagram NOT

accurately drawn

Diagram NOT

accurately drawn

Diagram NOT

accurately drawn

9. The diameter of a circle is 12 centimetres.

(a) Work out the circumference of the circle.

Give your answer, in centimetres, correct to 1 decimal place.

..............................

(3 marks)

10. Here is a tile in the shape of a semicircle.

The diameter of the semicircle is 8 cm.

Work out the perimeter of the tile.


..................................... cm

(3 marks)

11.

The radius of this circle is 8 cm.

Work out the circumference of the circle.


.............................. cm

(3 marks)

12 cm

Diagram drawn accurately

NOT

8 cm

8 cm

Diagram NOT

accurately drawn

Diagram NOT

accurately drawn

12.


A circle has a radius of 6 cm.

A square has a side of length 12 cm.

Work out the difference between the area of the circle and the area of the square.

Give your answer correct to one decimal place.

......................................

(4 marks)

13. The top of a table is a circle.

The radius of the top of the table is 50 cm.

(a) Work out the area of the top of the table.

………………………cm2

(2)

The base of the table is a circle.

The diameter of the base of the table is 40 cm.

(b) Work out the circumference of the base of the table.

………………………cm

(2)

(4 marks)

12 cm

12

cm

6 cm

14.


The diagram shows two small circles inside a large circle.

The large circle has a radius of 8 cm.

Each of the two small circles has a diameter of 4 cm.

(a) Write down the radius of each of the small circles.

............................. cm

(1)

(b) Work out the area of the region shown shaded in the diagram.


...................................... cm2

(4)

(5 marks)

4 cm

4 cm

8 cm


AREA OF COMPOUND

SHAPES






Instructions






Information






Advice





1.


Work out the area of the shape.

....................................... cm2

(Total 3 marks)

2.

The diagram shows a shape.


…………………………… cm2

(Total 4 marks)

5 cm

7 cm

7 cm

4 cm

20 cm

9 cm

4 cm

8 cm


NOT

3. Here is a trapezium.


Work out the area of the trapezium.

........................... cm2

(Total 2 marks)

4. The diagram shows a wall with a door in it.

Work out the shaded area.

…………………m2

(3)

(Total 3 marks)

6 cm

10 cm

5 cm


NOT

4 m

3 m

1 m

2 m

5. The diagram shows a 6-sided shape made from a rectangle and a right-angled triangle.

Work out the total area of the 6-sided shape.

...........................cm2

(Total 3 marks)

12 cm

7 cm

6 cm

2 cmDiagram accurately drawn

NOT

6.

The diagram shows 3 small rectangles inside a large rectangle.

The large rectangle is 10 cm by 8 cm.

Each of the 3 small rectangles is 4 cm by 2 cm.

Work out the area of the region shown shaded in the diagram.

………………………cm2

(Total 3 marks)

4 cm

2 cm

4 cm

2 cm

4 cm

2 cm

10 cm

8 cm


NOT

7.



.................... cm2

(Total 4 marks)

9cm

12cm

5cm

7cm

8.


The diagram shows a rectangle inside a triangle.

The triangle has a base of 12 cm and a height of 10 cm.

The rectangle is 5 cm by 3 cm.

Work out the area of the region shown shaded in the diagram.

.................................. cm2

(Total 3 marks)

9.


The diagram shows the plan of a field.

The farmer sells the field for £3 per square metre.

Work out the total amount of money the farmer should get.

£ .....................................

(Total 5 marks)

75m

100m

160m

30m


ROTATION






Instructions






Information






Advice





1.

On the grid, rotate triangle A 180° about O.

Label your new triangle B.

(2)

(Total 2 marks)

5

4

3

2

1

–1

–2

–3

–4

–5

54321–1–2–3–4–5

A

O x

y

2.

On the grid, rotate the shaded shape P one quarter turn anticlockwise about

O.

Label the new shape Q.

(3)

(Total 3 marks)

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–6 –5 –4 –3 –2 –1O

1 2 3 4 5 6x

y

P

3.

Rotate the triangle a quarter turn anticlockwise, centre O.

(Total 2 marks)

T

A

Ox

y

B

4.

Rotate the triangle a half turn about the point O.

(Total 2 marks)

y

xO

5.

Rotate triangle R a half turn about the point O.

Label the new triangle T.

(2)

(Total 2 marks)

x

y

O

A

B

R

6.

Describe fully the single transformation that maps shape P onto shape Q.

………………………………………………………………………………

…………………….…………………………………………………………

……………..………………….……………………………………………

…………………………..………………….………………………………

(Total 3 marks)

x

y

–2–3–4 –1 1 2 3 4

6

5

4

3

2

1

–1

–2

–3

O

P

Q

7.

Describe fully the single transformation that will map shape P onto shape Q.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

(Total 3 marks)

y

P

Q

–6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 x

7

6

5

4

3

2

1

O

–1

–2

–3

–4

–5


REFLECTION






Instructions






Information






Advice





1.

Reflect triangle R in the line AB.

Label the new triangle S.

(2)

(Total 2 marks)

x

y

O

A

B

R

2.

Triangle A is reflected in the x-axis to give triangle B.

Draw the triangle B and label it B.

Triangle B is reflected in the line x = 1 to give triangle C.

Draw the triangle C and label it C.

(Total 4 marks)

O 2

2

–2

–4

–6

–8

x

y

4

6

8

–2–4–6–8 4 6 8

x = 1

A

3.

Reflect the triangle in the line y = 1

(Total 2 marks)

6

5

4

3

2

1

1 2 3 4 5 6

–1

–2

–3

–4

–5

–6

–1–2–3–4–5–6O

x

y

y = 1

4.

Triangle A is reflected in the y axis to give triangle B.

Draw the triangle B and label it B.

Triangle B is then reflected in the x axis to give triangle C.

Draw the triangle C and label it C.

(Total 4 marks)

5

4

3

2

1

–1

–2

–3

–4

–5

–5 –4 –3 –2 –1 1 2 3 4 5

A

x

y

O

5.

Triangle T has been drawn on the grid.

Reflect triangle T in the y-axis.

Label the new triangle A.

(2)

(Total 2 marks)

–6 –5 –4 –3 –2 –1 1 2 3 4 5 6O

y

x

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

T

6.

Reflect Shape A in the y axis.

Label your new shape B.

(2)

(Total 2 marks)

y

A

–6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 x

7

6

5

4

3

2

1

O

–1

–2

–3

–4

–5

7.

On the grid, reflect triangle P in the y-axis.

Label the new shape, Q.

(1)

The line AB is drawn on the grid.

(b) On the grid, reflect triangle P in the line AB.

Label the new shape, R.

(1)

(Total 2 marks)

x

y

–2–3–4–5–6 –1 1 2 3 4 5 6

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

O

A B

P


ENLARGEMENT






Instructions






Information






Advice





1. On the grid, enlarge the shape with a scale factor of 2.

(Total 2 marks)

2.

On the grid, enlarge the shape with a scale factor of 2

(Total 2 marks)

3.

Enlarge the shaded triangle by a scale factor 2, centre 0.

(Total 3 marks)

7

6

5

4

3

2

1

–1

–2

–3

–4

–1–2–3–4

y

x321 7654 8

O

4.

On the grid, enlarge the shaded triangle by a scale factor of 2, centre C.

(Total 3 marks)

C

5.

On the grid, enlarge the shaded shape by scale factor of 2, centre (1,1).

(Total 3 marks)

y

8

7

6

5

4

3

2

1

O 1 2 3 4 5 6 7 8 9 10 x

6.

Describe fully the single transformation which takes shape A onto shape B.

………………………………………………………………………………

…………………….…………………………………………………………

(Total 3 marks)

Ox

y

A

B

7.

(c) Describe fully the single transformation which maps triangle T onto

triangle C.

...................................................................................................................

...................................................................................................................

(3)

(Total 3 marks)

1 2 3 4 5 6 7 8 9 10 11 12O

y

x

12

11

10

9

8

7

6

5

4

3

2

1

T

C


TRANSLATION






Instructions






Information






Advice





1.

On the grid, translate the shaded shape P by 2 units to the right and 3 units

up.

Label the new shape R.

(Total 2 marks)

2. Translate shape P 3 squares to the left and 2 squares down.

(Total 1 mark)

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–6 –5 –4 –3 –2 –1O

1 2 3 4 5 6x

y

P

P

3.

Translate triangle P by the vector .

Label the new triangle B.

(2)

(Total 2 marks)

x

y

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–6 –5 –4 –3 –2 –1 O 1 2 3 4 5 6

P

1

6

4.

Describe fully the single transformation that will map shape P onto

shape Q.

...................................................................................................................

...................................................................................................................

...................................................................................................................

(2)

(Total 2 marks)

x

P

Q

4

2

3

1

y

–4 –2–3 –1 2 41 3O

5.

On the grid, translate triangle P by the vector

Label the new triangle Q.

(2)

(Total 2 marks)

30

28

26

24

22

20

18

16

14

12

10

8

6

4

2

2 4 6 8 10 12 14 16 18 20 22 24 x

y

O

P

3

8

6.

Translate the triangle by the vector

(Total 2 mark)

7

6

5

4

3

2

1

–1

–2

–6 1–5 2–4 3–3 4–2 5–1 6

y

xO

3

4

7.

Describe fully the single transformation that will map shape P onto shape Q.

...........................................................................................................................................

...........................................................................................................................................

(2)

(Total 2 marks)

8.

Translate shape A by

2

8.

Label the new shape B.

(Total 2 marks)

9.

Translate the triangle by

2

3

(Total 2 marks)

______________________________________________________________________________


MIXED

TRANSFORMATIONS






Instructions






Information






Advice





1.

Triangle A and triangle B are drawn on the grid.

(a) Describe fully the single transformation which maps triangle A onto triangle B.

.....................................................................................................................................................

.....................................................................................................................................................

(3)

(b) Reflect triangle A in the line x = 4

(2)

(5 marks)

2.

Triangle P is drawn on a coordinate grid.

The triangle P is reflected in the line x = –1 and then reflected in the line y = 1 to give triangle Q.

Describe fully the single transformation which maps triangle P onto triangle Q.

............................................................................................................................................................

............................................................................................................................................................

(3 marks)

3.

(a) Rotate triangle A 90 clockwise, centre O.

(2)

(b) Enlarge triangle B by scale factor 3, centre (1, 2).

(3)

(5 marks)

4.

Describe fully the single transformation that maps shape P onto shape Q.

............................................................................................................................................................

............................................................................................................................................................

(3 marks)

5.

Describe fully the single transformation that maps triangle P onto triangle Q.

......................................................................................................................................................

......................................................................................................................................................

(3 marks)

6. (a)

Reflect shape P in the line y = x

(2)

(b)

Describe fully the single transformation that maps triangle A onto triangle B.

.....................................................................................................................................................

.....................................................................................................................................................

(2)

(4 marks)

7.

Shape P is reflected in the line x = –1 to give shape Q.

Shape Q is reflected in the line y = 0 to give shape R.

Describe fully the single transformation that maps shape P onto shape R.

............................................................................................................................................................

............................................................................................................................................................

(3 marks)

8.

Rotate the shaded shape 900 clockwise about the point (1, -1).

(3 marks)


NETS, PLANS &

ELEVATIONS






Instructions






Information






Advice





1. The diagrams show some solid shapes and their nets.

An arrow has been drawn from one solid shape to its net.

Draw an arrow from each of the other solid shapes to its net.

(3 marks)

2. The diagram shows some nets and some solid shapes.

An arrow has been drawn from one net to its solid shape.

Draw an arrow from each of the other nets to its solid shape.

(3 marks)

3. Here are the plan and front elevation of a prism.

The front elevation shows the cross section of the prism.

On the grid below, draw a side elevation of the prism.

(3)

(Total 3 marks)

Plan

Front elevation

4. The diagram shows a sketch of a solid object.

The solid object is made from five centimetre cubes.


(a) On the grid of centimetre squares, draw the elevation of the solid object in the

direction marked with an arrow.

Elevation

(2)

(b) On the grid of centimetre squares, draw the plan of the solid object.

Plan

(2)

(Total 4 marks)

5. The diagram shows a solid object made of 6 identical cubes.

(a) On the grid below, draw the side elevation of the solid object from the direction of

the arrow.

(2)

(b) On the grid below, draw the plan of the solid object.

(2)

(Total 4 marks)

6. Here are the plan and front elevation of a solid shape.

(a) On the grid below, draw the side elevation of the solid shape.

(2)

(b) In the space below, draw a sketch of the solid shape.

(2)

(Total 4 marks)

Plan Front Elevation

7. The diagram represents a solid made from 5 identical cubes.

On the grid below, draw the view of the solid from direction A.

(Total 2 marks)

A


SYMMETRY






Instructions






Information






Advice





1. (a) On the shape, draw all the lines of symmetry.

(2)

The shape below has rotational symmetry.

(b) Write down the order of rotational symmetry.

.....................................

(1)

(Total 3 marks)

2. Here is a rectangle.

(a) Draw all the lines of symmetry of this rectangle.

(2)

Here is a regular pentagon.

(a) Write down the order of rotational symmetry of this regular pentagon.

.....................................

(1)

Here is a shape.

(b) Write down the order of rotational symmetry of this shape.

.....................................

(1)

(Total 4 marks)

3. (a) Shade one more square to make a pattern with 1 line of symmetry.

(1)

(b) Shade one more square to make a pattern with rotational symmetry of order 2

(1)

(Total 2 marks)

4. Here are five shapes.

Two of these shapes have only one line of symmetry.

(a) Write down the letter of each of these two shapes.

........................... and ........................

(2)

Two of these shapes have rotational symmetry of order 2

(b) Write down the letter of each of these two shapes.

........................... and ........................

(2)

(Total 4 marks)

5. (a) This shape has rotational symmetry.

Mark with a cross () the centre of rotation.

(1)

(b)

Complete this shape so that it has rotational symmetry of order 4

(1)

(Total 2 marks)

______________________________________________________________________________

6. (a) Shade two more triangles to make a pattern with 1 line of symmetry.

(1)

(b) Shade two more triangles to make a pattern with rotational symmetry of order 3

(1)

(Total 2 marks)

7. Here is a square.

(a) On the square, draw all the lines of symmetry.

(2)

Here is a rectangle.

(b) Write down the order of rotational symmetry of the rectangle.

......................................................

(1)

(Total 3marks)

______________________________________________________________________________

8. Here is a parallelogram.

(a) Write down the order of rotational symmetry of the parallelogram.

(1)

..............................................................

Here is a rectangle.

(b) On the rectangle, draw all the lines of symmetry.

(1)

(Total 2 marks)

9. Here are four road signs.

Two of these road signs have one line of symmetry.

(a) Write down the letters of each of these two road signs.

.............. and .............

(2)

Only one of these four road signs has rotational symmetry.

(b) (i) Write down the letter of this road sign. .......................

(ii) Write down its order of rotational symmetry. ………………

(2)

(Total 4 marks)

______________________________________________________________________________

10. Here is a shape.

(a) Draw all the lines of symmetry on this shape.

(2)

A

C

B

D

30

Here is a regular hexagon.

(b) Write down the order of rotational symmetry of this regular hexagon.

..............................................

(1)

(Total 3 marks)

______________________________________________________________________________

11. (a)

Shade one more square to make a pattern with 1 line of symmetry.

(1)

(b)

Shade one more square to make a pattern with rotational symmetry of order 2

(1)

(Total 2 marks)

______________________________________________________________________________


TWO WAY TABLES






Instructions






Information






Advice





1. The two-way table shows some information about the number of students in a school.

Year Group Total

9 10 11

Boys 125 407

Girls 123

Total 303 256 831

Complete the two-way table.

(3 marks)

2. A factory makes three sizes of bookcase.

The sizes are small, medium and large.

Each bookcase can be made from pine or oak or yew.

The two-way table shows some information about the number of bookcases the factory

makes in one week.

Small Medium Large Total

Pine 7 23

Oak 16 34

Yew 3 8 2 13

Total 20 14


(3 marks)

3. The two-way table gives some information about how 100 children travelled to school

one day.

Walk Car Other Total

Boy 15 14 54

Girl 8 16

Total 37 100

(a) Complete the two-way table.

(3)

One of the children is picked at random.

(b) Write down the probability that this child walked to school that day.

.....................................

(1)

One of the girls is picked at random.

(c) Work out the probability that this girl did not walk to school that day.

.....................................

(2)

(6 marks)

4. The two-way table gives some information about how 100 children travelled to school

one day.

Walk Car Other Total

Boy 15 14 54

Girl 8 16

Total 37 100

(a) Complete the two-way table.

(3)

One of the children is picked at random.

(b) Write down the probability that this child walked to school that day.

.....................................

(1)

(4 marks)

5.

The diagram shows some 3-sided, 4-sided and 5-sided shapes.

The shapes are black or white.

(a) Complete the two-way table. (3)

Black White Total

3-sided shape 4 5

4-sided shape 2

5-sided shape 0

Total 11

Ed takes a shape at random.

(b) Write down the probability the shape is white and 3-sided.

.....................

(2)

(5 marks)

6. The two-way table shows some information about the number of boys, girls and teachers at three

schools.

School A School B School C Total

Boys 85 29 54

Girls 31 47 171

Teachers 13 5

Total 191 366


(4 marks)

7. 80 children went on a school trip.

They went to London or to York.

23 boys and 19 girls went to London.

14 boys went to York.

(a) Use this information to complete the two-way table.

London York Total

Boys

Girls

Total

(3)

One of these 80 children is chosen at random.

(b) What is the probability that this child went to London?

........................................

(1)

(4 marks)

8. Felicity asked 100 students how they came to school one day.

Each student walked or came by bicycle or came by car.

49 of the 100 students are girls.

10 of the girls came by car.

16 boys walked.

21 of the 41 students who came by bicycle are boys.

Work out the total number of students who walked to school.

.........................................................

(4 marks)

9. Janice asks 100 students if they like biology or chemistry or physics best.

38 of the students are girls.

21 of these girls like biology best.

18 boys like physics best.

7 out of the 23 students who like chemistry best are girls.

Work out the number of students who like biology best.

............................................................

(4 marks)

10. 56 students were asked if they watched tennis yesterday.

20 of the students are boys.

17 girls watched tennis yesterday.

32 students did not watch tennis yesterday

One of these students is to be chosen at random.

Write down the probability that the student chosen will be a boy who watched tennis yesterday.


.................................

(4 marks)


PIE CHARTS






Instructions






Information






Advice





1. The table gives information about the numbers of fish in a lake.

Fish Frequency

Perch 10

Bream 23

Carp 39

Draw an accurate pie chart to show this information.

(4 marks)

2. Mrs Yusuf went shopping at a superstore.

The pie chart shows information about the money she spent on petrol, on clothes, on food and on

other items.

(a) What did she spend most money on?

.....................................

(1)

(b) What fraction of the money she spent was on petrol?

.....................................

(1)

Mrs Yusuf spent £25 on petrol at the superstore.

(c) In total, how much money did she spend?

£ ...................................

(2)

(4 marks)

3. Harry asked each student in his class how they travelled to school that day.

He used the results to draw this pie chart.

(a) How did most of the students travel to school?

..............................................

(1)

Harry asked a total of 24 students.

(b) Work out the number of students who cycled to school.

..............................................

(2)

(3 marks)

______________________________________________________________________________

4. Sally recorded the musical instrument played by each of 30 students in the school orchestra.

The table shows her results.

One of the students in the school orchestra is chosen at random.

(a) Find the probability that this student plays the flute.

(2)

........................................................................................

(b) Draw an accurate pie chart to show the information shown in the table.

(4)

(6 marks)

5. Some children were asked to name their favourite flavour of ice cream.

The pie chart and table show some information about their answers.

Use the pie chart to complete the table.

Flavour Number of children Angle of sector

vanilla 12 90°

mint .................................. 45°

strawberry 14 ..................................

chocolate .................................. 120°

(3 marks)

6. Noreen carries out a survey of some students.

The pie chart shows some information about their favourite holiday.

5 students said that walking is their favourite holiday.

(a) How many students took part in the survey?

....................................

(2)

Noreen chooses one of these students at random.

(b) Write down the probability that this student’s favourite holiday is cycling. .........................

(1)

(3 marks)

7. The pie charts show some information about the numbers of medals won by Germany and by the

Russian Federation in the 2010 Winter Olympics.

Medals won by Germany Medals won by the Russian Federation

Germany won 7 bronze medals.

(a) How many gold medals did Germany win?

..............................................

(2)

(b) Graham says,

‘The pie charts show that Germany won more gold medals than the Russian Federation’.

Is Graham right? ......................

You must explain your answer.

.....................................................................................................................................................

.....................................................................................................................................................

(1)

(3 marks)

8. The table gives some information about the birds Paula sees in her garden one day.

Bird Frequency

Magpie 15

Thrush 10

Starling 20

Sparrow 27

Complete the accurate pie chart.

(3 marks)

9. The pie chart shows some information about the time Gill spent working in her garden one month.

(a) What fraction of the time did Gill spend cutting the grass?

.........................................

(1)

Gill spent 7 hours weeding.

(b) How much time did Gill spend planting?

.......................................... hours

(3)

(4 marks)


SCATTER GRAPHS

Materials required for examination

Ruler graduated in centimetres and




Instructions






Information






Advice





1. The scatter graph shows some information about 8 cars.

For each car it shows the engine size, in litres, and the distance, in kilometres, the car travels on one

litre of petrol.

(a) What type of correlation does the scatter graph show?

..............................................................................................

(1)

A different car of the same type has an engine size of 2.5 litres.

(b) Estimate the distance travelled on one litre of petrol by this car.

.............................................. kilometres

(2)

(3 marks)

______________________________________________________________________________

2. The scatter graph shows information about the height and the arm length of each of 8 students in

Year 11.

(a) What type of correlation does this scatter graph show?

..............................................................

(1)

A different student in Year 11 has a height of 148 cm.

(b) Estimate the arm length of this student.

..............................................................cm

(2)

(3 marks)

______________________________________________________________________________

3. The scatter graph shows information about 10 apartments in a city.

The graph shows the distance from the city centre and the monthly rent of each apartment.

The table shows the distance from the city centre and the monthly rent for two other apartments.

Distance from the city centre (km) 2 3.1

Monthly rent (£) 250 190

(a) On the scatter graph, plot the information from the table.

(1)

(b) Describe the relationship between the distance from the city centre and the monthly rent.

.....................................................................................................................................................

.....................................................................................................................................................

(1)

An apartment is 2.8 km from the city centre.

(c) Find an estimate for the monthly rent for this apartment.

£ ......................................................

(2)

(4 marks)

4. The scatter graph shows information about the height and the weight for nine students.

The table shows the height and the weight for three more students.

Height in cm 135 155 170

Weight in kg 70 75 85


(1)

(b) What type of correlation does this scatter graph show?

.....................................

(1)

(c) The weight of another student is 80 kg.

Estimate the height of this student.

.....................................cm

(2)

(4 marks)

______________________________________________________________________________

100

90

80

70

60

50

40

30

20

10

0110 120 130 140 150 160 170

Weightin kg

Height in cm

5. On a particular day, a scientist recorded the air temperature at 8 different heights above sea level.

The scatter diagram shows the air temperature, y °C, at each of these heights, x km, above sea level.

(a) Using the scatter diagram, write down the air temperature recorded at a height of 2.5 km above

sea level.

................................. °C

(1)

(b) Describe the correlation between the air temperature and the height above sea level.

........................................................

(1)

(c) Find an estimate of the height above sea level when the air temperature is 0 °C.

........................... km

(2)

(4 marks)

Air temperature at different heights above sea level

Air

temperature

(°C)

20

18

16

14

12

10

8

6

4

2

0

0 0.5 1.0 1.5 2.0 2.5 3.0

y

x

Height above sea level (km)

0.5 1.0 1.5 2.0 2.5 3.0

6. Some students took a mathematics test and a science test.

The scatter graph shows information about the test marks of eight students.

The table shows the test marks of four more students.

Mark in mathematics test 14 25 50 58

Mark in science test 21 23 38 51


(2)

(b) Describe the correlation between the marks in the mathematics test and the marks in the science

test.

…………………………………………………..

(1)

Josef was absent for the mathematics test but his mark in the science test was 45

(c) Estimate Josef’s mark in the mathematics test.

…………………………..

(2)

(5 marks)

______________________________________________ ____________________________

60

50

40

30

20

10

00 10 20 30 40 50 60

Mark in mathematics test

Markinsciencetest

7. The scatter graph shows the maths mark and the art mark for each of 15 students.

(a) What type of correlation does this scatter graph show?

(1)

...........................................................................

(b) Draw a line of best fit on the scatter graph.

(1)

Sarah has not got a maths mark.

Her art mark is 23

(c) Use your line of best fit to estimate a maths mark for Sarah.

(1)

...........................................................................

