4MA1 Mathematics A: January 2020 Paper 1HHigher Tier Paper 1
4MA1/1H
Pearson Edexcel International GCSE Mathematics A, January 2020, Higher Tier Paper 1.
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Pearson Edexcel International GCSE 4MA1 Mathematics A past paper 1H, Higher Tier Paper 1, January 2020. 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 4MA1/1H January 2020 paper so it reads well on any screen. Diagrams and tables are shown from the original.
- 1
The point A has coordinates (5, −4) The point B has coordinates (13, 1)
(a)Work out the coordinates of the midpoint of AB.
( , )[2]
Line L has equation y = 2 − 3x
(b)Write down the gradient of line L.
[1]
Line L has equation y = 2 − 3x
(c)Does the point with coordinates (100, −302) lie on line L? You must give a reason for your answer.
[1]
- 2
Find the lowest common multiple (LCM) of 28 and 105
[2]
- 3
The diagram shows a shape.
Loading diagram…From page 5 of the paper. The shape has area 129 cm2
Work out the value of x.
x = [4]
- 4
The table shows information about the weights, in kilograms, of 40 babies.
Loading diagram…From page 6 of the paper. (a)Write down the modal class.
[1]
(b)Work out an estimate for the mean weight of the 40 babies.
kg[4]
One of the 40 babies is going to be chosen at random.
(c)Find the probability that this baby has a weight of more than 5 kg.
[2]
- 5
120 children go on an activity holiday. The ratio of the number of girls to the number of boys is 3 : 5
On Sunday, all the children either go sailing or go climbing.
1625 of the boys go climbing.
Twice as many girls go sailing as go climbing.
Work out how many children go sailing on Sunday.
[6]
- 6
(a)Write 7.8 × 10−4 as an ordinary number.
[1]
(b)Work out 5.6 × 102.8 × 10−3
Give your answer in standard form.
[2]
- 7
(a)Expand and simplify (m − 8)(m + 5)
[2]
(b)Factorise fully 5y + 20y2
[2]
(c)Simplify ( p2 + 3)0
[1]
(d)Solve 3(2x − 5) = 9 − x2
Show clear algebraic working.
x = [4]
- 8
y
Loading diagram…From page 10 of the paper. On the grid, enlarge the shaded shape with scale factor 12 and centre (1, 2)[2]
- 9
Here is a right-angled triangle.
Loading diagram…From page 11 of the paper. Calculate the length of PQ. Give your answer correct to 3 significant figures.
cm[3]
- 10
The shaded region in the diagram is bounded by three lines. The equation of one of the lines is given.
Loading diagram…From page 12 of the paper. Write down the three inequalities that define the shaded region.
[3]
- 11
Max invests $6000 in a savings account for 3 years. The account pays compound interest at a rate of 1.5% per year for the first 2 years.
The compound interest rate changes for the third year. At the end of 3 years, there is a total of $6311.16 in the account.
Work out the compound interest rate for the third year. Give your answer correct to 1 decimal place.
%[3]
- 12
A total of 80 men and women took part in a race. The cumulative frequency graph gives information about the times, in minutes, they took for the race.
Loading diagram…From page 14 of the paper. (a)Use the graph to find an estimate for the interquartile range.
minutes[2]
60% of the men took 50 minutes or less for the race. No women took 50 minutes or less for the race.
(b)Work out an estimate for the number of men who took part in the race.
[3]
- 13
The diagram shows a solid cube. The cube is placed on a table so that the whole of one face of the cube is in contact with the table.
Loading diagram…From page 16 of the paper. w cm accurately drawn
Loading diagram…From page 16 of the paper. The cube exerts a force of 56 newtons on the table. The pressure on the table due to the cube is 0.14 newtons/cm2
Loading diagram…From page 16 of the paper. Work out the volume of the cube.
cm3[4]
- 14
The diagram shows parallelogram EFGH.
Loading diagram…From page 17 of the paper. EF = 9.3 cm FG = 14.7 cm Angle EFG = 106°
(a)Work out the area of the parallelogram. Give your answer correct to 3 significant figures.
cm2[2]
(b)Work out the length of the diagonal EG of the parallelogram. Give your answer correct to 3 significant figures.
cm[3]
- 15Loading diagram…
From page 18 of the paper. The diagram shows a cuboid of volume V cm3
(a)Show that V = 15 + 16x − x2 − 2x3[3]
There is a value of x for which the volume of the cuboid is a maximum.
(b)Find this value of x. Show your working clearly. Give your answer correct to 3 significant figures.
x = [5]
Loading diagram…From page 20 of the paper. - 16
P =
a = 58.4 correct to 3 significant figures. c = 20 correct to 2 significant figures. d = 3.6 correct to 2 significant figures.
Work out the upper bound for the value of P. Show your working clearly. Give your answer correct to 2 decimal places.
[3]
- 17
(a)Show that 6 + 2 12 = 12 7 + 4 3
Show each stage of your working.[3]
(b)Simplify fully 27a
Loading diagram…From page 21 of the paper. [3]
- 18
There are 16 sweets in a bowl.
4 of the sweets are blackcurrant. 5 of the sweets are lemon. 7 of the sweets are orange.
Anna, Ravi and Sam each take at random one sweet from the bowl.
Work out the probability that the 5 lemon sweets are still in the bowl.
[4]
- 19
The diagram shows a cuboid ABCDEFGH.
Loading diagram…From page 23 of the paper. EH = 9 cm, HG = 5 cm and GB = 6 cm.
Work out the size of the angle between AH and the plane EFGH. Give your answer correct to 3 significant figures.
Loading diagram…From page 23 of the paper. [4]
- 20
The curve C has equation y = 4(x − 1)2 − a where a > 4
Using the axes below, sketch the curve C. On your sketch show clearly, in terms of a,
(i)the coordinates of any points of intersection of C with the coordinate axes,
(ii)the coordinates of the turning point.
Loading diagram…From page 24 of the paper. [4]
- 21
The functions f and g are such that
Loading diagram…From page 25 of the paper. The function h is such that h(x) = fg(x) for x −2
Express the inverse function h−1(x) in the form h−1(x) = …
h−1(x) = [5]
- 22
Triangle HJK is isosceles with HJ = HK and JK = 80
H is the point with coordinates (−4, 1) J is the point with coordinates ( j, 15) where j < 0 K is the point with coordinates (6, k)
M is the midpoint of JK. The gradient of HM is 2
Find the value of j and the value of k.
j =
k = [6]