# 4MA1 Mathematics A Oct/Nov 2020 Paper 1HR (Higher Tier Paper 1)

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

- Page: https://mathvsarham.com/past-papers/4ma1/2020-oct-nov-paper-1hr/
- PDF: https://mathvsarham.com/papers/4ma1/4MA1_oct-nov_2020_paper_1HR_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International GCSE
- Subject: 4MA1 Mathematics A (https://mathvsarham.com/past-papers/4ma1/)
- Session: Oct/Nov 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
Show that 3 3/4 × 7/9 = 2 11/12 [3]

Question 2
Using ruler and compasses only, construct the bisector of angle ABC. You must show all your construction lines.
[Diagram or table: see page 3 of the paper]
[2]

Question 3
(a) Simplify h^7× h^2
Answer: ____ [1]
G = c^2– 4c
(b) Find the value of G when c = –5
Answer: G = ____ [2]
(c) Solve 5x − 3/4 = 2x + 3
Show clear algebraic working.
Answer: x = ____ [3]

Question 4
The table gives information about the length of time, in minutes, that each of 60 students took to travel to school on Monday.
[Diagram or table: see page 5 of the paper]
(a) Write down the modal class interval.
Answer: ____ [1]
(b) Work out an estimate for the mean length of time taken by these 60 students to travel to school on Monday. Give your answer correct to one decimal place.
Answer: ____ _minutes [4]

Question 5
In 2017, the population of a village was 7500 In 2019, the population of the village was 8265
(a) Work out the percentage increase in the population of the village from 2017 to 2019
Answer: ____ % [3]
In a sale, normal prices are reduced by 30% The sale price of a T‑shirt was 31.50 euros.
(b) Work out the normal price of the T‑shirt.
Answer: ____ _euros [3]

Question 6
Point A has coordinates (–3, 11) Point B has coordinates (47, b) The midpoint of AB has coordinates (a, –19)
Find the value of a and the value of b.
Answer: a = ____
Answer: b = ____ [2]

Question 7
Pedro drove from Toulouse to Montpellier in 2 hours 42 minutes. He drove at an average speed of 90 km/hour.
Janine drove from Toulouse to Montpellier along the same route as Pedro. The journey took her 3 hours.
Work out Janine’s average speed for the journey.
Answer: ____ _km/hour [4]

Question 8
Harold bought an antique clock for £1200 The clock increased in value by 8% per year.
Find the value of the clock exactly 3 years after Harold bought the clock. Give your answer correct to the nearest £.
Answer: £ ____ [3]

Question 9
A box is put on a horizontal table.
The face of the box in contact with the table is a square of side 1.5 metres. The pressure on the table due to the box is 34.8 newtons/m^2
Work out the force exerted by the box on the table. pressure =
[Diagram or table: see page 8 of the paper]
Answer: ____ _newtons [3]

Question 10
Alex makes 80 cakes to sell. He makes chocolate cakes, lemon cakes and fruit cakes where
[Diagram or table: see page 9 of the paper]
all of the chocolate cakes
3/4 of the lemon cakes
7/8 of the fruit cakes
The profit he makes on each cake he sells is shown in the table.
[Diagram or table: see page 9 of the paper]
Work out the total profit that Alex makes from the cakes he sells.
Answer: £ ____ [5]

Question 11
The frequency table gives information about the ages of the 80 people in a train carriage.
[Diagram or table: see page 10 of the paper]
(a) Complete the cumulative frequency table.
[Diagram or table: see page 10 of the paper]
[1]
(b) On the grid, draw a cumulative frequency graph for your table.
80
70
60
50
[Diagram or table: see page 11 of the paper]
[2]
(c) Use your graph to find an estimate for the median age of the people in the train carriage.
Answer: ____ _years [2]

Question 12
Solve the simultaneous equations
[Diagram or table: see page 12 of the paper]
Show clear algebraic working.
Answer: x = ____
Answer: y = ____ [4]

Question 13
The curve C has equation y = 5x^3– x^2– 6x + 4
(a) Find dy/dx
Answer: dy/dx = ____ [2]
There are two points on the curve C at which the gradient of the curve is 2
(b) Find the x coordinate of each of these two points. Show clear algebraic working.
Answer: ____ [4]

Question 14
Expand and simplify (4x + 1)(x – 3)(5x + 6)
Answer: ____ [3]

Question 15
[Diagram or table: see page 15 of the paper]
B, D, E and F are points on a circle. ABC is the tangent to the circle at B.
Angle EDF = 40° Angle FBC = 70°
Prove that the tangent ABC is parallel to EF. Give a reason for each stage of your working. [4]

Question 16
The functions f and g are defined as
[Diagram or table: see page 16 of the paper]
(a) Write down the value of x that must be excluded from any domain of g
Answer: ____ [1]
(b) Find gf(2.6)
Answer: ____ [2]
(c) Solve fg(x) = 2
Answer: x = ____ [3]
(d) Express the inverse function g^–1 in the form g^–1 : x  ...
Answer: g^–1 : x  ____ [3]

Question 17
The diagram shows a prism ABCDEFGH with a horizontal base.
[Diagram or table: see page 17 of the paper]
The base of the prism, EFGH, is a square of side 12 cm. Trapezium ADEF is a cross section of the prism where AF and DE are vertical edges.
DE = CH = 10 cm AD = BC = 15 cm
(a) Work out the size of the angle between CF and the base EFGH. Give your answer correct to one decimal place.
[Diagram or table: see page 17 of the paper]
Answer: ____ [3]
(b) Work out the length of BE. Give your answer correct to one decimal place.
Answer: ____ cm [3]

Question 18
In an arithmetic series, the 6th term is 39 In the same arithmetic series, the 19th term is 7.8
Work out the sum of the first 25 terms of the arithmetic series.
Answer: ____ [4]

Question 19
The diagram shows rectangle ABCD with rectangle EFGH cut out to form the shaded region.
[Diagram or table: see page 19 of the paper]
AD = 8.3 cm correct to one decimal place DC = 7.2 cm correct to one decimal place EH = 6.2 cm correct to one decimal place HG = 5.3 cm correct to one decimal place
Work out the upper bound of the area of the shaded region. Show your working clearly.
Answer: ____ _cm^2 [3]

Question 20
A curve has equation y = f(x) There is only one maximum point on the curve. The coordinates of this maximum point are (–3, 4)
Write down the coordinates of the maximum point on the curve with equation
(i) y = f(x) – 6
Answer: ( ____ , ____ )
(ii) y = f(2x)
Answer: ( ____ , ____ )
[Diagram or table: see page 21 of the paper]
[2]

Question 21
Given that M =_2
find the values of n for which M = 2
Answer: ____ [5]

Question 22
The diagram shows a regular octagon ABCDEFGH.
[Diagram or table: see page 22 of the paper]
Each side of the octagon has length 10 cm.
Find the area of the shaded region ACDEH. Give your answer correct to the nearest cm^2
Answer: ____ cm^2 [6]

Question 23
In a bag, there are only
[Diagram or table: see page 24 of the paper]
Jean is going to take at random two beads from the bag.
The probability that Jean will take two beads of the same colour is 3/8
Find the total number of beads in the bag. Show clear algebraic working.
Answer: ____ [4]