(3 marks)


FREQUENCY

POLYGONS






Instructions






Information






Advice





1. The table shows some information about the heights (h cm) of 60 plants.

Height (h cm) Frequency

20 < w ≤ 30 8

30 < w ≤ 40 13

40 < w ≤ 50 25

50 < w ≤ 60 10

60 < w ≤ 70 4

Draw a frequency polygon to show this information.

(4 marks)

Frequency

20 30 40 50 60 70

30

20

0

10

Height ( cm) h

2. The table shows some information about the weights, in kg, of 100 boxes.

Weight of box (w kg) Frequency

0 < w 4 10

4 < w 8 17

8 < w 12 28

12 < w 16 25

16 < w 20 20


(4 marks)

3. 30 students ran a cross-country race.

Each student’s time was recorded.

The table shows information about these times.

Time

(t minutes)

Frequency

10 < t < 14 2

14 < t < 18 5

18 < t < 22 12

22 < t < 26 8

26 < t < 30 3

On the grid, draw a frequency polygon to show this information.

(4 marks)

10 20 30 40

Number

of

students

15

10

5

0

0

Time (t minutes)

4. The table shows some information about the weights (w grams) of 60 apples.

Weight (w grams) Frequency

100 ≤ w< 110 5

110 ≤ w< 120 9

120 ≤ w< 130 14

130 ≤ w< 140 24

140 ≤ w< 150 8


(4 marks)

Frequency

100 110 120 130 140 150

30

20

0

10

Weight ( grams)w

5. The frequency table gives information about the times it took some office workers to get to

the office one day.

Time (t minutes) Frequency

0 < t 10 4

10 < t 20 8

20 < t 30 14

30 < t 40 16

40 < t 50 6

50 < t 60 2

(a) Draw a frequency polygon for this information.

(3)

(b) Write down the modal class interval.

..............................................

(1)

One of the office workers is chosen at random.

(c) Work out the probability that this office worker took more than 40 minutes to get to the office.

..............................................

(2)

(6 marks)

______________________________________________________________________________

6. The table gives information about the lengths of the branches on a bush.

Length(Lcm) Frequency

0 L <10 20

10 L < 20 12

20 L < 30 10

30 L < 40 8

40 L < 50 6

50 L < 60 0

(a) Draw a frequency polygon to show this information.

(3)


.....................................

(1)

One of the branches is chosen at random.

(c) Work out the probability that this branch less than 20 cm long.

..............................................

(2)

(6 marks)

______________________________________________________________________________

7. In one month, Janet travelled by bus 25 times and by train 25 times.

The grouped frequency table records the number of minutes (x minutes) late each of her buses

and trains were.

(a) On the grid below draw two frequency polygons to illustrate this data.

(3)

(b) Use your polygons to compare the lateness of buses and trains and comment on any differences

you observe.

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

(2)

(5 marks)

______________________________________________________________________________

Minutes late Bus Train

0 5x 5 9

5 10x 15 6

10 15x 4 6

15 20x 1 2

20 25x 0 3


STEM & LEAF

DIAGRAMS






Instructions






Information


each question.




Advice





1. 3. Here are the ages, in years, of 15 students.

19 18 20 25 37

33 21 17 29 20

42 18 23 37 22

Show this information in an ordered stem and leaf diagram.

(3 marks)

__________________________________________________________________________

2. Jo measured the times in seconds it took 18 students to run 400 m.

Here are the times.

67 78 79 98 96 103

75 85 94 92 61 80

82 86 90 95 90 89

(a) Draw an ordered stem and leaf diagram to show this information.

(3)

(b) Work out the median.

..................................... seconds

(2)

(5 marks)

3. Here are the speeds, in miles per hour, of 16 cars.

31 52 43 49 36 35 33 29

54 43 44 46 42 39 55 48

Draw an ordered stem and leaf diagram for these speeds.

(4 marks)

__________________________________________________________________________

4. Here are some people’s ages in years.

62 27 33 44 47

30 22 63 67 54

69 56 63 50 25

31 63 42 48 51

In the space below, draw an ordered stem and leaf diagram to show these ages.

(4 marks)

5. Jim did a survey on the lengths of caterpillars he found on a field trip.

Information about the lengths is given in the stem and leaf diagram.

1 3 5 7 7 Key: 5|2 means 5.2

cm

2 0 6 8 8 8 9

3 1 5 5 5 5 6 8 9

4 1 5

5 2

Work out the median.

............................... cm

(2 marks)

__________________________________________________________________________

6. Here are the times, in minutes, taken to solve a puzzle.

5 10 15 12 8 7 20 35 24 15

20 33 15 24 10 8 10 20 16 10

(a) In the space below, draw a stem and leaf diagram to show these times.

(3)

(b) Find the median time to solve this puzzle.

………………………. mins

(2)

___________________________________________________________________(5marks)

7. Jan measures the heights, in millimetres, of 20 plants in her greenhouse.

Here are her results.

178 189 147 147 166

167 153 171 164 158

189 166 165 155 152

147 158 148 151 172

Complete the stem and leaf diagram to show this information.

Stem Leaf

__________________________________________________________________(4 marks)

8. Anil counted the number of letters in each of 30 sentences in a newspaper.

Anil showed his results in a stem and leaf diagram.

0 8 8 9

1 1 2 3 4 4 8 9

2 0 3 5 5 7 7 8

3 2 2 3 3 6 6 8 8

4 1 2 3 3 5

Key 4 1 stands for 41 letters

(a) Write down the number of sentences with 36 letters. ..............................

(1)

(b) Work out the range. ..............................

(1)

(c) Work out the median.

..............................

(2)

(4 marks)

9. Here are the weights, in kilograms, of 15 parcels.

1.1 1.7 2.0 1.0 1.1 0.5 3.3 2.0

1.5 2.6 3.5 2.1 0.7 1.2 0.6

Draw a stem and leaf diagram to show this information.

(Total 3 marks)

10. Janine recorded the times, in seconds, for each of 15 people to do a puzzle.


90 81 78 83 68

75 79 81 69 87

76 91 67 73 81

(a) Complete the ordered stem and leaf diagram and key to show these results.

(3)

Janine says “To find the median time, you add all the results and divide by 15”

Janine is wrong.

(b) (i) Explain how to find the median.

.....................................................................................................................

.....................................................................................................................

....................................................................................................................

....................................................................................................................

.....................................................................................................................

(ii) Find the median.

...................................... s

(2)

(Total 5 marks)

11. Here are the ages, in years, of 15 teachers.

35 52 42 27 36

23 31 41 50 34

44 28 45 45 53

(a) Draw an ordered stem and leaf diagram to show this information.

You must include a key.

(3)

One of these teachers is picked at random.

(b) Work out the probability that this teacher is more than 40 years old.

....................................

(2)

(Total 5 marks)

Key:


PROBABILITY






Instructions






Information






Advice





1.

The diagram shows a fair spinner in the shape of a rectangular octagon.

The spinner can land on A or B or C.

Marc spins the spinner.

Write down the probability that the spinner will land on A.

.............................

(Total 2 marks)

2. Ishah spins a fair 5-sided spinner.

She then throws a fair coin.

(a) List all the possible outcomes she could get.


(1, head).........................................................................................................

........................................................................................................................

.......................................................................................................................

(2)

Ishah spins the spinner once and throws the coin once.

(b) Work out the probability that she will get a 1 and a head.

.....................................

(1)

(Total 3 marks)

A

A

A

B

B B

B

C

3. There are eight marbles in a bag.

Four marbles are blue (B),

two marbles are red (R)

and two marbles are green (G).

Steve takes a marble at random from the bag.

(a) On the probability scale, mark with the letter B, the probability that

Steve will take a blue marble.

(1)

(b) On the probability scale, mark with the letter G, the probability that

Steve will take a green marble.

(1)

(c) On the probability scale, mark with the letter Y, the probability that

Steve will take a yellow marble.

(1)

(Total 3 marks)

G

R

B

BG

BR

B

2

10 1

2

10 1

2

10 1

4. Lucy uses some letter cards to spell the word “NOVEMBER”.

Lucy takes one of these cards at random.

Write down the probability that Lucy takes a card with a letter E.

..........................

(Total 2 marks)

5. Here are some statements.

Draw an arrow from each statement to the word which best describes its

likelihood.


(Total 3 marks)

N O V E M B E R

A head is obtained when a fair coin is thrown

once.

A number less than 7 will be scored when an

ordinary six-sided dice is rolled once.

It will rain every day for a week next July in

London.

A red disc is obtained when a disc is taken at

random from a bag containing 9 red discs and 2

blue discs.

Certain

Likely

Even

Unlikely

Impossible

6. There are three beads in a bag.

One bead is red, one bead is white and one bead is yellow.

Sarah takes, at random, a bead from the bag.

She looks at its colour and then puts the bead back in the bag.

On the probability line,

(i) mark with the letter R the probability that Sarah takes a red bead.

(ii) mark with the letter B the probability that Sarah takes a black

bead.

(2)

(Total 2 marks)

7. A bag contains some beads which are red or green or blue or yellow.

The table shows the number of beads of each colour.

Colour Red Green Blue Yellow

Number of

beads 3 2 5 2

Samire takes a bead at random from the bag.

Write down the probability that she takes a blue bead.

............................

(Total 2 marks)

RW

Y

0 112

8.

Here is a fair 7-sided spinner.

The spinner is to be spun once.

The spinner will land on one of the colours.

(a) On which colour is the spinner most likely to land?

........................................

(1)

(b) Write down the probability that the spinner will land on green.

........................................

(1)

(Total 2 marks)

9. On the probability scale below, mark

(i) with the letter S, the probability that it will snow in London in June,

(ii) with the letter H, the probability that when a fair coin is thrown once it

comes down heads,

(iii) with the letter M, the probability that it will rain in Manchester next

year.

(Total 3 marks)

yellow

green

red

white

red

green

red

0 1

10. Joshua rolls an ordinary dice once.

It has faces marked 1, 2, 3, 4, 5 and 6.

(a) Write down the probability that he gets

(i) a 6,

………………………

(ii) an odd number,

………………………

(iii) a number less than 3,

………………………

(iv) an 8.

………………………

(4)

Ken rolls a different dice 60 times. This dice also has six faces.

The table gives information about Ken’s scores.

Score on dice Frequency

1 9

2 11

3 20

4 2

5 8

6 10

(b) Explain what you think is different about Ken’s dice.

...................................................................................................................

...................................................................................................................

(1)

(Total 5 marks)

11. Emily has a bag of 20 fruit flavour sweets.

7 of the sweets are strawberry flavour,

11 are lime flavour,

2 are lemon flavour.

Emily takes at random a sweet from the bag.

Write down the probability that Emily

(a) takes a strawberry flavour sweet,

...........................(1)

(b) does not take a lime flavour sweet,

...........................(1)

(c) takes an orange flavour sweet.

...........................(1)

(Total 3 marks)

12. (a) On the probability scale below, mark with a cross (×)

the probability that it will rain on at least one day in London in 2008.

(1)

(b) On the probability scale below, mark with a cross (×)

the probability that you will get a 10 when you roll an ordinary 6-sided

dice.

(1)

(c) On the probability scale below, mark with a cross (×)

the probability that you will get a head when you throw a coin.

(1)

(Total 3 marks)

0 11

2

0 11

2

0 11

2


PERCENTAGES






Instructions






Information






Advice





1. Wayne bought an engagement ring for Tracy.

The total cost of the ring was £420 plus VAT at 17 %.

(a) Work out the cost of the ring.

£ …………………………

(2)

Wayne invited 96 people to an engagement party.

Only 60 of the people invited came to the party.

(b) Express 60 as a percentage of 96.

………………………… %

(2)

(Total 4 marks)

2. A doctor has 12 000 patients.

4560 of these patients are male.

What percentage of these patients are female?

................................. %

(3)

(Total 3 marks)

21

3. Martin had to buy some cleaning materials.

The cost of the cleaning materials was £64.00 plus VAT at 17 %.

Work out the total cost of the cleaning materials.

£ .......................

(Total 2 marks)

4. There are 800 students at Prestfield School.

45% of these 800 students are girls.

(a) Work out 45% of 800

..........................

(2)


(b) Write 176 out of 800 as a percentage.

......................%

(2)

(Total 4 marks)

2

1

5. Alistair sells books.

He sells each book for £7.60 plus VAT at 17 %.

He sells 1650 books.

Work out how much money Alistair receives.

£…………………….

(Total 4 marks)

6. A hotel has 56 guests.

35 of the guests are male.

(a) Work out 35 out of 56 as a percentage.

.................................. %

(2)

40% of the 35 male guests wear glasses.

(b) Write the number of male guests who wear glasses as a fraction of the 56 guests.


....................................

(4)

(Total 6 marks)

2

1

7. The cost of a compact disc holder is 25p.

John has £15 to spend.

(a) What is the greatest number of compact disc holders that John can buy for £15?

...........................

(3)

A compact disc player costs £50 plus 17½% VAT.

(b) Calculate the total cost of the compact disc player.

£ ...........................

(3)

(Total 6 marks)

8. Work out 28% of £85 000

£ ..................................

(Total 2 marks)

9. Work out 45% of 800

............................

(Total 2 marks)

Compact disc player£50 + VAT

10. Bytes is a shop that sells computers and digital cameras.

In 2003, Bytes sold 620 computers.

In 2004, Bytes sold 708 computers.

Work out the percentage increase in the number of computers sold.

Give your answer to an appropriate degree of accuracy.

..................................... %

(4)

11. Calculate 36% of £4500

£ ………………...

(Total 2 marks)

12. In April 2004, the population of the European Community was 376 million.

In April 2005, the population of the European Community was 451 million.

Work out the percentage increase in population.


..................................%

(Total 3 marks)

13. The cost of a radio is the list price plus VAT at .

The list price of a radio is £240

Work out the cost of the radio.

£ ..................................

(Total 3 marks)

14. Linda’s mark in a maths test was 36 out of 50

Find 36 out of 50 as a percentage.

............................. %

(Total 2 marks)

15. Ann buys a dress in a sale.

The normal price of the dress is reduced by 20%.

The normal price is £36.80

Work out the sale price of the dress.

£ ..........................

(Total 3 marks)

%2

117

16. William’s salary is £24 000

His salary increases by 4%.

Work out William’s new salary.

£ ............................

(Total 3 marks)

17. The table shows the number of mobile phones sold in a shop in April and in May.

April May

85 91

Work out the percentage increase in the number of mobile phones sold from April to

May.


................................ %

(Total 3 marks)


HCF, LCM &

PRODUCT OF PRIMES






Instructions






Information






Advice





1. Write 140 as the product of its prime factors.

..............................................................................

(2 marks)

2. Write 720 as a product of its prime factors.

.....................................

(2 marks)

3. (a) Express the following numbers as products of their prime factors.

(i) 60,

.............................

(ii) 96.

.............................

(4)

(b) Find the Highest Common Factor of 60 and 96.

.............................

(1)

(c) Work out the Lowest Common Multiple of 60 and 96.

............................

(2)

(7 marks)

4. (a) Express 120 as the product of powers of its prime factors.

……………………………

(3)

(b) Find the Lowest Common Multiple of 120 and 150.

……………………………

(2)

(5 marks)

5. (a) Express 108 as the product of powers of its prime factors.

.........................

(3)

(b) Find the Highest Common Factor (HCF) of 108 and 24

..........................

(1)

(4 marks)

6. (a) Work out the Highest Common Factor (HCF) of 24 and 64

.....................................

(2)

(b) Work out the Lowest Common Multiple (LCM) of 24 and 64

.....................................

(2)

(4 marks)

7. (a) Find the Highest Common Factor of 75 and 90.

……………………………

(2)

(b) Find the Lowest Common Multiple of 75 and 90.

……………………………

(2)

(4 marks)

8. (a) Express 84 as a product of its prime factors.

................................

(3)

(b) Find the Highest Common Factor (HCF) of 84 and 35

................................

(2)

(5 marks)

9. (a) Express 56 as the product of its prime factors.

.....................................

(2)

(b) Find the Lowest Common Multiple of 56 and 98

.....................................

(2)

(4 marks)

10. Find the Highest Common Factor (HCF) of 84 and 180

......................................

(3 marks)

11. Find the Highest Common Factor (HCF) of 32 and 80

..................................

(3 marks)

12. (a) Find the Lowest Common Multiple (LCM) of 24 and 36

.....................................

(2)

James thinks of two numbers.

He says “The Highest Common Factor (HCF) of my two numbers is 3

The Lowest Common Multiple (LCM) of my two numbers is 45”

(b) Write down two numbers that James could be thinking of.

................. and ..................

(3)

(5 marks)


PLACE VALUE






Instructions






Information






Advice





1. Using the information that

19 × 24 = 456

write down the value of

(a) 19 × 240

.....................................

(1)

(b) 19 × 2.4

.....................................

(1)

(c) 1.9 × 2.4

.....................................

(1)

(d) 456 ÷ 190

.....................................

(1)

(4 marks)

2. Given that 48.6 × 35 = 1701


(a) 4.86 × 3.5

.....................................

(1)

(b) 486 × 35

.....................................

(1)

(c) 4.86 × 3.5

.....................................

(1)

(d) 17.01 ÷ 35

.....................................

(1)

(4 marks)

3. Given that 32 × 14 = 448


(a) 32 × 1.4

....................................

(1)

(b) 0.32 × 14

....................................

(1)

(c) 0.32 × 0.14

....................................

(1)

(d) 448 ÷ 320

....................................

(1)

(4 marks)

4. Use the information that

257 × 34 = 8738

to find the value of

(a) 2.57 × 34

…………………….

(1)

(b) 25.7 × 3.4

…………………….

(1)

(c) 2.57 × 0.34

…………………….

(1)

(d) 873.8 ÷ 2.57

…………………….

(1)

(4 marks)


65 × 423 = 27 495

find the value of

(i) 6.5 × 423

......................................

(ii) 0.65 × 423

......................................

(iii) 0.65 × 4.23

......................................

(iv) 274.95 ÷ 65

......................................

(4 marks)


73 × 154 = 11 242


(i) 73 × 1.54

............................

(ii) 73 × 1.54

............................

(iii) 7.3 × 1.54

............................

(iv) 112 420 ÷ 0.73

.............................

(4 marks)


322 × 48 = 15 456


(a) 3.22 × 4.8

.....................................

(1)

(b) 3.22 × 0.48

.....................................

(1)

(c) 0.322 × 0.48

.....................................

(1)

(d) 15 456 ÷ 4.8

.....................................

(1)

(4 marks)


38 × 323 = 12 274

find the value of

(i) 3.8 × 32.3

……………

(ii) 0.38 × 32.3

……………

(iii) 12 274 ÷ 380

……………

(iv) 37 × 323

……………

(4 marks)


97 × 123 = 11 931


(i) 0.97 × 123 000 .................................

(ii) 11.931 ÷ 9.7 .................................

(2 marks)


4.8 × 34 = 163.2


(a) 48 × 34

....................................

(1)

(b) 4.8 × 3.4

....................................

(1)

(c) 163.2 ÷ 48

....................................

(1)

(3 marks)

11. 32 × 129 = 4128

Write down the value of

(i) 3.2 × 1.29

……………………………

(ii) 32 × 1 290

……………………………

(iii) 0.32 × 129 000

……………………………

(3 marks)


56 × 29 = 1624


(i) 56 × 0.29

……………………………

(ii) 5.6 × 0.29

……………………………

(iii) 1624 ÷ 0.29

……………………………

(3 marks)


214 × 49 = 10486


(a) 2.14 × 49 ………………………

(1)

(b) 1048.6 ÷ 2.14 ………………………

(1)

(2 marks)


91× 121 = 11011


(i) 9.1 × 12.1

…………………..

(ii) 0.91 × 121 000

…………………..

(iii) 11.011 ÷ 9.1

…………………..

(3 marks)


13 × 17 = 221

to write down the value of

(i) 1.3 × 1.7

..........................

(ii) 22.1 ÷ 1700

..........................

(2 marks)


43 × 97 = 4171


(i) 4.3 × 9.7

..........................

(ii) 4.3 × 0.97

..........................

(iii) 41.71 ÷ 43

..........................

(3 marks)


84 × 63 = 5292


(i) 8.4 × 0.63

..........................

(ii) 0.84 × 0.63

..........................

(iii) 52.92 ÷ 6.3

..........................

(3 marks)


NEGATIVE NUMBERS






Instructions






Information






Advice





1. Sally wrote down the temperature at different times on 1st January 2003.

Time Temperature

midnight – 6 °C

4 am –10 °C

8 am – 4 °C

noon 7 °C

3 pm 6 °C

7 pm –2 °C

(a) Write down

(i) the highest temperature,

.......................°C

(ii) the lowest temperature.

(2)

(b) Work out the difference in the temperature between

(i) 4 am and 8 am,

.......................°C

(ii) 3 pm and 7 pm.

.......................°C

(2)

At 11 pm that day the temperature had fallen by 5 °C from its value at 7 pm.

(c) Work out the temperature at 11 pm.

.......................°C

(1)

(5 marks)

2. The table shows temperatures at midnight and midday on one day in five cities.

City Midnight

temperature

Midday

temperature

Belfast −3 °C 4 °C

Cambridge −1 °C 4 °C

Edinburgh −7 °C −1 °C

Leeds −6 °C 3 °C

London −2 °C 6 °C

(a) Which city had the lowest midnight temperature?

........................................

(1)

(b) How many degrees higher was the midnight temperature in Cambridge than the

midnight temperature in Leeds?

......................... °C

(1)

(c) Which city had the greatest rise in temperature from midnight to midday?

........................................

(1)

(3 marks)

3. At midnight, the temperature was –8°C.

By 10 00, the temperature had increased by 6°C.

(a) Work out the temperature at 10 00

.......................°C

(1)

By midday, the temperature was 4°C.

(b) Work out the difference between the temperature at midday and the temperature at

midnight.

.......................°C

(2)

(5 marks)

4. The table shows the temperatures in four cities at noon one day.

Oslo −13°C

New York −5°C

Cape Town 9°C

London 2°C

(a) Write down the highest temperature.

...................... °C

(1)

(b) Work out the difference in temperature between Oslo and New York.

...................... °C

(1)

(c) Work out the difference in temperature between Cape Town and Oslo.

.............................. °C

(1)

At 8 pm the temperature in London was 3°C lower than the temperature at noon.

(d) Work out the temperature in London at 8 pm.

...................... °C

(1)

(4 marks)

5. The table shows the temperatures at midnight in 6 cities during one night in 2006

City Temperature

Berlin 5°C

London 10°C

Moscow –3°C

New York 2°C

Oslo –8°C

Paris 7°C

(a) Write down the city which had the lowest temperature.

.....................................

(1)

(b) Work out the difference in temperature between London and Moscow.

.................................°C

(2)

(1)

(4 marks)


By 9 am the next morning, the temperature had increased by 3°C.

(a) Work out the temperature at 9 am the next morning.

…………………….°C

(1)

At midday, the temperature was 7°C.

(b) Work out the difference between the temperature a midday and the temperature at

midnight.

…………………….°C

(2)

(3 marks)

7. The table shows the midday temperatures in 4 different cities on Monday.

City Midday temperature (°C)

Belfast 5

Cardiff –1

Glasgow –6

London –4

(a) Which city had the lowest temperature? ………………...

(1)

(b) Work out the difference between the temperature in Cardiff and the temperature in

Belfast.

………………... C

(1)

By Tuesday, the midday temperature in London had risen by 7 °C.

(c) Work out the midday temperature in London on Tuesday.

………………... C

(1)

(3 marks)

8.

City Temperature

Cardiff –2 °C

Edinburgh –4 °C

Leeds 2 °C

London –1 °C

Plymouth 5 °C

The table gives information about the temperatures at midnight in 5 cities.

(a) Write down the lowest temperature. ........................................ °C

(1)

(b) Work out the difference in temperature between Cardiff and Plymouth.

........................................ °C

(1)

(c) Work out the temperature which is halfway between –1°C and 5°C.

........................................ °C

(1)

(3 marks)

9. Samina recorded the maximum temperature and the minimum temperature on each of six days in

January.

The table shows her results.

Mon Tues Wed Thurs Fri Sat

Maximum temperature 1 °C 3 °C 2 °C 0 °C 3 °C 4 °C

Minimum temperature –4 °C –2 °C –4 °C –5 °C –3 °C –2 °C

(a) Write down the lowest temperature.

.............................................. °C

(1)

(b) Work out the difference between the maximum temperature on Wednesday and the minimum

temperature on Wednesday.

.............................................. °C

(1)

The minimum temperature on Sunday was 5 °C higher than the minimum temperature on Saturday.

(c) Work out the minimum temperature on Sunday.

.............................................. °C

(1)

(3 marks)

10. The table shows the temperature on the surface of each of five planets.

Planet Temperature

Venus 480 °C

Mars – 60 °C

Jupiter – 150 °C

Saturn – 180 °C

Uranus – 210 °C

(a) Work out the difference in temperature between Mars and Jupiter.

…………………°C

(1)

(b) Work out the difference in temperature between Venus and Mars.

…………………°C

(1)

(c) Which planet has a temperature 30 °C higher than the temperature on Saturn?

