# 4MA1 Mathematics A January 2019 Paper 1HR (Higher Tier Paper 1)

Pearson Edexcel International GCSE 4MA1 Mathematics A past paper 1HR, Higher Tier Paper 1, January 2019. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/4ma1/2019-january-paper-1hr/
- PDF: https://mathvsarham.com/papers/4ma1/4MA1_january_2019_paper_1HR_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International GCSE
- Subject: 4MA1 Mathematics A (https://mathvsarham.com/past-papers/4ma1/)
- Session: January 2019
- 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
Show that 1 2/3 + 2 3/4 = 4 5/12 [3]

Question 2
There are 60 children in a club.
In the club, the ratio of the number of girls to the number of boys is 3 : 1
3
[Diagram or table: see page 4 of the paper]
What fraction of the 60 children play a musical instrument? [4]

Question 3
[Diagram or table: see page 5 of the paper]
S is the point on PR such that angle RSQ = 90° RQ = 14 cm RS = 10 cm SP = 5 cm
Work out the length of PQ.
[Diagram or table: see page 5 of the paper]
[4]

Question 4
a, a, b and 40 are four numbers.
a is the least number. 40 is the greatest number.
The range of the four numbers is 14 The median of the four numbers is 30
Work out the value of a and the value of b.
[Diagram or table: see page 6 of the paper]
[3]

Question 5
The Shanghai Maglev Train takes 8 minutes to travel a distance of 30.5 kilometres.
Work out the average speed of the train. Give your answer in kilometres per hour.
[Diagram or table: see page 7 of the paper]
[3]

Question 6
The diagram shows the triangle PQR.
[Diagram or table: see page 8 of the paper]
In the diagram, all the angles are in degrees.
RP = RQ
Find the value of y. Show clear algebraic working.
[Diagram or table: see page 8 of the paper]
[4]

Question 8
Solve the simultaneous equations
[Diagram or table: see page 10 of the paper]
Show clear algebraic working.
[Diagram or table: see page 10 of the paper]
[3]

Question 9
N = 480 ´ 10^9
(a) Write N as a number in standard form. [1]
(b) Write N as a product of powers of its prime factors. Show your working clearly. [3]
(c) Find the largest factor of N that is an odd number. [1]
[Diagram or table: see page 13 of the paper]
The boys and the girls have some coins.
The mean number of coins that the boys have is 5.5 The girls have a total of 18 coins.
Work out the mean number of coins the 20 children have.
[Diagram or table: see page 14 of the paper]
The numerators of the fractions form the sequence of whole numbers 1 2 3 4 … The denominators of the fractions form the sequence of odd numbers 1 3 5 7 …
(a) Write down an expression, in terms of n, for the nth term of this sequence of fractions. [2]
(b) Using algebra, prove that when the square of any odd number is divided by 4 the remainder is 1 [3]
[Diagram or table: see page 15 of the paper]
(a) Find dy/dx
[Diagram or table: see page 15 of the paper]
[2]
The curve C has two turning points.
(b) Work out the x coordinates of the two turning points. Show your working clearly. [3]
(c) Show that the x-axis is a tangent to the curve C. [2]
[Diagram or table: see page 16 of the paper]
euros, of 120 apartments in 2015
[Diagram or table: see page 16 of the paper]
(a) Find an estimate for the number of these apartments with a value of 80 thousand euros or less in 2015 [1]
The table gives information about the values, in thousands of euros, of the same 120 apartments in 2018
[Diagram or table: see page 17 of the paper]
(b) On the grid opposite, draw a cumulative frequency diagram for this information. [2]
(c) Find an estimate for the increase in the median value for these apartments from 2015 to 2018
[Diagram or table: see page 17 of the paper]
[2]
[Diagram or table: see page 18 of the paper]
[2]
(b) Expand and simplify 4n(n – 3)(n + 5) [2]
(c) Factorise 4c^2– 9d^2 [1]
(d) Simplify fully_2
[Diagram or table: see page 18 of the paper]
[3]
[Diagram or table: see page 19 of the paper]
7 of the beads are red. 3 of the beads are green. 2 of the beads are yellow.
Lucy takes at random a bead from the bag and keeps it. Then Julian takes at random a bead from the bag.
(a) Work out the probability that they each take a yellow bead. [2]
(b) Work out the probability that the beads they take are not the same colour. [3]
(b) Show that the ratio
[Diagram or table: see page 21 of the paper]
is the same as the ratio
[Diagram or table: see page 21 of the paper]
[3]
[Diagram or table: see page 21 of the paper]
Show your working clearly.
[Diagram or table: see page 22 of the paper]
B, C, D and E are points on a circle.
AB is the tangent at B to the circle. AB is parallel to ED. Angle ABE = 73°
Work out the size of angle DCE. Give a reason for each stage of your working.
[Diagram or table: see page 22 of the paper]
[Diagram or table: see page 23 of the paper]
M is the midpoint of the edge GH.
Find the size of the angle between the line MA and the plane ABCD. Give your answer correct to 1 decimal place.
[Diagram or table: see page 23 of the paper]
[Diagram or table: see page 24 of the paper]
The perimeter of the triangle is k cm.
Given that x = y − 1 find the value of k. Show your working clearly.
[Diagram or table: see page 24 of the paper]
[Diagram or table: see page 25 of the paper]
ABX and DCX are straight lines. → → AB = a BC = b → Find EX in terms of a and b. Give your answer in its simplest form.
[Diagram or table: see page 26 of the paper]
(a) Find the value of p for which f^−1(p) = k
[Diagram or table: see page 26 of the paper]
[3]
The function g is defined as g(x) = x^2 for x > 0
(b) Given that gf(a) = k for k > 1 find an expression for a in terms of k.
[Diagram or table: see page 26 of the paper]
[3]