# 4MA1 Mathematics A January 2020 Paper 1HR (Higher Tier Paper 1)

Pearson Edexcel International GCSE 4MA1 Mathematics A past paper 1HR, Higher Tier Paper 1, January 2020. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/4ma1/2020-january-paper-1hr/
- PDF: https://mathvsarham.com/papers/4ma1/4MA1_january_2020_paper_1HR_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International GCSE
- Subject: 4MA1 Mathematics A (https://mathvsarham.com/past-papers/4ma1/)
- Session: January 2020
- Paper: 1HR (Higher Tier Paper 1)
- Component code: 4MA1/1HR
- 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
Brendon, Asha and Julie share some money in the ratios 3 : 2 : 6 The total amount of money that Asha and Julie receive is $36
Work out the amount of money that Brendon receives.
Answer: $ ____ [3]

Question 2
Show that 3 1/5 × 2 5/8 = 8 2/5 [3]

Question 3
(a) Make a the subject of d = g + 2ac
Answer: ____ [2]
(b) Factorise fully 9ef − 12f
Answer: ____ [2]
(c) Expand and simplify (x + 2)(x − 5)
Answer: ____ [2]
(d) Simplify fully × n/n_5
Answer: ____ [2]

Question 4
B = {b, l, u, e}
G = {g, r, e, y}
W = {w, h, i, t, e}
(a) List all the members of the set
(i) B ∪ G
Answer: ____
(ii) W ∩ G′
Answer: ____ [2]
Serena writes down the statement B ∩ G ∩ W = ∅
(b) Is Serena’s statement correct? You must give a reason for your answer.
Answer: ____ [1]

Question 5
The diagram shows Yuen’s garden.
[Diagram or table: see page 6 of the paper]
The garden is in the shape of a semicircle of radius 7.2 m. Yuen is going to cover his garden with grass seed.
Yuen has 12 boxes of grass seed. Each box of grass seed contains enough seed to cover 6 m^2 of the garden.
Has Yuen enough grass seed for his garden? Show your working clearly. [3]

Question 6
Solve x^2 − 5x − 36 = 0 Show clear algebraic working.
Answer: ____ [3]

Question 7
In a sale, the normal price of a hat is reduced by 15% The sale price of the hat is 20.40 euros.
Work out the normal price of the hat.
Answer: ____ _euros [3]

Question 8
5 children are playing on a trampoline. The mean weight of the 5 children is 28 kg.
2 of the children get off the trampoline. The mean weight of these 2 children is 26.5 kg.
Work out the mean weight of the 3 children who remain on the trampoline.
Answer: ____ _kg [3]

Question 9
Pablo made a solid gold statue.
He melted down some gold blocks and used the gold to make the statue. Each block of gold was a cuboid, as shown below.
[Diagram or table: see page 9 of the paper]
The mass of the statue is 5.73 kg. The density of gold is 19.32 g/cm^3
Work out the least number of gold blocks Pablo melted down in order to make the statue. Show your working clearly.
Answer: ____ [5]

Question 10
The diagram shows a regular hexagon, ABCDEF, and an isosceles triangle, GHJ.
[Diagram or table: see page 10 of the paper]
The perimeter of the hexagon is equal to the perimeter of the triangle.
Find the length of each side of the hexagon. Show clear algebraic working.
Answer: ____ _cm [5]

Question 11
The weight of a cat is 4.3 kg correct to 2 significant figures.
(a) Write down the upper bound of the weight of the cat.
Answer: ____ _kg [1]
(b) Write down the lower bound of the weight of the cat.
Answer: ____ _kg [1]
G = e − f
e = 17 correct to the nearest integer f = 9.4 correct to one decimal place
(c) Work out the upper bound for the value of G.
Answer: ____ [2]

Question 12
The cumulative frequency graph gives information about the waiting times, in minutes, of people with appointments at Hospital A.
[Diagram or table: see page 12 of the paper]
(a) Use the graph to find an estimate of the median waiting time at Hospital A.
Answer: ____ _minutes [1]
(b) Use the graph to find an estimate of the interquartile range of the waiting times at Hospital A.
Answer: ____ _minutes [2]
At a different hospital, Hospital B, the median waiting time is 28 minutes and the interquartile range of the waiting times is 19 minutes.
(c) Compare the waiting times at Hospital A with the waiting times at Hospital B.
Answer: ____ [2]
[Diagram or table: see page 13 of the paper]