…………………….

(1)

The temperature on Pluto is 20 °C lower than the temperature on Uranus.

(d) Work out the temperature on Pluto. …………………°C (1)

(4 marks)

11. The table shows the highest and lowest temperatures one day in London and Moscow.

Highest Lowest

London 8°C –6°C

Moscow –3°C –8°C

(a) Work out the difference between the lowest temperature in London and the lowest

temperature in Moscow.

.................... °C

(1)

(b) Work out the difference between the highest and lowest temperature in London.

.................... °C

(1)

(2 marks)


By 9 am the next morning, the temperature had increased by 3°C.

(a) Work out the temperature at 9 am the next morning.

……………………….°C

(1)

At midday, the temperature was 7°C.

(b) Work out the difference between the temperature at midday and the temperature at

midnight.

……………………….°C

(2)

(c) Work out the temperature which is halfway between –5°C and 7°C.

……………………….°C

(1)

(4 marks)


ESTIMATION






Instructions






Information






Advice





1. Work out an estimate for the value of

5.1 × 98

............................

(2 marks)

2. Estimate the value of

..........................

(2 marks)


……………………..

(2 marks)

198

40168

8.92.3

637

4. Which is the best estimate for the value of

..........................

(3 marks)


..........................

(3 marks)

98.21.2

2.509.37

1.2

7.513.38

6. Work out an estimate for

....................................

(3 marks)


.................................

(3 marks)

1.39.5

7.291.10

6.97

19.8 813


...........................................

(4 marks)


...........................................

(4 marks)

523.0

31279.5

23.0

9.6410


...........................

(4 marks)


....................................

(4 marks)

21.0

1.48.29

51.0

96.9302


....................................

(4 marks)


..........................................

(4 marks)

195.0

904.5412

207.0

86.321


.....................................

(4 marks)

15. (a) Write down an estimate for

60

..........................................

(1)

(b) Write down an estimate for

90

..........................................

(1)

(c) Write down an estimate for

130

..........................................

(1)

(d) Write down an estimate for

150

..........................................

(1)

(4 marks)

051.0

1918.6


UTILITY BILLS






Instructions






Information






Advice





1. Mr Johnson works out the cost of the gas he used last year.

At the start of the year, the gas meter reading was 8569 units.

At the end of the year, the gas meter reading was 9872 units.

Each unit of gas he used cost 44p.

Work out the total cost of the gas he used last year.

£ ……………………………

(Total 4 marks)

2. Mr Holland uses 367 units of electricity in one month.

He pays 5.84p for each unit of electricity.

Mr Holland also pays a fixed charge of £6.14 for the month.

Work out the total amount he pays.

£ ……………………………

(Total 4 marks)

3. Here are two readings from a gas meter.

0 1 9 6 2 0 2 1 5 9

January April

The difference in the meter readings gives the number of units of gas used.

The cost of gas is 21p for each unit of gas used.

Work out the cost of gas used.

Give your answer in pounds (£).

£ …………………

(Total 4 marks)

4. Alison travels by car to her meetings.

Alison’s company pays her 32p for each mile she travels.

One day Alison writes down the distance readings from her car.

Start of the day: 2430 miles

End of the day: 2658 miles

Work out how much the company pays Alison for her day’s travel.

£……………………

(Total 4 marks)

5. Peter works out the cost of the gas he used last year.




Work out the cost of the gas he used last year.

£ ……………………………

(Total 4 marks)

*6. Here is part of Gary’s electricity bill.

Electricity bill

New reading 7155 units

Old reading 7095 units

Price per unit 15p

Work out how much Gary has to pay for the units of electricity he used.

(Total 4 marks)

7. Mr Shah is working out the cost of the electricity he used in April.

Mr Shah has to pay

21.3p for each of the first 70 units used in April

and 10.2p for each of all the other units used in April.

Work out the total cost of the electricity he used in April.

........................................................................................

(Total 4 marks)


ALGEBRA:

COLLECTING LIKE

TERMS






Instructions






Information






Advice





1. Simplify

(i) c + c + c + c

.................................

(ii) p × p × p × p

.................................

(iii) 3g + 5g

.................................

(iv) 2r × 5p

.................................

(4)

(Total 4 marks)

2. (a) Simplify 5p + 2q – 3p – 3q

.....................................

(2)

(b) Simplify

(i) 3g + 5g

.................................

(ii) 2r × 5p

.................................

(2)

(Total 4 marks)

3. (a) Simplify y + y

..........................

(1)

(b) Simplify p2 + p2 + p2

..........................

(1)

(Total 2 marks)

4. Simplify

(a) c + c + c

………………………

(1)

(b) e + f + e + f + e

………………………

(1)

(c) 2a + 3a

………………………

(1)

(d) 2xy + 3xy – xy

………………………

(1)

(e) 3a + 5b – a + 2b + 8

(2)

(Total 6 marks)

5. (a) Simplify

2x × y × 3

……………………………

(1)

(b) Simplify

5x + 3y - 2x + y

……………………………

(2)

(c) Simplify y × y × y

.....................................

(1)

(Total 4 marks)

6. (a) Simplify 5bc + 2bc – 4bc

................................

(1)

(b) Simplify 4x + 3y – 2x + 2y

................................

(2)

(c) Simplify m × m × m

................................

(1)

(d) Simplify 3n × 2p

................................

(1)

(Total 5 marks)

7. (a) Simplify a + a + a + a

.....................

(1)

(b) Simplify 3 × b × 4

.....................

(1)

(c) Simplify completely 4a + 5b – 2a + b

.....................................

(2)

(Total 4 marks)

8. (a) Simplify 2a + 7b – 3b + a

.................................

(2)

(b) Simplify x3 + x3

.................................

(1)

(Total 3 marks)

9. (a) Simplify 4p × 5q

....................................

(1)

(b) Simplify d × d × d × d

....................................

(1)

(Total 2 marks)

10. Simplify

(i) 5g – 2g

....................................

(1)

(ii) p × p

....................................

(1)

(Total 2 marks)

11. (a) Simplify 3p + 2q – p + 2q

……………………..

(2)

(b) Simplify 3y2 – y2

……………………..

(1)

(c) Simplify 5c + 7d – 2c – 3d

……………………..

(2)

(d) Simplify 4p × 2q

……………………..

(1)

(Total 6 marks)

12. (a) Simplify d + d + d + d + d

....................................

(1)

(b) Simplify y2 + y2

....................................

(1)

(c) Simplify

(i) 3a + 4b – 2a – b

................................

(2)

(ii) 5x2 + 2x – 3x2 – x

................................

(2)

(Total 6 marks)

13. (a) Simplify 4x + 7y + 2x – 3y

…………………………

(2)

(b) Simplify 2pq + pq

…………………………

(1)

(Total 3 marks)

14. (a) Simplify

(i) e + f + e + f + e

..........................

(1)

(ii) p2 + p2 + p2

..........................

(1)

(Total 2 marks)

15. (a) Simplify

(i) e + f + e + f + e + f + e

..........................

(1)

(ii) p2 + p2 + p2

..........................

(1)

(Total 2 marks)

16. (a) Simplify 2x + 2x

.....................................

(1)

(b) Simplify 5y – 2y

.....................................

(1)

(c) Simplify 2 × 4p

.....................................

(1)

(Total 3 marks)

17. (a) Simplify c + c + c

..............................................

(1)

(b) Simplify 2e × 3f

..............................................

(1)

(c) Simplify 9p + 2t – 2p + 3t

..............................................

(2)

(Total 4 marks)

18. (a) Simplify f + f + f + f – f

..............................................

(1)

(b) Simplify 2m × 3

..............................................

(1)

(c) Simplify 3a + 2h + a + 3h

....................................................................

(2)

(Total 4 marks)

19. (a) Simplify a + a + a + a

..........................................

(1)

(b) Simplify 3 × c × d

..........................................

(1)

(c) Simplify 3ef + 5ef – ef

..........................................

(1)

(Total 3 marks)

20. (a) Simplify d + d + d + d + d

(1)

..............................................................

(b) Simplify 3 × m × 2

(1)

..............................................................

(c) Simplify 6k + 3j – 2k + 5j

(2)

..............................................................

(Total 4 marks)


ALGEBRA:

EXPAND & FACTORISE






Instructions






Information






Advice





1. (a) Factorise 8x – 20

..........................

(1)

(b) Factorise fully 10x2 – 15xy

..........................

(2)

(3 marks)

2. (a) Factorise 3x + 12

.....................................

(1)

(b) Factorise fully 2x2 − 4xy

.....................................

(2)

(c) Expand and simplify 3(2a + 5) + 5(a – 2)

..............................................

(2)

(5 marks)

3. (a) Expand 3(2y – 5)

..............................................

(1)

(b) Factorise completely 8x2 + 4xy

..............................................

(2)

(3 marks)

4. (a) Expand 4(3x + 5)

......................................................................

(1)

(b) Expand and simplify 3(x – 4) – 2(x + 5)

......................................................................

(2)

(3 marks)

5. (a) Factorise x2 + 7x

..........................................

(2)

(b) Expand x(x + 2)

..........................................

(2)

(c) Factorise completely 2y2 – 4y

.....................................

(2)

(6 marks)

6. (a) Expand 3(4x + y)

(2)

......................................................

(b) Expand 5p(p – 3)

(2)

......................................................

(c) Factorise completely 8y2 – 24xy

..........................................

(2)

(6 marks)

7. (a) Expand and simplify 3(x + 4) + 2(5x – 1)

..........................................

(2)

(b) Factorise completely 6y2 – 9xy

..........................................

(2)

(4 marks)

8. (a) Factorise fully 6y2 + 12y

(2)

...........................................................................

(b) Factorise 5x – 10

..........................

(1)

(c) Factorise fully 2p2 – 4pq

..........................

(2)

(5 marks)


.....................................

(2)

(b) Factorise 5x + 10

.....................................

(1)

(c) Factorise x2 − 7x

.....................................

(1)

(4 marks)

10. (a) Expand x(x + 2)

.....................................

(2)

(b) Factorise 15x – 10

.....................................

(2)

(c) Expand and simplify 2(x – y) – 3(x – 2y)

.....................................

(2)

(6 marks)

11. (a) Factorise 4x + 10

(1)

........................................................................................

(b) Factorise fully 6y2 + 12y

(2)

........................................................................................

(c) Factorise 4 + 6x

.....................................

(2)

(5 marks)

12. (a) Expand 3(2y – 5)

..............................................

(1)


..............................................

(2)

(c) Factorise 4x + 10y

..............................................

(2)

(5 marks)

13. (a) Expand 3(x + 4)

..........................................

(1)

(b) Expand x(x2 + 2)

..........................................

(2)

(c) Factorise x2 – 6x

..........................................

(1)

(4 marks)

14. (a) Factorise p2 + p

………………………………

(1)

(b) Factorise x2 + 7x

..............................................

(1)

(c) Expand and simplify 4(x – 3) – 2(1 – x)

………………………………

(2)

(4 marks)

15. (a) Factorise 4x + 10y

..............................................

(1)

(b) Factorise x2 + 7x

..............................................

(1)

(c) Expand x2(x + 5)

..........................................

(2)

(4 marks)

16. (a) Expand 5(2y – 3)

.................................

(1)

(b) Expand the brackets p(q – p2)

...................................

(1)

(c) Expand and simplify 5(3p + 2) – 2(5p – 3)

...................................

(2)

(4 marks)

17. (a) Expand 3(2g – 1)

.....................................

(1)

(b) Expand 2d(d + 3)

.....................................

(2)

(c) Factorise p 2 + 6p

…………………….

(2)

(5 marks)

18. (a) Multiply out 7(n – 3)

………………………

(1)

(b) Expand 5(2y – 3)

.................................

(1)

(c) Expand and simplify

2(3x + 4) – 3(4x – 5)

.................................

(2)

(4 marks)

19. (a) Expand y(y3 + 2y)

…………………….

(2)

(b) Factorise completely 6x2 – 9xy

…………………….

(2)

(c) Expand and simplify 5(3p + 2) – 2(5p – 3)

..................................

(2)

(6 marks)

20. Expand the brackets

(i) 4(2x – 3)

................................

(2)

(ii) p(q – p2)

................................

(2)

(ii) t(3t2 + 4)

………………………

(2)

(6 marks)

21. (a) Factorise 3t – 12

…………………………

(2)

(b) Factorise y2 + y

…………………………

(1)

(c) Expand and simplify 3(2x – 1) – 2(2x – 3)

.

(2)

(6 marks)


ALGEBRA:

SOLVING EQUATIONS






Instructions






Information






Advice





1. (a) Solve 2y = 8

y = ………….......

(1)

(b) Solve t – 4 = 7

t = ………….......

(1)

(c) Solve 4

x = 3

x = ………….......

(1)

(3 marks)

2. (a) Solve 3

y= 6

y = …………………

(1)

(b) Solve 7y = 54

y = …………………

(1)

(c) Solve 2t – 5 = 9

t = ………….......

(2)

(4 marks)

3. (a) Solve 4w = 20

w = …………………

(1)

(b) Solve x − 6 = 3

x = …………………

(1)

(c) Solve 3

y= 7

y = …………………

(1)

(3 marks)

4. (a) Solve 3x = 12

x = ...............................

(1)

(b) Solve y – 7 = 5

y = ...............................

(1)

(c) Solve 2t + 8 = 3

t = ................................

(2)

(d) Solve 5

2y = 4

y = .....................................

(2)

(3 marks)

5. (a) Solve 6g = 18

g = ..........................................

(1)

(b) Solve y + 5 = 12

y = ..............................................

(1)

(c) Solve 4

x = 3

x = ..............................................

(1)

(d) Solve 5h + 7 = 17

h = ..........................................

(2)

(5 marks)

6. (a) Solve b – 7 = 12

b = .............................................

(1)

(b) Solve 5e = 40

e = .............................................

(1)

(c) Solve 4m + 6 = 15

m = .............................................

(2)

(d) Solve 5w – 6 = 10

w = ..............................................

(2)

(6 marks)

7. (a) Solve 4x + 1 = 9

x = ........................................

(2)

(b) Solve 2x – 5 = 4

x = ……………………………

(2)

(c) Solve 2y – 1 = 12

y = ........................................

(2)

(6 marks)

8. (a) Solve 4x + 1 = 19

x = ........................................

(2)

(b) Solve 4x + 3 = 19

x = ……………………………

(2)

(c) Solve 2q + 7 = 1

q = ........................................

(2)

(6 marks)

9. (a) Solve x + x + x = 15

x = ........................................

(2)

(b) Solve 6x – 7 = 38

x = ……………………………

(2)

(c) Solve 7x + 18 = 74

x = ........................................

(2)

(6 marks)

10. (a) Solve 2y + 3 = 8

y = ........................................

(2)

(b) Solve 5(t – 3) = 25

t = ……………………………

(2)

(c) Solve 4(5y – 2) = 48

y = ........................................

(2)

(6 marks)

11. Solve 13x + 1 = 11x + 9

x = .....................................

(3 marks)

12. Solve 5t – 4 = 3t + 6

t = .....................................

(3 marks)

13. Solve 4y + 3 = 2y + 8

(3 marks)

14. Solve 5y + 1 = 3y + 13

y = .....................................

(3 marks)

15. Solve 3y + 10 = 5y + 3

y = .....................................

(3 marks)

16. Solve 2y + 17 = 6y + 5

y = .....................................

(3 marks)


CHANGING THE

SUBJECT OF A

FORMULA Materials required for examination Items included with question papers





Instructions






Information






Advice





1. Make p the subject of the formula m = 3n + 2p

p = ...............................

(Total 2 marks)

2. Make c the subject of the formula a = 3c – 4

c = ……………………………

(Total 2 marks)

3. Make b the subject of the formula P = 2a + 2b

b = .....................................

(Total 2 marks)

4. Make c the subject of the formula f = 3c – 4

c = ..............................

(Total 2 marks)

5. Make t the subject of the formula

u = 7t + 30

t = ..........................

(Total 2 marks)

6. Make t the subject of the formula v = u + 5t

t = ………………..

(Total 2 marks)

7. Make y the subject of the formula

x = 3y + 2

…………………………

(Total 2 marks)

8. Rearrange y = x + 1 to make x the subject.

.....................................

(Total 2 marks)

9. Make a the subject of the formula s = + 8u

a = .............................

(Total 2 marks)

2

1

4

a

10. Make u the subject of the formula

D = ut + kt2

u = ...................................

(Total 2 marks)

11. Make s the subject of the formula v2 = u2 + 2as

s = .................................

(Total 2 marks)

12. Make t the subject of the formula

2(t – 5) = y

t = ....................................

(Total 3 marks)

13. Make n the subject of the formula m = 5n – 21

n = ........................................................

(Total 2 marks)

14. Make q the subject of the formula P = 2q + 10

q = .....................................

(Total 2 marks)

15. When you are h feet above sea level, you can see d miles to the horizon,

where

d =

Make h the subject of the formula d =

h =................................

(Total 2 marks)

2

3h

2

3h


ALGEBRA:

INEQUALITIES






Instructions






Information






Advice





1. –1 n < 4

n is an integer.

Write down all the possible values of n.

........................................................

(2 marks)

2. (a) x > −3

Show this inequality on the number line.

(2)

(b) Solve the inequality 7y - 34 8

...........................................

(2)

(c) Write down the integer values of x that satisfy the inequality

–2 x < 3

..........................................................................

(2)

(6 marks)

3. –2 n < 5

n is an integer.

(a) Write down all the possible values of n.

..........................................................................

(2)

(b) Solve the inequality 4x + 1 > 11

..........................................................................

(2)

(4 marks)

4. (a) On the number line below, show the inequality –2 < y < 3

(1)

(b) Here is an inequality, in x, shown on a number line.

Write down the inequality.

.........................................................

(2)

(c) Solve the inequality 4t – 5 > 11

.....................................

(2)

(5 marks)

5. (a) n is an integer.

–1 n < 4

List the possible values of n.

...........................................................................................

(2)

(b)

Write down the inequality shown in the diagram.

..............................................

(2)

(c) Solve 3y – 2 > 13

..............................................

(2)

(6 marks)

6. –3 < n ≤ 1

n is an integer.


..........................................

(2)

(b) Solve the inequality 3p – 7 > 11

..........................................

(2)

(4 marks)

7. n is an integer.

−3 < n < 4


……………………………………….

(2)

(b) Solve 2x - 7 ≤ 11

………………………………

(2)

(4 marks)

8. (a) (i) Solve the inequality

5x – 7 < 28

………………………

(ii) On the number line, represent the solution set to part (i).

(3)

n is an integer such that –4 2n < 3.

(b) Write down the possible values of n.

…………………………

(3)

(6 marks)

–5 –4 –3 –2 –1 0 1 2 3 4 5

9. (i) Write down the inequality shown on the number line.

.........................................

(ii) Show the inequality x > 1 on the number line below.

(3 marks)

10. (i) Solve the inequality 7x – 3 > 18

..............................

x is a whole number such that 7x – 3 > 18

(ii) Write down the smallest value of x.

..............................

(4 marks)

x 543210–1–2x

x 543210–1–2x

11. (a) Solve 5x + 12 < 17

(2)

x = ..................................................................

(b) Solve the inequality 3(2y + 1) > 10

(2)

...........................................................................

(4 marks)

12. (a) Solve the inequality 4x – 3 < 7

………………

(2)

An inequality is shown on the number line.

(b) Write down the inequality.

…………………………

(2)

(c) n is a whole number such that

6 3n 15

List all the possible values of n.

…………………(2)

(6 marks)

–4 –3 –2 –1 0 1 2 3 4

13. m is an integer such that –2 < m 3

(a) Write down all the possible values of m.

.............................................................................................

(2)

(b) Solve 7x – 9 < 12

..............................................

(2)

(4 marks)


TRIAL &

IMPROVEMENT






Instructions






Information






Advice





1. The equation x3 + 3x = 41

has a solution between 3 and 4

Use a trial and improvement method to find this solution.



x = ...............................

(4 marks)

2. The equation

x3 – 6x = 72





x = ..............................................

(4 marks)

______________________________________________________________________________

3. The equation

x3 – 3x = 15





x = ..........................................

(4 marks)

___________________________________________________________________________

4. The equation

x3 + 5x = 67




You must show ALL your working.

x = ...........................................

(4 marks)

5. The equation

x3 + 2x = 42





x = ....................

(4 marks)

___________________________________________________________________________

6. The diagram shows a cuboid.

Diagram NOT

accurately drawn

A cuboid has a square base of side x cm.

The height of the cuboid is (x + 4) cm.

The volume of the cuboid is 150 cm3.

(a) Show that x3 + 4x

2 = 150

(2)

The equation x3 + 4x

2 = 150 has a solution between 4 and 5

(b) Use a trial and improvement method to find this solution.



(4)

x= ....................................................................

(6 marks)

7. The diagram shows a cube and a cuboid.

All the measurements are in cm.

The volume of the cube is 100 cm3 more than the volume of the cuboid.

(a) Show that x3 – 10x = 100

(2)

(b) Use a trial and improvement method to find the value of x.



x = ..............................................

(4)

(6 marks)

______________________________________________________________________________


ALGEBRA: INDICES






Instructions






Information






Advice





1. (a) Simplify m3 × m

6

.....................................

(1)

(b) Simplify 2

8

p

p

.....................................

(1)

(c) Simplify (2n3)4

.....................................

(2)

(4 marks)


7

(1)

......................................................

(b) Simplify x0

(1)

......................................................

(c) Simplify 2

1

)16( 6y

(2)

......................................................

(4 marks)

3. (a) Simplify m5 ÷ m

3

.................................................

(1)

(b) Simplify 5x4y

3 × x

2y

.................................................

(2)

(3 marks)

4. (a) Simplify a4 × a

5

..............................

(1)

(b) Simplify 2

86

5

45

ef

fe

.........................................

(2)

(c) Write down the value of 2

1

9

.........................................

(1)

(4 marks)


4

……………………………………

(1)

(b) Simplify y7 ÷ y

5

……………………………………

(1)

(c) Simplify (m3)5

.....................................

(2)

(4 marks)

6. Simplify fully

(a) p2 × p

7

…………………………(1)

(b)

........................................(2)

(c) (2xy3)5

.................................................(2)

(4 marks)

3

54 23

q

qq

7. (a) Simplify 15y6 ÷ 3y

2

……………………………

(2)

(b) Simplify 7wx2 × 3w

3x

……………………………

(2)

(4 marks)

8. Work out the value of

(a) (22)3

.................................

(1)

(b) (3)2

.................................

(1)

(c) 924

.................................

(2)

(d) 4–2

.................................

(1)

(5 marks)

9. (a) Write down the value of

....................

(1)

(b) Simplify

(i)

...................................

(ii) (y4)3

...................................

(2)

(3 marks)

2

1

49

2

6

x

x

10. Simplify

………..……

(2 marks)

11. 75 × 76 = 73 × 7k

Find the value of k.

k = ……………

(2 marks)

12. (a) Simplify p3 × p2

.................................

(1)

(b) Simplify

.................................

(2)

(3 marks)


(i)

……………………………

(ii) 3-2

……………………………

(2 marks)

32

73

3

15

ba

ba

2

43

q

qqq

21

36

14. (a) Write as a power of 7

(i) 78 ÷ 73

......................

(ii)

......................

(3)

(b) Write down the reciprocal of 2

......................

(1)

(4 marks)

15. (a) Simplify

12y3 ÷ 3y5

……………………………

(2)

(b) Simplify

2w3x2 × 3w4x

……………………………

(2)

(4 marks)


(i) 42

.....................................

(ii)

.....................................

(iii) 3 × 23

.....................................

(3 marks)

7

77 32

64

17. Simplify

(i) x4 × x5

………………………

(ii)

………………………

(iii) 3s2t3 × 4s4t2

………………………

(iv) (q3)4

………………………

(6 marks)

18. Simplify fully

(i) (p3)3

.................................

(ii)

.................................

(4 marks)

19. Work out

(i) 40

.................................

(ii) 4–2

.................................

(iii)

.................................

(4 marks)

3

8

p

p

3

54 23

q

qq

2

3

16

20. (a) Find the value of

(i) 64°

……………………..

(ii)

…………………….

(iii)

…………………….

(4 marks)

2

1

64

3

2

64


ALGEBRA:

FORMING AND

SOLVING EQUATIONS






Instructions






Information






Advice





1.

In the diagram, all measurements are in centimetres.

ABC is an isosceles triangle.

AB = 2x

AC = 2x

BC = 10

(a) Find an expression, in terms of x, for the perimeter of the triangle.

Simplify your expression.

………………………

(2)

The perimeter of the triangle is 34 cm.

(b) Find the value of x.

x =………………………

(2)

(4 marks)

A

B C

2x

10

2x


2.


The lengths, in cm, of the sides of the triangle are 3(x – 3), 4x – 1 and 2x + 5

(a) Write down, in terms of x, an expression for the perimeter of the triangle.

....................... cm

(2)

The perimeter of the triangle is 49 cm.

