1.
WASSCE mock · Core Mathematics
If \(23_{x} = 1111_{2}\), find the value of \(x\).
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WASSCE mock exam
Core Mathematics — WASSCE Maths Mock
50 questions to work through. Answer them here, or take the whole thing timed with an account.
2.
WASSCE mock · Core Mathematics
If \(21_{x} = 111_{2}\), find the value of \(x\).
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3.
WASSCE mock · Core Mathematics
If \(41_{x} = 10101_{2}\), find the value of \(x\).
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4.
WASSCE mock · Core Mathematics
Which of the following equals \(101101_{2}\) when expressed in base 8?
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5.
WASSCE mock · Core Mathematics
What is the decimal value of \(7B_{16}\)?
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6.
WASSCE mock · Core Mathematics
If \(23_{x}=43_{10}\), find the value of \(x\).
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7.
WASSCE mock · Core Mathematics
If \(34_{x}=2A_{12}\) (where \(A_{12}=10_{10}\)), find \(x\).
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8.
WASSCE mock · Core Mathematics
A die is rolled once. Find the probability of obtaining a number less than \(3\).
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9.
WASSCE mock · Core Mathematics
A die is rolled once. What is the probability of obtaining an even number?
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10.
WASSCE mock · Core Mathematics
A fair coin is tossed twice. What is the probability of obtaining at least one head?
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11.
WASSCE mock · Core Mathematics
Two fair dice are rolled. What is the probability that the sum is \(9\)?
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12.
WASSCE mock · Core Mathematics
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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13.
WASSCE mock · Core Mathematics
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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14.
WASSCE mock · Core Mathematics
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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15.
WASSCE mock · Core Mathematics
If \(y\) varies as \(x^{2}\) and \(y=3\) when \(x=\sqrt{2}\), find \(y\) when \(x=2\).
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16.
WASSCE mock · Core Mathematics
If \(y\) varies directly as \(x^{2}\) and \(y=8\) when \(x=4\), find \(y\) when \(x=6\).
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17.
WASSCE mock · Core Mathematics
If \(y\) varies inversely as \(x^{2}\) and \(y=5\) when \(x=2\), find \(y\) when \(x=5\).
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18.
WASSCE mock · Core Mathematics
\(y\) 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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19.
WASSCE mock · Core Mathematics
If \(y\propto x^{3}\) and \(y=54\) when \(x=3\), find \(x\) when \(y=128\).
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20.
WASSCE mock · Core Mathematics
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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21.
WASSCE mock · Core Mathematics
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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22.
WASSCE mock · Core Mathematics
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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23.
WASSCE mock · Core Mathematics
If \(p = x + \frac{1}{x}\) and \(r = x^{3} + \frac{1}{x^{3}}\), express \(r\) in terms of \(p\).
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24.
WASSCE mock · Core Mathematics
If \(p = x - \frac{1}{x}\) and \(r = x^{3} - \frac{1}{x^{3}}\), express \(r\) in terms of \(p\).
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25.
WASSCE mock · Core Mathematics
If \(x + \frac{1}{x} = 5\), find the value of \(x^{3} + \frac{1}{x^{3}}\).
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26.
WASSCE mock · Core Mathematics
If \(p = x + \frac{1}{x}\) and \(s = x^{4} + \frac{1}{x^{4}}\), express \(s\) in terms of \(p\).
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27.
WASSCE mock · Core Mathematics
If \(p = x - \frac{1}{x}\) and \(t = x^{4} + \frac{1}{x^{4}}\), express \(t\) in terms of \(p\).
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28.
WASSCE mock · Core Mathematics
The interior angle of a regular polygon is twice its exterior angle. How many sides does the polygon have?
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29.
WASSCE mock · Core Mathematics
The interior angle of a regular polygon is three times its exterior angle. How many sides has the polygon?
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30.
WASSCE mock · Core Mathematics
Each exterior angle of a regular polygon is \(40^{\circ}\). How many sides has the polygon?
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31.
WASSCE mock · Core Mathematics
The sum of the interior angles of a regular polygon is \(1260^{\circ}\). How many sides does it have?
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32.
WASSCE mock · Core Mathematics
Each interior angle of a regular polygon is \(150^{\circ}\). How many sides has the polygon?
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33.
WASSCE mock · Core Mathematics
Each interior angle of a regular polygon is \(168^{\circ}\). How many sides has the polygon?
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34.
WASSCE mock · Core Mathematics
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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35.
WASSCE mock · Core Mathematics
If \(A = \frac{1}{2}b(a + b)\), make \(a\) the subject of the relation.
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36.
WASSCE mock · Core Mathematics
If \(S = \frac{1}{2}c(a + c)\), make \(a\) the subject of the relation.
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37.
WASSCE mock · Core Mathematics
If \(V = \frac{1}{3}\pi r^{2}h\), make \(h\) the subject of the relation.
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38.
WASSCE mock · Core Mathematics
If \(P = 2\pi r(r + h)\), express \(h\) in terms of \(P\) and \(r\).
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39.
WASSCE mock · Core Mathematics
If \(M = \frac{2ab}{a + b}\), make \(b\) the subject.
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40.
WASSCE mock · Core Mathematics
If \(Q = \frac{2a + b}{a - b}\), make \(a\) the subject of the relation.
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41.
WASSCE mock · Core Mathematics
If \(R = \frac{a^{2} - b^{2}}{a + b}\), make \(a\) the subject.
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42.
WASSCE mock · Core Mathematics
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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43.
WASSCE mock · Core Mathematics
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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44.
WASSCE mock · Core Mathematics
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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45.
WASSCE mock · Core Mathematics
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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46.
WASSCE mock · Core Mathematics
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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47.
WASSCE mock · Core Mathematics
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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48.
WASSCE mock · Core Mathematics
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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49.
WASSCE mock · Core Mathematics
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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50.
WASSCE mock · Core Mathematics
Among 60 students, 35 take Mathematics and 30 take Biology; 20 take both. How many take neither subject?
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