IGCSE Edexcel 3H June 2013

1 The table shows information about the mark scored on an examination question by each
of 40 students.

Work out the mean mark.

2 (a) Work out the value of \[\frac{√7.4}{9.8 − 2.1}\]
Give your answer as a decimal.
Write down all the figures on your calculator display.

(b) Give your answer to part (a) correct to 2 significant figures.

3 (a) Multiply out 6(n − 2)

(b) Factorise p² − 5p

(c) Solve\[\frac{7x − 3}{2}\] = x
Show clear algebraic working.

4

ABCDEF is a hexagon.
G is a point on AF.
H is a point on BC.
GH is parallel to AB.
(a) Give a reason why x = 107

(b) Work out the value of y.

5
 
The shape in the diagram is made from a rectangle and a right-angled triangle.
The diagram shows, in terms of x and y, the lengths, in centimetres, of the sides of the
rectangle and of the triangle.
The perimeter, P cm, of the shape is given by the formula
P = 12x + 2y
(a) Work out the value of x when P = 43 and y = 6.5

(b) Find, in terms of x and y, a formula for the area, A cm², of the shape.
Give your answer as simply as possible.

6 An airline increases the prices of its flights by 8%.
(a) Before the increase, the price of a flight to Cairo was £475.
Work out the price of a flight to Cairo after the increase.

(b) The increase in price of a flight to Mumbai was £48
Work out the price of a flight to Mumbai after the increase.

7 S = {s, q, u, a, r, e}
V = {a, e, i, o, u}
List the members of the set
(i) S ∩ V

(ii) S ∪ V

8 

A solid cylinder has a radius of 5.1cm and a height of 3.7cm.
Work out the total surface area of the cylinder.
Give your answer correct to 3 significant figures.

10

Work out the value of x.
Give your answer correct to 1 decimal place.

12 The cumulative frequency table shows information about the diameters of 60 oranges.


(a) On the grid, draw a cumulative frequency graph for the table.

(b) Use your graph to find an estimate for the median diameter of the 60 oranges.

13


A, B, C and D are points on a circle.
PA is a tangent to the circle.
Angle PAD = 39°
Angle BCD = 103°
Calculate the size of angle ADB.

14 (a) Simplify 4p³q⁵ × 6p²q

(b) Simplify (5x²y⁴)³

(c) Factorise 9a² - b²

15


The diagram shows two straight lines.
The equations of the lines are y = x − 1 and 2x + 3y = 12
(a) Write down the solution of the simultaneous equations
                                                 y = x − 1 and 2x + 3y = 12

(b) Find an equation of the line which is parallel to the line with equation 2x + 3y = 12
and passes through the point (0, 10)

(c) On the grid, mark with a cross (×) each point which satisfies both these inequalities
y > x - 1 and 2x + 3y < 12 and whose coordinates are positive integers.

16


Triangle ABC is similar to triangle PQR.
AB corresponds to PQ.
AC corresponds to PR.
AB = 8 cm.
AC = 5cm.
PQ = 14 cm.
(a) Calculate the length of PR

The area of triangle ABC is 16 cm²
(b) Calculate the area of triangle PQR.

17 Parveen travels to school either by bicycle or by bus.
The probability that, on any day, she will travel by bicycle is 0.7
When she travels by bicycle, the probability that she will be late for school is 0.2
When she travels by bus, the probability that she will be late for school is 0.1
(a) Calculate the probability that, on a randomly chosen day, Parveen will travel by bus
and be late for school.

(b) Calculate the probability that, on a randomly chosen day, Parveen will not be late for
school.

18 


P and Q are two points on a coast.
P is due North of Q.
A ship is at the point S.
PS = 2.9 km.
The bearing of the ship from P is 062°
The bearing of the ship from Q is 036°
Calculate the distance QS.
Give your answer correct to 3 significant figures.

19 (a) Correct to the nearest millimetre, the length of a side of a regular hexagon is 3.6 cm.
Calculate the upper bound for the perimeter of the regular hexagon.

(b) Correct to 1 significant figure, the area of a rectangle is 80 cm²
Correct to 2 significant figures, the length of the rectangle is 12 cm.
Calculate the lower bound for the width of the rectangle.
Show your working clearly.

20

The diagram shows a rectangle.
The length of the rectangle is x cm.
The length of a diagonal of the rectangle is 8 cm.
The perimeter of the rectangle is 20 cm.
(a) Show that x² - 10x + 18 = 0

(b) Solve x² - 10x + 18 = 0
Give your solutions correct to 3 significant figures.
Show your working clearly.

21 Here is a shape.


The shape is made from triangle ABC and a sector of a circle, centre C and radius CA.
CA = 7 cm.
CB = 16 cm.
Angle ACB = 150°
Calculate the area of the shape.
Give your answer correct to 3 significant figures.

22 Make y the subject of \[\frac{y}{x}\]+\[\frac{2y}{x+4}\] = 3
Show your working clearly and give your answer as simply as possible.