IGCSE Edexcel 4H January 2014

1 A school has 840 pupils and 40 teachers.
(a) Find the ratio of the number of pupils to the number of teachers.
Give your ratio in the form n : 1

In Year 11 at the school, the ratio of the number of pupils who study Chemistry to the
number of pupils who study Physics is 3 : 2
(b) 105 pupils in Year 11 study Chemistry.
Work out the number of pupils in Year 11 who study Physics.

For the 105 pupils who study Chemistry, the ratio of the number of boys to the number of
girls is 4 : 3
(c) Work out the number of girls in Year 11 who study Chemistry

2

The diagram shows a solid prism.
The cross section of the prism is a trapezium.
The lengths of the parallel sides of the trapezium are 11 cm and 7 cm.
The perpendicular distance between the parallel sides of the trapezium is 10 cm.
The length of the prism is 12 cm.
(a) Work out the area of the trapezium.

(b) Work out the volume of the prism.

3 Solve 6 (3y + 5) = 39
Show clear algebraic working.

4 The table gives information about the numbers of goals scored by a football team in
30 matches.

Find the mean number of goals scored.

5 The diagram shows a shape P, and a shape Q.



Describe fully the single transformation which maps shape P onto shape Q.

6 (a) Simplify k × k × k × k × k

(b) Expand 2(7t – 3)

(c) Expand and simplify fully
(i) 4(2y + 6) – 3(2y – 7)

(ii) (x – 6)(x – 4)

(d) Simplify fully \[\frac{v⁴×v⁷}{v⁵}\]

7 A square hole is cut from a circular piece of card.


The square has sides of length 3.2 cm.
The diameter of the circular piece of card is 10 cm.
Work out the area of the shaded region.
Give your answer correct to 3 significant figures.

8 Express 825 as a product of its prime factors.

9 E = {positive whole numbers less than 13}
A = {even numbers}
B = {multiples of 3}
C = {prime numbers}
(a) List the members of the set
(i) A ∩ B

(ii) B ∪ C

(b) Is it true that 14 ∈ A?
Explain your answer.

10 The mean of four numbers is 2.6
One of the four numbers is 5
Find the mean of the other three numbers.

11 The table shows the land areas, in km², of four countries.

(a) Which country has the largest land area?

(b) Calculate the total land area, in km², of all four countries.
Give your answer in standard form.

Population density is calculated by the formula

(c) In one year, the population of Ethiopia was 7.91 × 10⁷
Calculate the population density of Ethiopia for that year.

12

The diagram shows an equilateral triangle ABC and an isosceles triangle BCD.
AB = AC = BC = CD.
Angle ABD = x°
Express the size of angle ACD in terms of x°, giving your answer as simply as possible.
Give a reason for each step in your working.

13 Factorise fully 4(x – 5)²+ 3 (x – 5

14 Peter wants to pass his driving test.
The probability that he passes at his first attempt is 0.7
When Peter passes his driving test, he does not take it again.
If he fails, the probability that he passes at the next attempt is 0.8
(a) Complete the probability tree diagram for Peter’s first two attempts.

(b) Calculate the probability that Peter needs exactly two attempts to pass his driving
test.

(c) Calculate the probability that Peter passes his driving test at his third or fourth
attempt.

15 A farmer has 120 metres of fencing.
He is going to make a rectangular enclosure PQRS with the fencing.
He is also going to divide the enclosure into two equal parts by fencing along MN.

The width of the enclosure is x metres.
The length of the enclosure is y metres.
(a) (i) Show that y = 60 – 1.5x

The area of the enclosure PQRS is A m²
(ii) Show that A = 60x – 1.5x²

(b) Find \[\frac{dA}{dx}\]

(c) Find the maximum value of A.

16 The histogram shows information about the times, t minutes, customers spent in
a post office.

28 customers spent 2 minutes or less in the post office.
Calculate an estimate for the number of customers who spent between 5 and 14 minutes
in the post office.

17 A circular clock face, centre O, has a minute hand OA and an hour hand OB.
OA = 10 cm.
OB = 7 cm.
Calculate the length of AB when the hands show 5 o’clock.
Give your answer correct to 3 significant figures.

18 A rectangular lawn has a length of 3x metres and a width of 2x metres.
The lawn has a path of width 1 metre on three of its sides.


The total area of the lawn and the path is 100 m²
(a) Show that 6x² + 7x – 98 = 0

(b) Calculate the area of the lawn.
Show clear algebraic working

19

The diagram shows part of a regular polygon.
The interior angle and the exterior angle at a vertex are marked.
The size of the interior angle is 7 times the size of the exterior angle.
Work out the number of sides of the polygon.

20 Show that the recurring decimal

21 There are 1300 sheets of paper, correct to the nearest 100 sheets, in a pile.
Each sheet is of equal thickness.
The height of the pile is 160 mm, correct to the nearest 10 mm.
Calculate the upper bound, in millimetres, for the thickness of one sheet of paper

22 Solve the simultaneous equations
2x – y = 7
x² + y²= 34
Show clear algebraic working.

23 A pyramid has a horizontal square base ABCD with sides of length 230 metres.
M is the midpoint of AC.
The vertex, T, is vertically above M.
The slant edges of the pyramid are of length 218 metres.
Calculate the height, MT, of the pyramid.
Give your answer correct to 3 significant figures.