Question 13
(a) Use algebra to show that 0.572 = 63/110 [2]
Given that y is a prime number,
(b) express 3/2 − in the form a + b/c − y where a, b and c are integers.
[Diagram or table: see page 13 of the paper]
Answer: ____ [2]

Question 14
[Diagram or table: see page 14 of the paper]
A, B and C are points on a circle, centre O. Angle ABC = 38°
Work out the size of angle OAC. Give a reason for each stage of your working.
[Diagram or table: see page 14 of the paper]
Answer: ____ [4]

Question 15
The diagram shows two right-angled triangles, DEF and EFG.
[Diagram or table: see page 15 of the paper]
Work out the length of EG. Give your answer correct to 3 significant figures.
Answer: ____ _cm [4]

Question 16
Steffi is going to play one game of tennis and one game of chess.
The probability that she will win the game of tennis is 0.6 The probability that she will win both games is 0.42
Work out the probability that she will not win either game.
Answer: ____ [4]

Question 17
The function f is such that f(x) = (x − 4)^2 for all values of x.
(a) Find f(1)
Answer: ____ [1]
(b) State the range of the function f.
Answer: ____ [1]
The function g is such that g(x) = 4/x + 3 x ≠ −3
(c) Work out fg(2)
Answer: ____ [2]

Question 18
The diagram shows the graph of y = f(x) for −4  x  12
[Diagram or table: see page 18 of the paper]
The point P on the curve has x coordinate 2
(a)(i) Use the graph to find an estimate for the gradient of the curve at P.
Answer: ____ [3]
(ii) Hence find an equation of the tangent to the curve at P. Give your answer in the form y = mx + c
Answer: ____ [2]
The equation f(x) = k has exactly two different solutions for −4  x  12
(b) Use the graph to find the two possible values of k.
Answer: ____ _, ____ [2]

Question 19
Frequency density
[Diagram or table: see page 19 of the paper]
The histogram gives information about the heights of all the Year 11 students at a school.
There are 160 students in Year 11 with a height between 155 cm and 170 cm.
Work out the total number of students in Year 11 at the school.
Answer: ____ [4]

Question 20
The diagram shows a frustum of a cone and a sphere.
The frustum is made by removing a small cone from a large cone. The cones are similar.
[Diagram or table: see page 20 of the paper]
The height of the small cone is h cm. The height of the large cone is 2h cm. The radius of the base of the large cone is r cm.
The radius of the sphere is r cm.
Given that the volume of the frustum is equal to the volume of the sphere,
find an expression for r in terms of h. Give your expression in its simplest form.
Answer: r = ____ [5]

Question 21
The diagram shows the prism ABCDEF with cross section triangle ABC.
[Diagram or table: see page 22 of the paper]
Angle BEC = 40° and angle ACB is obtuse. AC = 6 cm and CE = 13 cm
The area of triangle ABC is 22 cm^2
Calculate the length of AB. Give your answer correct to one decimal place.
Answer: ____ _cm [6]

Question 22
The graph of y = a cos(x + b)° for 0  x  360 is drawn on the grid. y 3
2
1
[Diagram or table: see page 23 of the paper]
(a) Find the value of a and the value of b.
Answer: a = ____
Answer: b = ____ [2]
Another curve C has equation y = f(x) The coordinates of the minimum point of C are (4, 5)
(b) Write down the coordinates of the minimum point of the curve with equation
(i) y = f(2x)
Answer: ( ____ , ____ )
(ii) y = f(x) − 7
Answer: ( ____ , ____ ) [2]

Question 23
A particle moves along a straight line. The fixed point O lies on this line. The displacement of the particle from O at time t seconds, t  0, is s metres where
[Diagram or table: see page 24 of the paper]
At time T seconds the velocity of P is V m/s where V  −5
Find an expression for T in terms of V.
Give your expression in the form where k and m are integers to be found.
[Diagram or table: see page 24 of the paper]
Answer: T = ____ [6]