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

Pearson Edexcel International GCSE 4MA1 Mathematics A past paper 1HR, 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-1hr/
- PDF: https://mathvsarham.com/papers/4ma1/4MA1_may-june_2022_paper_1HR_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International GCSE
- Subject: 4MA1 Mathematics A (https://mathvsarham.com/past-papers/4ma1/)
- Session: May/June 2022
- 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
Here is a biased spinner.
[Diagram or table: see page 3 of the paper]
When the spinner is spun once, the probabilities that it lands on red or on yellow or on green are given in the table.
[Diagram or table: see page 3 of the paper]
(a) Work out the probability that the spinner lands on red or on yellow.
Answer: ____ [1]
Yang is going to spin the spinner 300 times.
(b) Work out an estimate for the number of times the spinner will land on purple.
Answer: ____ [3]

Question 2
In a warehouse there are two types of shelves, type R and type S.
These two types of shelves are arranged into shelving units that form a sequence of patterns.
Here are the first three terms in the sequence.
[Diagram or table: see page 4 of the paper]
The width of each type R shelf is 2.4 m and the width of each type S shelf is 3.5 m
(a) Work out the total width of a shelving unit that has 6 type R shelves.
Answer: ____ m [2]
A shelving unit has n type R shelves. The total width of this shelving unit is W metres.
(b) Find an expression for W in terms of n Give your answer in its simplest form.
Answer: W = ____ [2]

Question 3
Here are five cards.
Each card has a number written on it.
[Diagram or table: see page 5 of the paper]
The mean of the five numbers is 12
Work out the value of x
Answer: x = ____ [3]

Question 4
The language department of a college has 180 students. Each student studies exactly one of French, German, Italian or Spanish.
15 students study French. 45% of the students study German.
Express the percentage of students studying Italian or Spanish as a percentage of those studying French or German.
Answer: ____ % [4]

Question 5
(a) Expand 3c^3(c + 4)
Answer: ____ [2]
(b)(i) Factorise x^2+ 8x – 9
Answer: ____ [2]
(ii) Hence, solve x^2+ 8x –9 = 0
Answer: ____ [1]

Question 6
Show that 2 2/3 + 3 3/4 = 6 5/12 [3]

Question 7
The diagram shows a solid cylinder made from iron.
[Diagram or table: see page 9 of the paper]
The cylinder has diameter 18 cm and height 3.5 cm The mass of the cylinder is 7.04 kg
Work out the density of the iron. Give your answer in g/cm^3 correct to 2 significant figures.
Answer: ____ g/cm^3 [3]

Question 8
Jane bought a new car for $18 000 The car depreciates in value by 15% each year.
Work out the value of the car at the end of 4 years. Give your answer correct to the nearest $
Answer: $ ____ [3]

Question 9
Solve the inequality 3 – 4x  11
Answer: ____ [2]

Question 10
Line L is drawn on the grid.
[Diagram or table: see page 11 of the paper]
Find an equation for L Give your answer in the form y = mx + c
Answer: ____ [3]

Question 11
The diagram shows a quadrilateral ABCD
[Diagram or table: see page 12 of the paper]
In the diagram, ABC and DAC are right‑angled triangles.
[Diagram or table: see page 12 of the paper]
The area of quadrilateral ABCD is 31.5 cm^2
Work out the length of AD
[Diagram or table: see page 13 of the paper]
Answer: ____ cm [6]

Question 12
P = 3^3 × 5^2 × 7 Q = 3^2 × 5 × 7^2
(a) Write down the highest common factor (HCF) of P and Q
Answer: ____ [1]
P = 3^3 × 5^2 × 7 Q = 3^2 × 5 × 7^2
(b) Work out the value of P^3 × Q Give your answer in the form 3^x × 5^y × 7^z where x, y and z are positive integers.
Answer: ____ [2]

Question 13
Here is the number of runs scored by a baseball team in each of its 15 games this season.
The number of runs have been arranged in order of size.
[Diagram or table: see page 15 of the paper]
Work out the interquartile range of the number of runs.
Answer: ____ [2]

Question 14
Solve the simultaneous equations
[Diagram or table: see page 16 of the paper]
Show clear algebraic working.
Answer: x = ____
Answer: y = ____ [4]

Question 15
[Diagram or table: see page 17 of the paper]
P, Q, R and S are points on a circle with centre O
PS is a diameter of the circle.
Angle PQR = 136°
Work out the size of angle RPS
[Diagram or table: see page 17 of the paper]
Answer: ____ [3]

Question 16
(a) Expand and simplify (3x – 1)(x + 2)(3x + 1)
Answer: ____ [3]
(b) Simplify fully  2x/ /
[Diagram or table: see page 18 of the paper]
Answer: ____ [3]

Question 17
Here is a parallelogram PQRS, in which angle SPQ is acute.
[Diagram or table: see page 19 of the paper]
PQ = 6.1 cm PS = 3.8 cm
The area of the parallelogram is 18 cm^2
Work out the length of QS Give your answer correct to 3 significant figures.
Answer: ____ cm [5]

Question 18
The diagram shows a cube ABCDEFGH with sides of length 6 cm.
[Diagram or table: see page 20 of the paper]
T is the midpoint of AB and V is the midpoint of CH
Work out the distance from T to V in a straight line through the cube. Give your answer in the form a cm where a is an integer.
Answer: ____ cm [4]

Question 19
The histogram gives information about the height, h cm, of each tree in part of a forest.
Frequency density
[Diagram or table: see page 21 of the paper]
There are no trees for which h  200 and for which h > 800
The number of trees for which 300 < h  400 is 8 fewer than the number of trees for which 400 < h  500
Work out an estimate for the number of trees in this part of the forest that have a height greater than 500 cm.
Answer: ____ [3]

Question 20
The diagram shows two similar metal statues.
[Diagram or table: see page 22 of the paper]
The volume of statue B is 20% less than the volume of statue A
The surface area of statue B is k% less than the surface area of statue A
Work out the value of k Give your answer correct to 3 significant figures.
Answer: k = ____
3 + 8 [4]

Question 21
Express_2 in the form p + q where p and q are integers. 2 − 1
Show each stage of your working clearly.
Answer: ____ [4]

Question 22
The diagram shows a sketch of part of the curve with equation y = x^2– p/x where p is a
positive constant.
[Diagram or table: see page 24 of the paper]
For all values of p, the curve has exactly one turning point and this turning point is a minimum shown as the point T in the sketch.
For the curve where the x coordinate of T is –3
(a) find the value of p
Answer: p = ____ [4]
The line with equation y = k is a tangent to the curve with equation y = x^2– 16/x
(b) Find the value of k
Answer: k = ____ [3]

Question 23
(a) Express 2x^2– 12x + 3 in the form a(x + b)^2+ c where a, b and c are integers.
Answer: ____ [3]
The curve C has equation y = 2(x + 4)^2– 12(x + 4) + 3
The point M is the minimum point on C
(b) Find the coordinates of M
Answer: ( ____ , ____ ) [2]

Question 24
Elliot has x counters.
Each counter has one red face and one green face.
Elliot spreads all the counters out on a table and sees that the number of counters showing a red face is 5
Elliot then picks at random one of the counters and turns the counter over. He then picks at random a second counter and turns the counter over.
The probability that there are still 5 counters showing a red face is 19/32
Work out the value of x Show clear algebraic working.
Answer: x = ____ [5]

Question 25
The sum of the first 10 terms of an arithmetic series is 4 times the sum of the first 5 terms of the same series.
The 8th term of this series is 45
Find the first term of this series. Show clear algebraic working.
Answer: ____ [5]