Level 6 Easter Revision Pack - Toot Hill School · Title: Microsoft Word - Level 6 Easter Revision Pack.doc Author: PArmann Created Date: 2/24/2006 4:32:01 PM

Year 9 mathematics level 6: holiday revision pack DAY 1

1 toot hill school | level 6 holiday revision | question booklet

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Mental Questions

1. Look at the diagram. The lines marked with arrows are parallel. What is the size of angle p?

º

p

100º

2. Round three point seven nine five to one decimal place.

3.795

3. Five per cent of a number is sixteen. What is twenty-five per cent of the number?

5% 16

4. Look at the equation on your answer sheet. What is the value of a?

32 – 2 = 24a

5. Estimate the value of nine point two multiplied by two point nine.

9.2 2.9



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Speed bumps

Bumps are built on a road to slow cars down. The stem-and-leaf diagrams show the speed of 15 cars before and after the bumps were built.

Use the diagrams to write the missing numbers in these sentences.

Before the bumps:

The maximum speed was ………………… mph, and

…………………… cars went at more than 30mph.

After the bumps:

The maximum speed was ………………… mph, and

………………… cars went at more than 30mph. 2 marks



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Straight line graph

The graph shows the straight line with equation y = 3x – 4

(a) A point on the line y = 3x – 4 has an x-coordinate of 50. What is the y-coordinate of this point?

............................... 1 mark

(b) A point on the line y = 3x – 4 has a y-coordinate of 50. What is the x-coordinate of this point?

............................... 1 mark

(c) Is the point ( –10, –34 ) on the line y = 3x – 4?

Yes No Show how you know.

1 mark



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Solutions

Look at this equation.

14y – 51 = 187 + 4y

Is y = 17 the solution to the equation?

Yes No Show how you know.

1 mark



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Mental Questions

1. When a equals minus three and b equals minus seven, what is the value of a minus b?

a b

a b = –3 = –7

–

2. The mean of three numbers is six. Two of the numbers are fice. What is the third number? 5 5 ...........

3. A circle has a radius of six centimetres.

Give an approximate value for the circumference of the circle.

6 cm

cm

4. Round two point six nine four to one decimal place.

2.694

5. Look at the trapezium. Angle a is one hundred and ten degrees.

What is the size of angle b?

a

b

º



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Cuboid

I join six cubes face to face to make each 3-D shape below.

Then I join the 3-D shapes to make a cuboid. Draw this cuboid on the grid below.

2 marks



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Simplify

Write these expressions as simply as possible.

9 – 3k + 5k = ..............................

1 mark k2 + 2k + 4k = ..............................

1 mark



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Enlargement

Look at the rectangle drawn on a square grid. Draw an enlargement of this rectangle with scale factor 2 Use point A as the centre of enlargement.

A

2 marks



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Mental Questions

1. Solve the equation, t plus three-fifths equals one.

t + = 135

2. Last month my telephone bill was thirty pounds.

This month it is twenty per cent more. How much is this month’s bill?

£ £30 20%

3. Look at the expression on your answer sheet.

Its value is eighty-two. Write an expression using a and b with a value of forty-one.

6 + 4 82a b

4. Ten out of thirty-six people said they ate toast for breakfast.

What angle should represent this on a pie chart?

1036

º

5. Look at the circle with radius three.

One of the values below is its area. Put a ring round the correct value.

3

3π

12π 15π

6π 9π



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Sums and products

Write the missing numbers in the table. The first row is done for you.

First

number Second number

Sum of first and second

numbers

Product of first and second

numbers

3 6 9 18

5 –3 1 mark

–8 –5 1 mark



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Shading

The shapes below are drawn on square grids.

shape A shape B shape C (a) Is shape A an equilateral triangle? Tick ( ) Yes or No.

Yes No Explain your answer.

1 mark (b) Is shape B a kite?


1 mark (c) Is shape C a square?


