# 4MA1 Mathematics A May/June 2025 Paper 1HR (Higher Tier Paper 1)

Pearson Edexcel International GCSE 4MA1 Mathematics A past paper 1HR, Higher Tier Paper 1, May/June 2025. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/4ma1/2025-may-june-paper-1hr/
- PDF: https://mathvsarham.com/papers/4ma1/4MA1_may-june_2025_paper_1HR_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International GCSE
- Subject: 4MA1 Mathematics A (https://mathvsarham.com/past-papers/4ma1/)
- Session: May/June 2025
- Paper: 1HR (Higher Tier Paper 1)
- Component code: 4MA1/1HR
- 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
Find the lowest common multiple (LCM) of 45 and 70
Answer: ____ [2]

Question 2
The length of a ship is 142.8 m, correct to 1 decimal place.
(i) Write down the lower bound of the length of the ship.
Answer: ____ m [1]
(ii) Write down the upper bound of the length of the ship.
Answer: ____ m [1]

Question 3
Show that 2 1/4  15/7  3 6/7 [3]

Question 4
Here is a biased 5-sided spinner. When the spinner is spun, it can land on blue or on green or on purple or on red or on yellow.
[Diagram or table: see page 5 of the paper]
The table gives information about the probability of the spinner landing on each colour.
[Diagram or table: see page 5 of the paper]
Sophie spins the spinner once.
(a) Work out the probability that the spinner lands on blue or on green or on purple.
Answer: ____ [1]
Max spins the spinner 350 times.
(b) Work out an estimate for the number of times the spinner lands on red.
Answer: ____ [4]

Question 5
E  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
A  2, 4, 6, 8, 10, 12
B  3, 6, 9, 12
C  1, 3, 5, 7, 9, 11
(a) List the members of the set
(i) A ∪ B
Answer: ____
(ii) Bʹ
Answer: ____ [2]
E  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
A  2, 4, 6, 8, 10, 12
B  3, 6, 9, 12
C  1, 3, 5, 7, 9, 11
(b) Write a symbol from the box on each dotted line to make each of the following a true statement.
(i) Answer: A  C  ____
(ii) Answer: 13 ____ E [2]

Question 6
[Diagram or table: see page 7 of the paper]
(a) Write down the inequality shown on the number line.
Answer: ____ [2]
(b) Solve the inequality 7a  5  3a  28 Show clear algebraic working.
Answer: ____ [2]

Question 7
Change a speed of 50x metres per second to a speed in kilometres per hour.
Answer: ____ _km/h [3]

Question 8
(a) Simplify a^6 × a^10
Answer: ____ [1]
(b) Simplify c^30 ÷ c^12
Answer: ____ [1]
(c)(i) Factorise y^2  10 y  21
Answer: ____ [2]
(ii) Hence, solve y^2  10 y  21  0
Answer: ____ [1]

Question 9
The diagram shows triangle PQR
[Diagram or table: see page 9 of the paper]
Work out the length of QR Give your answer correct to 3 significant figures.
Answer: ____ _cm [3]

Question 10
The diagram shows two water containers. One is a cuboid and one is a cylinder.
[Diagram or table: see page 10 of the paper]
The cuboid measures 35 cm by 28 cm by 20 cm The surface of the water in the cuboid is 9 cm above the base of the cuboid.
The cylinder has a radius of 10 cm and a height of 33 cm The cylinder is completely full of water.
Izzy is going to pour all the water from the cylinder into the cuboid.
Show that the cuboid will not be completely full of water. [3]

Question 11
Zhou invests some money for 2 years. He invests $2500 with Bank A and $3000 with Bank B.
[Diagram or table: see page 11 of the paper]
4% per year compound interest for 2 years
Zhou receives more interest from Bank A than from Bank B.
How much more?
Answer: $ ____ [5]

