# 4MA1 Mathematics A January 2021 Paper 2HR (Higher Tier Paper 2)

Pearson Edexcel International GCSE 4MA1 Mathematics A past paper 2HR, Higher Tier Paper 2, January 2021. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/4ma1/2021-january-paper-2hr/
- PDF: https://mathvsarham.com/papers/4ma1/4MA1_january_2021_paper_2HR_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International GCSE
- Subject: 4MA1 Mathematics A (https://mathvsarham.com/past-papers/4ma1/)
- Session: January 2021
- Paper: 2HR (Higher Tier Paper 2)
- Component code: 4MA1/2HR
- Time allowed: 120 minutes
- Total marks: 100
- Pages: 24

## Question paper text

Extracted automatically from the PDF; diagrams are missing and notation may be imperfect.

Question 1
w = 5y^2– y^3
(a) Work out the value of w when y = –2
Answer: w = ____ [2]
(b) Factorise fully 8p^2– 2p
Answer: ____ [2]
(c) Expand 4t(3t – 2)
Answer: ____ [2]
(d) Expand and simplify (5x – 2)(x + 4)
Answer: ____ [2]

Question 2
The diagram shows a rectangle ABCD and a semicircle with diameter AB where AB = 12 cm. The point E lies on DC and also on the semicircle.
[Diagram or table: see page 4 of the paper]
Work out the area of the shaded region. Give your answer correct to 3 significant figures.
Answer: ____ cm^2 [3]

Question 3
E = {21, 22, 23, 24, 25, 26, 27, 28, 29, 30} A = {22, 24, 26, 28, 30} B = {21, 24, 27, 30}
(a) List the members of the set
(i) A ∩ B
Answer: ____
(ii) Aʹ
Answer: ____ [2]
C = {23, 25, 29}
(b) Using set notation, find an expression for C in terms of A and B.
Answer: ____ [1]

Question 4
(a) Simplify (3k^2)^4
Answer: ____ [2]
(b) Simplify (21m^4 n) ÷ (3n^–5)
Answer: ____ [2]

Question 5
Here is a shape P drawn on a grid of squares.
[Diagram or table: see page 6 of the paper]
(a) On the grid, rotate shape P 180° about the point (–3, 2) Label the new shape Q. [2]
(b) On the grid, translate shape P by the vector 10/ 8 
Label the new shape R. [1]
Here are triangle T and triangle U drawn on a grid of squares.
[Diagram or table: see page 7 of the paper]
(c) Describe fully the single transformation that maps triangle T onto triangle U.
Answer: ____ [3]

Question 6
On Wednesday, the price of 1 litre of petrol was £1.26 The price of petrol on Wednesday was 5% more than the price of petrol on the previous Monday.
Calculate the price of 30 litres of petrol on the previous Monday.
Answer: £ ____ [3]

Question 7
The shaded region R, shown in the diagram below, is bounded by the straight line with equation y = 3x – 2 and by two other straight lines.
Write down the three inequalities that define region R.
[Diagram or table: see page 8 of the paper]
Answer: ____ [3]

Question 8
The table gives the length of the coastline, in kilometres, of each of five oceans.
[Diagram or table: see page 9 of the paper]
(a) Which ocean has the greatest length of coastline?
Answer: ____ [1]
(b) Calculate the difference between the length of the Atlantic Ocean’s coastline and the length of the Southern Ocean’s coastline. Give your answer in standard form.
Answer: ____ km [2]

Question 9
Solve x^2– 21x + 20 = 0 Show your working clearly.
Answer: ____ [3]

Question 10
A mathematics teacher at a school asked a group of students how far, in kilometres, each student had travelled to get to school that day.
The table gives information about their answers.
[Diagram or table: see page 10 of the paper]
The teacher calculated that an estimate for the mean distance travelled by the whole group of students was 4.25 km.
Work out the value of x. Show your working clearly.
Answer: x = ____ [4]

Question 11
A circle centre O has radius 9 cm.
[Diagram or table: see page 11 of the paper]
Calculate the perimeter of the shaded sector of the circle. Give your answer correct to 3 significant figures.
Answer: ____ cm [4]

Question 12
Solve the simultaneous equations 2x + 7y = 17
Show clear algebraic working.
Answer: x = ____
Answer: y = ____ [4]

Question 13
The diagram shows two hot air balloons. A is a point on the base of one of the balloons and B is a point on the base of the other balloon.
[Diagram or table: see page 12 of the paper]
The distance between A and B is 500 metres. The angle of depression of B from A is 23°
Calculate the vertical height of A above B. Give your answer correct to one decimal place.
Answer: ____ _metres [3]

Question 14
Simon bought a house at the beginning of 2018 The value of Simon’s house had decreased by 15% by the end of 2018
The house increased in value during both 2019 and 2020 The percentage increases in the value of the house during 2019 and 2020 were the same.
The value of Simon’s house at the end of 2020 was 2.85% greater than the amount he paid for his house at the beginning of 2018
Calculate the percentage increase in the value of the house during 2019
Answer: ____ % [4]

Question 15
Prove algebraically that the product of any two odd numbers is always an odd number. [4]

Question 16
Two events A and B are such that n(A) = 62 n(B) = 30 and n(A ∪ B) = 68
Given that n(E ) = 80
(a) complete the Venn diagram to show the number of elements in each region.
[Diagram or table: see page 15 of the paper]
Answer: ____
Answer: ____ [2]
An element is chosen at random from E.
(b) Using the Venn diagram, find the probability that this element is in
(i) A ∩ B
Answer: ____ [1]
(ii) A ∪ Bʹ
Answer: ____ [2]

Question 17
The functions f and g are defined as
f(x) = x^2+ 6 g(x) = x – 10
(a) Find fg(3)
Answer: ____ [2]
(b) Solve the equation fg(x) = f(x) Show clear algebraic working.
Answer: ____ [3]
The function h is defined as
[Diagram or table: see page 16 of the paper]
(c) State the value of x that cannot be included in the domain of h
Answer: ____ [1]
(d) Express the inverse function h^–1 in the form h^–1(x) = ...
Answer: h^–1(x) = ____ [3]

Question 18
Solve the equation
[Diagram or table: see page 17 of the paper]
Show clear algebraic working.
Answer: ____ [5]

Question 19
(a) Simplify 8^2 ×^3 4^6 Give your answer in the form 2^a where a is an integer. Show each stage of your working clearly.
Answer: ____ [3]
Given that n^/^5^4// =  1/ 2 where n > 0
[Diagram or table: see page 18 of the paper]
(b) find the value of n.
Answer: n = ____ [4]

Question 20
A, B and C are points on a circle with centre O.
[Diagram or table: see page 19 of the paper]
Angle ABC = 75°
The area of the shaded segment is 200 cm^2
Calculate the radius of the circle. Give your answer correct to 3 significant figures.
Answer: ____ cm [5]

Question 21
A bag contains n beads. 6 of the beads are red and the rest are blue.
Ravi is going to take at random 2 beads from the bag.
The probability that the 2 beads will be of the same colour is 9/17
Using algebra, and showing each stage of your working, calculate the value of n.
Answer: n = ____ [6]

Question 22
ABC is an isosceles triangle in a horizontal plane. The point T is vertically above B.
[Diagram or table: see page 22 of the paper]
Angle ABC = 140° AB = BC = 8 cm TB = 10 cm M is the midpoint of AC.
Calculate the size of the angle between MT and the horizontal plane ABC. Give your answer correct to one decimal place.
[Diagram or table: see page 23 of the paper]
Answer: ____ [4]