MrJacksonMaths Higher Calculator Paper I

Name

For Edexcel

GCSE MathematicsPaper 4I (Calculator)

Higher TierTime: 1 hour and 45 minutes

Materials required

Ruler, protractor, compasses,pen, pencil, eraser.Tracing paper may be used.

Instructions and Information for Candidates

Write your name in the box at the top of the page.Answer all the questions in the spaces provided in this question paper.The marks for each question and for each part of a question are shown in brackets.The total number of marks for this paper is 100. There are 24 questions in this paper.Calculators may be used.If your calculator does not have a π button, take the value of π to be 3.142 unless thequestion instructs otherwise.

Advice to Candidates

Show all stages in any calculation.Work steadily through the paper. Do not spend too long on one question.If you cannot answer a question, leave it and attempt the next one.Return at the end to those you have left out.

Written by Shaun Armstrong

Only to be copied for use in the purchaser's school or college

EH4I 09 Page 1 © Churchill Maths Limited

GCSE Mathematics

Formulae: Higher Tier

Volume of a prism = area of cross section × length

Volume of sphere = 43 πr3 Volume of cone = 1

3 πr2h

Surface area of sphere = 4πr2 Curved surface area of cone = πrl

In any triangle ABC The Quadratic Equation

The solutions of ax2 + bx + c = 0where a ≠ 0, are given by

x = −b± b2−4ac

2a

Sine Rule a

sin A =

bsin B

= c

sinC

Cosine Rule a2 = b2 + c2 – 2bc cos A

Area of triangle = 12 ab sin C


sectioncross

length

r

l h

r

c B

C

A

b a

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Q1

Q2

Answer ALL TWENTY FOUR questions.

Write your answers in the spaces provided.

You must write down all the stages in your working.

1. Solve 5x = 2x + 9

x = ……………………

(Total 2 marks)

2. Alistair stores his files in boxes and trays.

He has x boxes.He has 2 more trays than he has boxes.

(a) Write down an expression, in terms of x, for the number of trays he has.

…………………………(1)

Each box has 10 files in it.Each tray has 3 files in it.

(b) Find an expression, in terms of x, for the total number of files he has.Give your answer in its simplest form.

…………………………(2)

(Total 3 marks)


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Q3

To work From work

Walk

Walk

Walk

Bus

3. The probability that Mr. Evans walks to work is 0.45

(a) What is the probability that Mr. Evans does not walk to work?

……………………(1)

Mr. Evans travels to work by walking, going on the bus or by getting a taxi.He also travels home from work by walking, going on the bus or by getting a taxi.

(b) Complete the table below to show all the ways in which Mr. Evans can travel to and from work on one day. Two are done for you.

(2)

(Total 3 marks)


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Q4

SideFront

4.

The diagram shows a solid shape.

(a) Sketch the front elevation of the shape from the direction shown.

(2)

(b) Sketch the side elevation of the shape from the direction shown.

(2)

(Total 4 marks)


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Q5

Q6

5. (a) Use your calculator to work out the value of 12.7 8.0319.7 − 7.12

Write down all the figures on your calculator display.

………………………………(2)

(b) Write your answer to part (a) correct to 2 decimal places.

…………………………(1)

(Total 3 marks)

6. (a) Simplify 6y × 2y

…………………………(1)

(b) Expand and simplify 6(z + 2) – 3(z – 5)

…………………………(2)

(Total 3 marks)


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Q7

7. Karen wants to find out about the number of birthday cards pupils in her class receive.

(a) Design a suitable question that she could use.You should include response boxes.

(2)

Ruth wants to find out about the type of birthday cake pupils in her class would like.

She asks each pupil in her class this question.

“What birthday cake would you like?”

(b) Write down two reasons why this is not a good question.

First reason …………………………………………………………………………

………………………………………………………………………………………

Second reason ………………………………………………………………………

………………………………………………………………………………………(2)

(Total 4 marks)


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Q8

Q9

8. Whilst on holiday in New York, Erina bought an MP3 player for $72.99

The same MP3 player would have cost her £49.99 at home.

The exchange rate was £1 = $1.85

Work out how much she saved, giving your answer in pounds.

£ ………………………

(Total 3 marks)

9. Before going on holiday, Joe, Paul and Tim do housework to earn some extra money.

Paul earns £6 more than Joe and Tim earns twice as much as Joe.Altogether, Joe, Paul and Tim earn £90.

Work out how much Paul earns.

£ ………………………

(Total 5 marks)


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Q10

10. 25 children took part in a sponsored walk.

The table gives information about the amount of money they raised.

Money raised (£P) Number of children

10 ≤ P < 20 5

20 ≤ P < 30 8

30 ≤ P < 40 7

40 ≤ P < 50 4

50 ≤ P < 60 1

(a) Work out an estimate for the mean amount of money raised by the children.

£ ……………………(4)

(b) Find the class interval in which the median lies.

…………………………(1)

When the money raised was checked, it was found that one child who thought he had raised £28 had actually raised £32.

(c) Will this change the interval in which the median lies?Explain your answer.

………………………………………………………………………………………

………………………………………………………………………………………(2)

(Total 7 marks)


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Q11

1.5 m

1.8 m

80 cm

1.6 m

11. Diagram NOTaccurately drawn

A garden shed is in the shape of a prism.

The cross-section of the prism is a trapezium which is shaded in the diagram.

Work out the volume of the shed in cubic metres.

