Practice for P2 June 2015 - KellyMathskellymaths.com/assets/Year11/practice-paper-for-p2-2015.pdf · Practice for P2 June 2015 Date: ... Q4. On the grid, draw the graph of y = 3 x

Name: _______________________________________________

Practice for P2 June 2015

Date:

Time: 4 hours 6 minutes Total marks available: 246 Total marks achieved: ______ @stephenbodman

Q1.f = 3g + 7h

(a) Work out the value of f when g = −5 and h = 2

f = ...........................................................(2)

(b) Factorise 3x + 6

...........................................................(1)

(c) Expand and simplify 5(y − 2) + 2(y − 3)

...........................................................(2)

(d) Simplify m5 × m3

...........................................................(1)

(e) Simplify

...........................................................(1)

(Total for question = 7 marks)

Q2.(a) Expand and simplify (p + 9)(p – 4)

..............................................................................................................................................(2)

(b) Solve = 4w + 2

w = . . . . . . . . . . . . . . . . . . . . . . (3)

(c) Factorise x2 – 49

..............................................................................................................................................(1)

(d) Simplify (9x8y3)½

..............................................................................................................................................(2)

(Total for Question is 8 marks)

Q3.Make p the subject of the formula y = 3p2 – 4

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


Q4.On the grid, draw the graph of y = 3x – 2 for values of x from –1 to 3.


Q5.The equation

x3 – 6x = 72

has a solution between 4 and 5

Use a trial and improvement method to find this solution. Give your answer correct to one decimal place. You must show all your working.

x = . . . . . . . . . . . . . . . . . . . . . .


Q6.p2 =

x = 8.5 × 109 y = 4 × 108

Find the value of p. Give your answer in standard form correct to 2 significant figures.

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


Q7.Solve

3x2 – 4x – 2 = 0

Give your solutions correct to 3 significant figures.

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


Q8.The equation

x3 − 3x = 15


Use a trial and improvement method to find this solution. Give your answer correct to 1 decimal place. You must show all your working.

x =. . . . . . . . . . . . . . . . . . . . .


Q9.The equation

x3 + 2x = 110


Use a trial and improvement method to find this solution. Give your answer correct to one decimal place. You must show ALL your working.

x = . . . . . . . . . . . . . . . . . . . . . .


Q10.(a) Factorise 6 + 9x ..............................................................................................................................................

(1)

(b) Factorise y2 – 16

.............................................................................................................................................. (1)

(c) Factorise 2p2 – p – 10

.............................................................................................................................................. (2)


Q11.The equation x3 − 2x = 125


Use a trial and improvement method to find this solution. Give your answer correct to 1 decimal place. You must show all your working.

x = ...........................................................

(Total for question = 4 marks) Q12.On the grid, draw the graph of y = 2x − 3 for values of x from −2 to 3


Q13.Solve 3x2 − 5x − 1 = 0 Give your solutions correct to 3 significant figures.

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

(Total for question = 3 marks) Q14.(a) Factorise x2 + 7x

.............................................................................................................................................. (1)

(b) Factorise y2 – 10y + 16

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

(2)

*(c) (i) Factorise 2t2 + 5t + 2

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

(ii) t is a positive whole number. The expression 2t2 + 5t + 2 can never have a value that is a prime number. Explain why.

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

(3)


Q15.

Simon went for a cycle ride. He left home at 2 pm.

The travel graph represents part of Simon's cycle ride.

At 3 pm Simon stopped for a rest.

(a) How many minutes did he rest?

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

(1)

(b) How far was Simon from home at 5 pm?

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

(1)

At 5 pm Simon stopped for 30 minutes. Then he cycled home at a steady speed. It took him 1 hour 30 minutes to get home.

(c) Complete the travel graph.

(2)


Q16.

(a) Expand and simplify 3(x + 4) + 2(5x− 1)

.............................................................................................................................................. (2)

(b) Expand and simplify (2x + 1)(x − 4)

.............................................................................................................................................. (2)

(c) Factorise completely 6y2 − 9xy

.............................................................................................................................................. (2)


Q17.

