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Name: _________________
Sec 2 Mock Exam Set 1
Paper 1
Paper 1 (50 marks)
Answer all questions.
Electronic calculators can be used in this paper.
All working must be shown clearly. Omission of essential working will result in loss of marks.
1
Given that the actual area of a 2 km2 pond is represented by 8 cm2 on a map,
a) Find the scale of the map in the form of 1: n.
[2]
b) If the actual length of a bridge across the pond is 350 m, find the length of the bridge on the
map.
[1]
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2
Given that P is directly proportional to R2, and P = 250 and R = 5, find
a) An equation connecting P and R.
[2]
b) The value(s) of R when P = 40.
[2]
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3
The diagram shows a quadrilateral PQRS in which BDC = 90°, AB = 84cm,
BD = 5 cm, DC = 12 cm and AC = 85 cm. The diagram is not drawn to scale.
5 cm
12 cm
a) Find the length of BC.
[1]
b) Determine if ABC is a right-angled triangle.
[2]
c) Find the shortest distance from B to AC.
Correct your answer to 3 significant figures.
[2]
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4
In the diagram, ∆ABC is similar to ∆PQR. Given that PR = 120 cm, QR = 100 cm,
AB = 62.5 cm and BC = 40 cm.
Calculate the length of
a)PQ
[1]
b) AC
[1]
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3𝑦
2𝑦
Express 𝑦 2 −9 − 𝑦+3 as a single fraction in its simplest form.
5
𝐴+2𝑥
6 a) Given that 𝑦 = √
𝑥
, make x the subject of the formula.
b) Hence, find the value of x, given that A = 49 and y = 10.
[3]
[2]
[1]
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7 a) Simplify p2 – (p+q) (p-q).
[2]
b) Using your answer in part (i), write down the value of
1234567892 – 123456797 × 123456781.
[2]
c) Factorise completely 9(x + 2)2 – (x − 1)2.
[3]
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8 a) Given that x2 + y2 = 36 and xy =9, find the value of (x – y)2.
b) Hence or otherwise, find the value of (2x – 2y)2.
[2]
[2]
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9 a) Factorise completely 18p2 − 8,
[2]
18𝑝2 −8
b) Hence or otherwise, simplify 6𝑝2 −14𝑝−12 .
[3]
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10 There are 20 green balls and x brown balls in a bag. A ball is drawn at random from the bag.
a) Write down, in terms of x, an expression for the probability that the ball drawn is brown. [1]
b) Given that this probability is
9
19
, find the value of x.
[2]
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11 Joshua randomly tosses an eight-sided die, numbered 1 to 8, five times. The mean of the
results is 4.8, median is 4 and the mode is 4. The difference between the smallest and the largest
result is 7. Given that the smallest result he obtained is not a prime number.
Find the results of each of the five tosses.
[3]
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12
There are 30 students in the hall, x of them are girls.
a) Write down in terms of x, the probability that a student chosen at random from the group is
a) i) a girl,
[1]
a) ii) a boy.
[1]
b) 8 more girls and 14 more boys entered the hall. The probability of choosing a girl from the
3
hall becomes 13 . Find the value of x.
[2]
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13
The diagram shows a square pyramid with base ABCD. The diagonals intersect at O.
The vertex E is vertically above O and AC = √50 cm and OE = 7 cm.
Calculate
a) the length of AB,
[1]
b) the volume of the pyramid,
[1]
c) if the pyramid is melted and recasted to form a sphere, find the radius of the sphere.
[2]
O
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Paper 2
Paper 2 (50 marks)
Answer all questions.
Electronic calculators can be used in this paper.
All working must be shown clearly. Omission of essential working will result in loss of marks.
1 Two ships, Alpha and Beta leave a port at the same time and travel in opposite directions.
The speed of Alpha at x km/h is 8km/h more than Beta at y km/h.
At the end of 2.5 days, the ships are 4320 km apart. Assume the ships sail for 24 hours a day.
a) By forming a pair of simultaneous equations, find the speed of each of the two ships.
[2]
b) Calculate how much longer it will take Beta to reach a destination 1780 km away from the
port if they leave the port at the same time. Give your answer in hour(s) and minutes, correct to
the nearest minute.
[2]
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2 a) i) Factorise 25 – p2,
[1]
25−𝑝2
ii) Hence or otherwise, simplify 15+3𝑝.
[2]
b) It is given that v2 = u2 – 2gh.
i) Find v when u = 30, g = 9.8 and h = 24,
[1]
ii) Express u in terms of g, h and v.
[2]
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3
3
If 1 is subtracted from the numerator and denominator of a fraction, the value obtained is 4.
4
If 1 is added to the numerator and denominator, the resulting value is 5 . Find the fraction.
[3]
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4 The distribution of marks obtained by students in a Mathematics class test is given in the
stem and leaf diagram below. The total marks is 40.
a) i) Find the total number of students who sat for the test,
[1]
ii) Find the modal mark for the test,
[1]
iii) Find the median mark for the test
[2]
b) If remedial lessons are to be given to students who scored below 25 marks, find the
percentage of students who have to attend remedial. Correct your answers to 3 significant
figures.
[2]
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5 a) Express 462 as a product of its prime factors.
[1]
b) Find the smallest whole number n for which 462n is a multiple of 1512.
[2]
c) Explain why 1512 is not a perfect cube.
[2]
d) Find the value of e, given that
1512
𝑒
is a perfect square.
[2]
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6 The diagram below shows a signboard DC placed at the top of a building BC. B is vertically
below C and  CAB = 25°. Given that AB = 120 m and AD = 145 m, find the height of the
signboard.
[4]
25
120 m
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7 The force of attraction, F Newtons, between two magnets is inversely proportional to the
square of the distance, d cm, between them. When the magnets are 8 cm apart, the force of
attraction is 10 Newtons.
a) Find a formula for F in terms of d.
[1]
b) Given that the force of attraction between the two magnets is 25 Newtons, find the distance
between the magnets.
[2]
c) When the magnets are at a certain distance apart, the force of attraction is 12 Newtons. Write
down the force when the distance is doubled.
[3]
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In the diagram, it is given that line AB is parallel to line DE. Find the value of x and y.
12 cm
8
[3]
40 cm
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9
Answer the whole of this question on a single sheet of graph paper.
The variables x and y are connected by the equation y = 2x2 + 2x – 1. Some of the corresponding
values of x and y are given in the table below.
x
y
−1.5
0.5
−1
−1
−0.5
−1.5
0
−1
0.5
0.5
1.5
6.5
a) Calculate the value of p.
2
p
2.5
16.5
[1]
b) Using a scale of 4 cm to represent 1 unit, draw a horizontal axis for −4 ≤ x ≤ 4. Using a scale
of 5 cm to 2 units, draw a vertical axis for −2 ≤ y ≤ 18. On your axes, plot the points given in the
table and join them with a smooth curve.
[3]
c) Write down the equation of the line of symmetry for the curve.
[1]
d) Using your graph to find
i) the value of y when x = −2,
[1]
ii) the minimum value of y.
[1]
ei) On the same axes, draw the line y = −x + 2 for −4 ≤ x ≤ 4.
[2]
eii) Write down the x-values of the intersection points of the line and the curve.
[2]
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