………………………… m3

(Total 3 marks)


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Q12

12. The students on a trip had to choose between going to a museum or to the cinema.

35 of the students were in year 10 and the rest were in year 11.

16 of the year 10 students chose to go to the museum.

15 of all the students on the trip chose to go to the museum.

Work out the fraction of year 11 students who chose to go to the museum.Give your answer as a fraction in its simplest form.

……………………

(Total 4 marks)


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Q13

1

2

4

3

5

y

–1

–3

–2

O 1 2 43 5 x–1–2–3

13.

y = 13 x

3y + 5x = 15

The graphs of the lines y = 13 x and 3y + 5x = 15 have been drawn on the grid.

(a) Use the graphs to write down an approximate solution to the simultaneous equations

y = 13 x

3y + 5x = 15

x = ……………………

y = ……………………(2)

The point P satisfies all three of these inequalities.

x ≥ 2 y ≥ 13 x 3y + 5x ≤ 15

The coordinates of P are both integers.

(b) Write down the coordinates of P.

( …… , …… )(1)

(Total 3 marks)


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Q14

14. Here are some patterns made from white and grey squares.

Pattern number 1 Pattern number 2 Pattern number 3 Pattern number 4

(a) Write down an expression, in terms of n, for

(i) the number of grey squares in pattern number n,

…………………………

(ii) the number of white squares in pattern number n.

…………………………(3)

(b) Work out how many grey squares there are in the pattern with 41 white squares.

…………………………(3)

(Total 6 marks)


P

R

48°

T

S

Q

O

54°

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In the diagram, P, Q, R and S are points on a circle.The centre of the circle, O, is on PR and the point T is where PR and QS intersect.

Angle PQS = 48°.Angle PSQ = 54°.

(a) (i) Work out the size of angle PRQ.

°…………………

(ii) Give a reason for your answer.

…………………………………………………………………………………

…………………………………………………………………………………(2)

(b) (i) Work out the size of angle RQS.

°…………………


…………………………………………………………………………………

…………………………………………………………………………………(2)


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Q15

Q16

17

37

56

21

45

58

22

46

63

26

49

65

30

51

68

31

54

80

(c) (i) Work out the size of angle PTS.

°…………………


…………………………………………………………………………………

…………………………………………………………………………………(2)

(Total 6 marks)

16. Here are 18 cards with numbers on.

(a) Complete this two-way table for the numbers on the cards.

(1)

One of the cards is picked at random and then replaced.A second card is picked at random and then replaced.

(b) Work out the probability that both cards picked had odd numbers that are less than 50 on them.

………………………(3)

(Total 4 marks)


Number less than 50

Number more than 50

Even number

Odd number 6

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Q17

P

R

Q

12 cm

10 cm69°


The diagram shows triangle PQR.

PQ = 12 cm.PR = 10 cm.Angle PRQ = 69°.

Find the size of angle QPR.Give your answer to an appropriate degree of accuracy.

°…………………………

(Total 4 marks)


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Q18

18.

(a) Reflect shape A in the line x = 3 and label the image B.(2)

(b) Describe fully the single transformation that maps shape A onto shape C.

………………………………………………………………………………………

………………………………………………………………………………………(3)

(Total 5 marks)


1 2 43 5 x

y

–2 –1 6 7O–3

–3

–4

–2

–1

8

1

2

4

3

5

6

C

A

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Q19

Q20

19. Solve the equation

x2 – 4x + 2 = 0

Give your answers correct to 3 significant figures.

x = ……………… or x = ………………

(Total 3 marks)

20. Mansur has two fair dice.

One of the dice has 4 red sides, 1 blue side and 1 yellow side.The other has 2 red sides, 3 blue sides and 1 yellow side.

Mansur rolls both dice.

Work out the probability that both dice show the same colour.

………………………

(Total 4 marks)


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Q21

A

C

E

B

D

17 cm

17 cm

15 cm

7 cm


BED is a straight line.Angle AEB = Angle CBD = 90°.AB = 17 cm.AE = 15cm.CD = 17 cm.DE = 7 cm.

Prove that triangle ABE and triangle BCD are congruent.

(Total 3 marks)


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Q22

22. The period of a pendulum is the time it takes to swing from left to right and back again.

The period, T seconds, of a pendulum is directly proportional to the square root of its length, l cm.

When l = 25, T = 1.

(a) Find a formula for T in terms of l.

T = …………………………(3)

(b) Find the value of l when T = 1.5

l = ……………………(2)

(Total 5 marks)


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Q23

23. At the start of 1998, Mr. Prince's house was worth £140 000

In the three years after the start of 1998, house prices where Mr. Prince lives increased by 10% per year. Since then, they have increased by 6% per year.

(a) Work out the value of his house at the start of 2001.

£ …………………………(3)

(b) Find the year in which Mr. Prince's house was first worth more than £200 000You must show all your working.

…………………………(3)

(Total 6 marks)


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Q24

A C

37°

B24. Diagram NOTaccurately drawn

In triangle ABC, AB = BC.Angle ABC = 37° correct to the nearest degree.

(a) Work out the upper bound for the size of angle BAC.

°…………………………

(2)

The length of AB is 16 cm correct to the nearest cm.

(b) Work out the lower bound for the perimeter of triangle ABC.Give your answer correct to 3 significant figures.

………………………… cm(5)

(Total 7 marks)

TOTAL FOR PAPER: 100 MARKS

END


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MrJacksonMaths Higher Calculator Paper I