(b) Work out the value of x.

x = ....................

(2)

(4 marks)

3( – 3)x2 + 5x

4 – 1x

3.


In the diagram, all measurements are in centimetres.

The lengths of the sides of the quadrilateral are

2r + 5

2r

4r – 3

r

(a) Find an expression, in terms of r, for the perimeter of the quadrilateral.

Give your expression in its simplest form.

.........................................

(2)

The perimeter of the quadrilateral is 65 cm.

(b) Work out the value of r.

r = .....................................

(2)

(4 marks)

4.

Diagram NOT

accurately drawn

The sizes of the angles, in degrees, of the triangle are

2x + 7

2x

x + 18

(a) Use this information to write down an equation in terms of x.

.............................................................................

(2)

(b) Use your answer to part (a) to work out the value of x.

x = .................................

(2)

(4 marks)

5.


In this quadrilateral, the sizes of the angles, in degrees, are

x + 10

2x

2x

50

(a) Use this information to write down an equation in terms of x.

..............................................................................

(2)

(b) Work out the value of x.

x = ............................

(3)

(5 marks)

A

x+10

B 2 x D

2x

C

50

6.


ABCD is a parallelogram.

AD = (x + 4) cm,

CD = (2x – 1) cm.

The perimeter of the parallelogram is 24 cm.

(i) Use this information to write down an equation, in terms of x.

…………………………………………………….

(ii) Solve your equation.

x = ……………………………

(4 marks)

A D

B C

( + 4) cmx

(2 – 1) cmx

7. The perimeter of this triangle is 19 cm.

All lengths on the diagram are in centimetres.


Work out the value of t.

t = ……………………………

(3 marks)

8.


The diagram shows a triangle.

The sizes of the angles, in degrees, are

3x

2x

x + 30


x = ...................

(3 marks)

( + 4)t

( – 1)t

( + 3)t

3x

2x x + 30

9.


The diagram shows a rectangle.

All the measurements are in centimetres.

(a) Explain why 4x + 1 = 2x + 12

.....................................................................................................................................

.....................................................................................................................................

(1)

(b) Solve 4x + 1 = 2x + 12

x = ........................................

(2)

(c) Use your answer to part (b) to work out the perimeter of the rectangle.

........................................ cm

(2)

(5 marks)

4 + 1 x

2 + 12 x

x x


SEQUENCES






Instructions






Information






Advice





1. Here are the first 5 terms of an arithmetic sequence.

6, 11, 16, 21, 26

Find an expression, in terms of n, for the nth term of the sequence.

.................................................

(Total 2 marks)

2. Here are the first five terms of a number sequence.

3 8 13 18 23

(a) Write down the next two terms of the sequence.

............, ............

(2)

(b) Explain how you found your answer.

..................................................................................................................

(1)

(c) Explain why 387 is not a term of the sequence.

..................................................................................................................

..................................................................................................................

(1)

(Total 4 marks)


126 122 118 114 110

(a) Write down the next two terms of the number sequence.

…………… , ……………

(1)


…………………………………………………………………………

(1)

The 20th term of the number sequence is 50

(c) Write down the 21st term of the number sequence.

……………………..

(1)

(Total 3 marks)


3 7 11 15 19

(a) Work out the 8th term of the number sequence.

.........................................

(1)

(b) Write down an expression, in terms of n, for the nth term of the number

sequence.

.........................................

(2)

(Total 3 marks)

5. The first five terms of an arithmetic sequence are

2 9 16 23 30

Find, in terms of n, an expression for the nth term of this sequence.

............................................

(Total 2 marks)


2 7 12 17 22

Write down, in terms of n, an expression for the nth term of this sequence.

....................................

(Total 2 marks)

7. Here are the first five terms of an arithmetic sequence.

1 3 7 11 15

(a) Find, in terms of n, an expression for the nth term of this sequence.

………….……………………..

(2)

In another arithmetic sequence the nth term is 8n 16

John says that there is a number that is in both sequences.

(b) Explain why John is wrong.

…………………………………………………….…………………….

…………………………………………………………………………..

(2)

(Total 4 marks)

8. The first four terms of an arithmetic sequence are

21 17 13 9


.............................

(Total 2 marks)

9. The nth term of a sequence is 2n2

(i) Find the 4th term of the sequence.

...............................................................

(ii) Is the number 400 a term of the sequence?

............................


...........................................................................................................................................

...........................................................................................................................................

(Total 3 marks)


3 9 15 21 27

(a) Find an expression, in terms of n, for the nth term of this sequence.

....................................................................

(2)

Ben says that 150 is in the sequence.

(b) Is Ben right?

You must explain your answer.

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

(1)

(Total 3 marks)


2 9 16 23 30

(a) Write down the 12th term of this sequence.

………………………..

(1)

(b) Find, in terms of n, an expression for the nth term of this sequence.

…………………………………

(2)

(Total 3 marks)

12. The first four terms of an arithmetic sequence are

21 17 13 9


.............................

(Total 2 marks)


6, 11, 16, 21, 26

Find an expression, in terms of n, for the nth term of the sequence.

.................................................

(Total 2 marks)


2 9 16 23 30


............................................

(Total 2 marks)


3 8 13 18 23

(a) Write down the next two terms of the sequence.

............, ............

(2)


..................................................................................................................

(1)

(c) Explain why 387 is not a term of the sequence.

..................................................................................................................

..................................................................................................................

..................................................................................................................

(1)

(Total 4 marks)


3 7 11 15 19

(a) Write down an expression, in terms of n, for the nth term of this

sequence.

..........................................

(2)

Adeel says that 319 is a term in the number sequence.

(b) Is Adeel correct?

You must justify your answer.

..................................................................................................................

..................................................................................................................

(2)

(Total 4 marks)

17. Here are some patterns made up of dots.

(a) In the space below, draw Pattern number 4.

(1)

(b) Complete the table.

Pattern

number

1 2 3 4 5

Number of

dots

10 14 18

(1)

(c) How many dots are used in Pattern number 10?

..........................

(1)

(Total 3 marks)

Pattern number 1 Pattern number 2 Pattern number 3


STRAIGHT LINE

GRAPHS






Instructions






Information






Advice





1. (a) Complete the table of values for y = 2x + 5

x –2 –1 0 1 2

y 1 5

(2)

(b) On the grid, draw the graph of y = 2x + 5 for values of x from x = –2 to x = 2

(2)

(4 marks)

______________________________________________________________________________

2. (a) Complete the table of values for y = 2x − 3

x –1 0 1 2 3 4

y –3 –1

(2)

(b) On the grid, draw the graph of y = 2x − 3

(2)

(4 marks)

O

y

x –1 1 2 3 4

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

3. (a) Complete the table of values for y = 2x + 1

x –2 –1 0 1 2 3

y –1 1

(2)

(b) On the grid, draw the graph of y = 2x + 1

(2)

(c) Use your graph to find

(i) the value of y when x = –1.5 y = ..................

(ii) the value of x when y = 6 x = ..................

(2)

(6 marks)

4. On the grid, draw the graph of y = 3x – 2 for values of x from –1 to 3

(4 marks)

______________________________________________________________________________

5. On the grid, draw the graph of y = 3 – 2x from x = −2 to x = 4

y

7

6

5

4

3

2

1

-2

-1 O

-1

1 2 3 4 x

-2

-3

-4

-5

(4 marks)

____________________________________________________________________________

6. On the grid, draw the graph of y = 3x + 2

(4)

(4 marks)

x

y

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–2 –1 O 1 2

7. On the grid, draw the graph of x + y = 5

(4)

(4 marks)

y

x–1 O 1 2 3

8

7

6

5

4

3

2

1


SOLVNG

SIMULTANEOUS

EQUATIONS

GRAPHICALLY






Instructions






Information






Advice





1. The graphs of the straight lines with equations 3y + 2x = 12 and y = x – 1

have been drawn on the grid.

Use the graphs to solve the simultaneous equations

3y + 2x = 12

y = x –1

x = .....................................

y = .....................................

(2)

(Total 2 marks)

x

y

8

6

4

2

O 2 4 6 8

3 + 2 = 12y x

y x = –1

2. The straight line y + 2x = 5 has been drawn on the grid.

(a) Complete this table of values for y = 2x – 1

x –1 0 1 2 3 4

y –1 3 5

(2)

(b) On the grid, draw the graph of y = 2x – 1

(2)

(c) Use your diagram to solve the simultaneous equations

y + 2x = 5

y = 2x – 1

x = ....................................

y = ....................................

(2)

(Total 6 marks)

y

–3 –2 –1 O 1 2 3 4 x

8

6

4

2

–2

–4

3.

The diagram shows graphs of y = x + 2

and 2y + 3x = 12

(a) Use the diagram to solve the simultaneous equations

y = x + 2

2y + 3x = 12

x = ................... y = ....................

(2)

(Total 2 marks)

7

6

5

4

3

2

1

1 2 3 4 5 6 7O

x

y

2

1

2

1

4.


The diagram shows two straight lines intersecting at point A.

The equations of the lines are

y = 4x – 8

y = 2x + 3

Work out the coordinates of A.

(.................., ..................)

(Total 3 marks)

y x = 4 – 8

A

y

xO

y x = 2 + 3


DRAWING

QUADRATIC GRAPHS






Instructions






Information






Advice





1. (a) Complete the table of values for y = x2 + x.

x –3 –2 –1 0 1 2 3

y 6 2 0 6

(2)

(b) On the grid, draw the graph of y = x2 + x.

(2)

(Total 4 marks)

12

10

8

6

4

2

1 2 3

–2

–4

–6

–8

–10

–12

–1–2–3O

x

y

2. (a) Complete the table for y = x2 – 2x – 4

x –2 –1 0 1 2 3 4

y 4 –4 –5 –1

(2)

(b) On the grid, draw the graph of y = x2 – 2x – 4

(2)

(Total 4 marks)

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

4321–1–2

y

xO

3. (a) Complete the table of values for y = x2 – 4x + 2

x –1 0 1 2 3 4 5

y 2 –1 –1 7

(2)

(b) On the grid, draw the graph of y = x2 – 4x + 2

(2)

(Total 4 marks)

x –1 O 1 2 3 4 5

y

8

7

6

5

4

3

2

1

–1

–2

–3

–4

4. (a) Complete the table of values for y = x2 – 3x – 1.

x 2 1 0 1 2 3 4

y 3 1 3 3

(2)

(b) On the grid below, draw the graph of y = x2 – 3x – 1.

(2)

(c) Use your graph to find an estimate for the minimum value of y.

…………………………… (1)

(Total 5 marks)

x

y

–2 –1 1 2 3 4O

10

9

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

5. (a) Complete the table of values for y = x2 – 3

x –2 –1 0 1 2 3

y 1 –3 –2

(2)

(b) On the grid, draw the graph of y = x2 – 3

(2)

(Total 4 marks)

7

6

5

4

3

2

1

–1

–2

–3

–4

–2 –1 1 2 3

y

x

6. (a) Complete the table for y = x2 – 3x + 1

x –2 –1 0 1 2 3 4

y 11 1 –1 1 5

(2)

(b) On the grid below, draw the graph of y = x2 – 3x + 1

(2)

(c) Use your graph to find an estimate for the minimum value of y.

y = …………………… (1)

12

11

10

9

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–2 –1 1 2 3 4 x

y

O

(Total 5 marks)

7. (a) Complete the table of values for y = x2 – 3x – 1

x –2 –1 0 1 2 3

y 3 –1 –3

(2)

(b) On the grid, draw the graph of y = x2 – 3x – 1

(2)

(Total 4 marks)

10

8

6

4

2

–2

–4

–2 –1 1 2 3O

y

x


DISTANCE TIME

GRAPHS






Instructions






Information






Advice





1. Here is part of a travel graph of Siân’s journey from her house to the shops and back.

(a) Work out Siân’s speed for the first 30 minutes of her journey.

Give your answer in km/h.

............................. km/h

(2)

Siân spends 15 minutes at the shops.

She then travels back to her house at 60 km/h.

(b) Complete the travel graph.

(2)

(Total 4 marks)

20

18

16

14

12

10

8

6

4

2

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80

Time in minutes

Distancein kmfrom

Si n’shouse

â

2. Anil cycled from his home to the park.

Anil waited in the park.

Then he cycled back home.

Here is a distance-time graph for Anil’s complete journey.

(a) At what time did Anil leave home?

..........................

(1)

(b) What is the distance from Anil’s home to the park?

................... km

(1)

(c) How many minutes did Anil wait in the park?

..........................

(1)

(Total 3 marks)

8

6

4

2

00900 0910 0920 0930 0940 0950 1000 1010

Time of day

Distancefromhome(km)

3. A man left home at 12 noon to go for a cycle ride.

The travel graph represents part of the man’s journey.

At 12.45pm the man stopped for a rest.

(a) For how many minutes did he rest?

……………minutes

(1)

(b) Find his distance from home at 1.30pm.

………………….km

(1)

The man stopped for another rest at 2pm.

He rested for one hour.

Then he cycled home at a steady speed. It took him 2 hours.

(c) Complete the travel graph.

(2)

4. Margaret went on a cycle ride.

The travel graph shows Margaret’s distance from home on this cycle ride.

(a) How far had Margaret cycled after 30 minutes?

................................... km

(1)

After 60 minutes, Margaret stopped for a rest.

(b) For how many minutes did she rest?

........................... minutes

(1)

(c) How far did Margaret cycle in total on her ride?

................................... km

(1)

(Total 3 marks)

5. Judy drove from her home to the airport.

She waited at the airport.

Then she drove home.

Here is the distance-time graph for Judy’s complete journey.

(a) What is the distance from Judy’s home to the airport?

........................ km

(1)

(b) For how many minutes did Judy wait at the airport?

......................... minutes

(1)

(c) Work out Judy’s average speed on her journey home from the airport.

Give your answer in kilometres per hour.

...................... kilometres per hour

(2)

(Total 4 marks)

1400 1430 1500 1530 1600 1630

Time of day

50

40

30

20

10

0

Distance

from home

(km)

6. Jamie travelled 20 km from his home to his friend’s house.

Jamie then spent some time at his friend’s house before returning home.

Here is the travel graph for part of Jamie’s journey.

(a) Write down the time that Jamie left home.

………………...

(1)

(b) Write down Jamie’s distance from home at 10 20

.............................. km

(1)

Jamie left his friend’s house at 11 10 to return home.

(c) Work out the time in minutes Jamie spent at his friend’s house.

...................... minutes

(1)

Jamie returned home at a steady speed.

He arrived home at 11 50

(d) Complete the travel graph.

(1)

10 00 10 20 10 40 11 00 11 20 11 40 12 00

(e) Work out Jamie’s average speed on his journey from his home to his friend’s

house.

Give your answer in kilometres per hour.

......................... kilometres per hour

(2) (Total 6 marks)

7. James left home at 10 00 am.

He walked to the swimming pool.

On the way to the swimming pool he stopped to talk to a friend.

Here is the distance-time graph for his complete journey.

(a) For how many minutes did James stop and talk to his friend?

…………………………… minutes

(1)

(b) What is the distance from James’ home to the swimming pool?

…………………………… km

(1)

(Total 2 marks)

5

4

3

2

1

0

10 00 11 00 12 00Time

Distance in kmfrom

James’ home

8. Robert left school at 3 30 pm.

He walked home.

On the way home, he stopped to talk to a friend.

His sister, Sarah, left the same school at 3 45 pm.

She cycled home using the same route as Robert.

Here are the distance-time graphs for Robert’s and Sarah’s complete journeys.

(a) Find the distance Robert walked during the first 10 minutes of his journey.

................................. km

(1)

(b) Find the total time that Robert stopped to talk to his friend.

................................. minutes

(1)

(c) Write down the distance that Robert had walked when Sarah cycled past him.

................................. km

(1)

3

2

1

0330 340 350 400

Distancefromschool(km)

Time(pm)

9. Here is a travel graph of Siân’s journey from her house to the library and back to her

house.

(a) How far is Siân from her house at 09 30?

...................... km

(1)

The library is 20 km from Siân’s house.

(b) (i) At what time did Siân arrive at the library?

......................

(ii) How long did Siân spend at the library?

...................... minutes

(2)

Siân left the library at 10 30 to travel back to her house.

(c) At what time did Siân arrive back at her house?

......................

(1)

0

2

4

6

8

10

12

14

16

18

20

Dis

tance

fro

m S

iân’s

ho

use

(km

)

Time

11 3011 0010 3010 0009 3009 00

10. Pete visited his friend and then returned home.

The travel graph shows some information about Pete’s journey.

(a) Write down the time that Pete started his journey.

..................................

(1)

At 2.30 pm Pete stopped for a rest.

(b) (i) Find his distance from home when he stopped for this rest.

....................... km

(ii) How many minutes was this rest?

....................... minutes

(2)

Pete stayed with his friend for one hour.

He then returned home.

(c) Work out the total distance travelled by Pete on this journey.

....................... km

(2)

(Total 5 marks)

Distance

from

home in km

0

2

4

6

8

10

12

14

16

18

Time of day

7pm6pm5pm4pm3pm2pm1pm

11. Here are six temperature/time graphs.

Each sentence in the table describes one of the graphs.

Write the letter of the correct graph next to each sentence.


The temperature starts at 0°C and keeps rising. B

The temperature stays the same for a time and then falls.

The temperature rises and then falls quickly.

The temperature is always the same.

The temperature rises, stays the same for a time and then falls.

The temperature rises, stays the same for a time and then rises

again.

(Total 3 marks)

Otime

temperature

°C

temperature

°C

temperature

°C

temperature

°C

temperature

°C

temperature

°C

Otime

A B

Otime

Otime

C D

Otime

Otime

E F


PYTHAGORAS

THEOREM






Instructions






Information


each question.




Advice





1.

PQR is a right-angled triangle.

PQ = 16 cm.

PR = 8 cm.

Calculate the length of QR.


............................... cm

(3 marks)

2.

XYZ is a right-angled triangle.

XY = 3.2 cm.

XZ = 1.7 cm.

Calculate the length of YZ.


…………………………. cm

(3 marks)


NOT

3.2 cm

1.7 cm

X Y

Z

3.

ABC is a right-angled triangle.

AB = 8 cm,

BC = 11 cm.

Calculate the length of AC.


…………………………… cm

(3 marks)

4.

Angle MLN = 90°.

LM = 3.7 m.

MN = 6.3 m.

Work out the length of LN.


LN = ……….…………….. m

(3 marks)

8 cm

11 cmB C

A

3.7 m

6.3 mM N

L

Diagram NOT

accurately drawn

Diagram NOT

accurately drawn

5.

ABCD is a rectangle.

AC = 17 cm.

AD = 10 cm.

Calculate the length of the side CD.


................................... cm

(3 marks)

6.


The diagram shows three cities.

Norwich is 168 km due East of Leicester.

York is 157 km due North of Leicester.

Calculate the distance between Norwich and York.

Give your answer correct to the nearest kilometre.

................................ km

(3 marks)

10 cm17 cm

A B

CD

Diagram Taccurately drawn

NO

7.

Diagram NOT

accurately drawn

A rectangular television screen has a width of 45 cm and a height of 34 cm.

Work out the length of the diagonal of the screen.

Give your answer correct to the nearest centimetre.

................................. cm

(4 marks)

8.


Work out the length, in centimetres, of AM.


…………………… cm

(3 marks)

7 cm 7 cm

A

MB C

8 cm

9.


ABCD is a trapezium.

AD is parallel to BC.

Angle A = angle B = 90.

AD = 2.1 m, AB = 1.9 m, CD = 3.2 m.

Work out the length of BC.


………………………… m

(4 marks)

10.



AC = 6 cm.

BC = 9 cm.

Work out the length of AB.


............................. cm

(3 marks)

A D

B C

1.9 m

2.1 m

3.2 m

B

9 cm

A C6 cm

11.


In triangle ABC,

AB = 10 cm

AC = 20 cm

angle BAC = 90°



You must state the units in your answer.

........................... ..................

(4 marks)

12.

Diagram NOT

accurately drawn

In the triangle XYZ

XY = 5.6 cm

YZ = 10.5 cm

angle XYZ = 90

Work out the length of XZ.

........................................ cm

(3 marks)

B

CA

10 cm

20 cm

X

YZ

10.5 cm

5.6 cm

13. ABCD is a trapezium.

AD = 10 cm

AB = 9 cm

DC = 3 cm

Angle ABC = angle BCD = 90°



.............................................. cm

( 5 marks)

14. A ladder is 6 m long.

The ladder is placed on horizontal ground, resting against a vertical wall.

The instructions for using the ladder say that the bottom of the ladder must not be closer than 1.5 m

from the bottom of the wall.

How far up the wall can the ladder reach?


.................................................................................. m

(4 marks)


SURFACE AREA






Instructions






Information






Advice





1. The diagram shows a cuboid of dimensions 10cm × 8cm × 5cm.


Work out the total surface area of the cuboid.

State the units with your answer.

…………………….

(Total 4 marks)

2. The diagram shows a solid cuboid which is 5 cm by 4 cm by 3 cm.


What is the total surface area of this cuboid?


…………………….

(Total 4 marks)

8 cm

10 cm

5 cm

3 cm

4 cm5 cm

3. Here is a cuboid.


What is the total surface area of the cuboid?


…………………….

(Total 4 marks)

4.

Work out the surface area of the triangular prism.


…………………….

(Total 4 marks)

5 cm

6 cm

10 cm

5.


What is the total surface area of the triangular prism?



…………………….

(Total 4 marks)

5cm

3cm

10cm

4cm

6.


Work out the total surface area of the triangular prism.

........................... cm2

(Total 3 marks)

3 cm5 cm

4 cm

7 cm

7.


Work out the total surface area of the triangular prism.

Give the units with your answer.

.......................................................

(Total 4 marks)

3 cm5 cm

4 cm

7 cm

8.


The diagram shows a right-angled triangular prism.


................................... cm2

(Total 3 marks)

5 cm

13 cm

20 cm

12 cm

9.

Diagram NOT

accurately drawn

Work out the total surface area of the L-shaped prism.


.....................................

(Total 4 marks)


VOLUME OF PRISM






Instructions






Information






Advice





1. Here is a cuboid.

Work out the volume of the cuboid.

............................................................................

(3 marks)

______________________________________________________________________________

*2. The diagram shows two fish tanks, each in the shape of a cuboid.

45 cm

35 cm

35 cm

30 cm

95 cm 65 cm

Finley fills both fish tanks with water.

Which fish tank holds the most water?

You must show all your calculations.

(4 marks)

______________________________________________________________________________

Diagram NOT

accurately drawn

A

B

3. The diagram shows a prism.

Work out the volume of the prism.

...................................................cm3

(4 marks)

______________________________________________________________________________

4. Here is a solid prism.


.......................................... cm3

(4 marks)

___________________________________________________________________________

5.

Work out the volume of the triangular prism.

.........................................

(4 marks)

6.

Calculate the volume of the triangular prism.

…................................

(4 marks)

______________________________________________________________________________

4 cm5 cm

3 cm

7 cm


NOT

7. The diagram shows a triangular prism.

BC = 4 cm, CF = 12 cm and angle ABC = 90º.

The volume of the triangular prism is 84 cm3.

Work out the length of the side AB of the prism.

…................................

(4 marks)

______________________________________________________________________________

8. The diagram shows a triangular prism.

The cross-section of the prism is a trapezium.

The lengths of the parallel sides of the trapezium are 8 cm and 6 cm.

The distance between the parallel sides of the trapezium is 5 cm.

The length of the prism is 20 cm.


…................................

(4 marks)

_____________________________________________________________________________

9.

A skip is in the shape of a prism with cross-section ABCD.

AD = 2.3 m, DC = 1.3 m and BC = 1.7 m.

The width of the skip is 1.5 m.

(a) Calculate the area of the shape ABCD.

…................................

(2 marks)

b) Calculate the volume of the skip.

…................................

(3 marks)

_____________________________________________________________________________


VOLUME AND SURFACE

AREA OF CYLINDER






Instructions






Information


each question.




Advice





1.


A cylinder has a height of 24 cm and a radius of 4 cm.

Work out the volume of the cylinder.


…………………………… cm3

(Total 2 marks)

4 cm

24 cm

2. A can of drink is in the shape of a cylinder.

The can has a radius of 4 cm and a height of 15 cm.

Calculate the volume of the cylinder.


…………………………

(Total 3 marks)

3.


A solid cylinder has a radius of 6 cm and a height of 20 cm.

Calculate the volume of the cylinder.


...................................... cm3

(Total 2 marks)


NOT

15 cm

4 cm

6 cm

20 cm

4.


The diagram shows a piece of wood.

The piece of wood is a prism of length 350 cm.

The cross-section of the prism is a semi-circle with diameter 1.2 cm.

Calculate the volume of the piece of wood.


………………………… cm3

(Total 4 marks)

1.2 cm

350 cm

5.


The diagram shows a prism of length 90 cm.

The cross section, PQRST, of the prism is a semi-circle above a rectangle.

PQRT is a rectangle.

