4MA1 Mathematics A: May/June 2018 Paper 2HHigher Tier Paper 2
4MA1/2H
Pearson Edexcel International GCSE Mathematics A, May/June 2018, Higher Tier Paper 2.
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Pearson Edexcel International GCSE 4MA1 Mathematics A past paper 2H, Higher Tier Paper 2, May/June 2018. 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 May/June 2018 paper so it reads well on any screen. Diagrams and tables are shown from the original.
- 1
(a)Make a the subject of the formula M = ac – bd
[2]
(b)Solve the inequality 5x – 4 39
[2]
(c)Factorise fully 18e2 f3– 12e3 f
[2]
- 2
Work out the difference between the largest share and the smallest share when 3450 yen is divided in the ratios 2 : 6 : 7
yen[3]
- 3
Gopal is paid 20 000 rupees each month. Jamuna is paid 19 200 rupees each month.
Gopal and Jamuna are both given an increase in their monthly pay. After the increase, they are both paid the same amount each month.
Gopal was given an increase of 8%
Work out the percentage increase that Jamuna was given.
%[4]
- 4
Show that 3 47 − 158 = 1 5356[3]
- 5
In the diagram below, P and Q are points on a circle with centre O.
Loading diagram…From page 6 of the paper. QT is a tangent to the circle. Angle OPQ = 18q
Work out the size of angle PQT. Give a reason for each stage of your working.
Loading diagram…From page 6 of the paper. [3]
- 6
The diagram shows two cylinders, A and B.
Loading diagram…From page 7 of the paper. Cylinder A has height 1.6 m and radius 0.56 m.
(a)Work out the curved surface area of cylinder A. Give your answer in m2 correct to 3 significant figures.
m2[2]
Cylinder B is mathematically similar to cylinder A. The height of cylinder B is 0.6 m.
(b)Work out the radius of cylinder B.
m[2]
- 7
The students in Class A and in Class B take the same examination.
There are 28 students in Class A and 32 students in Class B. The mean score for all the students in both classes is 72.6 The mean score for the students in Class A is 75
(a)Work out the mean score for the students in Class B.
[4]
The lowest score in Class A is 39 The range of scores for Class A is 57 The lowest score in Class B is 33 The range of scores for Class B is 60
(b)Find the range of scores for all the students in both classes.
[3]
- 8Loading diagram…
From page 9 of the paper. Work out the value of x. Give your answer correct to 3 significant figures.
x = [3]
- 9
Solve the simultaneous equations
Loading diagram…From page 9 of the paper. Show clear algebraic working.
x =
y =
Loading diagram…From page 10 of the paper. [3]
- 10Loading diagram…
From page 10 of the paper. (a)Find the value of n.
n = [2]
(13–6)4 × 135= 13k
(b)Find the value of k.
k = [2]
- 11
A solid metal sphere has radius 1.5 cm. The mass of the sphere is 109.6 grams.
Work out the density of the sphere. Give your answer correct to 3 significant figures.
g/cm3[3]
- 12Loading diagram…
From page 12 of the paper. The diagram shows a hexagon ABCDEF. BC is parallel to ED.
Work out the size of the obtuse angle DEF.
Loading diagram…From page 12 of the paper. [5]
- 13
Felix has 10 cards. There are 5 red cards, 4 blue cards and 1 green card.
Felix takes at random one of the cards. He does not replace the card. Felix then takes at random a second card.
(a)Complete the probability tree diagram.
Loading diagram…From page 13 of the paper. Loading diagram…From page 13 of the paper. 5
Loading diagram…From page 13 of the paper. 10
Loading diagram…From page 13 of the paper. Loading diagram…From page 13 of the paper. 10
Loading diagram…From page 13 of the paper. [2]
(b)Work out the probability that Felix takes at least one blue card and no green card.
[3]
- 14
(a)Complete the table of values for y = x3– 2x2– 3x + 4
Loading diagram…From page 14 of the paper. [2]
(b)On the grid, draw the graph of y = x3– 2x2– 3x + 4 for values of x from –2 to 3
Loading diagram…From page 14 of the paper. [2]
(c)By drawing a suitable straight line on the grid, find estimates for the solutions of the equation x3– 2x2– x + 1 = 0 Give your solutions correct to 1 decimal place.
[4]
- 15
e = 8.31 correct to 2 decimal places f = 0.65 correct to 2 decimal places
Work out the lower bound for the value of e – f Show your working clearly.
[2]
- 16
R is proportional to t2 The graph shows the relationship between R and t for 0 - t - 4
Loading diagram…From page 16 of the paper. (a)Find a formula for R in terms of t.
[3]
Given also that R = 85x
(b)show that t is inversely proportional to x for t 0[2]
- 17Loading diagram…
From page 18 of the paper. (a)Find dydx
dydx = [2]
C is the curve with equation y = x3– 2x2– 15x + 5
(b)Work out the range of values of x for which C has a negative gradient.
[4]
- 18
A triangle has sides of length 8 cm, 10 cm and 14 cm.
Work out the size of the largest angle of the triangle. Give your answer correct to 1 decimal place.
Loading diagram…From page 19 of the paper. [3]
- 19
The diagram shows a triangular prism.
Loading diagram…From page 20 of the paper. AF = 10 cm, AB = 24 cm and BC = 8 cm. Angle FAB = angle ADC = angle BCD = 90q
Work out the size of the angle between the line BE and the plane ABCD. Give your answer correct to 1 decimal place.
Loading diagram…From page 20 of the paper. [3]
- 20
The histogram shows information about the birth weights of some babies.
Loading diagram…From page 21 of the paper. 6 of these babies had a birth weight less than 2.5 kg or greater than 4 kg.
Work out the number of babies who had a birth weight between 2.5 kg and 4 kg.
[3]
- 21
(a)Show that 45 + 20 = 5 5 Show your working clearly.[2]
(b)Express 23 − 1 in the form p + q
where p and q are integers. Show your working clearly.
[2]
(c)Express x2+ 6 2 x – 1 in the form (x + a)2+ b Show your working clearly.
[2]
- 22Loading diagram…
From page 23 of the paper. A, D, B and E are points on a circle, centre O. AFBC, OEC and OFD are straight lines.
AF = 7 cm, FB = 4 cm, BC = 5 cm, FD = 2 cm and CE = x cm.
Work out the value of x. Show your working clearly.
x = [6]
- 23
The sum of the first 48 terms of an arithmetic series is 4 times the sum of the first 36 terms of the same series.
Find the sum of the first 30 terms of this series.
[5]