# 4MA1 Mathematics A May/June 2022 Paper 1H (Higher Tier Paper 1)

Pearson Edexcel International GCSE 4MA1 Mathematics A past paper 1H, Higher Tier Paper 1, May/June 2022. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/4ma1/2022-may-june-paper-1h/
- PDF: https://mathvsarham.com/papers/4ma1/4MA1_may-june_2022_paper_1H_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International GCSE
- Subject: 4MA1 Mathematics A (https://mathvsarham.com/past-papers/4ma1/)
- Session: May/June 2022
- Paper: 1H (Higher Tier Paper 1)
- Component code: 4MA1/1H
- 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
Here are the first five terms of an arithmetic sequence.
[Diagram or table: see page 3 of the paper]
(a) Find an expression, in terms of n, for the nth term of this sequence.
Answer: ____ [2]
The nth term of another arithmetic sequence is 3n + 5
(b) Find an expression, in terms of m, for the (2m)th term of this sequence.
Answer: ____ [1]

Question 2
Here is a biased 4-sided spinner.
[Diagram or table: see page 4 of the paper]
The table gives the probabilities that, when the spinner is spun once, it will land on 1 or it will land on 3
[Diagram or table: see page 4 of the paper]
The probability that the spinner will land on 2 is equal to the probability that the spinner will land on 4
Ravina is going to spin the spinner a number of times.
Ravina works out that an estimate for the number of times the spinner will land on 3 is 45
Work out an estimate for the number of times the spinner will land on 4
Answer: ____ [4]

Question 3
(a) Find the highest common factor (HCF) of 56 and 84 Show your working clearly.
Answer: ____ [2]
(b) Find the lowest common multiple (LCM) of 60 and 72 Show your working clearly.
Answer: ____ [2]

Question 4
The diagram shows parts of three regular polygons, A, B and C, meeting at a point.
[Diagram or table: see page 6 of the paper]
Polygon B has n sides.
Work out the value of n.
Answer: n = ____ [4]

Question 5
(a) Expand and simplify (n − 6)(n + 4)
Answer: ____ [2]
(b) Solve 2x − 3 = 3x − 5/4
Show clear algebraic working.
Answer: x = ____ [3]

Question 6
Asha bought an apartment.
The table gives information about the value of apartments, in euros, and the annual service charge band.
Value (x euros) Service charge band
[Diagram or table: see page 8 of the paper]
0 < x < 400 000 E
In 2021, the value of Asha’s apartment was 634 400 euros.
The value of Asha’s apartment had increased by 4% from its value in 2020
(a) Has the annual service charge band changed for Asha’s apartment? Show your working clearly. [3]
Pam bought a boat.
In each year after Pam bought the boat, the value of the boat depreciated by 15%
(b) Work out the total percentage by which the value of the boat had depreciated by the end of the second year after Pam bought the boat.
Answer: ____ _% [3]

Question 7
A cylinder is placed on the ground.
[Diagram or table: see page 9 of the paper]
The height of the cylinder is 18 cm.
The force exerted by the cylinder on the ground is 72 newtons. The pressure on the ground due to the cylinder is 1.4 newtons / cm^2
force
[Diagram or table: see page 9 of the paper]
Work out the volume of the cylinder. Give your answer correct to 3 significant figures.
Answer: ____ _cm^3 [4]

Question 8
(a) Write 0.000 089 in standard form.
Answer: ____ [1]
(b) Write 8.34 × 10^4 as an ordinary number.
Answer: ____ [1]

Question 9
(a) Simplify 8 × (4t)^0
Answer: ____ [1]
x^6÷ x^−5 = x ^p
(b) Find the value of p
Answer: p = ____ [1]
(c) Simplify fully (2k^2 m^4)^3
Answer: ____ [2]

Question 10
Two circles, C_1 and C_2 , are drawn on a centimetre grid, with a scale of 1 cm for 1 unit on each axis.
The centre of circle C_1 is at the point with coordinates (–1, 3) and the radius of C_1 is 13 cm.
The centre of circle C_2 is at the point with coordinates (7, 18) and the radius of C_2 is 6 cm.
(a) Work out the distance between the centre of C_1 and the centre of C_2
Answer: ____ _cm [3]
(b) Explain why circle C_1 intersects circle C_2
Answer: ____ [1]

Question 11
(a) Factorise 9x^2 − 4y^2
Answer: ____ [2]
(b) Express 7/8 − x + 3/4x as a single fraction in its simplest form.
Answer: ____ [3]

