gcse mathematics - the "life cloud · gcse mathematics formulae: higher tier volume of a prism...

Name

For Edexcel

GCSE MathematicsPaper 4A (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 27 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

EH4A 09 © 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

LeaveBlank

Q1

Q2

7.2 cm

2.8 cm

4.6 cm

Answer ALL TWENTY SEVEN questions.

Write your answers in the spaces provided.

You must write down all the stages in your working.

1. Gary plays two games of table tennis.Each game is either won or lost.

The probability that he loses both games is 0.28The probability that he wins exactly one game is 0.3

Work out the probability that he wins both games.

………………………

(Total 2 marks)

2. Diagram NOTaccurately drawn

The diagram shows a replacement blade for a knife.The blade is in the shape of a trapezium.

Find the area of this trapezium.Give the units with your answer.

…………………………

(Total 3 marks)


LeaveBlank

Q3

Front

3. The diagram shows a 3-D shape made from cubes.

(a) On the grid, draw the front elevation of the shape from the direction shown.

(2)

(b) On the grid, draw the plan of the shape.

(2)

(Total 4 marks)


LeaveBlank

Q4

Q5

4. Angela recorded the resting pulse, in beats per minute, of 20 people.

Here are her results.

72 63 54 64 80 60 67 63 75 78

61 78 72 57 63 57 66 83 71 69

Draw an ordered stem and leaf diagram to show her results.You should include a key.

(Total 3 marks)

5. (a) Use your calculator to work out the value of 3.13

…………………………(1)

(b) Kath says

“squaring a number always makes it bigger”.

Give an example to show that Kath is wrong.

………………………………………………………………………………………

………………………………………………………………………………………(2)

(Total 3 marks)


LeaveBlank

Q6

6. Here are four fair spinners.

Spinner A Spinner B Spinner C Spinner D

In each part of this question a statement is made.

Write down the letter of the spinner for which the statement is true.

(a) The probability of getting a 4 is 12 .

Spinner ………………(1)

(b) It is impossible to get a 3.


(c) The probability of getting a 2 is the same as the probability of getting a 5.


(d) The probability of getting a 4 is twice the probability of getting a 6.


(Total 4 marks)


12

44

3

4

11

46

2

3

22

56

3

5

14

56

4

5

LeaveBlank

Q7

Q8

7. (a) Use your calculator to work out the value of 9.6− 2.32

0.16

Write down all the figures on your calculator display.

………………………………(2)

(b) Write your answer to part (a) correct to an appropriate degree of accuracy.

…………………………(1)

(Total 3 marks)

8. The table shows the heights of pupils in a class.

Height (h cm) Frequency

100 < h ≤ 110 6

110 < h ≤ 120 9

120 < h ≤ 130 8

130 < h ≤ 140 5

140 < h ≤ 150 1

Find the class interval in which the median lies.

………………………………

(Total 2 marks)


LeaveBlank

Q9

2x + 1

3x – 2

2x – 1

x


The diagram shows a quadrilateral.

The lengths of the sides are given in centimetres.

(a) Find an expression, in terms of x, for the perimeter of the quadrilateral.Give your answer in its simplest form.

……………………… cm(2)

The perimeter of the quadrilateral is 34 cm.

(b) Find the length of the longest side of the quadrilateral.

……………………… cm(3)

(Total 5 marks)


LeaveBlank

4 m

2.5 m

6 m

2 m

1 m

Q10

10. Bill and Ben are decorators.

Bill charges £70 per wall to hang wallpaper.

Ben charges £6 per square metre covered to hang wallpaper.

Diagram NOTaccurately drawn

The diagram shows the dimensions of Brian's dining room.He wants wallpaper hung on all four walls except for the door which is shaded.

Work out who will charge less to hang the wallpaper, Bill or Ben, and by how much.You must show all your working.

…………………………………………………………………

(Total 5 marks)


LeaveBlank

Q11

11. The equation

x3 – x = 100

has a solution between 4 and 5.

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 4 marks)


LeaveBlank

Q12

1 2 43 5 6 7 8 x

1

2

4

3

5

6

7

8

y

O

C

B

A

12.

Describe fully the single transformations which will map

(a) triangle A onto triangle B,

………………………………………………………………………………………(2)

(b) triangle A onto triangle C.

………………………………………………………………………………………

………………………………………………………………………………………(3)

(Total 5 marks)


LeaveBlank

Q13

Q14

17 cm

62 cm

13. (a) Solve x 3

4 = 2

x = ……………………(2)

(b) Factorise 9 – y2

………………………………(2)

(Total 4 marks)


A rectangle has sides of length 17 cm and 62 cm.

Calculate the length of a diagonal of the rectangle.Give your answer correct to 3 significant figures.

………………………… cm

(Total 3 marks)


LeaveBlank

Q15

a b

D

A CB

O


OAB is a triangle.