RST is a semi-circle with diameter RT.

PQ = RT = 60 cm.

PT = QR = 45 cm.

Calculate the volume of the prism.


State the units of your answer.

........................... ...................

(Total 5 marks)

6.


The diagram shows a solid cylinder.

The cylinder has a diameter of 12 cm and a height of 18 cm.

Calculate the total surface area of the cylinder.


………………………… cm2

(Total 4 marks)

12 cm

18 cm

7.


The diagram shows a solid cylinder.

The radius of the cylinder is 9.3 cm.

Its height is 12.4 cm.

Calculate the total surface area of the cylinder.


................... cm2

(Total 4 marks)

9.3 cm

12.4 cm

8.


The diagram shows a cylinder with a height of 10 cm and a radius of 4 cm.

(a) Calculate the volume of the cylinder.


............................

(3)

The cylinder is solid.

(b) Calculate the total surface area of the cylinder.


............................

(3)

(Total 6 marks)


SIMILAR SHAPES






Instructions






Information






Advice





1. Shapes ABCD and EFGH are mathematically similar.

Diagrams NOT accurately drawn

(a) Calculate the length of BC.

........................... cm

(2)

(b) Calculate the length of EF.

........................... cm

(2)

(Total 4 marks)

120°

A

B

C

D

G

120°

E

F

H

7.5 cm

8 cm

6 cm 9 cm

2.

Triangles ABC and PQR are mathematically similar.

Angle A = angle P.

Angle B = angle Q.

Angle C = angle R.

AC = 4 cm.

BC = 12 cm.

PR = 6 cm.

PQ = 15 cm.

(a) Work out the length of QR.

................................cm

(2)

(b) Work out the length of AB.

................................cm

(2)

(Total 4 marks)

3.

Triangles ABC and DEF are similar.

AB = 4 cm.

AC = 9 cm.

DE = 6 cm.

EF = 10.5 cm.

(a) Work out the length of DF.

(2)

...................................................... cm

(b) Work out the length of BC.

(2)

...................................................... cm

(Total 4 marks)

4. The diagram shows two similar triangles.

In triangle ABC, AB = 10 cm and AC = 18 cm.

In triangle PQR, PQ = 6 cm and QR = 12 cm.

Angle ABC = angle PQR.

Angle CAB = angle RPQ.

(a) Calculate the length of BC.

.......................... cm

(2)

(b) Calculate the length of PR.

.......................... cm

(2)

(Total 4 marks)

5.

Triangle ABC is similar to triangle ADE.

AC = 15 cm.

CE = 6 cm.

BC = 12.5 cm.

Work out the length of DE.

............................... cm

(Total 3 marks)

*6.

Pictures NOT

accurately drawn

A 20 Euro note is a rectangle 133 mm long and 72 mm wide.

A 500 Euro Note is a rectangle 165 mm long and 82 mm wide.

Show that the two rectangles are not mathematically similar.

(Total 3 marks)

7. The diagram shows two similar solids, A and B.

Solid A has a volume of 80 cm3.

(a) Work out the volume of solid B.

....................................cm3

(2)

Solid B has a total surface area of 160 cm2.

(b) Work out the total surface area of solid A.

....................................cm2

(2)

(Total 4 marks)


COMPOUND

MEASURES






Instructions






Information






Advice





1. Adam cycled 24 km in 2 hours.

Work out his average speed.

........................... km/h

(Total 2 marks)

2. Stuart drives 180 km in 2 hours 15 minutes.

Work out Stuart’s average speed.

..................................... km/h

(Total 3 marks)

3. Joe travelled 60 miles in 1 hour 30 minutes.

Work out Joe’s average speed.

Give your answer in miles per hour.

........................... miles per hour

(Total 2 marks)

4. The distance from Liverpool to Prague is 1200 km.

A flight from Liverpool to Prague lasts 4 hours.

Work out the average speed of the aeroplane.

………………………. km/h

(Total 2 marks)

5. Mia drove a distance of 343 km.

She took 3 hours 30 minutes.

Work out her average speed.

Give your answer in km/h.

........................ km/h

(Total 3 marks)

6. The distance from London to New York is 3456 miles.

A plane takes 8 hours to fly from London to New York.

Work out the average speed of the plane.

........................... miles per hour

(Total 2 marks)

7. A car travels for 3 hours.

Its average speed is 75 km/h.

Work out the total distance the car travels.

.............................. km

(Total 2 marks)

8. Daniel leaves his house at 07 00.

He drives 87 miles to work.

He drives at an average speed of 36 miles per hour.

At what time does Daniel arrive at work?

…………………………

(Total 3 marks)

9. Fred runs 200 metres in 21.2 seconds.

(a) Work out Fred’s average speed.


................................. metres per second

(2)

(b) Round off your answer to part (a) to an appropriate degree of accuracy.

................................. metres per second

(1)

(Total 3 marks)

10. A plane flies 1400 kilometres in 2 hours 20 minutes.

Calculate the average speed, in km/h, of the plane.

................................. km/h

(Total 3 marks)

11. John travelled 30 km in 1.5 hours.

Kamala travelled 42 km in 2 hours.

Who had the greater average speed?


....................................

(Total 3 marks)

12. The mass of 5 m3 of copper is 44 800 kg.

(a) Work out the density of copper.

…………………………… kg/m3

(2)

The density of zinc is 7130 kg/m3.

(b) Work out the mass of 5 m3 of zinc.

………………………… kg

(2)

(Total 4 marks)

13. A silver chain has a volume of 5 cm3.

The density of silver is 10.5 grams per cm3.

Work out the mass of the silver chain.

………………………grams

(Total 2 marks)

14. The density of concrete is 2.3 grams per cm3.

(a) Work out the mass of a piece of concrete with a volume of 20 cm3.

............................... grams

(2)

480 grams of a cheese has a volume of 400 cm3.

(b) Work out the density of the cheese.

.................. grams per cm3

(2)

(Total 4 marks)

15. The volume of a gold bar is 100 cm3.

The density of gold is 19.3 grams per cm3.

Work out the mass of the gold bar.

.................................... grams

(Total 2 marks)


LOCI &

CONSTRUCTIONS






Instructions






Information






Advice





1. Here is a sketch of a triangle.

In the space below, use ruler and compasses to construct this triangle accurately. You

must show all construction lines.

(3 marks)

5.7 cm 4.2 cm

6.3 cm

2.

ABC is a triangle.

AB = 8 cm.

AC = 1 cm.

Angle A = 43°.

In the space below, make an accurate drawing of triangle ABC.

(3 marks)

7 cm

C

BA 8 cm

43°


NOT

3. The diagram shows a sketch of triangle ABC.

BC = 7.3 cm.

AC = 8 cm.

Angle C = 38°.

(a) Make an accurate drawing of triangle ABC.

(3)

(b) Measure the size of angle A on your diagram.

.........................°

(1)

(4 marks)

38°A

B

C8 cm

7.3 cm


NOT

4. In the space below, use ruler and compasses to construct an equilateral triangle with

sides of length 6 centimetres.

You must show all your construction lines.

(3 marks)

5. Use the ruler and compasses to construct the perpendicular to the line segment AB that

passes through the point P.

You must show all construction lines.

(3 marks)

6.

Use ruler and compasses to construct the bisector of angle PQR.


(3 marks)

×

A

P

B

7.


(a) Make an accurate drawing of triangle ABC.

(3)

(b) Measure the size of the angle at C in your triangle.

........................................°

(1)

(4 marks)

60º 30º

A B

C

6.5 cm

8.

Diagram NOT

accurately drawn

(a) Make an accurate drawing of this triangle.

(2)

(b) Measure the length of the line AC on your drawing.

You must state the units.

………………...

(2)

The size of the angle in the triangle at C is 90°.

(c) Write down the mathematical name for this type of angle.

………………...

(1)

(5 marks)

C

6.5 cmBA

60°30°

9.

Make an accurate drawing of the quadrilateral ABCD in the space below.

(4 marks)

120°

5 cm

4 cm

8 cmA B

C

D


NOT

10.


ABC is a triangle.

AB = 8 cm.

AC = 6 cm.

BC = 10 cm.

Use ruler and compasses to construct an accurate drawing of triangle ABC.


(3 marks)

8 cm6 cm

10 cm

A

B C

11. Here is a sketch of a rhombus.


The rhombus has a side of length 6 cm.

One angle of the rhombus is 50°.

Another angle of the rhombus is 130°.

Use a ruler and a protractor to make an accurate drawing of the rhombus.

(4 marks)

50º 130º

6 cm


BEARINGS






Instructions






Information






Advice





1.

Work out the bearing of B from A.

................................... °

(2 marks)

2.

(a) Write down the bearing of A from P.

..................................

(b) Work out the bearing of B from P.

..................................

(3 marks)

______________________________________________________________________________

140

60

P

A

N

B

3.

(a) Measure and write down the bearing of B from A.

……………………°

(1)

(b) On the diagram, draw a line on a bearing of 107° from A.

(1)

(2 marks)

____________________________________________________________________________

4. The diagram shows the position of two ports P and Q on a map.

(a) Measure the bearing of Q from P.

................................... °

(1)

A rock R is on a bearing of 150° from Q.

On the map R is 6 cm from Q.

(b) Mark the position of R with a cross (×) and label it R.

(2)

(3 marks)

North

B

A

5. The diagram shows the position of a lighthouse L and a harbour H.

The scale of the diagram is 1 cm represents 5 km.

(a) Work out the real distance between L and H.

.............................................. km

(1)

(b) Measure the bearing of H from L.

..............................................°

(1)

A boat B is 20 km from H on a bearing of 040°

(c) On the diagram, mark the position of boat B with a cross (×).

Label it B.

(2)

(4 marks)

______________________________________________________________________________

6. The diagram shows the positions of two villages, Beckhampton (B) and West Kennett (W).

Scale: 4 cm represents 1 km.

(a) Work out the real distance, in km, of Beckhampton from West Kennett.

.......................................... km

(2)

The village, Avebury (A), is on a bearing of 038 from Beckhampton.

On the diagram, A is 6 cm from B.

(b) On the diagram, mark A with a cross (×).

Label the cross A.

(2)

(4 marks)

___________________________________________________________________________

7. The diagram shows the position of two boats, P and Q.

The bearing of a boat R from boat P is 0600

The bearing of boat R from boat Q is 3100

In the space above, draw an accurate diagram to show the position of boat R.

Mark the position of boat R with a cross (). Label it R.

(3 marks)

8. The diagram shows the positions of two telephone masts, A and B, on a map.

(a) Measure the bearing of B from A.

........................................ °

(1)

Another mast C is on a bearing of 160° from B.

On the map, C is 4 cm from B.

(b) Mark the position of C with a cross () and label it C.

(2)

(3 marks)

9. The bearing of a ship from a lighthouse is 050°

Work out the bearing of the lighthouse from the ship.

..............................................°

(2 marks)

______________________________________________________________________________


PROBABILITY AND

RELATIVE

FREQUENCY






Instructions






Information






Advice





1. The probability that a biased dice will land on a five is 0.3

Megan is going to roll the dice 400 times.

Work out an estimate for the number of times the dice will land on a five.

..............................................

_______________________________________________________________________(2 marks)

2. Jack sows 300 wildflower seeds.

The probability of a seed flowering is 0.7

Work out an estimate for the number of these seeds that will flower.

......................................................

________________________________________________________________________(2 marks)

3. Angel Ltd manufacture components for washing machines. The probability that a component

will be made within a tolerance of one tenth of a millimetre is 0.995.

Angel Ltd. manufacture 10 000 components each day.

Work out an estimate for the number of components that will not be within the tolerance of

one tenth of a millimetre each day.

________________________________________________________________________(2 marks)

4. Four teams, City, Rovers, Town and United play a competition to win a cup. Only one

team can win the cup.

The table below shows the probabilities of City or Rovers or Town winning the cup.

City Rovers Town United

0.38 0.27 0.15 x


.........................

________________________________________________________________________(2 marks)

5. Mia spins a spinner.

The spinner can land on red or green or blue or pink.

The table shows each of the probabilities that the spinner will land on red or green or

blue.

Colour Red Green Blue Pink

Probability 0.4 0.1 0.2

Work out the probability that the spinner will land on pink.

.....................................

________________________________________________________________________(2 marks)

6. A bag contains some sweets.

The flavours of the sweets are either strawberry or chocolate or mint or orange.

Sarah is going to take one sweet at random from the bag.

The table shows the probability that Sarah will take a strawberry sweet or a mint sweet or

an orange sweet.

Flavour Strawberry Chocolate Mint Orange


Work out the probability that Sarah will take a chocolate sweet.

.............................

( 2 marks)

7. A bag contains only red, green and blue counters.

The table shows the probability that a counter chosen at random from the bag will be red

or will be green.

Colour Red Green Blue

Probability 0.5 0.3

Mary takes a counter at random from the bag.

(a) Work out the probability that Mary takes a blue counter.

..........................

(2)

The bag contains 50 counters.

(b) Work out how many green counters there are in the bag.

..........................

(2)

________________________________________________________________________(4 marks)

8. A bag contains counters which are blue or red or green or yellow.

Mark takes a counter at random from the bag.

The table shows the probabilities he takes a blue counter or a red counter or a yellow

counter.

Colour Blue red green yellow


(a) Work out the probability that Mark takes a green counter.

..........................

(2)

Mark puts the counter back into the bag.

Laura takes a counter at random from the bag.

She looks at its colour then puts the counter back into the bag.

She does this 50 times.

(b) Work out an estimate for the number of times Laura takes a red counter.

..........................

(2)

________________________________________________________________________(4 marks)

9. Marco has a 4-sided spinner.

The sides of the spinner are numbered 1, 2, 3 and 4

The spinner is biased.

The table shows the probability that the spinner will land on each of the numbers 1, 2 and

3

Number 1 2 3 4


(a) Work out the probability that the spinner will land on the number 4

.....................................

(2)

Marco spins the spinner 100 times.

(b) Work out an estimate for the number of times the spinner will land on the number 2

.....................................

(2)

________________________________________________________________________(4 marks)

10. A box contains bricks which are orange or blue or brown or yellow.

Duncan is going to choose one brick at random from the box.

The table shows each of the probabilities that Duncan will choose an orange brick or a

brown brick or a yellow brick.

Colour Orange Blue Brown Yellow


Work out the probability that Duncan will choose a blue brick.

……………………………

________________________________________________________________________(2 marks)

4

1

2

3

11. Riki has a packet of flower seeds.

The table shows each of the probabilities that a seed taken at random will grow into a

flower that is pink or red or blue or yellow.

Colour pink red blue yellow white

Probability 0.15 0.25 0.20 0.16

(a) Work out the probability that a seed taken at random will grow into a white flower.

.....................................

(2)

There are 300 seeds in the packet.

All of the seeds grow into flowers.

(b) Work out an estimate for the number of red flowers.

.....................................

(2)

________________________________________________________________________(4 marks)

12. There are only red counters, blue counters, white counters and black counters in a bag.

The table shows the probability that a counter taken at random from the bag will be red or blue.

Colour red blue white black

Probability 0.2 0.5

The number of white counters in the bag is the same as the number of black counters in the bag.

Tania takes at random a counter from the bag.

(a) Work out the probability that Tania takes a white counter.

...................................................

(2)

There are 240 counters in the bag.

(b) Work out the number of red counters in the bag.

...................................................

(2)

________________________________________________________________________(4 marks)

13. A bag contains some balls which are red or blue or green or black.

Yvonne is going to take one ball at random from the bag.

The table shows each of the probabilities that Yvonne will take a red ball or a blue ball or

a black ball.

Colour Red Blue Green Black


Work out the probability that Yvonne will take a green ball.

..........................

________________________________________________________________________(2 marks)

14. Here is a four-sided spinner. The spinner is biased.

The table shows the probabilities that the spinner will land on 1 or on 3

Number 1 2 3 4

Probability 0.2 0.1

The probability that the spinner will land on 2 is the same as the probability that the spinner will land

on 4

(a) Work out the probability that the spinner will land on 4

..........................................

(3)

Shunya is going to spin the spinner 200 times.

(b) Work out an estimate for the number of times the spinner will land on 3

..........................................

(2)

________________________________________________________________________(5 marks)

15. Here is a 4-sided spinner.

The sides of the spinner are labelled 1, 2, 3 and 4.


The probability that the spinner will land on each of the numbers 2 and 3 is given in the table.

The probability that the spinner will land on 1 is equal to the probability that it will land on 4.

Number 1 2 3 4

Probability x 0.3 0.2 x

(a) Work out the value of x. x = ………………….

(2)

Sarah is going to spin the spinner 200 times.

(b) Work out an estimate for the number of times it will land on 2

…………………….

(2)

________________________________________________________________________(4 marks)

16. Here is a 4-sided spinner.

The sides of the spinner are labelled 1, 2, 3 and 4.


The probability that the spinner will land on each of the numbers 2 and 3 is given in the table.

The probability that the spinner will land on 1 is equal to the probability that it will land on 4.

Number 1 2 3 4

Probability x 0.46 0.28 x

Sarah is going to spin the spinner 500 times.

Work out an estimate for the number of times it will land on 4

…………………….

____________________________________________________________________(5 marks)


FREQUENCY TABLES






Instructions






Information






Advice





1. Amanda collected 20 leaves and wrote down their lengths, in cm.


5 6 5 2 4 5 8 7 5 4

7 6 4 3 5 7 6 4 8 5

(a) Complete the frequency table to show Amanda’s results.

Length in cm Tally Frequency

2

3

4

5

6

7

8

(2)

(b) Write down the modal length .………………………cm (1)

(c) Work out the range. .………………………cm (1)

(4 marks)

2. Rosie had 10 boxes of drawing pins.

She counted the number of drawing pins in each box.

The table gives information about her results.

Number of

drawing pins Frequency

29 2

30 5

31 2

32 1

Work out the mean number of drawing pins in a box.

.................................

(3 marks)

3. Andy did a survey of the number of cups of coffee some pupils in his school had drunk

yesterday.

The frequency table shows his results.

Number of cups of

coffee Frequency

2 1

3 3

4 5

5 8

6 5

(a) Work out the number of pupils that Andy asked. .....................................

(2)

(b) Work out the mean number of cups of coffee drunk. .....................................

(3)

(5 marks)

4. 20 students scored goals for the school hockey team last month.

The table gives information about the number of goals they scored.

Goals scored Number of

students

1 9

2 3

3 5

4 3

(a) Write down the modal number of goals scored.

..........................

(1)

(b) Work out the range of the number of goals scored.

..........................

(1)

(c) Work out the mean number of goals scored.

..........................

(3)

(5 marks)

5. Bob asked each of 40 friends how many minutes they took to get to work.

The table shows some information about his results.

Time taken (m minutes) Frequency

0 < m 10 3

10 < m 20 8

20 < m 30 11

30 < m 40 9

40 < m 50 9

a) Work out an estimate for the mean time taken.

.............................................. minutes (4)

b) State the modal class interval

.............................................. (1)

c) Find the group containing the median

.............................................. (2)

(7 marks)

______________________________________________________________________________

6. The table shows information about the numbers of hours 40 children watched television one

evening.

(a) Find the class interval that contains the median.

(1)

...........................................................................

(b) Work out an estimate for the mean number of hours.

(4)

.............................................................. hours

(5 marks)

7. 80 people work in Jenny’s factory.

The table shows some information about the annual pay of these 80 workers.

Annual pay (£x) Number of workers

10 000 < x 14 000 32

14 000 < x 16 000 24

16 000 < x 18 000 16

18 000 < x 20 000 6

20 000 < x 40 000 2

(a) Write down the modal class interval.

..............................................

(1)

(b) Find the class interval that contains the median.

..............................................

(2)

(c) Work out an estimate for the mean annual pay.

..............................................

(3)

(d) Why is your answer to part (c) and estimate?

..................................................................................................................................................................

..................................................................................................................................................................

..................................................................................................................................................................

(1)

(7 marks)

______________________________________________________________________________

8. Caleb measured the heights of 30 plants.

The table gives some information about the heights, h cm, of the plants.

Height (h cm) of plants Frequency

00 < h 10 2

10 < h 20 8

20 < h 30 9

30 < h 40 7

40 < h 50 4

(a) Work out an estimate for the mean height of a plant.

..............................................

(3)


..............................................

(1)

(c) Find the class interval that contains the median.

..............................................

(2)

(d) Why is your answer to part (a) and estimate?

..................................................................................................................................................................

..................................................................................................................................................................

..................................................................................................................................................................

(1)

(7 marks)

9. Marcus collected some pebbles.

He weighed each pebble.

The grouped frequency table gives some information about weights.

Weight (w grams) Frequency

50 w < 60 5

60 w < 70 9

70 w < 80 22

80 w < 90 27

90 w < 100 17

(a) Work out an estimate for the mean weight of the pebbles.

..............................................

(3)


..............................................

(1)

(c) Find the class interval that contains the median.

..............................................

(2)

(d) Why is your answer to part (a) and estimate?

..................................................................................................................................................................

..................................................................................................................................................................

..................................................................................................................................................................

(1)

(7 marks)


QUESTIONNAIRE

Materials required for examination

Ruler graduated in centimetres and




Instructions






Information






Advice





Notes:

1. Make sure that your questions include a TIME FRAME; e.g. Day, Week, Month...

2. Always have an option for ZERO or NONE

3. DO NOT have OVERLAPPING INTERVALS

4. Include at least 4 tick boxes

5. Your last Interval should be: More than .....

1. Sam wants to find out the types of film people like best.

He is going to ask whether they like comedy films or action films or science fiction films or musicals

best.

(a) Design a suitable table for a data collection sheet he could use to collect this information.

(2)

Sam collects his data by asking 10 students in his class at school.

This might not be a good way to find out the types of film people like best.

(b) Give one reason why.

.....................................................................................................................................................

.....................................................................................................................................................

(1)

(3 marks)

______________________________________________________________________________

2. Alison wants to find out how much time people spend reading books.

She is going to use a questionnaire.

Design a suitable question for Alison to use in her questionnaire.

(2 marks)

______________________________________________________________________________

3. Pradeep wants to find out how much time people spend playing sport.

He uses this question on a questionnaire.

(a) Write down two things wrong with this question.

1...................................................................................................................................................

.....................................................................................................................................................

2...................................................................................................................................................

.....................................................................................................................................................

(2)

(b) Design a better question for Pradeep’s questionnaire to find out how much time people spend

playing sport.

(2)

(4 marks)

______________________________________________________________________________

4. Guy wants to find out how much time people spend watching television.

He will design a questionnaire.

Design a suitable question for Guy’s questionnaire.

(2 marks)

5. Paula wants to find out how much money people spend buying CDs.

She uses this question on a questionnaire.

How much money do you spend buying CDs?

£10 – £30 £30 – £50 £50 – £70 more than £70

(a) Write down two things wrong with this question.

1 .................................................................................................................................................

.....................................................................................................................................................

2 ..................................................................................................................................................

.....................................................................................................................................................

(2)

Paula asks 100 people in a CD store to do her questionnaire.

(b) Her sample is biased.

Explain why.

.....................................................................................................................................................

.....................................................................................................................................................

(1)

(3 marks)

______________________________________________________________________________

6. The manager of a department store has made some changes.

She wants to find out what people think of these changes.

She uses this question on a questionnaire.

“What do you think of the changes in the store?”

Excellent Very good Good

(a) Write down what is wrong about this question.

......................................................................................................................................................

......................................................................................................................................................

......................................................................................................................................................

(1)

This is another question on the questionnaire.

“How much money do you normally spend in the store?”

A lot Not much

(b) Write down one thing that is wrong with this question.

......................................................................................................................................................

......................................................................................................................................................

......................................................................................................................................................

(1)

(Total 2 marks)

______________________________________________________________________________

7. The local council is planning to build a new swimming pool.

The councillors want to get the views of the local people.

Councillor Smith suggests taking a sample from the people who attend the local sports centre.

(a) Explain why this would not be a good sample.

......................................................................................................................................................

......................................................................................................................................................

......................................................................................................................................................

(1)

Councillor Singh suggests taking a simple random sample of 100 people.

(b) Describe how the council could take a simple random sample.

......................................................................................................................................................

......................................................................................................................................................

......................................................................................................................................................

(1)

The council decided to use a questionnaire to find out how often people would use the swimming

pool.

(c) Design a question the council could use on their questionnaire.

(1)

(Total 4 marks) ____________________________________________________________________________

8. Gordon is going to open a restaurant.

He wants to know how often people eat out at a restaurant.

He designs a questionnaire.


(a) Write down two things that are wrong about this question.

1.........................................................................................................................................................

...........................................................................................................................................................

2.........................................................................................................................................................

............................................................................................................................................................

(2)

(b) Design a more suitable question Gordon could use to find out how often people eat out at a

restaurant.

(2)

Gordon asks his family “Do you agree that pizza is better than pasta?”

This is not a good way to find out what people who might use his restaurant like to eat.

(c) Write down two reasons why this is not a good way to find out what people who might use his

restaurant like to eat.

