GCSE Mathematics
Practice Paper 2023
Bonus Paper
Higher Tier
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Answer ALL questions.
Write your answers in the spaces provided.
You must write down all the stages of your working.
1.
Work out
54.6 × 4.3
………………………..
(3 marks)
2.
100 adults were asked how they keep fit.
Each adult goes to the gym, runs or cycles.
45 of these adults are female.
30 of the 52 adults who go to the gym are female.
35 adults run.
9 males cycle.
How many females run?
………………………..
(3 marks)
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3.
The table shows information about the heights, in cm, of a group of year 8 girls.
This stem and leaf diagram shows some information about the heights, in cm, of a
group of 15 year 10 boys.
Compare the distribution of the heights of the girls with the distribution of the
heights of the boys.
………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………
(3 marks)
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4.
The diagram represents a solid made from seven centimetre cubes.
On the centimetre grid, draw a plan of the solid.
(2 marks)
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5.
The diagram shows the positions of three points, A, B and C, on a map.
The bearing of B from A is 070𝑜
Angle ABC is 50𝑜
AB = CB
Work out the bearing of C from A.
……………………………..…..……… o
(3 marks)
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6.
20 men, 10 women and 10 children are in a competition.
The mean score for the women is 15.6
The mean score for the children is 9.2
Jennifer says that the mean score for all 40 people is 11.2
(a) Work out the mean score for the men
……………………………..…..………
(3 marks)
Jennifer was wrong.
The mean score for all 40 people was actually 11.15
(b) How does this affect the mean score for the men?
…………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………
(1 mark)
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7.
When a biased 6-sided dice is thrown, the probability that it will land on 4 is 0.65
The biased dice is thrown twice.
Write down two things that are wrong with the probability diagram.
1 ………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………
2 ………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………
(2 marks)
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8.
ABCDEFGH is a regular octagon.
ADJ is a straight line.
Angle BAD = angle CDA
Show that angle CDJ = 135𝑜
(4 marks)
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9.
Maria has to cover 3 tanks completely with paint.
Each tank is in the shape of a cylinder with a top and a
bottom. The tank has a diameter of 1.6m and a height
of 1.8m.
Maria has 7 tins of paint.
Each tin of paint covers 5𝑚2
Has Maria got enough paint to cover completely the 3
tanks?
You must show how you get your answer.
.
(5 marks)
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10.
The pie charts give information about the ages, in years, of people living in two
towns, Adley and Bridford.
The ratio of the number of people living in Adley to the number of people living in
Bridford is given by the ratio of the areas of the pie charts.
What proportion of the total number of people living in these two towns live in
Adley and are aged 0 – 19?
Give your answer correct to 3 significant figures.
……………………………………….
(3 marks)
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11.
Jack bought a new boat for £12 500
The value, £V, of Jack's boat at the end of n years is given by the formula
𝑉 = 12500 × (0.85)𝑛
(a) At the end of how many years was the value of Jack's boat first less than 50% of
the value of the boat when it was new?
……………………………………….
(2 marks)
A savings account pays interest at a rate of R% per year.
Jack invests £5500 in the account for one year.
At the end of the year, Jack pays tax on the interest at a rate of 40%.
After paying tax, he gets £79.20
(b) Work out the value of R.
……………………………………….
(3 marks)
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12.
In London, 1 litre of petrol costs 108.9p
In New York, 1 US gallon of petrol costs $2.83
1 US gallon = 3.785 litres
£1 = $1.46
In which city is petrol better value for money, London or New York?
You must show your working.
………………………………………..
(3 marks)
13.
The diagram shows a prism placed on a horizontal floor.
The prism has height 3 m
The volume of the prism is 18 𝑚3
The pressure on the floor due to the prism is 75 newtons/𝑚2
Work out the force exerted by the prism on the floor.
…………………………………… newtons
(3 marks)
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14.
The box plot shows information about the length of time, in minutes, some people
waited to see a doctor at a hospital on Monday.
(a) Work out the interquartile range of the information in the box plot.
………………………………………..
(2 marks)
Becky says, "50% of the people waited for at least 2 hours."
(b) Is Becky correct? Explain why.
....................................................................................................................................
....................................................................................................................................
....................................................................................................................................
(1 mark)
The table gives information about the length of time, in minutes, some people
waited to see a doctor at the same hospital on Tuesday.
Becky was asked to compare the distribution of the lengths of times people waited
on Monday with the distribution of the lengths of times people waited on Tuesday.
She wrote, "People had to wait longer on Tuesday than on Monday."
(c) Give one reason why Becky may be wrong.
....................................................................................................................................
....................................................................................................................................
....................................................................................................................................
(1 mark)
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15.
√5(√8 + √18) can be written in the form 𝑎√10 where a is an integer.
Find the value of a.
a = ……………………………………..
(3 marks)
16.
The diagram shows a solid shape.
The shape is a cone on top of a hemisphere.
The height of the cone is 10 cm.
The base of the cone has a diameter of 6 cm.
The hemisphere has a diameter of 6 cm.
The total volume of the shape is kπ cm3, where k is an integer.
Work out the value of k.
k = ……………………………..………
(4 marks)
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17.
In the diagram ABC and DEFG are parallel lines.
Angle ABE = x°
EB = EF
1
Show that 𝑤 = 90 + 𝑥
2
Give a reason for each stage of your working.
(4 marks)
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18.
(a) Write 2x2 + 16x + 35 in the form a(x + b)2 + c where a, b, and c are integers.
……………………….…………………..
(3 marks)
(b) Hence, or otherwise, write down the coordinates of the turning point of the
graph of y = 2x2 + 16x + 35
……………………….…………………..
(1 mark)
19.
Here is the graph of y = sin x° for −180 ≤ x ≤ 180
On the grid, sketch the graph of y = sin x° − 2 for −180 ≤ x ≤ 180
(2 marks)
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20.
The diagram shows a right-angled triangle.
All the measurements are in centimetres.
The area of the triangle is 27.5 cm2
Work out the length of the shortest side of the triangle.
You must show all your working.
……………………….………………….. cm
(4 marks)
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21.
The diagram shows a pyramid with base ABC.
CD is perpendicular to both CA and CB.
Angle CBD = 34°
Angle ADB = 45°
Angle DBA = 60°
BC = 20 cm.
Calculate the size of the angle between the line AD and the plane ABC.
Give your answer correct to 1 decimal place.
……………………….………………….. o
(5 marks)
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22.
S is a geometric sequence.
(a) Given that (√𝑥 − 1), 1 and (√𝑥 + 1), are the first three terms of S, find the
value of x.
You must show all your working.
……………………….…………………..
(3 marks)
(b) Show that the 5th term of S is 7 + 5√2
(2 marks)
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23.
Solve algebraically the simultaneous equations
2x2 − y2 = 17
x + 2y = 1
(5 marks)
End of Paper
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