WASSCE Maths Mock
Contains Maths Questions from WASSCE 2022, 2023 and 2024. Use this Exam to examine your preparedness towards the 2025 BECE Exam Paper
Question 1
If \(23_{x} = 1111_{2}\), find the value of \(x\).
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Question 2
If \(21_{x} = 111_{2}\), find the value of \(x\).
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Question 3
If \(41_{x} = 10101_{2}\), find the value of \(x\).
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Question 4
Which of the following equals \(101101_{2}\) when expressed in base 8?
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Question 5
What is the decimal value of \(7B_{16}\)?
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Question 6
If \(23_{x}=43_{10}\), find the value of \(x\).
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Question 7
If \(34_{x}=2A_{12}\) (where \(A_{12}=10_{10}\)), find \(x\).
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Question 8
A die is rolled once. Find the probability of obtaining a number less than \(3\).
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Question 9
A die is rolled once. What is the probability of obtaining an even number?
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Question 10
A fair coin is tossed twice. What is the probability of obtaining at least one head?
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Question 11
Two fair dice are rolled. What is the probability that the sum is \(9\)?
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Question 12
A card is drawn from a standard 52-card deck. What is the probability that it is a heart or a king?
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Question 13
Two fair dice are rolled. What is the probability that the product of the two numbers is a multiple of \(3\)?
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Question 14
A box contains 4 red, 3 blue and 5 green balls. A ball is drawn, replaced, and a second drawn. What is the probability that the two balls are of different colours?
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Question 15
If \(y\) varies as \(x^{2}\) and \(y=3\) when \(x=\sqrt{2}\), find \(y\) when \(x=2\).
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Question 16
If \(y\) varies directly as \(x^{2}\) and \(y=8\) when \(x=4\), find \(y\) when \(x=6\).
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Question 17
If \(y\) varies inversely as \(x^{2}\) and \(y=5\) when \(x=2\), find \(y\) when \(x=5\).
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Question 18
\(y\) varies jointly as \(x\) and \(\sqrt{z}\). If \(y=24\) when \(x=3\) and \(z=16\), find \(y\) when \(x=5\) and \(z=9\).
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Question 19
If \(y\propto x^{3}\) and \(y=54\) when \(x=3\), find \(x\) when \(y=128\).
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Question 20
If \(y\) varies as \(x^{4}\) and inversely as \(\sqrt{z}\), and \(y=32\) when \(x=2\) and \(z=4\), find \(y\) when \(x=3\) and \(z=9\).
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Question 21
Given that \(p = x - \frac{1}{x}\) and \(q = x^{2} + \frac{1}{x^{2}}\), express \(q\) in terms of \(p\).
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Question 22
Given that \(p = x + \frac{1}{x}\) and \(q = x^{2} + \frac{1}{x^{2}}\), express \(q\) in terms of \(p\).
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Question 23
If \(p = x + \frac{1}{x}\) and \(r = x^{3} + \frac{1}{x^{3}}\), express \(r\) in terms of \(p\).
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Question 24
If \(p = x - \frac{1}{x}\) and \(r = x^{3} - \frac{1}{x^{3}}\), express \(r\) in terms of \(p\).
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Question 25
If \(x + \frac{1}{x} = 5\), find the value of \(x^{3} + \frac{1}{x^{3}}\).
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Question 26
If \(p = x + \frac{1}{x}\) and \(s = x^{4} + \frac{1}{x^{4}}\), express \(s\) in terms of \(p\).
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Question 27
If \(p = x - \frac{1}{x}\) and \(t = x^{4} + \frac{1}{x^{4}}\), express \(t\) in terms of \(p\).
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Question 28
The interior angle of a regular polygon is twice its exterior angle. How many sides does the polygon have?
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Question 29
The interior angle of a regular polygon is three times its exterior angle. How many sides has the polygon?
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Question 30
Each exterior angle of a regular polygon is \(40^{\circ}\). How many sides has the polygon?
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Question 31
The sum of the interior angles of a regular polygon is \(1260^{\circ}\). How many sides does it have?
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Question 32
Each interior angle of a regular polygon is \(150^{\circ}\). How many sides has the polygon?
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Question 33
Each interior angle of a regular polygon is \(168^{\circ}\). How many sides has the polygon?
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Question 34
The ratio of the interior angle to the exterior angle of a regular polygon is \(5:1\). How many sides has the polygon?
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Question 35
If \(A = \frac{1}{2}b(a + b)\), make \(a\) the subject of the relation.
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Question 36
If \(S = \frac{1}{2}c(a + c)\), make \(a\) the subject of the relation.
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Question 37
If \(V = \frac{1}{3}\pi r^{2}h\), make \(h\) the subject of the relation.
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Question 38
If \(P = 2\pi r(r + h)\), express \(h\) in terms of \(P\) and \(r\).
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Question 39
If \(M = \frac{2ab}{a + b}\), make \(b\) the subject.
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Question 40
If \(Q = \frac{2a + b}{a - b}\), make \(a\) the subject of the relation.
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Question 41
If \(R = \frac{a^{2} - b^{2}}{a + b}\), make \(a\) the subject.
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Question 42
An arc of a circle \(50\text{ cm}\) long subtends an angle \(75^{\circ}\) at the centre of the circle. Find, correct to three significant figures, the radius of the circle. \([\text{Take }\pi=\frac{22}{7}]\)
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Question 43
An arc of a circle \(44\text{ cm}\) long subtends an angle \(40^{\circ}\) at the centre. Calculate the radius correct to three significant figures. \([\pi=\frac{22}{7}]\)
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Question 44
A circle has radius \(12\text{ cm}\). Find the length of the arc that subtends an angle of \(150^{\circ}\) at the centre. Give your answer correct to one decimal place. \([\pi=\frac{22}{7}]\)
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Question 45
In a circle of radius \(21\text{ cm}\), an arc is \(11\text{ cm}\) long. Calculate, correct to the nearest degree, the angle subtended by the arc. \([\pi=\frac{22}{7}]\)
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Question 46
In a circle of radius \(15\text{ cm}\), the length of an arc is \(18\text{ cm}\). Find the angle, in degrees (nearest whole number), that the arc subtends at the centre. \([\pi=\frac{22}{7}]\)
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Question 47
The area of a sector of a circle of radius \(14\text{ cm}\) is \(154\text{ cm}^{2}\). Calculate the angle of the sector. \([\pi=\frac{22}{7}]\)
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Question 48
In a class of 30 students, 18 take Mathematics, 5 take both Mathematics and Biology, and 8 take neither. How many take Biology?
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Question 49
In a class of 40 students, 25 study Mathematics, 7 study both Mathematics and Biology, and 5 study neither. How many study Biology?
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Question 50
Among 60 students, 35 take Mathematics and 30 take Biology; 20 take both. How many take neither subject?
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