1st reason .........................................................................................................................................

...........................................................................................................................................................

2nd reason ........................................................................................................................................

............................................................................................................................................................

(2)

(Total 6 marks)

_ ___________________________________________________________________________

"How often do you go to a restaurant?"

Never Sometimes Often

9. Gary wants to find out how much time teenagers spend listening to music.


(a) Write down two things wrong with this question. 1 .................................................................................................................................................. ..................................................................................................................................................... 2 .................................................................................................................................................. .....................................................................................................................................................

(2) (b) Design a better question for Gary’s questionnaire to find out how much time teenagers spend

listening to music.

(2)

(Total 4 marks)

10. Sophie wants to find out the amount of time people exercise.

She will use a questionnaire.

(a) Design a suitable question for Sophie to use in her questionnaire.

You must include some response boxes.

(2)

Sophie asks the people at her swimming pool to complete her questionnaire.

This may not be a suitable sample.

(b) Give a reason why.

..................................................................................................................................................... .....................................................................................................................................................

(1)

(Total 3 marks)


FUNCTIONAL MATHS






Instructions






Information






Advice





1. The diagram shows a patio in the shape of a rectangle.

The patio is 3.6 m long and 3 m wide.

Matthew is going to cover the patio with paving slabs.

Each paving slab is a square of side 60 cm.

Matthew buys 32 of the paving slabs.

(a) Does Matthew buy enough paving slabs to cover the patio?


..............................................

(3)

The paving slabs cost £8.63 each.

(b) Work out the total cost of the 32 paving slabs.

£ ..............................................

(3)

(6 marks)

______________________________________________________________________________

*2. Mr Weaver’s garden is in the shape of a rectangle.

In the garden

there is a patio in the shape of a rectangle

and two ponds in the shape of circles with diameter 3.8 m.

The rest of the garden is grass.

Mr Weaver is going to spread fertiliser over all the grass.

One box of fertiliser will cover 25 m2 of grass.

How many boxes of fertiliser does Mr Weaver need?


(5 marks)

______________________________________________________________________________

*3. Henry is thinking about having a water meter.

These are the two ways he can pay for the water he uses.

Henry uses an average of 180 litres of water each day.

Henry wants to pay as little as possible for the water he uses.

Should Henry have a water meter?

(5 marks)

______________________________________________________________________________

*4. Here is part of Gary’s electricity bill.

Electricity bill

New reading 7155 units

Old reading 7095 units

Price per unit 15p

Work out how much Gary has to pay for the units of electricity he used.

(4 marks)

______________________________________________________________________________

5. Peter works out the cost of the gas he used last year.




Work out the mean cost per month of the gas he used last year.

£ ……………………………

(5 marks)

6. Here is a diagram of Jim’s garden.

Jim wants to cover his garden with grass seed to make a lawn.

Grass seed is sold in bags.

There is enough grass seed in each bag to cover 20 m2 of garden.

Each bag of grass seed costs £4.99

Work out the least cost of putting grass seed on Jim’s garden.

£ .........................................................

(5 marks)

______________________________________________________________________________

7. Jon has a flower garden in the shape of a circle.

The diameter of the garden is 5 metres.

Jon wants to put fencing around the edge of the garden.

The fencing costs £1.80 per metre.

Work out the total cost of the fencing.

£..........................................

(5 marks)

8. The diagram shows a CD.

The CD is a circle of radius 6 cm.

CDs of this size are cut from rectangular sheets of plastic.

Each sheet is 1 metre long and 50 cm wide.

Work out the greatest number of CDs that can be cut from one rectangular sheet.

.....................................

(4 marks)

*9. Jenny fills some empty flowerpots completely with compost.

Diagram NOT

accurately drawn

Each flowerpot is in the shape of a cylinder of height 15 cm and radius 6 cm.

She has a 15 litre bag of compost.

She fills up each flowerpot completely.

How many flowerpots can she fill completely?


...........................................................................

( 6 marks)


STANDARD FORM






Instructions






Information






Advice





1. (a) Write the number 0.00037 in standard form.

(1)

...........................................................................

(b) Write 8.25 × 103 as an ordinary number.

(1)

...........................................................................

(c) Work out (2.1 × 108) × (6 × 10

-5).

Write your answer in standard form.

(2)

...........................................................................

(4 marks)

2. (a) Write 6.43 × 105 as an ordinary number.

.....................................

(1)

(b) Work out the value of 2 ×107 × 8 ×10

−12

Give your answer in standard form.

.....................................

(2)

(3 marks)


..............................................

(1)

(b) Write 6.7 × 10–5

as an ordinary number.

..........................................................................

(1)

(c) Work out the value of (3 × 107) × (9 × 10

6)


..........................................................................

(2)

(4 marks)


....................................................................

(1)

(b) Write 0.000 376 in standard form.

....................................................................

(1)

(c) Work out the value of (2.3 × 1012

) ÷ (4.6 × 103)


....................................................................

(2)

(4 marks)

______________________________________________________________________________

5. A floppy disk can store 1 440 000 bytes of data.

(a) Write the number 1 440 000 in standard form.

……………………………………

(1)

A hard disk can store 2.4 × 109 bytes of data.

(b) Calculate the number of floppy disks needed to store the 2.4 × 109 bytes of data.

……………………………………

(3)

(4 marks)

______________________________________________________________________________

6. (a) (i) Write 40 000 000 in standard form.

...................................

(ii) Write 3 x 10–5 as an ordinary number.

...................................

(2)


3 x 10–5 x 40 000 000


...................................

(2)

(4 marks) ______________________________________________________________________________

7. (a) Write the number 40 000 000 in standard form.

.................................

(1)

(b) Write 1.4 × 10–5 as an ordinary number.

.................................

(1)

(c) Work out

(5 × 104) × (6 × 109)


.................................

(2)

(4 marks) ______________________________________________________________________________


..........................................................................

(1)

(b) Write 0.0039 in standard form.

..........................................................................

(1)

(c) Write 0.25 × 107 in standard form.

..........................................................................

(1)

(d) Work out (3.2 × 105) × (4.5 × 104) in standard form.

..........................................................................

(2)

(5 marks) ______________________________________________________________________________

9. (a) (i) Write 7900 in standard form.

.....................................

(ii) Write 0. 00035 in standard form.

.....................................

(2)

(b) Work out


.....................................

(2)

(4 marks) ______________________________________________________________________________

10. (a) Write 30 000 000 in standard form.

.........................................................

(1)

(b) Write 2 × 10–3 as an ordinary number.

.........................................................

(1)

(2 marks) ______________________________________________________________________________

11. (a) Write 5.7× 10–4 as an ordinary number.

.........................................

(1)

(b) Work out the value of (7 × 104) × (3 × 105)


.........................................

(2)

(3 marks) ______________________________________________________________________________

5–

3

108

104

12. Write the following numbers in order of size.


0.038 × 102 3800 × 10

–4 380 0.38 × 10

–1

............................................................................................................................................................

(2 marks)

______________________________________________________________________________

13. The time taken for light to reach Earth from the edge of the known universe is 14 000 000 000 years.

Light travels at the speed of 9.46 × 1012

km/year.

Work out the distance, in kilometres, from the edge of the known universe to Earth.


……………………………… km

(3 marks)

______________________________________________________________________________

14. The surface area of Earth is 510 072 000 km2.

The surface area of Jupiter is 6.21795 × 1010 km2.

The surface area of Jupiter is greater than the surface area of Earth.

How many times greater?


...........................................

(3 marks)

15. p2 =

xy

yx

x = 8.5 × 109

y = 4 × 108

Find the value of p.

Give your answer in standard form correct to 2 significant figures.

..............................................

(4 marks)

_________________________________________________________________________________

16. y2 =

a = 3 × 108

b = 2 × 107

Find y.

Give your answer in standard form correct to 2 significant figures.

y = ...................................

(4 marks) ______________________________________________________________________________

ba

ab


COMPOUND INTEREST

AND DEPRECIATION






Instructions






Information






Advice





1. Toby invested £4500 for 2 years in a savings account.

He was paid 4% per annum compound interest.

How much did Toby have in his savings account after 2 years?

£ ............................

(Total 3 marks)

2. The value of a car depreciates by 35% each year.

At the end of 2007 the value of the car was £5460

Work out the value of the car at the end of 2006

£ ..................................

(Total 3 marks)

3. Mario invests £2000 for 3 years at 5% per annum compound interest.

Calculate the value of the investment at the end of 3 years.

£…………………….

(Total 3 marks)

4. Derek invests £154 500 for 2 years at 4% per year compound interest.

Work out the value of the investment at the end of 2 years.

£.......................

(3)

(Total 3 marks)

5. Henry invests £4500 at a compound interest rate of 5% per annum.

At the end of n complete years the investment has grown to £5469.78.

Find the value of n.

……………………

(Total 2 marks)

6. A company bought a van that had a value of £12 000

Each year the value of the van depreciates by 25%.

Work out the value of the van at the end of three years.

£ .......................

(3)

(Total 3 marks)

7. Bill invests £500 on 1st January 2004 at a compound interest rate of R% per

annum.

The value, £V, of this investment after n years is given by the formula

V = 500 × (1.045)n

(a) Write down the value of R.

R = …………………

(1)

(b) Use your calculator to find the value of Bill’s investment after 20 years.

£……………………..

(2)

(Total 3 marks)

8. Gwen bought a new car.

Each year, the value of her car depreciated by 9%.

Calculate the number of years after which the value of her car was 47% of

its value when new.

......................................

(Total 3 marks)

9. Liam invests £6200 for 3 years in a savings account.

He gets 2.5% per annum compound interest.

How much money will Liam have in his savings account at the end of 3 years?

£ ..............................................................

(Total 3 marks)

10. Toby invested £4500 for 2 years in a savings account.

He was paid 4% per annum compound interest.

(a) How much did Toby have in his savings account after 2 years?

£ ..............................

(3)

Jaspir invested £2400 for n years in a savings account.

He was paid 7.5% per annum compound interest.

At the end of the n years he had £3445.51 in the savings account.

(b) Work out the value of n.

...........................

(2)

(Total 5 marks)

*11 Viv wants to invest £2000 for 2 years in the same bank.

The International Bank

Compound Interest

4% for the first year

1% for each extra year

The Friendly Bank

Compound Interest

5% for the first year

0.5% for each extra year

At the end of 2 years, Viv wants to have as much money as possible.

Which bank should she invest her £2000 in?

(Total 4 marks)


REVERSE

PERCENTAGES






Instructions






Information






Advice





1. In a sale, normal prices are reduced by 20%.

SALE

20% OFF

Andrew bought a saddle for his horse in the sale.

The sale price of the saddle was £220.

Calculate the normal price of the saddle.

£……………………

(Total 3 marks)

2.

Jacob answered 80% of the questions in a test correctly.

He answered 32 of the questions correctly.

Work out the total number of questions in the test.

…………………..

(Total 3 marks)


The sale price of a CD player is £102

Work out the normal price of the CD player.

£.....................................

(Total 3 marks)

4. A garage sells cars.

It offers a discount of 20% off the normal price for cash.

Dave pays £5200 cash for a car.

Calculate the normal price of the car.

£ ..........................

(Total 3 marks)


The sale price of a saw is £12.75

Calculate the normal price of the saw.

£ .....................................

(Total 3 marks)


The sale price of a DVD player is £242.

Work out the normal price of the DVD player.

£ …………………………

(Total 3 marks)

7. The price of all rail season tickets to London increased by 4%.

(a) The price of a rail season ticket from Cambridge to London increased

by £121.60

Work out the price before this increase.

£ ..................................

(2)

(b) After the increase, the price of a rail season ticket from Brighton to

London was £2828.80

Work out the price before this increase.

£ ..................................

(3)

(Total 5 marks)


ALGEBRA: EXPAND & FACTORISE

QUADRATICS






Instructions






Information






Advice





1. (a) Factorise fully 2x2 − 4xy

.....................................

(2)

(b) Factorise p2 – 6p + 8

.....................................

(2)

(c) Simplify 2

)2( 2

x

x

.....................................

(1)

(d) Factorise x2 – 100

.....................................

(2)

(7 marks)

2. (a) Simplify x5 × x

4

...................

(1)

(b) Simplify y7 ÷ y

2

...................

(1)

(c) Expand and simplify 3(2a + 5) + 5(a – 2)

..............................................

(2)

(d) Expand and simplify (y + 5)(y + 7)

..............................................

(2)

(e) Factorise p2 – 6p + 5

..............................................

(2)

(8 marks)

3. (a) Expand and simplify (p + 9)(p – 4)

..............................................

(2)

(b) Factorise x2 – 11x + 18

.....................................................................

(2)

(c) Factorise x2 – 49

.....................................................................

(2)

(d) Simplify 2

1

38 )9( yx

..............................................

(2)

(8 marks)

4. (a) Expand 3(2y – 5)

..............................................

(1)


..............................................

(2)

(c) Expand and simplify (p + 7)(p – 8)

..............................................

(2)


.....................................................................

(2)

(7 marks)

5. (a) Expand 4(3x + 5)

......................................................................

(1)

(b) Expand and simplify 3(x – 4) – 2(x + 5)

......................................................................

(2)

(c) Expand and simplify (x + 4)(x + 6)

......................................................................

(2)

(5 marks)

6. (a) Factorise x2 + 7x

..............................................

(1)

(b) Factorise y2 – 10y + 16

...............................................................................

(2)

(c) Solve y2 – 10y + 16 = 0

...............................................................................

(2)

(5 marks)


..........................................

(2)

(b) Expand and simplify (2x + 1)(x – 4)

..........................................

(2)

(c) Factorise completely 6y2 – 9xy

..........................................

(2)

(6 marks)

8. (a) Expand x(x + 2)

..........................................

(2)

(b) Expand and simplify (x + 3)(x – 4)

....................................................................

(2)

(c) Factorise completely 2y2 – 4y

.....................................

(2)


.....................................

(2)

(8 marks)

9. (a) Expand and simplify (3x + 5)(4x − 1)

..........................................

(2)

(b) Factorise x2 − 3x − 10

....................................................................

(2)

(c) Solve x2 − 3x − 10 = 0

x = ..................................................................

(2)

(6 marks)

10. (a) Expand 3(4x + y)

(2)

......................................................

(b) Expand 5p(p – 3)

(1)

......................................................

(c) Expand and simplify (y + 8)(y – 3)

(2)

......................................................

(d) Expand and simplify (2t – 3)2

(2)

......................................................

(7 marks)

11. (a) Factorise fully 6y2 + 12y

(2)

...........................................................................

(b) Factorise k2 + 13k + 30

(2)

...........................................................................

(c) Solve k2 + 13k + 30 = 0

(2)

...........................................................................

(6 marks)


..........................

(1)

(b) Factorise fully 2p2 – 4pq

..........................

(2)

(c) Expand and simplify (t + 5)(t – 4)

...................................

(2)

(d) Factorise x2 + 17x + 60

...........................................................................

(2)

(e) Factorise x2 – 144

.....................................

(2)

(9 marks)


..........................

(1)

(b) Factorise fully 10x2 – 15xy

..........................

(2)

(c) Factorise x2 – 64

.....................................

(2)

(d) Expand and simplify (x + 7)(x – 5)

...................................

(2)

(e) Factorise x2 + 2x – 15

...........................................................................

(2)

(f) Solve x2 + 2x – 15 = 0

………………………………………….

(2)

(11 marks)


SOLVING

QUADRATICS BY

FACTORISING






Instructions






Information






Advice





1. (i) Factorise x2 – 4x – 45

.................................

(ii) Solve the equation

x2 – 4x – 45 = 0

.................................

(Total 3 marks)

2. (i) Factorise x2 – 7x + 12

.................................


x2 – 7x + 12 = 0

.................................

(Total 3 marks)

3. (a) Factorise x2 – 3x – 18

………………………

(2)

(b) Solve x2 – 3x – 18 = 0

x =………………………

or x =………………………

(1)

(Total 3 marks)

4. (a) Factorise x2 + 6x + 8

………………………

(2)

(b) Solve x2 + 6x + 8 = 0

x =………………………

or x =………………………

(1)

(Total 3 marks)

5. (a) Factorise x2 – x – 56

………………………

(2)

(b) Solve x2 – x – 56= 0

x =………………………

or x =………………………

(1)

(Total 3 marks)

6. (i) Factorise x2 + 9x + 20

.................................


x2 + 9x + 20 = 0

.................................

(Total 3 marks)

7. (i) Factorise x2 – 12x + 35

.................................


x2 – 12x + 35 = 0

.................................

(Total 3 marks)

8. (i) Factorise x2 – x – 72

.................................


x2 – x – 72 = 0

.................................

(Total 3 marks)

9. (a) Factorise x2 – 15x + 56

………………………

(2)

(b) Solve x2 – 15x + 56 = 0

x =………………………

or x =………………………

(1)

(Total 3 marks)

10. (a) Factorise x2 + 9x + 18

………………………

(2)

(b) Solve x2 + 9x + 18 = 0

x =………………………

or x =………………………

(1)

(Total 3 marks)

11. (a) Factorise x2 – 2x – 48

………………………

(2)

(b) Solve x2 – 2x – 48 = 0

x =………………………

or x =………………………

(1)

(Total 3 marks)

12. (i) Factorise x2 + 10x + 24

.................................


x2 + 10x + 24 = 0

.................................

(Total 3 marks)

13.

The diagram shows a trapezium.

The lengths of three of the sides of the trapezium are x – 5, x + 2 and x + 6.

All measurements are given in centimetres.

The area of the trapezium is 36 cm2.

(a) Show that x2 – x – 56 = 0

(4)

(b) (i) Solve the equation x2 – x – 56 = 0

…………………………

(ii) Hence find the length of the shortest side of the trapezium.

…………………… cm

(4)

(Total 8 marks)

x – 5

x + 6

x + 2


NOT


SIMULTANEOUS

EQUATIONS






Instructions






Information






Advice





1. Solve the simultaneous equations

3x + 2y = 4

4x + 5y = 17

x = .....................................................

y = .....................................................

(4 marks)

______________________________________________________________________________

2. Solve the equations

3x + 5y = 19

4x – 2y = –18

x = ............................

y = ............................

(4 marks)


3x + 4y = 200

2x + 3y = 144

x = ...............................

y = ...............................

(4 marks)

______________________________________________________________________________


5x + 2y = 11

4x – 3y = 18

x = ..............................................

y = ..............................................

(4 marks)

______________________________________________________________________________


4x – 3y = 11

10x + 2y = −1

x = ………………

y = ………………

(4 marks)

____________________________________________________________________________


3x + 7y = 26

4x + 5y = 13

x = .....................................

y = .....................................

(4 marks)

____________________________________________________________________________


6x – 2y = 33

4x + 3y = 9

x = ....................

y = ....................

(4 marks)

____________________________________________________________________________


INEQUALITIES

REGIONS






Instructions






Information






Advice





1. On the grid, shade the region that satisfies all three of these inequalities

y > –4 x < 2 y < 2x + 1


2. The region R satisfies the inequalities

x ≥ 2, y ≥ 1, x + y ≤ 6

On the grid below, draw straight lines and use shading to show the region R.

(Total 3 marks)

1

1

2

3

4

5

6

7

8

y

x2 3 4 5 6 7 8O

3. The graphs of the straight lines with equations

3y + 2x = 12 and

y = x – 1

have been drawn on the grid.

3y + 2x > 12 y < x – 1 x < 6

x and y are integers.

On the grid, mark with a cross (×), each of the four points which satisfies all

3 inequalities.

(Total 3 marks)

8

6

4

2

8642O

y

x

y = x – 1

3 + 2 = 12y x

4. On the grid, show by shading, the region which satisfies all three of the

inequalities.

x < 3 y > –2 y < x

Label the region R.

(Total 4 marks)

5. –2 < x 1 y > –2 y < x + 1


On the grid, mark with a cross ( ), each of the six points which satisfies all

these 3 inequalities.

(Total 3 marks)

–4–5 –3 –2 –1 1 2 3 4 5

4

3

2

1

–1

–2

–3

–4

Ox

y

6. (a) On the grid below, draw straight lines and use shading to show the

region R that satisfies the inequalities

x 2 y x x + y 6

(3)

The point P with coordinates (x, y) lies inside the region R.


(b) Write down the coordinates of all the points of R whose coordinates

are both integers.

.................................................................................................................

(2)

(Total 5 marks)

8

7

6

5

4

3

2

1

87654321x

y

O

7. 4x + 3y < 12, y < 3x, y > 0, x > 0

x and y are both integers.

On the grid, mark with a cross (×), each of the three points which

satisfy all these four inequalities.

(3)

(Total 5 marks)

5

4

3

2

1

–1

–2

–3

–4

–5

–5 –4 –3 –2 –1 1 2 3 4 5 x

y

O


TRIGONOMETRY






Instructions






Information






Advice





1.


Angle B = 90.

Angle A = 36.

AB = 8.7 cm.



................................................................. cm

(3 marks)

2.

Calculate the value of x.


..............................................

(3 marks)

Diagram NOT

accurately drawn

3.


PQR is a triangle.

Angle Q = 90°.

Angle R = 43°.

PR = 5.8 m.

Calculate the length of QR.


............................... m

(3 marks)

4.

PQR is a triangle.

Angle PQR = 900.

PQ = 12.5 cm.

QR = 5 cm.

Calculate the value of x.


.........................................

(3 marks)

R Q

P

5.8 m

43º

5 cm

12.5 cm

R

Q Px°


NOT

5.

LMN is a right-angled triangle.

MN = 9.6 cm.

LM = 6.4 cm.

Calculate the size of the angle marked x.


..............................................................

(3 marks)

______________________________________________________________________________

6.



x = ...............................

Diagram NOT

accurately drawn

(3 marks)

7.

PQR is a right-angled triangle.

PR = 12 cm.

QR = 4.5 cm.

Angle PRQ = 90°.



x = ....................................

(3 marks)

______________________________________________________________________________

8. Calculate the size of angle a in this right-angled triangle.


.....................................

(3 marks)

xP

12 cmR

Q

4.5 cm

a

6 m

5 m

Diagram NOT

accurately drawn

Diagram NOT

accurately drawn

9. PQR is a right-angled triangle.

PR = 8 cm.

QR = 12 cm.

(a) Find the size of the angle marked x.


......................... °

(3)

XYZ is a different right-angled triangle.

XY = 5 cm.

Angle Z = 32°.

(b) Calculate the length YZ.


..................... cm

(3)

(6 marks)

10. The diagram shows a quadrilateral ABCD.

AB = 16 cm.

AD = 12 cm.

Angle BCD = 40.

Angle ADB = angle CBD = 90.

Calculate the length of CD.


.............................................. cm

(5 marks)

11.

Diagram NOT

accurately drawn

ABC is a triangle.

ADC is a straight line with BD perpendicular to AC.

AB = 7 cm.

BC = 12 cm.

Angle BAD = 65°.



......................... cm

(6 marks)

A

B

C

12 cm7 cm

65º

D


CIRCLE THEOREMS






Instructions






Information






Advice





1.

A, B, C and D are points on the circumference of a circle.

Angle ABD = 54.

Angle BAC = 28.

(i) Find the size of angle ACD.

........................°


....................................................................................................................................................

....................................................................................................................................................

(3 marks)

2.

Diagram NOT

accurately drawn

A, B, C and D are points on the circumference of a circle, centre O.

Angle AOC = 168

Work out the size of angle ADC.

You must give reasons for your working.

.....................................................

(4 marks)

3.

A, B and D are points on the circumference of a circle, centre O.

BOD is a diameter of the circle.

BC and AC are tangents to the circle.

Angle OCB = 34°.

Work out the size of angle DOA.

.......................................... °

(4 marks)

4.


B and C are points on a circle, centre O.

AB and AC are tangents to the circle.

Angle BOC = 130°.

Work out the size of angle BAO.

..............................°

(4 marks)

O

C

B

A

5.


A and B are points on the circumference of a circle, centre O.

PA and PB are tangents to the circle.

Angle APB is 86°.


.........................°

(3 marks)

6.

R and S are two points on a circle, centre O.

TS is a tangent to the circle.

Angle RST = x.

Prove that angle ROS = 2x.

You must give reasons for each stage of your working.

(4 marks)

86°

x

O

A

B

P

R

x

O

S T

Diagram NOT

accurately drawn

7.

In the diagram, O is the centre of the circle.

A and C are points on the circumference of the circle.

BCO is a straight line.

BA is a tangent to the circle.

AB = 8 cm.

OA = 6 cm.

(a) Explain why angle OAB is a right angle.

.....................................................................................................................................................

.....................................................................................................................................................

(1)

(b) Work out the length of BC.

................................cm

(3)

(4 marks)

8.

A, B, C and D are points on a circle, centre O.

BC = CD.

Angle BCD = 130°.

(a) Write down the size of angle BAD.


...................................°

(2)

(b) Work out the size of angle ODC.


...................................°

(4)

(6 marks)

9.


In the diagram, A, B, C and D are points on the circumference of a circle, centre O.

