# 4MA1 Mathematics A May/June 2023 Paper 1HR (Higher Tier Paper 1)

Pearson Edexcel International GCSE 4MA1 Mathematics A past paper 1HR, Higher Tier Paper 1, May/June 2023. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/4ma1/2023-may-june-paper-1hr/
- PDF: https://mathvsarham.com/papers/4ma1/4MA1_may-june_2023_paper_1HR_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International GCSE
- Subject: 4MA1 Mathematics A (https://mathvsarham.com/past-papers/4ma1/)
- Session: May/June 2023
- 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
Write 2250 as a product of powers of its prime factors. Show your working clearly.
Answer: ____ [3]

Question 2
Here is a Venn diagram.
E
[Diagram or table: see page 4 of the paper]
(a) Write down the numbers that are in the set
(i) A
Answer: ____ [1]
(ii) B ∪ C
Answer: ____ [1]
Dominic writes down 9 ∉ C
(b) Explain why Dominic is correct.
Answer: ____ [1]

Question 3
ABCD and EFGH are similar quadrilaterals.
[Diagram or table: see page 5 of the paper]
(a) Work out the length of GH
Answer: ____ _cm [2]
(b) Work out the length of BC
Answer: ____ _cm [2]

Question 4
The diagram shows a shape made up of three semicircles, enclosing a right‑angled triangle.
[Diagram or table: see page 6 of the paper]
AB, BC and CA are each the diameter of a semicircle.
BC = CA = 6 cm.
Work out the perimeter of the shape. Give your answer correct to one decimal place.
Answer: ____ _cm [5]

Question 5
Each time Evie plays a game against her computer, she will win or lose.
For each game, the probability that Evie will win is 0.74 Evie is going to play 300 games against her computer.
Work out an estimate for the number of games that Evie will lose.
Answer: ____ [2]

Question 6
(a) Simplify m^10÷ m^3
Answer: ____ [1]
k ^n × k^4= k^12
(b) Write down the value of n
Answer: n = ____ [1]
(c) Simplify (3x^6 y^8)^2
Answer: ____ [2]

Question 7
(a) Expand 4x(x – 5)
Answer: ____ [1]
(b) Factorise y^2– 9y + 20
Answer: ____ [2]

Question 8
(a) Write 5.6 × 10^–3 as an ordinary number.
Answer: ____ [1]
(b) Work out 6  10/2.1  10__4__5
Give your answer in standard form.
Answer: ____ [2]

Question 9
Kazi buys a car for 700 000 taka. The value of the car depreciates by 12% each year.
Work out the value of the car at the end of 3 years. Give your answer correct to the nearest taka.
Answer: ____ _taka [3]

Question 10
[Diagram or table: see page 10 of the paper]
On the grid, enlarge the shaded shape with scale factor 1/3 and centre (1, 7) [2]

Question 11
The diagram shows a block of iron in the shape of a cuboid.
[Diagram or table: see page 11 of the paper]
The block has length w cm, width 5 cm and height 4 cm
The density of iron is 7.8 g / cm^3 The mass of the block is 1950 g
Work out the value of w
Answer: w = ____ [3]

Question 12
Moeen has a biased 6‑sided dice.
The table gives information about the probability that, when the dice is thrown, it will land on each number.
[Diagram or table: see page 12 of the paper]
(a) Show that x + y = 0.19 [2]
Given that 3x – y = 0.09
and x + y = 0.19
(b) work out the value of x and the value of y Show clear algebraic working.
Answer: x = ____
Answer: y = ____ [3]

Question 13
Novak is going to play two games of tennis.
The probability that he wins the first game is 0.7
If he wins the first game, the probability that he wins the second game is 0.9 If he loses the first game, the probability that he wins the second game is 0.4
(a) Complete the probability tree diagram.
[Diagram or table: see page 13 of the paper]
Answer: ____
[Diagram or table: see page 13 of the paper]
Answer: ____
[1]
(b) Work out the probability that Novak wins both games of tennis.
Answer: ____ [2]

