# 4MA1 Mathematics A May/June 2019 Paper 1HR (Higher Tier Paper 1)

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

- Page: https://mathvsarham.com/past-papers/4ma1/2019-may-june-paper-1hr/
- PDF: https://mathvsarham.com/papers/4ma1/4MA1_may-june_2019_paper_1HR_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International GCSE
- Subject: 4MA1 Mathematics A (https://mathvsarham.com/past-papers/4ma1/)
- Session: May/June 2019
- 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
The diagram shows a cylinder.
[Diagram or table: see page 3 of the paper]
The cylinder has radius 8.2 cm and height 10 cm. The cylinder is empty.
Pam pours 1.5 litres of water into the cylinder.
Work out the depth of the water in the cylinder. Give your answer correct to 1 decimal place.
Answer: ____ cm [3]

Question 2
Each interior angle of a regular polygon is 162°
Work out the number of sides the polygon has.
Answer: ____ [3]

Question 3
E = {11, 12, 13, 14, 15, 16, 17, 18, 19, 20} A = {even numbers} B = {multiples of 3}
List the members of the set
(i) A ˆ B
Answer: ____
(ii) A ‰ B
Answer: ____
(iii) Aމ
Answer: ____ [3]

Question 4
Solve 4x x
Answer: x = ____ [2]

Question 5
(a) Write 720 as a product of its prime factors. Show your working clearly.
Answer: ____ [3]
(b) Find the smallest whole number that 720 can be multiplied by to give a square number.
Answer: ____ [1]

Question 6
Lorenzo increases all the prices on his restaurant menu by 8%
Before the increase, the price of a dessert was $4.25
(a) Work out the price of the dessert after the increase.
Answer: $ ____ [3]
After the increase, the price of lasagne is $9.45
(b) Work out the price of lasagne before the increase.
Answer: $ ____ [3]

Question 7
The diagram shows isosceles triangle ABC.
[Diagram or table: see page 8 of the paper]
AB = AC = 7.5 cm. The height of the triangle is 6 cm.
Calculate the area of the triangle.
Answer: ____ cm^2 [4]

Question 8
There are 10 people in a lift. These 10 people have a mean weight of 79.2 kg.
3 of these people get out of the lift. These 3 people have a mean weight of 68 kg.
Work out the mean weight of the 7 people left in the lift.
Answer: ____ kg [3]

Question 9
(a) Simplify t^9÷ t^3
Answer: ____ [1]
(b) Simplify w^5 q w^7
Answer: ____ [1]
(c) Simplify (5xy^2)^3
Answer: ____ [2]

Question 10
Change 22 metres per second to a speed in kilometres per hour. Show your working clearly.
Answer: ____ km/h [3]

Question 11
3 years ago, the ratio of Tom’s age to Clemmie’s age was 2 : 7 Tom is now 15 years old and Clemmie is now x years old.
Find the value of x.
Answer: x = ____ [3]

Question 12
[Diagram or table: see page 11 of the paper]
A box, in the shape of a cuboid, is going to be put on a table.
The whole of one face of the box will be in contact with the table. The force exerted by the box on the table is always 105 newtons.
The box is 5 m by 4 m by 3 m.
The greatest pressure exerted by the box on the table is P newtons/m^2 The least pressure exerted by the box on the table is Q newtons/m^2
Work out the value of PíQ
Answer: ____ [3]

Question 13
(a) On the Venn diagram, shade the set (A ‰ B މˆ C
[Diagram or table: see page 12 of the paper]
[1]
(b) Use set notation to describe the shaded region in the Venn diagram below.
[Diagram or table: see page 12 of the paper]
Answer: ____ [1]

Question 14
Each day that Barney goes to college, he either goes by bus or he walks. The probability that Barney will go to college by bus on any day is 0.3
When Barney goes to college by bus, the probability that he will be late is 0.2 When Barney walks to college, the probability that he will be late is 0.1
(a) Complete the probability tree diagram.
[Diagram or table: see page 13 of the paper]
Answer: ____
[Diagram or table: see page 13 of the paper]
Answer: ____
[Diagram or table: see page 13 of the paper]
Answer: ____
[Diagram or table: see page 13 of the paper]
Answer: ____
[2]
Barney will go to college on 200 days next year.
(b) Work out an estimate for the number of days Barney will be late for college next year.
Answer: ____ [4]

Question 15
The straight line L_1 has equation 2y = 6xí
The straight line L_2 is perpendicular to L_1 DQGSDVVHVWKURXJKWKHSRLQW í
Find an equation for L_2 Give your answer in the form ay + bx = c
Answer: ____ [4]

Question 16
A particle P is moving along a straight line. The fixed point O lies on this line.
At time t seconds, the displacement, s metres, of P from O is given by
[Diagram or table: see page 15 of the paper]
At time t seconds, the velocity of P is v m/s.
(a) Find an expression for v in terms of t.
Answer: v = ____ [2]
(b) Find the time at which the acceleration of the particle is 6 m/s^2
Answer: ____ _seconds [3]

Question 17
The histogram shows information about the ages of all the passengers travelling on a plane. No one on the plane is older than 80 years.
[Diagram or table: see page 16 of the paper]
24 passengers on the plane are aged between 40 years and 60 years.
(a) Work out the total number of passengers on the plane.
Answer: ____ [3]
A passenger on the plane is picked at random.
(b) Work out an estimate for the probability that this person is older than 55 years.
Answer: ____ [2]

Question 18
(a) Expand and simplify (x + 2)(2x + 3)(x – 7) Show your working clearly.
Answer: ____ [3]
(b) Make m the subject of p^2 = x + m/2m − y
Answer: ____ [3]

Question 19
The 25th term of an arithmetic series is 44.5 The sum of the first 30 terms of this arithmetic series is 765
Find the 16th term of the arithmetic series. Show your working clearly.
Answer: ____ [5]

Question 20
a = 25 q 10^14^n where n is an integer.
Find an expression, in terms of n, for a^3/2 Give your answer in standard form.
Answer: ____ [3]

Question 21
A curve has equation y = f(x)
There is only one maximum point on the curve. The coordinates of this maximum point are (4, 3)
(a) Write down the coordinates of the maximum point on the curve with equation
(i) y = f(x – 5)
Answer: ( ____ , ____ )
(ii) y = 3f(x)
Answer: ( ____ , ____ ) [2]
Here is the graph of y = a sin(bx)° for 0 - x - 360
[Diagram or table: see page 20 of the paper]
(b) Find the value of a and the value of b.
Answer: a = ____
Answer: b = ____ [2]

Question 22
Solve the simultaneous equations
[Diagram or table: see page 21 of the paper]
y = 2x + 1
Show clear algebraic working.
Answer: ____ [5]

Question 23
[Diagram or table: see page 22 of the paper]
B, C, D and F are points on a circle. ABC, AFD, BFE and CDE are straight lines.
Work out the size of angle x. Show your working clearly.
[Diagram or table: see page 22 of the paper]
Answer: x = ____ [4]

Question 24
[Diagram or table: see page 23 of the paper]
P is the point on AB such that AP : PB = 3 : 1 Q is the point on AC such that OQP is a straight line.
Use a vector method to find AQ : QC Show your working clearly.
Answer: AQ : QC = ____ [5]

Question 25
A boat sails from point X to point Y and then to point Z.
Y is on a bearing of 280° from X. Z is on a bearing of 220° from Y.
The distance from X to Y is 3.5 km. The distance from Y to Z is 6 km.
Work out the bearing of Z from X. Give your answer correct to 1 decimal place.
[Diagram or table: see page 24 of the paper]
Answer: ____ [5]