Question 12
Rudolf goes to the gym.
The probability that he will use the treadmill is 0.8
When he uses the treadmill, the probability that he will use the cross trainer is 0.3 When he does not use the treadmill, the probability that he will use the cross trainer is 0.6
(a) Complete the probability tree diagram for this information.
[Diagram or table: see page 13 of the paper]
Answer: ____
[Diagram or table: see page 13 of the paper]
Answer: ____
Answer: ____ does not use
[Diagram or table: see page 13 of the paper]
Answer: ____
[Diagram or table: see page 13 of the paper]
Answer: ____ does not use
[2]
(b) Work out the probability that Rudolf uses both the treadmill and the cross trainer.
Answer: ____ [2]

Question 13
Antoine is going on holiday. He makes 3 separate payments to cover the total cost of his holiday.
The following table shows how much money Antoine pays to the holiday company.
[Diagram or table: see page 14 of the paper]
Payment 1 3/8 of the total cost
Payment 2 45% of the total cost
Payment 3 $406
Work out how much Antoine has to pay for Payment 2
Answer: $ ____ [5]

Question 14
The function f is defined as
[Diagram or table: see page 15 of the paper]
(a) Find f(10)
Answer: ____ [1]
(b) Express the inverse function f^−1 in the form f^−1 : x  …
Answer: f^−1 : x  ____ [3]

Question 15
Abraham is going to play a computer game. Abraham can win the game, draw the game or lose the game.
For any game that Abraham plays
the probability that he wins the game is 0.3 the probability that he draws the game is 0.5 the probability that he loses the game is 0.2
When Abraham wins a game, he scores +10 points. When Abraham draws a game, he scores 0 points. When Abraham loses a game, he scores −5 points.
Abraham plays 3 games and the points he scores in each of the 3 games are added together to get his total score.
Work out the probability that when he has played 3 games his total score is 0 points.
Answer: ____ [4]

Question 16
Without using a calculator, show that 12/2 − 1 − ( 2 = 2 32 + 12
Show your working clearly. [3]

Question 17
A particle P moves along a straight line. The fixed point O lies on this line.
The displacement of P from O at time t seconds, t  1, is s metres where
[Diagram or table: see page 18 of the paper]
The velocity of P at time t seconds, t  1, is v m / s
Work out the distance of P from O at the instant when v = 0
Answer: ____ _m [5]

Question 18
Here is triangle ABC
[Diagram or table: see page 19 of the paper]
Work out the value of x Give your answer correct to 3 significant figures.
Answer: x = ____ [5]

Question 19
[Diagram or table: see page 20 of the paper]
OAB is a sector S of a circle with centre O and radius (r + 7) metres. Angle AOB = 45°
A circle C has radius (r − 2) metres.
The area of sector S is twice the area of circle C
Find the value of r Show your working clearly.
[Diagram or table: see page 21 of the paper]
Answer: r = ____ [5]

Question 20
The diagram shows a sketch of part of the curve with equation y = f (x)
[Diagram or table: see page 21 of the paper]
There is one maximum point on this curve. The coordinates of this maximum point are (s, t)
Find, in terms of s and t, the coordinates of the maximum point on the curve with equation
(i) y = f (x − 2)
Answer: ( ____ , ____ ) [1]
(ii) y = 3f (x)
Answer: ( ____ , ____ ) [1]

Question 21
The histogram shows information about the total time, m minutes, taken by each child in a school to walk to school every day for one week.
[Diagram or table: see page 22 of the paper]
There are no children for whom m > 100 There are 10 children for whom m  20
Work out an estimate for the number of children for whom 50 < m  80
Answer: ____ [3]

Question 22
A solid is made from a cone and a hemisphere.
[Diagram or table: see page 23 of the paper]
The circular plane face of the hemisphere coincides with the circular base of the cone. The radius of the hemisphere and the radius of the circular base of the cone are both 20 cm.
The curved surface area of the cone is 580π cm^2
The volume of the solid is kπ cm^3
Work out the exact value of k
Answer: k = ____ [5]

Question 23
A polygon has n sides, where n > 5
When arranged in order of size, starting with the largest number, the sizes of the interior angles of the polygon, in degrees, are the terms of an arithmetic sequence.
Here are the first five terms of this sequence.
[Diagram or table: see page 24 of the paper]
Find the value of n Show clear algebraic working.
Answer: n = ____ [6]

Question 24
Express each of a, b and c in terms of q so that
[Diagram or table: see page 26 of the paper]
can be written as a − b (x − c)^2
Answer: a = ____
Answer: b = ____
Answer: c = ____ [4]