Question 14
The table gives information about the times taken by 80 people to run a race.
Time taken (t minutes) Frequency
[Diagram or table: see page 14 of the paper]
(a) Complete the cumulative frequency table.
Time taken (t minutes) Cumulative frequency
[Diagram or table: see page 14 of the paper]
[1]
(b) On the grid below, draw a cumulative frequency graph for your table.
[Diagram or table: see page 15 of the paper]
[2]
(c) Use your graph to find an estimate for the median time taken.
Answer: ____ _minutes [1]
(d) Use your graph to find an estimate for the interquartile range of the times taken.
Answer: ____ _minutes [2]

Question 15
[Diagram or table: see page 16 of the paper]
BCDEFG is a hexagon. AB, BC and CD are three sides of a regular n‑sided polygon.
Calculate the value of n Show your working clearly.
Answer: n = ____
[Diagram or table: see page 17 of the paper]
[4]

Question 16
Use algebra to show that 00.17. 1766 == 35/198 [2]

Question 17
F is inversely proportional to the square of r
F = 36 when r = 4
(a) Find a formula for F in terms of r
Answer: ____ [3]
(b) Work out the value of F when r = 48
Answer: ____ [1]

Question 18
Diego builds a fence using fence panels.
The total length of the fence is 50 metres, correct to the nearest 5 metres. The length of each fence panel is 1.3 metres, correct to the nearest 10 cm.
The cost of each fence panel is £8.65
Diego may only buy complete fence panels. Diego only pays for the number of panels he needs to build the fence.
Work out the greatest difference in the possible amounts that Diego could pay to build the fence. Show your working clearly.
Answer: £ ____ [4]

Question 19
The diagram shows a triangle ABC where A, B and C represent the positions of three towns.
C
[Diagram or table: see page 19 of the paper]
Pru travels directly from A to B and then directly from B to C
Yang travels directly from A to C
Given that the values for AB and BC are in kilometres,
work out how much further Pru travels than Yang travels. Give your answer in km, correct to one decimal place.
Answer: ____ _km [5]

Question 20
Curve C has equation y = f (x) The graph of curve C has one maximum point. The coordinates of this maximum point are (3, 5)
(a) Write down the coordinates of the maximum point on the curve with equation
(i) y = 2f (x)
Answer: ( ____ , ____ ) [1]
(ii) y = f (x) – 7
Answer: ( ____ , ____ ) [1]
(iii) y = f (–x)
Answer: ( ____ , ____ ) [1]
Curve L has equation y = x^2+ 7x + 20
 2  Curve L is transformed to curve S under the translation   0  
(b) Find an equation for S Give your answer in the form y = ax^2+ bx + c
Answer: y = ____ [4]

Question 21
The curve T has equation y = x^3– 2x^2– 9x + 15
(a) Find dy/dx
Answer: dy/dx = ____ [2]
(b) Find the range of values of x for which T has a positive gradient. Give your values correct to 3 significant figures. Show your working clearly.
Answer: ____ [4]

Question 22
Some people attend a concert. The histogram shows information about the ages of these people.
[Diagram or table: see page 22 of the paper]
Work out an estimate for the percentage of these people who are aged more than 55 years. Give your answer correct to one decimal place.
Answer: ____ % [4]

Question 23
Simplify  x^2  4   4x/  7x  2 /x  2x
[Diagram or table: see page 24 of the paper]
Give your answer in the form where a, b and c are integers.
[Diagram or table: see page 24 of the paper]
Answer: ____ [4]

Question 24
Given that
[Diagram or table: see page 25 of the paper]
find an expression for x in terms of n State any restrictions on n
Answer: ____ [5]

Question 25
Here is a triangle ABC
[Diagram or table: see page 26 of the paper]
(2x + 1) cm
[Diagram or table: see page 26 of the paper]
The area of the triangle is (x^2+ x – 3.75) cm^2
Find the size of the largest angle in triangle ABC Give your answer correct to the nearest degree.
[Diagram or table: see page 27 of the paper]
Answer: ____ [6]