4MA1 Mathematics A: January 2019 Paper 2HHigher Tier Paper 2
4MA1/2H
Pearson Edexcel International GCSE Mathematics A, January 2019, Higher Tier Paper 2.
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Pearson Edexcel International GCSE 4MA1 Mathematics A past paper 2H, Higher Tier Paper 2, January 2019. Open it online or download the question paper PDF free.
Sit this paper like the real exam
2 h · 100 marks
Questions
Rebuilt from the 4MA1/2H January 2019 paper so it reads well on any screen. Diagrams and tables are shown from the original.
- 1
A plane has a length of 73 metres.
A scale model is made of the plane. The scale of the model is 1 : 200
Work out the length of the scale model. Give your answer in centimetres.
Loading diagram…From page 3 of the paper. [3]
- 2
Here are the first five terms of an arithmetic sequence.
Loading diagram…From page 3 of the paper. Write down an expression, in terms of n, for the nth term of this sequence.[2]
- 3
There are 90 counters in a bag. Each counter in the bag is either red or blue so that
Loading diagram…From page 4 of the paper. Li is going to put some more red counters in the bag so that
Loading diagram…From page 4 of the paper. Work out the number of red counters that Li is going to put in the bag.[4]
- 4
E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} A = {odd numbers} A ∩ B = {1, 3} A ∪ B = {1, 2, 3, 4, 5, 6, 7, 9, 11, 12}
Draw a Venn diagram to show this information.
Loading diagram…From page 5 of the paper. [4]
- 5
Calvin has 12 identical rectangular tiles. He arranges the tiles to fit exactly round the edge of a shaded rectangle, as shown in the diagram below.
Loading diagram…From page 6 of the paper. Work out the area of the shaded rectangle.
Loading diagram…From page 6 of the paper. [5]
- 6
(a)Find the highest common factor (HCF) of 96 and 120[2]
C = 3 ´ 52
(b)Find the lowest common multiple (LCM) of A, B and C.[2]
- 7
Jenny invests $8500 for 3 years in a savings account. She gets 2.3% per year compound interest.
(a)How much money will Jenny have in her savings account at the end of 3 years? Give your answer correct to the nearest dollar.
Loading diagram…From page 8 of the paper. [3]
Rami bought a house on 1st January 2015
In 2015, the house increased in value by 15% In 2016, the house decreased in value by 8%
On 1st January 2017, the value of the house was $687 700
(b)What was the value of the house on 1st January 2015?
Loading diagram…From page 8 of the paper. [3]
- 8
A block of wood has a mass of 3.5 kg. The wood has density 0.65 kg/m3
(a)Work out the volume of the block of wood. Give your answer correct to 3 significant figures.
Loading diagram…From page 9 of the paper. [3]
(b)Change a speed of 630 kilometres per hour to a speed in metres per second.
Loading diagram…From page 9 of the paper. [3]
- 9
Solve the simultaneous equations
Loading diagram…From page 10 of the paper. [3]
- 11
Twenty students took a Science test and a Maths test.
Both tests were marked out of 50
The table gives information about their results.
Loading diagram…From page 12 of the paper. Use this information to compare the Science test results with the Maths test results. Write down two comparisons.
Loading diagram…From page 12 of the paper. [2]
- 12
(a)Simplify n0[1]
(b)Simplify (3x2 y5)3[2]
(c)Factorise fully 2e2– 18[2]
(d)Make r the subject of m = 6a + r5r[4]
- 13
The frequency table gives information about the numbers of mice in some nests.
Number of mice Frequency
Loading diagram…From page 14 of the paper. The mean number of mice in a nest is 7
Work out the value of x.
Loading diagram…From page 14 of the paper. [4]
- 14
Marcus plays two games of tennis. For each game, the probability that Marcus wins is 0.35
(a)Complete the probability tree diagram.
First game Second game
Loading diagram…From page 15 of the paper. [2]
(b)Work out the probability that Marcus wins at least one of the two games of tennis.[3]
- 15
The diagram shows a trapezium.
Loading diagram…From page 16 of the paper. All measurements shown on the diagram are in centimetres.
The area of the trapezium is 133 cm2
(a)Show that 8x2– 6x – 275 = 0[3]
(b)Find the value of x. Show your working clearly.
Loading diagram…From page 16 of the paper. [3]
- 16
The diagram shows two mathematically similar vases, A and B.
Loading diagram…From page 17 of the paper. A has a volume of 405 cm3 B has a volume of 960 cm3
B has a surface area of 928 cm2
Work out the surface area of A.
Loading diagram…From page 17 of the paper. [3]
- 17
f is the function such that f(x) = 4 – 3x
(a)Work out f(5)[1]
g is the function such that g(x) = 11 − 2x
(b)Find the value of x that cannot be included in any domain of g[1]
(c)Work out fg(−1.5)[2]
Loading diagram…From page 19 of the paper. - 18
P =
x = 8 correct to 1 significant figure a = 4.6 correct to 2 significant figures m = 20 correct to the nearest 10
Calculate the lower bound of P. Show your working clearly.[4]
- 19
The histogram shows information about the numbers of minutes some people waited to be served at a Post Office.
Loading diagram…From page 20 of the paper. Work out an estimate for the proportion of these people who waited longer than 20 minutes to be served.[3]
- 20Loading diagram…
From page 21 of the paper. A, B, C and D are points on a circle. PCQ is a tangent to the circle. AB = CB.
Angle BCQ = x°
Prove that angle CDA = 2x° Give reasons for each stage in your working.[5]
- 21
Line L has equation 4y – 6x = 33 Line M goes through the point A (5, 6) and the point B (−4, k)
L is perpendicular to M.
Work out the value of k.[4]
- 22
The diagram shows a cone.
Loading diagram…From page 23 of the paper. AB is a diameter of the cone. V is the vertex of the cone.
Given that
Loading diagram…From page 23 of the paper. work out the size of angle AVB. Give your answer correct to 1 decimal place.
Loading diagram…From page 23 of the paper. [6]
- 23
ABCD is a trapezium.
Loading diagram…From page 24 of the paper. DA = −2 DB = −1
Find the exact magnitude of BC[5]