OAB is a sector of a circle, centre O. The radius of the circle is 15 cm. The angle of the sector is 30°.Calculate the area o f sector OAB. Give your answer correct to 3 significant figures.

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

(Total for Question is 2 marks) Q18. 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.

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


Q19.

Calculate the value of x. Give your answer correct to 3 significant figures.

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


Q20.

Diagram NOT accurately drawn

LMN is a right-angled triangle. MN = 9.6 cm. LM = 6.4 cm.

Calculate the size of the angle marked x°. Give your answer correct to 1 decimal place.

. . . . . . . . . . . . . . . . . . . . . .°


Q21. x = 0.7

Work out the value of

Write down all the figures on your calculator display.

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


Q22.Here are the first five terms of an arithmetic sequence.

2 6 10 14 18

(a) Write down an expression, in terms of n, for the nth term of this sequence.

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

(2)

*(b) Is 86 a term in the sequence? You must give a reason for your answer.

(1)

(Total for question = 3 marks) Q23. (a) Expand and simplify (y − 2)(y − 5)

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

(2)

*(b) Prove algebraically that

(2n + 1)2 − (2n + 1) is an even number

for all positive integer values of n.

(3) (Total for Question is 5 marks)

Q24. Here are the first five terms of an arithmetic sequence.

4 9 14 19 24

(a) Find, in terms of n, an expression for the nth term of this sequence.

........................................................... (2)

Here are the first five terms of a different sequence.

2 2 0 −4 −10

An expression for the nth term of this sequence is 3n − n2

(b) Write down, in terms of n, an expression for the nth term of a sequence whose first five terms are

4 4 0 −8 −20

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


Q25. Here are the first four terms of an arithmetic sequence.

3 10 17 24

(a) Find, in terms of n, an expression for the nth term of this arithmetic sequence.

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

(2)

(b) Is 150 a term of this sequence? You must explain how you get your answer.

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

............................................................................................................................................. (2)

(Total for Question is 4 marks) Q26.(a) Solve 2x2 + 9x – 7 = 0


.............................................................................................................................................. (3)

(b) Solve 2⁄y2 + 9⁄y - 7 = 0


.............................................................................................................................................. (2)


Q27.

(a) Complete the table of values for y = x2 – 2x

(2)

(b) On the grid, draw the graph of y = x2 – 2x for values of x from –2 to 4

(2)

(c) Solve x2 – 2x – 2 = 1

.............................................................................................................................................. (2)


Q28. * The diagram shows a ladder leaning against a vertical wall.

The ladder stands on horizontal ground.

The length of the ladder is 6 m. The bottom of the ladder is 2.25 m from the bottom of the wall.

A ladder is safe to use when the angle marked y is about 75°.

Is the ladder safe to use? You must show all your working.


Q29.The diagram shows a solid prism.

On the centimetre square grid, draw the side elevation of the solid prism from the direction shown by the arrow.

(Total for Question is 2 marks) Q30.A circle has a diameter of 140 cm.

Work out the circumference of the circle.

Give your answer correct to 3 significant figures.

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


Q31. ABC is an isosceles triangle.

Work out the area of the triangle.

Give your answer correct to 3 significant figures.

........................................................... cm2 (Total for Question is 4 marks)

Q32. Here is a circle.


The diameter of the circle is 9 cm.

Work out the circumference of this circle. Give your answer correct to 3 significant figures.

...........................................................cm (Total for Question is 2 marks) Q33.

ABC is a right-angled triangle. AC = 6 cm AB = 13 cm

(a) Work out the length of BC. Give your answer correct to 3 significant figures.

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

(3)

PQR is a right-angled triangle. PR = 17 cm PQ = 25 cm

(b) Work out the size of angle RPQ. Give your answer correct to 1 decimal place.

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

(3)


Q34.

ABC is a triangle.

(a) Work out the area of triangle ABC. Give your answer correct to 3 significant figures.