1 mark



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Medicine

Doctors sometimes use this formula to calculate how much medicine to give a child.

c is the correct amount for a child, in ml

c = yay+12 a is the amount for an adult, in ml

y is the age of the child, in years

A child who is 4 years old needs some medicine. The amount for an adult is 20 ml. Use the formula to work out the correct amount for this child. You must show your working.

............................... 2 marks



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Mental Questions

1. Look at the numbers on your answer sheet. Put them in order of size starting with the smallest.

0.4 25%1

5

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

2. Look at the expression. Write it as simply as possible. 7 – n n2 2

3. What is the sum of the angles in a rhombus?

º

4. It takes me one and a half minutes to swim one length of the pool.

How many lengths can I swim in fifteen minutes?

lengths 15

5. To the nearest whole number, what is the square root of eighty-three

point nine?

83.9



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Solving an equation

Solve this equation. 75 + 2t = 100 – 2t

t = ………………… 2 marks



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Functions

(a) A function maps the number n to the number n + 2 Complete the missing values.

n → n + 2

4 → .................

................. → 20

1 mark (b) A different function maps the number n to the number 2n Complete the missing values.

n → 2n

4 → .................

................. → 20

1 mark (c) Many different functions can map the number 25 to the number 5 Complete the tables by writing two different functions.

n → ................. n → .................

25 → 5 25 → 5

2 marks



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Holiday

(a) In 1976 the average yearly wage was £3275 On average, people spent 17% of £3275 on their family holiday. How much is 17% of £3275? Show your working.

£ …………………… 2 marks

(b) In 2001 the average yearly wage was £21842 On average, people spent £1644 on their family holiday. What percentage of the average yearly wage is that? Show your working.

…………………… % 2 marks



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Mental Questions

1. A circle has radius r. What is the formula for the area of the circle?

2. Write an equation that shows that k is one more than twice m. k m is one more than twice

3. Look at the fractions. Which of them are less than a half? Ring your answers.

150

23

34

110

37

4. A club played twenty-four games in a season. They won the same number of games as they lost. Use the pie chart to work out how many games they won.

won

lost

drawn

5. Multiply minus six by minus two.



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Angle p

This shape has been made from two congruent isosceles triangles.

Not drawn accurately

What is the size of angle p?

p = …………………° 2 marks



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Cuboids

You can make only four different cuboids with 16 cubes.

Dimensions

Cuboid A

1 1 16

Cuboid B

1 2 8

Cuboid C

1 4 4

Cuboid D

2 2 4

(a) Which of the cuboids A and D has the larger surface area? Tick ( ) the correct answer below.

Cuboid A

Cuboid D

Both the same 1 mark

Explain how you know.

1 mark (b) Which cuboid has the largest volume? Tick ( ) the correct answer below.

Cuboid A

Cuboid B

Cuboid C

Cuboid D

All the same



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1 mark (c) How many of cuboid D make a cube of dimensions 4 × 4 × 4?

............................... 1 mark

(d) You can make only six different cuboids with 24 cubes. Complete the table to show the dimensions. Two have been done for you.

Dimensions

Cuboid E 1 1 24

Cuboid F 1 2 12

Cuboid G

Cuboid H

Cuboid I

Cuboid J

3 marks



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Same area

(a) The square and the rectangle below have the same area.

4 cm 2 cm

4 cm

y cm

Not drawnaccurately

Work out the value of y.

y = ………………… cm 1 mark

(b) The triangle and the rectangle below have the same area.

4 cm

4 cm

w cm6 cm

Not drawnaccurately

Work out the value of w. Show your working.

w = ………………… cm 2 marks



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Mental Questions

1. Your answer sheet shows the answer to thirty-four multiplied by fifty-six. Use this information to help you work out the answer to thirty-five multiplied by fifty-six.

