# 4MA1 Mathematics A May/June 2018 Paper 1HR (Higher Tier Paper 1)

Pearson Edexcel International GCSE 4MA1 Mathematics A past paper 1HR, Higher Tier Paper 1, May/June 2018. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/4ma1/2018-may-june-paper-1hr/
- PDF: https://mathvsarham.com/papers/4ma1/4MA1_may-june_2018_paper_1HR_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International GCSE
- Subject: 4MA1 Mathematics A (https://mathvsarham.com/past-papers/4ma1/)
- Session: May/June 2018
- 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
Here is a hexagon ABCDEF.
[Diagram or table: see page 3 of the paper]
CD is parallel to AF.
Work out the area of hexagon ABCDEF.
Answer: ____ _cm^2 [4]

Question 2
The table gives information about the times, in hours, some students spent doing sport one week.
Time (T hours) Frequency
[Diagram or table: see page 4 of the paper]
Calculate an estimate for the mean time these students spent doing sport. Give your answer in hours, correct to 1 decimal place.
Answer: ____ _hours [4]

Question 3
[Diagram or table: see page 5 of the paper]
(a) Reflect triangle S in the line y = x Label the new triangle R. [2]
(b) Translate triangle S by the vector ⎛ −4⎞/⎜
Label the new triangle T. [1]

Question 4
Anna and Lionel share $675 in the ratio 4 : 5
Lionel gives 3/5 of his share of the money to his mother.
How much money does Lionel give to his mother?
Answer: $ ____ [3]

Question 5
E = n^2+ n + 5
Ali thinks that the value of E will be a prime number for any whole number value of n.
Is Ali correct? You must give a reason for your answer.
Answer: ____ [2]

Question 6
[Diagram or table: see page 7 of the paper]
ABC and DEF are parallel lines.
BG = BE Angle DEG = 38° Angle GEB = 65°
Find the size of angle ABG.
[Diagram or table: see page 7 of the paper]
Answer: ____ [3]

Question 7
Here are the first four terms of an arithmetic sequence.
[Diagram or table: see page 8 of the paper]
(a) Find an expression, in terms of n, for the nth term of this sequence.
Answer: ____ [2]
(b) Write down an expression, in terms of n, for the (n + 1)th term of this sequence.
Answer: ____ [1]

Question 8
(a) Write 1 390 000 in standard form.
Answer: ____ [1]
(b) Write 0.005 in standard form.
Answer: ____ [1]

Question 9
Here is an empty pool in the shape of a cuboid.
[Diagram or table: see page 9 of the paper]
The width of the pool is 3 m. The length of the pool is 12 m. The top of the pool is 2.5 m above the base of the pool.
Jeb is going to put water in the pool. The level of the surface of the water will be 60 cm below the top of the pool.
Water flows into the pool at 400 litres per minute. 1 m^3= 1000 litres
How long will it take to fill the pool to 60 cm below the top of the pool? Give your answer in hours and minutes.
Answer: ____ _hours ____ _minutes [4]

Question 10
Solve
[Diagram or table: see page 10 of the paper]
Show clear algebraic working.
Answer: x = ____
Answer: y = ____ [3]

Question 11
Change a speed of 72 kilometres per hour to a speed in metres per second.
Answer: ____ _metres_per_second [3]

Question 12
A company makes cars.
In 2016, the company made 350 cars.
In the first 6 months of 2017, the company made 25 cars each month. In the last 6 months of 2017, the company made 45 cars each month.
(a) Work out the percentage increase in the number of cars the company made from 2016 to 2017
Answer: ____ _% [4]
The company’s income in 2017 was $500 000 more than the company’s income in 2016
The company’s income in 2017 was 8% more than the company’s income in 2016
(b) Work out the company’s income in 2016
Answer: $ ____ [3]

Question 13
Each month Edna spends all her income on rent, on travel and on other living expenses.
She spends 1/3 of her income on rent.
She spends 1/5 of her income on travel.
She spends $420 of her income on other living expenses.
Work out her income each month.
Answer: $ ____ [4]

Question 14
(a) Simplify (2e^2 f^3)^3
Answer: ____ [2]
(b) Expand and simplify (3xíy)(x + 3y)
Answer: ____ [2]
[Diagram or table: see page 13 of the paper]
(c) Find the value of k.
Answer: k = ____ [2]
(d) Simplify 2/4_n − 1/− 1
Answer: ____ [2]

Question 15
There are two bags of counters, bag X and bag Y.
There are 20 counters in bag X. 11 of the counters are blue and the rest are red.
There are 16 counters in bag Y. 9 of the counters are blue and the rest are red.
Arkady takes at random a counter from bag X and takes at random a counter from bag Y.
(a) Complete the probability tree diagram.
[Diagram or table: see page 14 of the paper]
Answer: ____
[Diagram or table: see page 14 of the paper]
[3]
(b) Work out the probability that the two counters are both red.
Answer: ____ [2]
(c) Work out the probability that the two counters are both red or are both blue.
Answer: ____ [3]

Question 16
[Diagram or table: see page 16 of the paper]
The points B, C, Y and X lie on a circle.
AXY and ABC are straight lines.
AX = 12 cm XY = x cm AB = x cm BC = 4 cm
(a) Show that x^2íx  [3]
(b) Find the length of AC. Show your working clearly. Give your answer correct to 3 significant figures.
Answer: ____ _cm [4]

Question 17
The table gives information about the areas, in hectares, of some farms in Spain.
[Diagram or table: see page 17 of the paper]
0  A - 20
20  A - 50
50  A - 100
100  A - 300
300  A - 350
On the grid, draw a histogram for this information.
4
3
[Diagram or table: see page 17 of the paper]
[3]

Question 18
Here is a quadrilateral PQRS.
[Diagram or table: see page 18 of the paper]
Angle SRQ is acute.
Work out the size of angle SQR. Give your answer correct to 1 decimal place.
[Diagram or table: see page 18 of the paper]
Answer: ____ [6]

Question 19
The curve shown in the diagram has equation
[Diagram or table: see page 19 of the paper]
The curve has a maximum point at A (a, b) The curve has a minimum point at B (c, d)
[Diagram or table: see page 19 of the paper]
Using differentiation, find the value of bíd Show your working clearly.
Answer: ____ [6]

Question 20
Two functions, f and g are defined as
[Diagram or table: see page 20 of the paper]
Given that h = fg
express the inverse function h^í in the form h^í: x 6 …
Answer: h^í: x 6 ____ [4]

Question 21
(a) Show that x(xí x + 1) = x^3íx [1]
(b) Prove that the difference between a whole number and the cube of this number is always a multiple of 6 [3]

Question 22
A 3-D shape consists of a hollow sphere made of metal.
The diagram shows a cross section drawn through the centre, O, of the sphere.
[Diagram or table: see page 22 of the paper]
The internal radius of the sphere is 1.2 m. The thickness of the metal is t cm.
The density of the metal is 2700 kg per m^3
The mass of the 3-D shape is 1980 kg.
Work out the value of t. Give your answer correct to 2 significant figures.
Answer: t = ____ [5]

Question 23
Work out the sum of the multiples of 3 between 1 and 1000
Answer: ____ [4]