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NameFor Edexcel
GCSE MathematicsPaper 4A (Calculator)
Higher TierTime: 1 hour and 45 minutes
Materials requiredRuler, protractor, compasses,pen, pencil, eraser.Tracing paper may be used.
Instructions and Information for CandidatesWrite 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 CandidatesShow 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 ArmstrongOnly to be copied for use in the purchaser's school or college
EH4A 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 πr2hSurface area of sphere = 4πr2 Curved surface area of cone = πrl
In any triangle ABC The Quadratic EquationThe solutions of ax2 + bx + c = 0where a ≠ 0, are given by
x = −b±b2−4ac 2a
Sine Rule asin A =
bsin B =
csinC
Cosine Rule a2 = b2 + c2 – 2bc cos A
Area of triangle = 12 ab sin C
EH4A Page 2 © Churchill Maths Limited
sectioncross
length
rl h
r
c B
C
A
b a
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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)
EH4A Page 3 © Churchill Maths Limited
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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)
EH4A Page 4 © Churchill Maths Limited
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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)
EH4A Page 5 © Churchill Maths Limited
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Q6
6. Zahir wants to change £300 into Euros (€).
There are two places where he can change his money.
Central Bank
£1 = €1.44
no fee
Travel Mart
£1 = €1.48
2% fee
(a) Work out how many Euros he would get at the Central Bank.
€ ……………………(2)
(b) Work out how much extra he would get at the Travel Mart after paying the fee.
€ ……………………(3)
(Total 5 marks)
EH4A Page 6 © Churchill Maths Limited
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Q7
Q8
7. (a) Simplify
(i) 2x × 3y
……………………
(ii) p4 ÷ p7
……………………(2)
(b) Make b the subject of the formula a = 3 + 5b
b = ………………………(2)
(Total 4 marks)
8. (a) Use your calculator to work out the value of 9.6 − 2.32
0.16
Write down all the figures on your calulator display.
………………………………(2)
(b) Write your answer to part (a) correct to an appropriate degree of accuracy.
…………………………(1)
(Total 3 marks)
EH4A Page 7 © Churchill Maths Limited
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Q9
9. 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)
EH4A Page 8 © Churchill Maths Limited
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Q10
2x + 1
3x – 2
2x – 1
x
10. Diagram NOTaccurately drawn
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)
EH4A Page 9 © Churchill Maths Limited
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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)
EH4A Page 10 © Churchill Maths Limited
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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)
EH4A Page 11 © Churchill Maths Limited
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Q13
Q14
17 cm
62 cm
13. (a) Solve x 3
4 = 2
x = ……………………(2)
(b) Factorise 9 – y2
………………………………(2)
(Total 4 marks)
14. Diagram NOTaccurately drawn
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)
EH4A Page 12 © Churchill Maths Limited
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Q15
a b
D
A CB
O
15. Diagram NOTaccurately drawn
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
(b) Find OC in terms of a and b.
…………………………(2)
D is the midpoint of OC.
(c) Express OD in terms of a and b.
…………………………(1)
(Total 4 marks)
EH4A Page 13 © Churchill Maths Limited
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Q16
P
R
132°
S
Q
O
63°
16. Diagram NOTaccurately drawn
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)
EH4A Page 14 © Churchill Maths Limited
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Q17
A
C
Y
B
X45°
17. Diagram NOTaccurately drawn
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)
EH4A Page 15 © Churchill Maths Limited
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Q18
Q19
18. Solve the simultaneous equations
3x + 2y = 112x − 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)
EH4A Page 16 © Churchill Maths Limited
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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)
EH4A Page 17 © Churchill Maths Limited
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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)
EH4A Page 18 © Churchill Maths Limited
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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)
23. Diagram NOTaccurately drawn
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)
EH4A Page 19 © Churchill Maths Limited
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Q24Amount 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)
EH4A Page 20 © Churchill Maths Limited
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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)
EH4A Page 21 © Churchill Maths Limited
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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
EH4A Page 22 © Churchill Maths Limited
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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
EH4A Page 23 © Churchill Maths Limited