. . . . . . . . . . . . . . . . . . . . . . cm2 (2)

(b) Work out the length of the side AB. Give your answer correct to 3 significant figures.

.............................................................................................................................................. (3)


Q35.* Saphia is organising a conference. People at the conference will sit at circular tables.

Each table has a diameter of 140 cm. Each person needs 60 cm around the circumference of the table.

There are 12 of these tables in the conference room. A total of 90 people will be at the conference.

Are there enough tables in the conference room?


Q36. Here is a plan of Martin's driveway.


Martin is going to cover his driveway with gravel. The gravel will be 6 cm deep.

Gravel is sold in bags. There are 0.4 m3 of gravel in each bag. Each bag of gravel costs £38

Martin gets a discount of 30% off the cost of the gravel.

Work out the total amount of money Martin pays for the gravel.

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


Q37.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?

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


Q38.Use a calculator to work out

Write down all the figures on your calculator display. Give your answer as a decimal.

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


Q39.* A company sells boxes to factories. Fred buys boxes. The boxes are sold in packs of 1000 Each pack costs £193.86

Fred orders 3 packs of boxes. He gets a discount on his total order.

The table shows the discount he will get.

Total Order Discount

£100 - £300 5% £301 - £400 10%

£401 and above 15%

Work out the total cost of the order after the discount. You must show your working.


Q40 160 cm of gold wire has a weight of 17.8 grams.

Work out the weight of 210 cm of the gold wire.

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


Q41. * In the UK, petrol cost £1.24 per litre. In the USA, petrol cost 3.15 dollars per US gallon.

1 US gallon = 3.79 litres £1 = 1.47 dollars

Was petrol cheaper in the UK or in the USA?


Q42. Bill's weight decreases from 64.8 kg to 59.3 kg.

Calculate the percentage decrease in Bill's weight. Give your answer correct to 3 significant figures.

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


Q43.Rob is learning about the planets.

Rob makes a model of the Sun. He also makes a model of the planet Jupiter.

Rob is going to hang the two models in the school hall.

Rob wants a distance of 16 m between the two models. The real distance between the planet Jupiter and the Sun is 8 × 108 km.

Work out the scale Rob should use. Give your answer in the form 1 : n

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


Q44. Mr Watkins needs to buy some oil for his central heating.

Mr Watkins can put up to 1500 litres of oil in his oil tank. There are already 850 litres of oil in the tank. Mr Watkins is going to fill the tank with oil.

The price of oil is 67.2p per litre. Mr Watkins gets 5% off the price of the oil.

How much does Mr Watkins pay for the oil he needs to buy?

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


Q45.

Calculate the value of

Write down all the figures on your calculator display. You must give your answer as a decimal.

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


Q46.* Viv wants to invest £2000 for 2 years in the same bank.

At the end of 2 years, Viv wants to have as much money as possible.

Which bank should she invest her £2000 in?


Q47. Sasha takes a music exam.

The table shows the result that Sasha can get for different percentages in her music exam.

Sasha gets 62 out of 80 in her music exam.

What result does Sasha get?

You must show your working.

........................................................... (Total for Question is 3 marks)

Q48. In a sale normal prices are reduced by 20%.

A washing machine has a sale price of £464

By how much money is the normal price of the washing machine reduced?

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


Q49. * The table gives some information about student attendance at a school on Friday.

The school has a target of 94% of students being present each day.

Did the school meet its target on Friday?

(Total for question = 3 marks) Q50.Derek buys a house for £150 000 He sells the house for £154 500

(a) Work out Derek's percentage profit.

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

(3)

Derek invests £154 500 for 2 years at 4% per year compound interest.

(b) Work out the value of the investment at the end of 2 years.

£ . . . . . . . . . . . . . . . . . . . . . .(3)


Q51.

(a) Use your calculator to work out

Write down all the figures on your calculator display. You must give your answer as a decimal.

...........................................................(2)

(b) Write your answer to part (a) correct to 1 significant figure.

...........................................................(1)


Q52. Pavel and Katie share some sweets in the ratio 3 : 8

Katie gets 32 sweets.

