# 4MA1 Mathematics A May/June 2022 Paper 2HR (Higher Tier Paper 2)

Pearson Edexcel International GCSE 4MA1 Mathematics A past paper 2HR, Higher Tier Paper 2, May/June 2022. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/4ma1/2022-may-june-paper-2hr/
- PDF: https://mathvsarham.com/papers/4ma1/4MA1_may-june_2022_paper_2HR_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International GCSE
- Subject: 4MA1 Mathematics A (https://mathvsarham.com/past-papers/4ma1/)
- Session: May/June 2022
- Paper: 2HR (Higher Tier Paper 2)
- Component code: 4MA1/2HR
- Time allowed: 120 minutes
- Total marks: 100
- Pages: 28

## Question paper text

Extracted automatically from the PDF; diagrams are missing and notation may be imperfect.

Question 1
[Diagram or table: see page 3 of the paper]
(a) Describe fully the single transformation that maps triangle A onto triangle B
Answer: ____ [3]
(b) On the grid above, translate triangle A by the vector −4/  
Label your triangle C [1]

Question 2
Write 1200 as a product of powers of its prime factors. Show your working clearly.
Answer: ____ [3]

Question 3
Alberto, Bill, Candela and Diana are four friends.
Here is some information about the height of each of these friends.
Alberto’s height is 158 cm. Bill’s height is 175 cm. Candela’s height is greater than Diana’s height.
The median height of these four friends is 160 cm. The range of the heights of these four friends is 21 cm.
Work out Candela’s height and Diana’s height.
Answer: Candela ____ cm
Answer: Diana ____ cm [3]

Question 4
E = {9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20} A = {multiples of 3} B = {odd numbers}
(a) List the members of the set
(i) A ∩ B
Answer: ____ [1]
(ii) A ∪ B
Answer: ____ [1]
(b) Is it true that 24 ∈ A?
Tick one of the boxes below.
Yes No
Give a reason for your answer.
Answer: ____ [1]
Set C has 4 members such that C ∩ B¢ = {10, 18}
(c) List the members of one possible set C
Answer: ____ [2]

Question 5
The diagram shows a shape made from a square ABCD and 4 identical semicircles.
[Diagram or table: see page 7 of the paper]
As shown in the diagram, the semicircles have AB, BC, CD and DA as diameters.
The area of the square is 36 cm^2
Calculate the total area of the shape. Give your answer correct to one decimal place.
Answer: ____ cm^2 [4]

Question 6
(a) Solve p = 3 p − 5/10
Show clear algebraic working.
Answer: p = ____ [3]
(b) Simplify a^0 where a > 0
Answer: ____ [1]
(c) Simplify fully
[Diagram or table: see page 8 of the paper]
Answer: ____ [2]
(d) Factorise fully 10c^3 d^2+ 15cd^4
Answer: ____ [2]
2^k_x

Question 7
[Diagram or table: see page 9 of the paper]
Find an expression for x in terms of k and n
Answer: x = ____ [2]

Question 8
A cinema increased the cost of an adult ticket by 12%
After the increase, the cost of an adult ticket was £18.20
Work out the cost of an adult ticket before the increase.
Answer: £ ____ [3]

Question 9
The table gives information about the population, correct to 2 significant figures, of each of five cities in 2018
[Diagram or table: see page 10 of the paper]
(a) Write 8.8 × 10^6 as an ordinary number.
Answer: ____ [1]
(b) Which of these cities had the least population in 2018?
Answer: ____ [1]
(c) Work out the difference between the population of Tokyo and the population of Ahmedabad in 2018 Give your answer in standard form correct to 2 significant figures.
Answer: ____ [2]

Question 10
The diagram shows triangle ABP inside the regular hexagon ABCDEF
[Diagram or table: see page 11 of the paper]
Work out the size of angle PAF Give your answer correct to 3 significant figures.
[Diagram or table: see page 11 of the paper]
Answer: ____ [5]

Question 11
The cumulative frequency table shows information about the ages of 60 people who went to a gym on Saturday.
[Diagram or table: see page 12 of the paper]
(a) On the grid, draw a cumulative frequency graph for the information in the table.
[Diagram or table: see page 12 of the paper]
[2]
(b) Use your graph to find an estimate for the median of the ages of these people.
Answer: ____ _years [1]
(c) Use your graph to find an estimate for the interquartile range of the ages of these people.
Answer: ____ _years [2]
(d) Use your graph to find an estimate for the number of these people who are older than 55 years.
Answer: ____ [2]

Question 12
[Diagram or table: see page 14 of the paper]
ACE and BCD are straight lines. AB is parallel to DE
Work out the value of x
Answer: x = ____ [3]