34 × 56 = 190435 × 56

2. What percentage of fifty pounds is thirty-five pounds?

% £ 50

3. Look at the equation. What is the value of x? 34 – 2 = 14x

4. Multiply out the brackets. 4(7 – )y

5. The instructions for a fruit drink say to mix one part blackcurrant juice with four parts water. I want to make one litre of this fruit drink. How much blackcurrant juice should I use? Give your answer in millilitres. ml 1 litre



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Rearrange

(a) Rearrange the equations. b + 4 = a

b = ………………………… 1 mark

4d = c

d = ………………………… 1 mark

m – 3 = 4k

m = ………………………… 1 mark

(b) Rearrange the equation to make t the subject. Show your working.

5(2 + t) = w

t = …………………… 2 marks



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Square cut

The diagram shows a square. Two straight lines cut the square into four rectangles. The area of one of the rectangles is shown.

Not drawn accurately Work out the area of the rectangle marked A.

…………………… cm2 2 marks



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Heron of Alexandria

About 2000 years ago, a Greek mathematician worked out this formula to find the area of any triangle.

For a triangle with sides a, b and c

Area = c)b)(sa)(ss(s −−−

where s = 2

cbas ++=

A triangle has sides, in cm, of 3, 5 and 6 Use a = 3, b = 5 and c = 6 to work out the area of this triangle.

…………………… cm2 2 marks



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Mental Questions

1. The net of a triangular prism is made from triangles and rectangles. How many of each shape are needed?

............... triangles

............... rectangles

2. I am going to throw a fair eight-sided dice, numbered twelve to nineteen.

What is the probability that I will throw a prime number?

12 to 19

3. I’m thinking of a number. I call it n.

I square my number then add four. Write an expression to show the result. n

4. What number is five cubed?

5. What is the volume of a cuboid measuring five centimetres by six centimetres by seven centimetres?

cm 5 cm by 6 cmby 7 cm

3



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Solving equations

Solve these equations. 8k − 1 = 15

k = ......................... 1 mark

2m + 5 = 10

m = ......................... 1 mark



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Number

I think of a number. I multiply this number by 8, then subtract 66 The result is twice the number that I was thinking of. What is the number I was thinking of?

……………………. 2 marks



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Hands

Here is some information about all the pupils in class 9A.

girls boys

right-handed 13 14

left-handed 1 2

A teacher is going to choose a pupil from 9A at random. (a) What is the probability that the pupil chosen will be a girl?

1 mark (b) What is the probability that the pupil chosen will be left-handed?

1 mark (c) The teacher chooses the pupil at random. She tells the class the pupil is left-handed. What is the probability that this left-handed pupil is a boy?

1 mark



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Mental Questions

1. On average, the driest place on earth gets only nought point five millimetres of rain every year. In total, how much rain would it expect to get in twenty years?

mm 0.5 mm

2. Jenny and Mark share some money in the ratio two to three.

Jenny’s share is one hundred and ten pounds. How much is Mark’s share?

£ 2 : 3

3. Twenty-one out of thirty-six pupils said they watched Top of the Pops.

What angle would show this on a pie chart? ° 21

36

4. On the grid, sketch the straight line with equation y equals three.

y4

2

00 2 4 x

5. The diagram shows a rhombus. The angle marked x is seventy-five degrees. What is the size of the angle marked y?

°

xy



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Thinking fractions

Calculate 53

65 ×

Show your working. Write your answer as a fraction in its simplest form.

2 marks



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Midpoint

(a) P is the midpoint of line AB.

What are the coordinates of point P?

P is (………… , …………) 1 mark

(b) Q is the midpoint of line MN. The coordinates of Q are ( 30, 50 )

What are the coordinates of points M and N?

M is (…………… , ……………)

1 mark

N is (…………… , ……………) 1 mark



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Spinning

A spinner has the numbers 1 to 4 on it.

The probability of spinning a number 4 is 0.1

The probability of spinning a number 1 is 0.6

The probability of spinning a number 2 is the same as the probability of spinning a number 3

Calculate the probability of spinning a number 3.