Angle BAD = 70°.

Angle BOD = x°.

Angle BCD = y°.

(a) (i) Work out the value of x.

x = ....................................


...............................................................................................................................

...............................................................................................................................

(2)

(b) (i) Work out the value of y.

y = ....................................


...............................................................................................................................

...............................................................................................................................

(2)

(4 marks)

O

D

C

B

A 70°

x°

y°

10.

The diagram shows a circle centre O.

A, B and C are points on the circumference.

DCO is a straight line.

DA is a tangent to the circle.

Angle ADO = 36°

(a) Work out the size of angle AOD.

..................................°

(2)

(b) (i) Work out the size of angle ABC.

..................................°


............................................................................................................................................

............................................................................................................................................

............................................................................................................................................

(3)

(4 marks)

11.

B, D and E are points on a circle centre O.

ABC is a tangent to the circle.

BE is a diameter of the circle.

Angle DBE = 35°.

(a) Find the size of angle ABD.


............................ °

(2)

(b) Find the size of angle DEB.


............................ °

(2)

(4 marks)

12.

P, Q and T are points on the circumference of a circle, centre O.

The line ATB is the tangent at T to the circle.

PQ = TQ.

Angle ATP = 58°.

Calculate the size of angle OTQ.

Give a reason for each stage in your working.

................................... °

(4 marks)

13. (a)

D, E and F are points on the circumference of a circle, centre O.

Angle DOF = 130°.

(i) Work out the size of angle DEF.

..........................°


...............................................................................................................................

...............................................................................................................................

(2)

(b)

In the diagram, A, B and C are points on the circumference of a circle, centre O.

Angle ABC = 85°.

(i) Work out the size of the angle marked x°. ................................ °


.....................................................................................................................................

.....................................................................................................................................

(2)

(4 marks)

FE

D

O 130º

A

85°

Ox°

C

B

*14.

S and T are points on the circumference of a circle, centre O.

PT is a tangent to the circle.

SOP is a straight line.

Angle OPT = 32°.



..............................................°

(Total 5 marks)

___________________________________________________________________________


CUMULATIVE

FREQUENCY & BOX

PLOTS






Instructions






Information






Advice





1. All the students in Mathstown school had a test.

The lowest mark was 18

The highest mark was 86

The median was 57

The lower quartile was 32

The interquartile range was 38

On the grid, draw a box plot to show this information.

(3 marks)

2. Sameena recorded the times, in minutes, some girls took to do a jigsaw puzzle.

Sameena used her results to work out the information in this table.

Minutes

Shortest time 18

Lower quartile 25

Median 29

Upper quartile 33

Longest time 44

(a) On the grid, draw a box plot to show the information in the table.

(2)

The box plot below shows information about the times, in minutes, some boys took to do the same

jigsaw puzzle.

(b) Compare the distributions of the girls’ times and the boys’ times.

.....................................................................................................................................................

.....................................................................................................................................................

.....................................................................................................................................................

.....................................................................................................................................................

(2)

(4 marks)

______________________________________________________________________________

3. This frequency table gives information about the ages of 60 teachers.

Age (A) in years Frequency

20 < A 30 12

30 < A 40 15

40 < A 50 18

50 < A 60 12

60 < A 70 3

(a) Complete the cumulative frequency table.

Age (A) in years Cumulative frequency

20 < A 30

20 < A 40

20 < A 50

20 < A 60

20 < A 70

(1)

(b) On the grid opposite, draw a cumulative frequency graph for this information.

(2)

(c) Use your cumulative frequency graph to find an estimate for the median age.

........................... years

(2)

(d) Use your cumulative frequency graph to find an estimate for the number of teachers older than

55 years.

.....................................

(2)

(7 marks)

4. Harry grows tomatoes.

This year he put his tomato plants into two groups, group A and group B.

Harry gave fertiliser to the tomato plants in group A.

He did not give fertiliser to the tomato plants in group B.

Harry weighed 60 tomatoes from group A.

The cumulative frequency graph shows some information about these weights.

(a) Use the graph to find an estimate for the median weight.

.............................................. g

(1)

The 60 tomatoes from group A

had a minimum weight of 153 grams

and a maximum weight of 186 grams.

(b) Use this information and the cumulative frequency graph to draw a box plot for the 60 tomatoes

from group A.

(3)

Harry did not give fertiliser to the tomato plants in group B.

Harry weighed 60 tomatoes from group B.

He drew this box plot for his results.

(c) Compare the distribution of the weights of the tomatoes from group A with the distribution of

the weights of the tomatoes from group B.

.....................................................................................................................................................

.....................................................................................................................................................

.....................................................................................................................................................

.....................................................................................................................................................

(2)

(6 marks)

______________________________________________________________________________

5. The table shows information about the speeds of 100 lorries.

Speed (s) in km/h Frequency

0 < s 20 2

20 < s 40 9

40 < s 60 23

60 < s 80 31

80 < s 100 27

100 < s 120 8

(a) Complete the cumulative frequency table for this information.

Speed (s) in km/h Cumulative

frequency

0 < s 20 2

0 < s 40

0 < s 60

0 < s 80

0 < s 100

0 < s 120

(1)

(b) On the grid, draw a cumulative frequency graph for your table.

(2)

(c) Find an estimate for the number of lorries with a speed of more than 90 km/h.

.....................................................

(2)

(5 marks)

______________________________________________________________________________

6. The grouped frequency table shows information about the weekly wages of 80 factory workers.

Weekly wage (£x) Cumulative

Frequency

100 < x 200 8

200 < x 300 15

300 < x 400 30

400 < x 500 17

500 < x 600 7

600 < x 700 3

(a) Complete the cumulative frequency table.

Weekly wage (£x) Cumulative

Frequency

100 < x 200

100 < x 300

100 < x 400

100 < x 500

100 < x 600

100 < x 700

(1)

(b) On the grid opposite, draw a cumulative frequency graph for your table.

(2)

(c) Use your graph to find an estimate for the interquartile range.

£ ........................................

(2)

(d) Use your graph to find an estimate for the number of workers with a weekly wage of more than

£530

........................................

(2)

(7 marks)

______________________________________________________________________________

7. Here are the times, in seconds, that 15 people waited to be served at Rose’s garden centre.

5 9 11 14 15 20 22 25 27 27 28 30 32 35 44

(a) On the grid, draw a box plot for this information.

(3)

The box plot below shows the distribution of the times that people waited to be served at Green’s

garden centre.

(b) Compare the distribution of the times that people waited at Rose’s garden centre and the

distribution of the times that people waited at Green’s garden centre.

…...........................................................................................................................................

…...........................................................................................................................................

…...........................................................................................................................................

…...........................................................................................................................................

(2)

(5 marks)

___________________________________________________________________________


PROBABILITY &

TREE DIAGRAMS






Instructions






Information






Advice





1. Hannah is going to play one badminton match and one tennis match.

The probability that she will win the badminton match is 10

9

The probability that she will win the tennis match is 5

2

(a) Complete the probability tree diagram.

(2)

(b) Work out the probability that Hannah will win both matches.

(2)

...........................................................................

(4 marks)

2. There are only red marbles and green marbles in a bag.

There are 5 red marbles and 3 green marbles.

Dwayne takes at random a marble from the bag.

He does not put the marble back in the bag.

Dwayne takes at random a second marble from the bag.


(2)

(b) Work out the probability that Dwayne takes marbles of different colours.

.....................................

(3)

(5 marks)

3. Wendy goes to a fun fair.

She has one go at Hoopla.

She has one go on the Coconut shy.

The probability that she wins at Hoopla is 0.4

The probability that she wins on the Coconut shy is 0.3


(2)

(b) Work out the probability that Wendy wins at Hoopla and also wins on the Coconut shy.

..............................................

(2)

(4 marks)

______________________________________________________________________________

4. There are 5 red pens, 3 blue pens and 2 green pens in a box.

Gary takes at random a pen from the box and gives the pen to his friend.

Gary then takes at random another pen from the box.

Work out the probability that both pens are the same colour.

......................................

(4 marks)

5. Carolyn has 20 biscuits in a tin.

She has

12 plain biscuits

5 chocolate biscuits

3 ginger biscuits

Carolyn takes at random two biscuits from the tin.

Work out the probability that the two biscuits were not the same type.

..............................................

(4 marks)

______________________________________________________________________________

6. Here are seven tiles.

Jim takes at random a tile.

He does not replace the tile.

Jim then takes at random a second tile.

(a) Calculate the probability that both the tiles Jim takes have the number 1 on them.

..............................................

(2)

(b) Calculate the probability that the number on the second tile Jim takes is greater than the number

on the first tile he takes.

..............................................

(3)

(5 marks)

______________________________________________________________________________

7. There are three different types of sandwiches on a shelf.

There are

4 egg sandwiches,

5 cheese sandwiches

and 2 ham sandwiches.

Erin takes at random 2 of these sandwiches.

Work out the probability that she takes 2 different types of sandwiches.

........................................

(5 marks)

______________________________________________________________________________


RECURRING

DECIMALS INTO

FRACTIONS






Instructions






Information






Advice





1. (a) Change to a decimal.

…………………….

(1)

(b) Prove that the recurring decimal =

(3)

(Total 4 marks)

2. Prove that the recurring decimal

(Total 3 marks)

11

3

93.0 33

13

33

1554.0

3. Express the recurring decimal as a fraction.

....................

(Total 3 marks)

4. Prove that can be written as the fraction

(Total 2 marks)

312.0

374.0 990

469

5. Prove that the recurring decimal

(Total 2 marks)

6. (a) Express as a fraction in its simplest form.

……………………………

(3)

99

1771.0

72.0

x is an integer such that 1 x 9

(b) Prove that

(2)

(Total 5 marks)

7. Change the recurring decimal to a fraction.

..........................

(Total 2 marks)

990.0

xx

32.0

8. (i) Convert the recurring decimal to a fraction.

……………………

(ii) Convert the recurring decimal 2. to a mixed number.


……………………

(Total 5 marks)

9. Convert the recurring decimal to a fraction.

.........................

(Total 3 marks)

63.0

631

541.2


.....................................

(Total 3 marks)

11. Express 0.3 as a fraction in its simplest form.

.....................................

(Total 3 marks)

621.0

82

12. The recurring decimal can be written as the fraction

Write the recurring decimal as a fraction.

............................................

(Total 2 marks)


Write your answer in its simplest form.

....................................

(Total 3 marks)

27.0 11

8

275.0

60.2


FRACTIONAL AND

NEGATIVE INDICES






Instructions






Information






Advice






(i)

……………………………

(ii) 32

……………………………

(Total 2 marks)


(a) 70

.....................................

(1)

(b) 4–1

.....................................

(1)

(Total 2 marks)

3. (a) Simplify 20

..............................

(1)

(b) Simplify 5–1

..............................

(1)

(Total 2 marks)

4. (a) Write down the value of 2–1

....................................

(1)

(b) Write down the value of

....................................

(1)

(Total 2 marks)

21

36

2

1

64


(i) 5°

.....................................

(ii) 4–2

.....................................

(iii)

.....................................

(Total 3 marks)

6. (a) Write down the value of

(i) 9°

.....................................

(ii) 169

.....................................

(2)

(b) Work out 64

.....................................

(2)

(Total 4 marks)


....................................

(1)

(b) Find the value of

....................................

(2)

(Total 3 marks)

2

1

100

2

1

3

2

2

1

36

3

2

8

8. Work out

(i) 40

.................................

(ii) 4–2

.................................

(iii)

.................................

(Total 3 marks)


(a)

..........................

(1)

(b) 90

...........................

(1)

(Total 2 marks)

10. (a) Evaluate

(i) 3–2

…………………………

(ii)

…………………………

(iii)

…………………………

(iv)

…………………………

(5)

2

3

16

2

1

25

2

1

36

3

2

27

4

3

81

16


(i) 64°

……………………..

(ii)

…………………….

(iii)

…………………….

(4)

(b)


n = ……………

(2)

(Total 6 marks)

2

1

64

3

2

64

n3273

12. (a) Work out 36 ÷ 3-7

.................................

(1)

(b) Write down the value of

.................................

(1)

(c) 3n =


n = ......................

(1)

(Total 3 marks)

13. (a) Simplify

(i) (3x2y)3

.....................................

(ii) (2t–3)–2

.....................................

(4)

2

1

36

9

1

14. x = 2p, y = 2q

(a) Express in terms of x and/or y,

(i) 2p + q

....................................

(ii) 22q

.....................................

(iii) 2p – 1

....................................

(3)

xy = 32

and 2xy2 = 32

(b) Find the value of p and the value of q.

p = ..............................

q = ..............................

(2)

(Total 5 marks)


.....................................

(1)

be written in the form 8k

(b) Find the value of k.

k = .....................................

(1)

can also be expressed in the form where m is a positive integer.

(c) Express in the form

.....................................

(2)

(d) Rationalise the denominator of

Give your answer in the form where p is a positive integer.

.....................................

(2)

(Total 6 marks)

3

1

88

88 2m

88 2m

88

1

p

2


SURDS






Instructions






Information






Advice





1. Express in the form a , where a and b are positive integers.

...................................

(Total 2 marks)

2. Rationalise

.....................................

(Total 2 marks)

2

6b

7

1

3. Expand and simplify

(3 + 15)2

Give your answer in the form n + m5, where n and m are integers.

.....................................

(Total 4 marks)


........................................

(Total 2 marks)

232–3

5. Rationalise the denominator of

....................................

(Total 2 marks)

6. Expand

Give your answer in the form where a and b are integers.

....................................

(Total 3 marks)

3

1

)31)(32(

3ba

7. Write in the form p + q , where p and q are integers.

p = ..….…….

q = ………….

(Total 4 marks)


(2 + )(7 – )

Give your answer in the form a + , where a and b are integers.

....................................

(Total 3 marks)

2

10 18 2

3 3

3b

9. Work out


.................................................

(Total 3 marks)

10. (a) Rationalise the denominator of 2

5

.....................................................

(2)

(b) Expand and simplify (2 + 3 )2 – (2 – 3 )

2

......................................................................................................

(2)

(Total 4 marks)

22

)3–5)(35(


DIRECT & INVERSE

PROPORTIONALITY






Instructions






Information






Advice





1. The weight of a piece of wire is directly proportional to its length.

A piece of wire is 25 cm long and has a weight of 6 grams.

Another piece of the same wire is 30 cm long.

Calculate the weight of the 30 cm piece of wire.

………………….. grams

(Total 2 marks)

2. A ball falls vertically after being dropped.

The ball falls a distance d metres in a time of t seconds.

d is directly proportional to the square of t.

The ball falls 20 metres in a time of 2 seconds.

(a) Find a formula for d in terms of t.

d = ...............................

(3)

(b) Calculate the distance the ball falls in 3 seconds.

.................................. m

(1)

(c) Calculate the time the ball takes to fall 605 m.

........................ seconds

(3)

(Total 7 marks)

3. The time, T seconds, it takes a water heater to boil some water is directly proportional

to the mass of water, m kg, in the water heater.

When m = 250, T = 600

(a) Find T when m = 400

T = .....................................

(3)

The time, T seconds, it takes a water heater to boil a constant mass of water is inversely

proportional to the power, P watts, of the water heater.

When P = 1400, T = 360

(b) Find the value of T when P = 900

T =.....................................

(3)

(Total 6 marks)

4. D is proportional to S2.

D = 900 when S = 20

Calculate the value of D when S = 25

D = .....................................

(Total 4 marks)

5. In a spring, the tension (T newtons) is directly proportional to its extension (x cm).

When the tension is 150 newtons, the extension is 6 cm.

(a) Find a formula for T in terms of x.

T = .................................

(3)

(b) Calculate the tension, in newtons, when the extension is 15 cm.

................................. newtons

(1)

(c) Calculate the extension, in cm, when the tension is 600 newtons.

................................. cm

(1)

(Total 5 marks)

6. d is directly proportional to the square of t.

d = 80 when t = 4

(a) Express d in terms of t.

…………………….

(3)

(b) Work out the value of d when t = 7

d = ………………….

(1)

(c) Work out the positive value of t when d = 45

t = ………………….

(2)

(Total 6 marks)

7. The distance, D, travelled by a particle is directly proportional to the square of the time, t,

taken.

When t = 40, D = 30

(a) Find a formula for D in terms of t.

D = .....................................

(b) Calculate the value of D when t = 64

.....................................

(1)

(c) Calculate the value of t when D = 12


.....................................

(2)

(Total 6 marks)

8. M is directly proportional to L3.

When L = 2, M = 160

Find the value of M when L = 3

.....................................

(Total 4 marks)

9. p is inversely proportional to m.

p = 48 when m = 9

Calculate the value of p when m = 12

..................................

(Total 2 marks)

10. r is inversely proportional to t.

r = 12 when t = 0.2

Calculate the value of r when t = 4.

……………………………

(Total 3 marks)

11. f is inversely proportional to d.

When d = 50, f = 256

Find the value of f when d = 80

f = ..................................

(Total 3 marks)

12. y is inversely proportional to x2.

Given that y = 2.5 when x = 24,

(i) find an expression for y in terms of x

y = ...............................

(ii) find the value of y when x = 20

y = ...............................

(iii) find a value of x when y = 1.6

x = ...............................

(Total 6 marks)

13. P is inversely proportional to d2.

P = 10 000 when d = 0.4

Find the value of P when d = 0.8

P = ...........................

(Total 3 marks)

14. The shutter speed, S, of a camera varies inversely as the square of the aperture setting, f.

When f = 8, S = 125

(a) Find a formula for S in terms of f.

..........................

(3)

(b) Hence, or otherwise, calculate the value of S when f = 4

S = ....................

(1)

(Total 4 marks)

15. q is inversely proportional to the square of t.

When t = 4, q = 8.5

(a) Find a formula for q in terms of t.

q = ......................................

(3)

(b) Calculate the value of q when t = 5

...............................

(1)

(Total 4 marks)

16. P is inversely proportional to V.

When V = 8, P = 5

(a) Find a formula for P in terms of V.

P = ...............................

(3)

(b) Calculate the value of P when V = 2

.....................................

(1)

(Total 4 marks)

17. The force, F, between two magnets is inversely proportional to the square of the distance, x,

between them.

When x = 3, F = 4.

(a) Calculate F when x = 2.

.................................

(4)

(b) Calculate x when F = 64.

.................................

(2)

(Total 6 marks)


UPPER AND LOWER

BOUNDS






Instructions






Information






Advice





1. The weight of a bag of potatoes is 25 kg, correct to the nearest kg.

(a) Write down the smallest possible weight of the bag of potatoes.

............................... kg

(1)

(b) Write down the largest possible weight of the bag of potatoes.

............................... kg

(1)

(Total 2 marks)

2. The length of a line is 63 centimetres, correct to the nearest centimetre.

(a) Write down the least possible length of the line.

........................................ centimetres

(1)

(b) Write down the greatest possible length of the line.

........................................ centimetres

(1)

(Total 2 marks)

3. A field is in the shape of a rectangle.

The length of the field is 340 m, to the nearest metre.

The width of the field is 117 m, to the nearest metre.

Calculate the upper bound for the perimeter of the field.

.............................................. m

(Total 2 marks)

4. The length of a rectangle is 30 cm, correct to 2 significant figures.

The width of a rectangle is 18 cm, correct to 2 significant figures.

(a) Write down the upper bound of the width.

(1)

................................................................. cm

(b) Calculate the upper bound for the area of the rectangle.

(2)

................................................................. cm

(Total 3 marks)

5.

The length of the rectangle is 35 cm correct to the nearest cm.

The width of the rectangle is 26 cm correct to the nearest cm.

Calculate the upper bound for the area of the rectangle.


.................................................................cm2

(Total 3 marks)

6. A field is in the shape of a rectangle.

The width of the field is 28 metres, measured to the nearest metre.

(a) Work out the upper bound of the width of the field.

......................... metres

(1)

The length of the field is 145 metres, measured to the nearest 5 metres.

(b) Work out the upper bound for the perimeter of the field.

......................... metres

(3)

(Total 4 marks)

7. Steve measured the length and the width of a rectangle.

He measured the length to be 645 mm correct to the nearest 5 mm.

He measured the width to be 400 mm correct to the nearest 5 mm.

Calculate the lower bound for the area of this rectangle.


............................ mm2

(Total 3 marks)

8. The average fuel consumption (c) of a car, in kilometres per litre, is given by the

formula

c = f

d

where d is the distance travelled, in kilometres, and f is the fuel used, in litres.

d = 163 correct to 3 significant figures.

f = 45.3 correct to 3 significant figures.

By considering bounds, work out the value of c to a suitable degree of accuracy.

You must show all of your working and give a reason for your final answer.

c = ............................

(Total 5 marks)

9. The voltage V of an electronic circuit is given by the formula

V = I R

where I is the current in amps

and R is the resistance in ohms.

Given that V = 218 correct to 3 significant figures,

R = 12.6 correct to 3 significant figures,

calculate the lower bound of I.

............................................

(Total 3 marks)

*10.

sm

t

s = 3.47 correct to 2 decimal places.

t = 8.132 correct to 3 decimal places.

By considering bounds, work out the value of m to a suitable degree of

accuracy.

You must show all your working and give a reason for your final answer.

(Total 5 marks)


QUADRATIC

FORMULA






Instructions






Information






Advice





1. Solve 3x2 + 7x – 13 = 0

Give your solutions correct to 2 decimal places.

x = ................................ or x = ................................

(3 marks)

2. Solve the equation

2x2 + 6x – 95 = 0

Give your solutions correct to 3 significant figures.

x = ...................................... or x = ......................................

(3 marks)

3. Solve x2 + 3x - 5 = 0


……………………….

(3 marks)

4. Solve this quadratic equation.

x2 – 5x – 8 = 0

Give your answers correct to 3 significant figures.

x = .....................................or x = .....................................

(3 marks)

5. (a) Solve x2 – 2x – 1 = 0

Give your solutions correct to 2 decimal places.

.......................................................

(3)

(b) Write down the solutions, correct to 2 decimal places, of 3x2 – 6x – 3 = 0

.......................................................

(2)

(5 marks)

6. (a) Solve x2 + x + 11 = 14


......................................................

(3)

y = x2 + x + 11

The value of y is a prime number when x = 0, 1, 2 and 3

The following statement is not true.

‘y = x2 + x + 11 is always a prime number when x is an integer’

(b) Show that the statement is not true.

.....................................................................................................................................

.....................................................................................................................................

(2)

(5 marks)

7. The diagram below shows a 6-sided shape.

All the corners are right angles.

All the measurements are given in centimetres.


The area of the shape is 95 cm2.

(a) Show that 2x2 + 6x – 95 = 0

(3)

(b) Solve the equation

2x2 + 6x – 95 = 0


x = ...................................... or x = ......................................

(3)

(6 marks)

x

2 x + 1

x

5

8. The diagram below shows a 6-sided shape.


All measurements are given in centimetres.


(a) Show that 6x2 + 17x – 39 = 0

(3)

(b) (i) Solve the equation

6x2 + 17x – 39 = 0

x = …………… or x = ……………

(ii) Hence work out the length of the longest side of the shape.

………………..cm

(4)

(7 marks)

9. The diagram shows a 6-sided shape.


All the measurements are given in centimetres.

Diagram NOT

accurately drawn


(a) Show that 9x2 – 17x – 85 = 0

(3)

(b) (i) Solve 9x2 – 17x – 85 = 0


x = .................................. or x = ..................................

(ii) Hence, work out the length of the shortest side of the 6-sided shape.

.................................. cm

(4)

(7 marks)

3x 3x + 4

x

2 – 7x


ALGEBRAIC

FRACTIONS






Instructions






Information






Advice





1. Simplify fully

....................................

(Total 3 marks)

107

62

2

xx

xx

2. Simplify fully

................................................

(Total 3 marks)

1572

1582

2

xx

xx

3. Simplify

.....................................

(Total 3 marks)

4. Simplify fully

..............................

(Total 3 marks)

62

92

p

p

14

362

2

x

xx

5. (a) Simplify

.....................................

(3)

(b) Write as a single fraction in its simplest form.

(3)

(Total 6 marks)

4+4+

4+22 xx

x

4–

2+

4+

1

xx

6. Simplify

....................................

(Total 3 marks)

23

122

2

xx

xx

7. Simplify fully

....................................

(Total 3 marks)

3

5

4

3

xx

8. Simplify fully

......................................................

(Total 3 marks)

43

1322

2

xx

xx


MORE DIFFICULT

REARRANGEING

FORMULAE






Instructions






Information






Advice





1. Rearrange a(q – c) = d to make q the subject.

q = ..........................................

(3)

(Total 5 marks)

2. (a) Make n the subject of the formula m = 5n – 21

n = ........................................................

(2)

(b) Make p the subject of the formula 4(p – 2q) = 3p + 2

p = ........................................................

(3)

(Total 5 marks)

3. P = πr + 2r + 2a

Make r the subject of the formula

r = ……………………

(Total 3 marks)

4. Make a the subject of the formula

2(3a c) = 5c + 1

……………………..