Question 13
The diagram shows a sector AOB of a circle with centre O
[Diagram or table: see page 15 of the paper]
Angle AOB = 67° OA = OB = 5.2 cm
Calculate the perimeter of the sector. Give your answer correct to 3 significant figures.
Answer: ____ cm [3]

Question 14
Ciara throws four fair six‑sided dice.
The faces of each dice are labelled with the numbers 1, 2, 3, 4, 5, 6
Work out the probability that at least one of the dice lands on an even number.
Answer: ____ [3]

Question 15
The diagram shows a kite ABCD
[Diagram or table: see page 17 of the paper]
Calculate the area of the kite. Give your answer correct to 3 significant figures.
Answer: ____ cm^2 [3]

Question 16
Here are nine graphs.
[Diagram or table: see page 18 of the paper]
Complete the table below with the letter of the graph that could represent each given equation. Write each answer on the dotted line.
[Diagram or table: see page 19 of the paper]
Answer: ____
[Diagram or table: see page 19 of the paper]
Answer: ____
[Diagram or table: see page 19 of the paper]
Answer: ____
[Diagram or table: see page 19 of the paper]
Answer: ____
[Diagram or table: see page 19 of the paper]
[3]

Question 17
Use algebra to show that 0.345 = 19/55 [2]

Question 18
Kaidan and Sonja went on two different car journeys.
For Kaidan’s journey distance = 80 km correct to the nearest 5 km time = 2.7 hours correct to 1 decimal place
For Sonja’s journey distance = 33 km correct to 2 significant figures time = 1 hour correct to the nearest 0.1 hour
Kaidan says, “My average speed could have been greater than Sonja’s average speed.”
By considering bounds, show that Kaidan is correct. Show your working clearly. [4]

Question 19
f(x) = x^2– 4
g(x) = 2x + 1
Solve fg(x) > 0 Show clear algebraic working.
Answer: ____ [4]

Question 20
The centre O of a circle has coordinates (4, 7)
The point A, on the circle, has coordinates (6, 11) and AOP is a diameter of the circle.
Find an equation of the tangent to the circle at the point P
Answer: ____ [4]

Question 21
Solve the simultaneous equations
[Diagram or table: see page 23 of the paper]
Show clear algebraic working.
Answer: ____ [5]

Question 22
The point A with coordinates (–3, 2) lies on the straight line with equation y = f(x)
(a) Find the coordinates of the image of the point A on the straight line with equation
(i) y = f(x) – 3
Answer: ( ____ , ____ ) [1]
(ii) y = f  x/ 2
[Diagram or table: see page 24 of the paper]
Answer: ( ____ , ____ ) [1]
Here is a sketch of part of the curve with equation y = g(x)
[Diagram or table: see page 24 of the paper]
The point B with coordinates ( p, q) lies on the curve.
(b) Find the coordinates of the image of the point B on the curve with equation
[Diagram or table: see page 24 of the paper]
where c is a constant.
Answer: ( ____ , ____ ) [2]
[Diagram or table: see page 25 of the paper]

Question 23
Express / x 20/− 36 − 2/x − 6 1/4 − x as a single fraction in its simplest form. _2  ×
Answer: ____ [3]

Question 24
The diagram shows a frustum of a cone, and a sphere.
The frustum, shown shaded in the diagram, is made by removing the small cone from the large cone. The small cone and the large cone are similar.
[Diagram or table: see page 26 of the paper]
The height of the small cone is h cm and the radius of the base of the small cone is r cm. The height of the large cone is kh cm and the radius of the base of the large cone is kr cm. The radius of the sphere is r cm.
The sphere is divided into two hemispheres, each of radius r cm.
Solid A is formed by joining one of the hemispheres to the frustum. The plane face of the hemisphere coincides with the upper plane face of the frustum, as shown in the diagram below.
Solid B is formed by joining the other hemisphere to the small cone that was removed from the large cone. The plane face of the hemisphere coincides with the plane face of the base of the small cone, as shown in the diagram below.
[Diagram or table: see page 26 of the paper]
The volume of solid A is 6 times the volume of solid B.
Given that k >^3 7
find an expression for h in terms of k and r
Answer: h = ____ [6]

Question 25
ABCD is a parallelogram and ADM is a straight line.
[Diagram or table: see page 28 of the paper]
AB = a BC = b DM = 1/2 b
K is the point on AB such that AK : AB = λ : 1 L is the point on CD such that CL : CD = μ : 1 KLM is a straight line.
Given that λ : μ = 1 : 2
use a vector method to find the value of λ and the value of μ
Answer: λ = ____
Answer: μ = ____ [5]