2 marks



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Mental Questions

1. Look at the equation. When x equals six, what is the value of y?

y x = 2

2. What is three point nine divided by two?

3.9

3. The longest bone in the human body is in the leg.

The average length of this bone in a man is fifty centimetres. In a woman it is ten per cent less. What is the average length of this bone in a woman?

cm 50 cm

4. A children’s sandpit is a cuboid measuring three metres by four metres by fifty centimetres. Which of the calculations on your answer sheet will give the volume of the sandpit? Put a ring round it.

3 m by 4 m by 50 cm

3 + 4 + 50 3 × 4 × 50

3 + 4 + 0.5 3 × 4 × 0.5

5. What is one third of three-quarters of one hundred?

100



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Puzzle

You can often use algebra to show why a number puzzle works. Fill in the missing expressions.

5

9

14

7

5

Think of a number

Add 4

Now add the number youwere first thinking of

Divide by 2

Subtract 2

n

n + 4

The answer is the number you were first thinking of

Example: Algebra:

2 marks



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Making zero

(a) Look at this information.

Two numbers multiply to make zero.

One of the statements below is true. Tick ( ) the true statement.

Both numbers must be zero.

At least one number must be zero.

Exactly one number must be zero.

Neither number can be zero.

1 mark (b) Now look at this information.

Two numbers add to make zero.

If one number is zero, what is the other number?

............................... 1 mark

If neither number is zero, give an example of what the numbers could be.

............................... and ……………………..

1 mark



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A level results

Here is some information about A levels in 2002.

English Mathematics

Number of students 72 000 54 000

Percentage gaining grade A 19% 37%

How many more students gained grade A in mathematics than in English?

……………………. 2 marks



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Mental Questions

1. On the grid, sketch the straight line with equation y equals x.

y4

2

00 2 4 x

2. Using three as an approximation for pi, what is the area of a circle with radius five centimetres?

cm 5 cm2

3. I can make a three-digit number from the digits two, three and four in six different ways. How many of these three-digit numbers are even?

4. I drive ten kilometres in twelve minutes.

What is my average speed in kilometres per hour? 10 km 12 minutes

km/h

5. Look at the expression on your answer sheet.

Multiply out the brackets.

2 ( + 4)a a



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Poplars

The scatter graph shows information about trees called poplars.

Height oftree (m)

6

5

4

3

2

1

00 1 2 3 4 5

Diameter of tree trunk (cm) (a) What does the scatter graph show about the relationship between the diameter of the tree trunk and the height of the tree?

1 mark (b) The height of a different tree is 3 m. The diameter of its trunk is 5 cm. Use the graph to explain why this tree is not likely to be a poplar.

1 mark



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(c) Another tree is a poplar. The diameter of its trunk is 3.2 cm. Estimate the height of this tree.

............................ m 1 mark

(d) Below are some statements about drawing lines of best fit on scatter graphs. For each statement, tick ( ) to show whether the statement is True or False. Lines of best fit must always...

go through the origin. True

False

have a positive gradient. True

False

join the smallest and the largest values. True

False

pass through every point on the graph. True

False

2 marks



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Dividing fractions

How many eighths are there in one quarter?

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

Now work out 43 ÷

81

............................... 3 marks



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Screens

The screens of widescreen and standard televisions look different. They have different proportions.

Keri starts to draw scale drawings of the televisions. For each, the height is 4.5 cm. What should the width of each scale drawing be?

The width of this scale drawing

should be ………………………….. cm

1 mark The width of this scale drawing

The width of this scale drawing

should be ………………………….. cm

1 mark

Documents

Level 6 Easter Revision Pack - Toot Hill School · Title: Microsoft Word - Level 6 Easter Revision Pack.doc Author: PArmann Created Date: 2/24/2006 4:32:01 PM