# 4MA1 Mathematics A January 2022 Paper 2H (Higher Tier Paper 2)

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

- Page: https://mathvsarham.com/past-papers/4ma1/2022-january-paper-2h/
- PDF: https://mathvsarham.com/papers/4ma1/4MA1_january_2022_paper_2H_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International GCSE
- Subject: 4MA1 Mathematics A (https://mathvsarham.com/past-papers/4ma1/)
- Session: January 2022
- Paper: 2H (Higher Tier Paper 2)
- Component code: 4MA1/2H
- 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
(a) Expand and simplify ( y + 4)(2 − y)
Answer: ____ [2]
(b) Factorise fully 15b^5 c − 35b^3 c^9
Answer: ____ [2]

Question 2
Show that 6 3/4 ÷ 2 4/7 = 2 5/8 [3]

Question 3
[Diagram or table: see page 5 of the paper]
Triangle ABC is similar to triangle PQR
[Diagram or table: see page 5 of the paper]
(a) Calculate the length of BC
Answer: ____ _cm [2]
(b) Write down an expression for y in terms of x
Answer: y = ____ [1]

Question 4
Each side of a regular octagon has a length of 18 mm, correct to the nearest 0.5 mm
[Diagram or table: see page 6 of the paper]
(a) Write down the lower bound of the length of each side of the octagon.
Answer: ____ _mm [1]
(b) Write down the upper bound of the length of each side of the octagon.
Answer: ____ _mm [1]

Question 5
The scale diagram shows the position on a map of a house, A
[Diagram or table: see page 7 of the paper]
House C is on a bearing of 110° from A The distance from A to C is 700 m
(a) Mark the position of C on the diagram with a cross (×) Label your cross C [3]
(b) Write the scale of the map in the form 1 : n
Answer: 1 : ____ [1]

Question 6
A bag contains only pink sweets, white sweets, green sweets and red sweets.
The table gives each of the probabilities that, when a sweet is taken at random from the bag, the sweet will be green or the sweet will be red.
[Diagram or table: see page 8 of the paper]
number of pink sweets : number of white sweets = 2 : 1
There are 28 red sweets in the bag.
Work out the number of white sweets in the bag.
Answer: ____ [5]

Question 7
Find the lowest common multiple (LCM) of 28, 42 and 63 Show your working clearly.
Answer: ____ [3]

Question 8
The table gives information about the average house price in England in 2018 and in 2019
[Diagram or table: see page 10 of the paper]
(a) Work out the percentage increase in the average house price from 2018 to 2019 Give your answer correct to one decimal place.
Answer: ____ _% [2]
The average house price in 2019 was 7.7% greater than the average house price in 2017
(b) Work out the average house price in 2017 Give your answer correct to 3 significant figures.
Answer: £ ____ [3]

Question 9
The frequency table gives information about the number of points scored by a player.
[Diagram or table: see page 11 of the paper]
The mean number of points scored is 2
Work out the value of x
Answer: x = ____ [4]

Question 10
Solve the simultaneous equations
[Diagram or table: see page 12 of the paper]
Show clear algebraic working.
Answer: x = ____
Answer: y = ____ [3]

Question 11
The diagram shows a regular 10-sided polygon, ABCDEFGHIJ
[Diagram or table: see page 13 of the paper]
Show that x = y [4]

Question 12
a = 6 × 10^40
Work out the value of a^3 Give your answer in standard form.
Answer: ____ [3]

Question 13
The shaded region in the diagram is bounded by three lines. The equation of one of the lines is given.
[Diagram or table: see page 15 of the paper]
Write down three inequalities that define the shaded region.
Answer: ____ [3]

Question 14
A zip wire is shown as the dashed line AC in the diagram.
[Diagram or table: see page 16 of the paper]
The zip wire is supported by two vertical posts AB and CD standing on horizontal ground.
[Diagram or table: see page 16 of the paper]
The zip wire makes an angle x with the horizontal, as shown in the diagram. The design of the zip wire requires the angle x to be at least 5°
Work out the least possible height of the post AB Give your answer correct to 3 significant figures.
Answer: ____ _m [3]

Question 15
Diyar recorded the distance, in kilometres, that he cycled each day for 11 days. Here are his results.
[Diagram or table: see page 17 of the paper]
Find the interquartile range of his results.
Answer: ____ _km [3]

Question 16
D, E, F and G are points on a circle, centre O
[Diagram or table: see page 18 of the paper]
EOG is a diameter of the circle.
Angle EGD = 42°
Calculate the size of angle DFG Give a reason for each stage of your working.
[Diagram or table: see page 18 of the paper]
Answer: Angle DFG = ____ [4]

Question 17
Show that 12/3 + 2
can be written in the form a + b where a and b are integers. [3]

Question 18
Prove that when the sum of the squares of any two consecutive odd numbers is divided by 8, the remainder is always 2 Show clear algebraic working. [3]

Question 19
[Diagram or table: see page 21 of the paper]
PTQ is a diameter of a circle. RTS is a chord of the circle.
[Diagram or table: see page 21 of the paper]
Calculate the radius of the circle.
Answer: ____ _cm [3]

Question 20
The histogram gives information about the heights, h cm, of some tomato plants.
Frequency density
[Diagram or table: see page 22 of the paper]
There are 12 tomato plants for which 75 < h  85 One of the tomato plants is selected at random.
Find an estimate for the probability that this tomato plant has a height greater than 82.5 cm
Answer: ____ [4]

Question 21
Part of the graph of y = 2x^2 − 4x − 1 is shown on the grid.
[Diagram or table: see page 23 of the paper]
(a) Use the graph to find estimates for the solutions of the equation 2x^2 − 4x − 1 = 0 Give your solutions correct to one decimal place.
Answer: ____ [2]
(b) By drawing a suitable straight line on the grid, find estimates for the solutions of the equation x^2 − x − 1 = 0 Show your working clearly. Give your solutions correct to one decimal place.
Answer: ____ [3]

Question 22
Here is a rectangle.
[Diagram or table: see page 24 of the paper]
Given that the area of the rectangle is less than 75 cm^2
find the range of possible values of x
Answer: ____ [5]

Question 23
The diagram shows triangle PQR
[Diagram or table: see page 25 of the paper]
Given that angle PQR is obtuse,
work out the area of triangle PQR Give your answer correct to 3 significant figures.
Answer: ____ _cm^2 [6]

Question 24
A particle P moves along a straight line that passes through the fixed point O
The displacement, x metres, of P from O at time t seconds, where t  0 , is given by
[Diagram or table: see page 26 of the paper]
The direction of motion of P reverses when P is at the point A on the line.
The acceleration of P at the instant when P is at A is a m /s^2
Find the value of a
Answer: a = ____ [5]

Question 25
The function g is defined as
[Diagram or table: see page 27 of the paper]
(a) Express the inverse function g^−1 in the form g^−1 : x  …
Answer: g^−1 : x  ____ [4]
(b) State the domain of g^−1
Answer: ____ [1]

Question 26
An arithmetic series has first term a and common difference d, where d is a prime number.
The sum of the first n terms of the series is S_n and
[Diagram or table: see page 28 of the paper]
S_2_m = 320
Find the value of d and the value of m Show clear algebraic working.
Answer: d = ____
Answer: m = ____ [5]