OA = a and OB = b.

(a) Express AB in terms of a and b.

…………………………(1)

C is the point on AB extended such that AB : BC = 3 : 2

D is the midpoint of OC.

(b) Find OD in terms of a and b.

…………………………(3)

(Total 4 marks)


LeaveBlank

Q16

P

R

132°

S

Q

O

63°


P, Q, R and S are points on a circle, centre O.

Angle PQR = 132°.Angle ORQ = 63°.

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

°……………………

(ii) Give a reason for your answer.

…………………………………………………………………………………

…………………………………………………………………………………(2)

(b) Work out the size of angle OPQ.

°……………………

(2)

(Total 4 marks)


LeaveBlank

Q17

A

C

Y

B

X45°


The diagram shows a vertical mast ABC.The mast is supported by cables attached to the horizontal ground at X and Y.

AB = BC.Angle BXA = 45°.

Find the size of angle CXA.

°…………………………

(Total 3 marks)


LeaveBlank

Q18

Q19

18. Solve the simultaneous equations

3x + 2y = 11

2x − 5y = 20

x = ……………………

y = ……………………

(Total 4 marks)

19. Diya's weight is 8% less than it was a month ago.He now weighs 52.9 kg.

Work out how much weight Diya has lost in the last month.

…………………… kg

(Total 3 marks)


LeaveBlank

Q20

1 2 43 5 6 7 8 x

1

2

4

3

5

6

7

8

y

O

20. (a) −4 < 2n ≤ 6

n is an integer.

Write down all the possible values of n.

………………………………(2)

(b) y > 0, y < 3x, y + 2x < 6

x and y are integers.

On the grid, mark with a cross (× ) each of the three points which satisfy all these three inequalities.

(3)

(Total 5 marks)


LeaveBlank

Q21

21. Mindy collects data on how pupils usually get to school.

The table shows her results.

Transport to school Number of pupils

Car 341

Bus 217

Train 32

Bike 65

Walk 156

Mindy wants some pupils to answer more questions about their journey to school.

She decides to ask a stratified sample of 60 pupils.

(a) Work out the number of pupils travelling to school by car who should be in her sample.

……………………(3)

Mindy needs 16 pupils travelling to school by bus in her sample.

(b) Describe a method she could use to obtain a random sample of 16 from the 217 pupils who travel by bus.

………………………………………………………………………………………

………………………………………………………………………………………

………………………………………………………………………………………(1)

(Total 4 marks)


LeaveBlank

Q22

Q23

x

8.4 cm7.1 cm

5.6 cm

22. A car journey takes 1 hour 10 minutes, correct to the nearest minute.

The car's average speed on the journey is 72 km/h, correct to 2 significant figures.

Work out the least distance the car could have travelled.

………………………… km

(Total 4 marks)


The diagram shows a triangle with sides of length 5.6 cm, 7.1 cm and 8.4 cm.

Find the size of the angle labelled x.

°…………………………

(Total 3 marks)


LeaveBlank

Q24

Amount spent (£A)100 200 400300 5000

24. Richard carried out a survey on the amount of money people spent online in a week.

The table shows his results.

Amount spent (£A) Frequency

0 ≤ A < 50 60

50 ≤ A < 100 25

100 ≤ A < 200 38

200 ≤ A < 300 17

300 ≤ A < 500 18

Draw a histogram for the information given in the table.

(Total 3 marks)


LeaveBlank

Q25

Q26

25. A mug of warm coffee is left on a table outside.

The temperature of the coffee, T °C, decreases by P % each minute. Its temperature after n minutes is given by the formula

T = 65 × (0.975)n

(a) Write down the value of T when n = 0.

T = …………………(1)

(b) Write down the value of P.

P = …………………(1)

(c) Find the temperature of the coffee after 20 minutes.Give your answer correct to 1 decimal place.

…………………… °C(2)

(Total 4 marks)

26. Simplify fully 2 x − x2

6 7 x x2

…………………………

(Total 3 marks)


LeaveBlank

y

xO

CB

A

27.

The diagram shows a sketch of the curve with equation y = 4 – x2

The maximum point of the curve is the point A.The curve crosses the x-axis at the points B and C.

(a) Find the coordinates of the points A, B and C.

A ( …… , …… )

B ( …… , …… )

C ( …… , …… )(3)

(b) On the set of axes on the next page, sketch and label the curves with equations

(i) y = 2(4 – x2)

(ii) y = 4 – (x + 2)2


LeaveBlank

Q27

–1

–2

1

3

4

5

6

y

–2 –1 1 2 3 4 5 x–5 –4 –3 O

2

7

9

8

(3)

(Total 6 marks)

TOTAL FOR PAPER: 100 MARKS

END


gcse mathematics - the "life cloud · gcse mathematics formulae: higher tier volume of a prism...

Documents