(Total 3 marks)

5. Make m the subject of the formula 2(2p + m) = 3 – 5m

m = ……………………………

(Total 3 marks)

6. Make x the subject of

5(x – 3) = y(4 – 3x)

x = .....................................

(Total 4 marks)

7. When you are h feet above sea level, you can see d miles to the horizon,

where

d =

Make h the subject of the formula

h =................................

(Total 4 marks)

2

3h

8. y =

Rearrange the formula to make t the subject.

t = ..................................

(Total 4 marks)

9. Make b the subject of the formula

.......................................................

(Total 4 marks)

tp

pt

–

2

5

72

b

ba

10.

Rearrange the formula to make a the subject.

a =.....................................

(Total 4 marks)

11.

Make x the subject of the formula.

x =................................

(Total 4 marks)

an

anP

2

q

p

cx

x

12. Rearrange

to make u the subject of the formula.


.....................................

(Total 5 marks)

fvu

111


SIMULTANEOUS

EQUATIONS WITH A

QUADRATIC






Instructions






Information






Advice






x2 + y2 = 29

y – x = 3

………………………………………………………

(Total 7 marks)

2. Bill said that the line y = 6 cuts the curve x2 + y2 = 25 at two points.

(a) By eliminating y show that Bill is incorrect.

(2)

(b) By eliminating y, find the solutions to the simultaneous equations

x2 + y2 = 25

y = 2x – 2

x = ........................ y = ...................

or x = ........................ y = ...................

(6)

(Total 8 marks)

3. By eliminating y, find the solutions to the simultaneous equations

x2 + y2 = 25

y = x – 7

x = .............................. y = ..............................

or x = .............................. y = ..............................

(Total 6 marks)

4. By eliminating y, find the solutions to the simultaneous equations

y – 2x = 3

x2 + y2 = 18

x =……………………. y =…………………….

or x =……………………. y =…………………….

(Total 7 marks)


x2 + y2 = 5

y = 3x + 1

x = .................... y = .....................

or x = .................... y = .....................

(Total 6 marks)


x + y = 4

x2 + y2 = 40

x =................., y = .................

or

x =................., y = .................

(Total 7 marks)

7. By eliminating x, find the solutions to the simultaneous equations

x – 2y = 1

x2 + y2 = 13

x = ……….., y = ……….

or x = ……….., y = ……….

(Total 7 marks)


TRANSFORMATION

OF GRAPHS






Instructions






Information






Advice





1. The graph of y = f(x) is shown on the grids.

(a) On this grid, sketch the graph of y = f(x) + 2

(2)

(b) On this grid, sketch the graph of y = – f(x)

(2)

(4 marks)

2.

The diagram shows part of the curve with equation y = f(x).

The coordinates of the maximum point of this curve are (2, 3).

Write down the coordinates of the maximum point of the curve with equation

(a) y = f(x – 2)

(......... , ..........)

(1)

(b) y = 2f(x)

(......... , ..........)

(1)

(2 marks)

3.

The curve with equation y = f(x) is translated so that the point at (0, 0) is mapped onto

the point (4, 0).

Find an equation of the translated curve.

.....................................

(2 marks)

y = f(x)

y

xO

(2, 3)

y

y = f(x)

2 4 6–2 O x

4. The graph of y = f(x) is shown on the grids.

(a) On this grid, sketch the graph of y = f(x) – 4

(2)

(b) On this grid, sketch the graph of y = f( x).

(2)

(4 marks)

y

2

4

6

8

10

12

–2

–4

–6

–8

–10

–12

–14

–16

–18

2 4 6 8 10–2–4–6–8–10 O x

2

1

y

2

4

6

8

10

12

–2

–4

–6

–8

–10

–12

–14

–16

–18

2 4 6 8 10–2–4–6–8–10 O x

5. The graph of y = f(x) is shown on each of the grids.

(a) On this grid, sketch the graph of y = f(x – 3)

(2)

(b) On this grid, sketch the graph of y = 2f(x)

(2)

(4 marks)

6. y = f(x)

The graph of y = f(x) is shown on the grid.

(a) On the grid above, sketch the graph of y = –f(x).

(2)

The graph of y = f(x) is shown on the grid.

The graph G is a translation of the graph of y = f(x).

(b) Write down the equation of graph G.

....................................................................

(2)

(4 marks)

7.

The diagram shows part of the curve with equation y = f(x).

The coordinates of the minimum point of this curve are (3, 1).

Write down the coordinates of the minimum point of the curve with equation

(a) y = f(x) + 3

(1)

(…………, …………)

(b) y = f(x – 2)

(1)

(…………, …………)

(c) y = f x21

(1)

(…………, …………)

(3 marks)

8.

The curve with equation y = f(x) is translated so that the point at (0, 0) is mapped onto the point (4,

0).

Find an equation of the translated curve.

.....................................

(2 marks)

9. This is a sketch of the curve with the equation y = f(x).

The only minimum point of the curve is at P(3, –4).

(a) Write down the coordinates of the minimum point of the curve with the equation

y = f(x – 2).

(............ , ............)

(2)

(b) Write down the coordinates of the minimum point of the curve with the equation

y = f(x + 5) + 6

(............ , ............)

(2)

(4 marks)


ENLARGEMENT:

NEGATIVE SCALE

FACTOR






Instructions






Information






Advice





1.

Enlarge the shaded triangle by a scale factor 1 , centre P.

(Total 3 marks)

3

2

1

–1

–2

–3

–4

–5

–4 –3 –2 –1 1 2 3 4 5x

y

O

P×

2

1

2.

Enlarge triangle A by scale factor –1 , centre O.

(Total 3 marks)

5

4

3

2

1

–1

–2

–3

–4

–5

5 6 74321–1–2–3–4–5

A

Ox

y

2

1

3.

Enlarge triangle A by scale factor – , centre (–1, –2).

Label your triangle B.

(Total 3 marks)

–5 –4 –3 –2 –1 3 4 5

5

4

3

2

1

–1

–2

–3

–4

–5

O x

y

A

1 2

2

1

4.

Enlarge shape T with scale factor 1.5, centre (0, 2).

(Total 3 marks)

x

y

–2–3–4–5–6–7 –1 1 2 3 4 5 6 7

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

O

T

5.

Enlarge the triangle by a scale factor of , centre O

(Total 2 marks)

y

xO

2

1–

6. The triangle ABC is to be enlarged, using E as the centre, to give the triangle

PQR. The line PQ is the image of the line BA.

(a) Write down the scale factor of the enlargement.

…………………………

(1)

(b) Complete the triangle PQR.

(1)

(Total 2 marks)

A B

C

E

P Q

7.

Enlarge triangle T, scale factor –2, centre O.

(Total 2 marks)

y

xO

T


SINE AND COSINE

RULES & AREA OF

TRIANGLES






Instructions






Information






Advice





1.

AB = 11.7 m.

BC = 28.3 m.

Angle ABC = 670.

(a) Calculate the area of the triangle ABC.


…………………………. m2

(2)

(b) Calculate the length of AC.


…………………………. m

(3)

(Total 5 marks)


NOT

67°

11.7 m

28.3 m

A

B C

2.

In triangle ABC,

AC = 7 cm,

BC = 10 cm,

angle ACB = 73°.

Calculate the length of AB.


……………………. cm

(Total 4 marks)

A B

C

7 cm10 cm

73°


NOT

3.

ABC is a triangle.

AB = 8 cm

BC = 14 cm

Angle ABC = 106

Calculate the area of the triangle.


………………..cm2

(Total 3 marks)

4.


The lengths of the sides of a triangle are 4.2 cm, 5.3 cm and 7.6 cm.

(a) Calculate the size of the largest angle of the triangle.


....................................°

(3)

(b) Calculate the area of the triangle.


............................... cm2

(3)

(Total 6 marks)

5.


In triangle ABC,

AC = 8 cm,

BC =15 cm,

Angle ACB = 70°.

(a) Calculate the length of AB.


................................ cm

(3)

(b) Calculate the size of angle BAC.


...................................°

(2)

(Total 5 marks)

B

A

C

8 cm

15 cm

70º

6.


ABC is a triangle.

AB = 12 m.

AC = 10 m.

BC = 15 m.

Calculate the size of angle BAC.


................................°

(Total 3 marks)

A

C

B

10 m12 m

15 m

7.

AB = 3.2 cm

BC = 8.4 cm

The area of triangle ABC is 10 cm2.

Calculate the perimeter of triangle ABC.

Give your answer correct to three significant figures.

..................... cm

(Total 6 marks)

3.2 cm

A

B C8.4 cm


NOT


3D PYTHAGORAS






Instructions






Information






Advice





1.

The diagram represents a cuboid ABCDEFGH.

AB = 5 cm.

BC = 7 cm.

AE = 3 cm.

Calculate the length of AG.


...................................... cm

(3)

A

B

CD

EF

G

H

3 cm

5 cm7 cm


NOT

2. A cuboid has length 3 cm, width 4 cm and height 12 cm.

Diagram NOT

accurately drawn

Work out the length of PQ.

..................................... cm

(Total 3 marks)

P

12 cm

Q

4 cm

3 cm

3. The diagram shows a pyramid. The apex of the pyramid is V.

Each of the sloping edges is of length 6 cm.

The base of the pyramid is a regular hexagon with sides of length 2 cm.

O is the centre of the base.

Calculate the height of V above the base of the pyramid.


………………..cm

(3)


SPHERES AND CONES






Instructions






Information






Advice





1.


The diagram represents a cone.

The height of the cone is 12 cm.

The diameter of the base of the cone is 10 cm.

Calculate the curved surface area of the cone.

Give your answer as a multiple of .

…………….. cm2

(Total 3 marks)

12 cm

10 cm

2.


The radius of the base of a cone is 5.7 cm.

Its slant height is 12.6 cm.

Calculate the volume of the cone.


…………………….. cm3

(Total 4 marks)

12.6 cm

5.7 cm

3.

Diagram NOT

accurately drawn

A cone has a base radius of 5 cm and a vertical height of 8 cm.

Calculate the volume of the cone.


................................. cm3

(2)

4. The diagram shows a child’s toy.

Diagram NOT

accurately drawn

The toy is made from a cone on top of a hemisphere.

The cone and hemisphere each have radius 7 cm.

The total height of the toy is 22 cm.

Work out the volume of the toy.


............................................................... cm3

(Total 3 marks)

5. The diagram shows a solid hemisphere of radius 8 cm.

Work out the total surface area of the hemisphere.


............................. cm2

(Total 3 marks)

6.

A rectangular container is 12 cm long, 11 cm wide and 10 cm high.

The container is filled with water to a depth of 8 cm.

A metal sphere of radius 3.5 cm is placed in the water.

It sinks to the bottom.

Calculate the rise in the water level.


..............................cm

(Total 4 marks)

12 cm

11 cm

3.5 cm

10 cm


NOT

7.

A frustum is made by removing a small cone from a similar large cone.

The height of the small cone is 20 cm.

The height of the large cone is 40 cm.

The diameter of the base of the large cone is 30 cm.

Work out the volume of the frustum.


.......................................... cm3

(Total 4 marks)


AREA OF SECTOR AND

LENGTH OF ARCS






Instructions






Information






Advice





1.


The diagram shows a sector of a circle, centre O.

The radius of the circle is 13 cm.

The angle of the sector is 150°.

Calculate the area of the sector.


.............................................. cm2

(Total 2 marks)

2.


The diagram shows a sector of a circle, centre O, radius 10 cm.

The arc length of the sector is 15 cm.

Calculate the area of the sector.

.......................... cm2

(Total 4 marks)

150º

O

13 cm13 cm

10 cm

10 cm

15 cm

O

3.


OAB is a sector of a circle, centre O.

Angle AOB = 60º.

OA = OB = 12 cm.

Work out the length of the arc AB.

Give your answer in terms of π.

.................................... cm

(Total 3 marks)

4.


The diagram shows a sector of a circle, centre O.


Angle AOB = 120°.

Work out the perimeter of the sector.

Give your answer in terms of π in its simplest form.

............................. cm

(Total 3 marks)

B

O

A

6 cm 6 cm

120°

5.


The diagram shows an equilateral triangle ABC with sides of length 6 cm.

P is the midpoint of AB.

Q is the midpoint of AC.

APQ is a sector of a circle, centre A.

Calculate the area of the shaded region.


........................................ cm2

(Total 4 marks)

6 cm 6 cm

Q

P

C A

B

6 cm

6.


The diagram shows a sector OABC of a circle with centre O.

OA = OC = 10.4 cm.

Angle AOC = 120°.

(a) Calculate the length of the arc ABC of the sector.


.....................................cm

(3)

(b) Calculate the area of the shaded segment ABC.


.....................................cm2

(4)

(Total 7 marks)

A

B

C

O

10.4 cm

120°

10.4 cm

7. The diagram shows a sector of a circle with centre O.


PRS is an arc of the circle.

PS is a chord of the circle.

Angle POS = 40°

Calculate the area of the shaded segment.


............................. cm2

(Total 5 marks)

8.

ABC is an arc of a circle centre O with radius 80 m.

AC is a chord of the circle.

Angle AOC = 35°.

Calculate the area of the shaded region.


............................... m2

(Total 5 marks)


VECTORS






Instructions






Information






Advice





1.

ABCDEF is a regular hexagon, with centre O.

OA = a , OB = b.

(a) Write the vector AB in terms of a and b.

.....................................

(1)

The line AB is extended to the point K so that AB : BK = 1 : 2

(b) Write the vector CK in terms of a and b.


.....................................

(3)

(4 marks)

2.

OAB is a triangle.

OA = a

OB = b

(a) Find AB in terms of a and b.

..............................................

(1)

P is the point on AB such that AP : PB = 3 : 1

(b) Find OP in terms of a and b.


..............................................

(3)

(4 marks)

3.

APB is a triangle.

N is a point on AP.

AB = a AN = 2b NP = b

(a) Find the vector PB , in terms of a and b.

.....................................................

(1)

B is the midpoint of AC.

M is the midpoint of PB.

*(b) Show that NMC is a straight line.

(4)

(5 marks)

4.

OAYB is a quadrilateral.

OA = 3a

OB = 6b

(a) Express AB in terms of a and b.

....................................................................

(1)

X is the point on AB such that AX : XB = 1 : 2

and BY = 5a – b

* (b) Prove that OX = 5

2 OY

(4)

(5 marks)

5.

Diagram NOT

accurately drawn

PQRS is a trapezium.

PS is parallel to QR.

QR = 2PS

PQ = a PS = b

X is the point on QR such that QX : XR = 3 : 1

Express in terms of a and b.

(i) PR

(2)

......................................................

(ii) SX

(3)

......................................................

(5 marks)

6.

OPQ is a triangle.

R is the midpoint of OP.

S is the midpoint of PQ.

OP = p and OQ = q

(i) Find OS in terms of p and q.

OS = ..........................

(ii) Show that RS is parallel to OQ.

(5 marks)

p

q

P

Q

R S

O


NOT

6.

OAB is a triangle.

OA = 2a

OB = 3b

(a) Find AB in terms of a and b.

AB = ............................

(1)

P is the point on AB such that AP : PB = 2 : 3

(b) Show that OP is parallel to the vector a + b.

(3)

(4 marks)


HISTOGRAMS






Instructions






Information






Advice





1. The table gives some information about the speeds, in km/h, of 100 cars.

Speed(s km/h) Frequency

60 < s 65 15

65 < s 70 25

70 < s 80 36

80 < s 100 24

(a) On the grid, draw a histogram for the information in the table.

(3)

(b) Work out an estimate for the number of cars with a speed of more than 85 km/h.

..............................................

(2)

(5 marks)

______________________________________________________________________________

2. The table gives information about the heights, h metres, of trees in a wood.

Height (h metres) Frequency

0 < h 2 7

2 < h 4 14

4 < h 8 18

8 < h 16 24

16 < h 20 10

Draw a histogram to show this information.

(3 marks)

______________________________________________________________________________

3. The histogram shows some information about the weights of a sample of apples.

Work out the proportion of apples in the sample with a weight between 140 grams and 200 grams.

..........................................

(4 marks)

___________________________________________________________________________

4. The table shows information about the lengths of time, t minutes, it took some students to do their

maths homework last week.

Time (t minutes) Frequency

0 < t 10 4

10 < t 15 8

15 < t 20 24

20 < t 30 16

30 < t 50 5

Draw a histogram for this information.

(Total 3 marks)

5. The table shows information about the total times that 35 students spent using their mobile phones

one week.

On the grid below, draw a histogram for this information.


6. The incomplete table and histogram give some information about the ages of the people who live in a

village.

(a) Use the information in the histogram to complete the frequency table below.

Age (x) in years Frequency

0 < x 10 160

10 < x 25

25 < x 30

30 < x 40 100

40 < x 70 120

(2)

(b) Complete the histogram.

(2)

(Total 4 marks)

______________________________________________________________________________

Frequencydensity

0 10 20 30 40 50 60 70

Age in years

7. The table shows the distribution of the ages of passengers travelling on a plane from London

to Belfast.

Age (x years) Frequency

0 < x 20 28

20 < x 35 36

35 < x 45 20

45 < x 65 30

On the grid below, draw a histogram to show this distribution.

(Total 3 marks)

______________________________________________ _____________________________

0 10 20 30 40 50 60 70

Age ( years)x


STRATIFIED

SAMPLING






Instructions






Information






Advice





1. The grouped frequency table shows information about the weights, in

kilograms, of 20 students, chosen at random from Year 11.

Weight (w

kg)

Frequenc

y

50 w < 60 7

60 w < 70 8

70 w < 80 3

80 w < 90 2


Work out an estimate for the number of students in Year 11 whose weight is

between 50 kg and 60 kg.

…………………………………

(Total 3 marks)

2. The table shows the number of students in each year group at a school.

Year group 7 8 9 10 11

Number of students 190 145 145 140 130

Jenny is carrying out a survey for her GCSE Mathematics project.

She uses a stratified sample of 60 students according to year group.

Calculate the number of Year 11 students that should be in her sample.

...............................................

(Total 3 marks)

3. A school has 450 students.

Each student studies one of Greek or Spanish or German or French.

The table shows the number of students who study each of these languages.

Language Number of

students

Greek 145

Spanish 121

German 198

French 186

An inspector wants to look at the work of a stratified sample of 70 of these

students.

Find the number of students studying each of these languages that should be

in the sample.

Greek ...........................

Spanish ........................

German ........................

French .........................

(Total 3 marks)

4. There are three age groups in a competition.

The table shows the number of competitors in each age group.

16-18

years

19-24

years

25+ years

120 250 200

John wants to do a survey of the competitors.

He uses a stratified sample of exactly 50 competitors according to each age

group.

Work out the number of competitors in each age group that should be in his

stratified

sample of 50.

16-18 years: ..................

19-24 years: ..................

25+ years: ..................

(Total 3 marks)

5. The table shows the number of boys and the number of girls in each year

group at

Springfield Secondary School.

There are 500 boys and 500 girls in the school.

Year

group

Number of

boys

Number of

girls

7 100 100

8 150 50

9 100 100

10 50 150

11 100 100

Total 500 500

Azez took a stratified sample of 50 girls, by year group.

Work out the number of Year 8 girls in his sample.

.....................................

(Total 2 marks)

6. The table gives information about the numbers of students in the two years

of a college course.

Male Female

First year 399 602

Second year 252 198

Anna wants to interview some of these students.

She takes a random sample of 70 students stratified by year and by gender.

Work out the number of students in the sample who are male and in the first

year.

.....................................

(Total 3 marks)

7. 258 students each study one of three languages.

The table shows information about these students.

Language studied

German French Spanish

Male 45 52 26

Female 25 48 62

A sample, stratified by the language studied and by gender, of 50 of the 258

students is taken.

(a) Work out the number of male students studying Spanish in the sample.

..........................

(2)

(b) Work out the number of female students in the sample.

..........................

(2)

(Total 4 marks)

8. (a) Explain what is meant by

(i) a random sample,

............................................................................................................................

(ii) a stratified sample.

...........................................................................................................................

.

(2)

The table shows some information about the members of a golf club.

Age

range

Male Female Total

Under 18 29 10 39

18 to 30 82 21 103

31 to 50 147 45 192

Over 50 91 29 120

Total number of members 454

The club secretary carries out a survey of the members.

He chooses a sample, stratified both by age range and by gender, of 90 of

the 454 members.

(b) Work out an estimate of the number of male members, in the age range

31 to 50, he would have to sample.

.................................................

(2)

(Total 4 marks)

9. Hamid wants to find out what people in Melworth think about the sports

facilities in the town.

Hamid plans to stand outside the Melworth sports centre one Monday

morning.

He plans to ask people going into the sports centre to complete a

questionnaire.

Carol tells Hamid that his survey will be biased.

(i) Give one reason why the survey will be biased.

…………………………………………………………………………

…...…….....……………………………………………………………

…………………....……………………………………………………

(ii) Describe one change Hamid could make to the way in which he is

going to carry out his survey so that it will be less biased.

…………………………………………………………………………

…………………………………………………………………………

…………………………………………………………………………

(Total 2 marks)

10. There are 970 students in Bayton High School.

Brian takes a random sample of 100 students.

He asks these 100 students which subject they like best.

They can choose English or Maths or Science.

Brian is going to use his results to work out an estimate of how many of the

970 students like English best.

Explain how.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(Total 2 marks)

11. 340 475 people live in Brinton.

A company carried out a survey.

It used a random sample of 1500 of the 340 475 people.

870 of this sample of 1500 people were male.

Work out an estimate for the number of females living in Brinton.

………………….

(Total 3 marks)

12. The table shows some information about the pupils at Statson School.

Year group Boys Girls Total

Year 7 104 71 175

Year 8 94 98 192

Year 9 80 120 200

Total 278 289 567

Kelly carries out a survey of the pupils at Statson School.

She takes a sample of 80 pupils, stratified by both Year group and gender.

(a) Work out the number of Year 8 boys in her sample.

………………….

(2)

(b) Describe a method that Kelly could use to take a random sample of

Year 8 boys.

………………………………………………………………………

………………………………………………………………………

………………………………………………………………………

(2)

(Total 4 marks)

13. The table gives information about the number of girls in each of four

schools.

School A B C D Total

Number of girls 126 82 201 52 461

Jenny did a survey of these girls.

She used a stratified sample of exactly 80 girls according to school.

Work out the number of girls from each school that were in her sample of

80.

Complete the table.

School A B C D Total

Number of girls 80

(Total 3 marks)

14. The table shows the number of boys in each of four groups.

Group A B C D Total

Number of boys 32 43 38 19 132

Jamie takes a sample of 40 boys stratified by group.

Calculate the number of boys from group B that should be in his sample.

.....................................

(Total 2 marks)

15. Melanie wants to find out how often people go to the cinema.

She gives a questionnaire to all the women leaving a cinema.

Her sample is biased.

Give two possible reasons why.

1 ........................................................................................................................

...........................................................................................................................

...........................................................................................................................

2 ........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(Total 2 marks)

16. The two-way table shows information about the number of students in a

school.

Year Group Total

7 8 9 10 11

Boys 126 142 140 135 125 670

Girls 134 140 167 125 149 715

Total 260 282 307 260 276 1385

Robert carries out a survey of these students.

He uses a sample of 50 students stratified by gender and by year group.

Calculate the number of girls from year 9 that are in his sample.

.....................................

(Total 2 marks)


PROOF






Instructions






Information






Advice





1. The nth even number is 2n.

The next even number after 2n is 2n + 2

(a) Explain why.

...................................................................................................................

...................................................................................................................

(1)

(b) Write down an expression, in terms of n, for the next even number after

2n + 2

.....................................

(1)

(c) Show algebraically that the sum of any 3 consecutive even numbers is

always a multiple of 6

(3)

(5 marks)

2. Prove that (3n + 1)2 – (3n –1)2 is a multiple of 4, for all positive integer

values of n.

(3 marks)

3. Prove, using algebra, that the sum of two consecutive whole numbers is always an

odd number.

(3 marks)

4. Prove that

(2n + 3)2 – (2n – 3)

2 is a multiple of 8

for all positive integer values of n.

(3 marks)

*5. Prove algebraically that the difference between the squares of any two

consecutive integers is equal to the sum of these two integers.

(4 marks)

6. Prove that (5n + 1)2 – (5n –1)2 is a multiple of 5, for all positive integer

values of n.

(3 marks)

7. If 2n is always even for all positive integer values of n, prove algebraically that

the sum of the squares of any two consecutive even numbers is always a multiple of 4.

(3 marks)

8. Prove that

(n + 1)2 – (n – 1)

2 + 1 is always odd for all positive integer values of n.

(3 marks)

9. Prove algebraically that the sum of the squares of any two consecutive numbers

always leaves a remainder of 1 when divided by 4.

(4 marks)

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Mathematics (Linear) 1MA0 READING SCALES...Young Person’s RAILCARD off normal price Lisa uses her railcard to buy a ticket. She gets off the normal price of the ticket. The normal