(a) How many sweets does Pavel get?

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

(2)

Katie also has a tin of chocolates.

There are 80 chocolates in the tin.

45% of the chocolates have toffee in the middle.

(b) Work out the number of chocolates that have toffee in the middle.

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

(2)

(Total for Question is 4 marks) Q53.(a) Write 7.8 × 10−4 as an ordinary number.

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

(1)

(b) Write 95 600 000 as a number in standard form.

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


Q54. Katie invests £200 in a savings account for 2 years.

The account pays compound interest at an annual rate of

3.3% for the first year 1.5% for the second year

(a) Work out the total amount of money in Katie's account at the end of 2 years.

£........................................................... (3)

Katie travels to work by train. The cost of her weekly train ticket increases by 12.5% to £225

Katie's weekly pay increases by 5% to £535.50

*(b) Compare the increase in the amount of money Katie has to pay for her weekly train ticket with the increase in her weekly pay.

(3)

(Total for Question is 6 marks) Q55.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)


Q56. In Holborn School there are 460 students in Key Stage 3 320 students in Key Stage 4 165 students in Key Stage 5

Nimer is carrying out a survey. He needs a sample of 100 students stratified by Key Stage.

Work out the number of students from Key Stage 3 there should be in the sample.

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


Q57.The table shows information about 1065 students.

Elena takes a stratified sample of 120 students by year group and by gender.

Work out the number of Year 8 female students in her sample.

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

(Total for Question is 2 marks) Q58. The table gives information about the temperature, T °C, at noon in a town for 50 days.

(a) Write down the modal class interval.

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

(1)

(b) Calculate an estimate for the mean temperature.

........................................................... ° C

(4)

(c) Draw a frequency polygon for the information in the table.

(2)

(Total for Question is 7 marks) Q59.Lorna carries out a survey about the number of times customers go to a shop.

She asks at random 100 customers how many times they went to the shop last month.

The table shows Lorna's results.

One of the 100 customers is chosen at random.

(a) What is the probability that this customer went to the shop 5 or more times?

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

(2)

Last month the shop had a total of 1500 customers.

(b) Work out an estimate for the number of customers who went to the shop exactly 2 times last month.

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

(2)

The owner of a different shop is carrying out a survey on the ages of his customers. He records the ages of the first 10 customers in his shop after 9 am one morning.

(c) This may not be a suitable sample. Give two reasons why.

1 .............................................................................................................................................

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

2 .............................................................................................................................................

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


Q60.(a) Max wants to take a random sample of students from his year group. (i) Explain what is meant by a random sample.

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

(ii) Describe a method Max could use to take his random sample.

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

(2) (b) The table below shows the numbers of students in 5 year groups at a school.

Year Number of students

9 239 10 257 11 248 12 190 13 206

Lisa takes a stratified sample of 100 students by year group.

Work out the number of students from Year 9 she has in her sample.

.............................................................................................................................................. (2)


Q61.(a) Explain what is meant by a stratified sample.

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

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

(1)

The table shows information about the ages of the people living in a village.

Mrs Parrish carries out a survey of these people. She uses a sample size of 50 people stratified by age group.

(b) Work out the number of people over 60 years of age in the sample.

........................................................... (2)


Q62. The frequency table gives information about the heights of some people.

Draw a frequency polygon for this information.

(Total for question = 2 marks) Q63. 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.

(2)

(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)


Q64. There are some green counters, some yellow counters, some blue counters and some red counters in a bag.

The table shows the probabilities that a counter taken at random from the bag will be green or yellow or red.

Mary takes at random a counter from the bag.

(a) Work out the probability that the counter will be blue.

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

(2)

Mary puts the counter back into the bag. There are 125 counters in the bag.

(b) Work out the number of green counters in the bag.

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

(2) (Total for question = 4 marks)

Documents

Practice for P2 June 2015 - KellyMathskellymaths.com/assets/Year11/practice-paper-for-p2-2015.pdf · Practice for P2 June 2015 Date: ... Q4. On the grid, draw the graph of y = 3 x