Question 12
The table gives information about the ages of 80 people in a cinema.
Age (n years) Frequency
[Diagram or table: see page 12 of the paper]
(a) Complete the cumulative frequency table.
Age (n years) Cumulative frequency
[Diagram or table: see page 12 of the paper]
[1]
(b) On the grid below, draw a cumulative frequency graph for your table.
[Diagram or table: see page 13 of the paper]
[2]
(c) Use your graph to find an estimate for the percentage of the 80 people who are more than 46 years of age. Give your answer correct to the nearest whole number.
Answer: ____ % [3]

Question 13
Here are the numbers of eggs laid by some hens on each of 11 days in June.
[Diagram or table: see page 14 of the paper]
Work out the interquartile range of the numbers of eggs.
Answer: ____ [2]

Question 14
Work out 6.7  10^135  3  10^134
Give your answer in standard form.
Answer: ____ [2]

Question 15
(a) Solve 5a  8/3  2a  5/4  23
Show clear algebraic working.
[Diagram or table: see page 15 of the paper]
Answer: ____ [4]
(b) Express / / in the form cy where c and n are numbers to be found.
[Diagram or table: see page 15 of the paper]
Answer: ____ [2]
[Diagram or table: see page 16 of the paper]

Question 16
Use algebra to show that the recurring decimal 0. 612 = 101/165 [2]

Question 17
Prove that, for any three numbers which are consecutive multiples of 4, the difference between the square of the largest number and the square of the smallest number is always a multiple of 64
Show clear algebraic working. [3]

Question 18
F is inversely proportional to the cube of r
F = 6 when r = 2
(a) Find a formula for F in terms of r
Answer: ____ [3]
(b) Find the value of r when F = 3072
Answer: r = ____ [2]

Question 19
Kannika has 9 counters. There is a number on each counter.
[Diagram or table: see page 19 of the paper]
Kannika puts the 9 counters in a bag. She takes at random a counter from the bag and does not replace the counter. She then takes at random a second counter from the bag.
Work out the probability that the sum of the numbers on the two counters is less than 5
Answer: ____ [3]

Question 20
The diagram shows cuboid ABCDEFGH
[Diagram or table: see page 20 of the paper]
Calculate the length of BC Give your answer correct to 3 significant figures.
Answer: ____ cm [3]

Question 21
The curve with equation y = f(x) has one turning point. The coordinates of this turning point are (−6, 9)
(a) Write down the coordinates of the turning point on the curve with equation y = f (3x)
Answer: ( ____ , ____ ) [1]
The curve C with equation y = g(x) is transformed to give the curve S with equation y = g(x + a) + b
The point (4, −5) on C is mapped to the point (1, −16) on S
(b) Write down the value of a and the value of b
Answer: a = ____
Answer: b = ____ [2]

Question 22
Solve the simultaneous equations
[Diagram or table: see page 22 of the paper]
Show clear algebraic working.
Answer: ____ [5]

Question 23
[Diagram or table: see page 23 of the paper]
PTR and QTS are chords of a circle.
[Diagram or table: see page 23 of the paper]
Find an expression for y in terms of x
Answer: y = ____ [5]

Question 24
The first 3 terms of an arithmetic series are
[Diagram or table: see page 24 of the paper]
where x and y are constants.
The sum of the first 9 terms of the series is 216
Find the value of x and the value of y Show clear algebraic working.
Answer: x = ____
Answer: y = ____ [6]

Question 25
[Diagram or table: see page 26 of the paper]
BAC is a sector of a circle, centre A
BCD is a sector of a circle, centre C
Angle BAC = 40° Angle BCD = 130° Area of shaded segment = 28 cm^2
Find the length of the arc BD Give your answer correct to 3 significant figures.
Answer: ____ _cm [6]

Question 26
R, S and T are three similar vases.
[Diagram or table: see page 28 of the paper]
The volume of vase S is 72.8% more than the volume of vase R
The height of vase R is h cm The height of vase T is 6h cm
The surface area of vase S is A cm^2 The surface area of vase T is kA cm^2
Work out the value of k
Answer: k = ____ [4]