Core Mathematics 2022 - WASSCE

WASSCE CORE MATHEMATICS

Question 1

Find the number of even integers between 11 and 97.

Question 2

Find the values of \(x\) for which \(\dfrac{1}{2x^{2}-13x+15}\) is not defined.

Question 3

**DIAGRAM WILL BE PROVIDED.** In the diagram, \(P,Q,R,S\) are points on the circle. If \(\angle PQS = 32^\circ\) and \(\angle PRQ = 61^\circ\), find \(\angle QPS\).

Question 4

The bearing of a point \(P\) from a point \(Q\) is \(065^\circ\). What is the bearing of \(Q\) from \(P\)?

Question 5

The 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. \([Take\ \pi=\frac{22}{7}]\)

Question 6

Find the truth set of \((3 + x)(1 - x) > 9 - x^{2}\).

Question 7

A bag contains 32 blue, 28 black and 20 red identical balls of same size. If a ball is picked at random, what is the probability that it is not red?

Question 8

Simplify: \(\frac{1}{2}(x-1)-\frac{1}{3}\left(\frac{1}{2}x-1\right)\).

Question 9

A woman buys 3 exercise books at GH₵ 0.4 each and 9 exercise books at GH₵ 0.2 each. What is the average cost of an exercise book?

Question 10

Given that \(4x + 6y = 5\) and \(2x + 4y = 3\), find the value of \((x + 2y)\).

Question 11

Simplify \(\dfrac{9-x^{2}}{3x-x^{2}}\), where \(x \ne 3\).

Question 12

Given that \(P \propto v^{2}x\) and \(x \propto vt\), express \(P\) in terms of \(v\) and \(t\).

Question 13

Express, correct to two significant figures \(\left(\frac{9}{28}-\frac{2}{7}\right)\).

Question 14

**DIAGRAM WILL BE PROVIDED.** Find the value of \(y\) in the diagram.

Question 15

If \((23)_{x} = (1111)_{two}\), find the value of \(x\).

Question 16

Dina and Rose were given GH₵ 875.08 to be shared in the ratio 3:2 respectively. If Rose shared her part of the money between Efua and Ama in the ratio 1:2 respectively, how much was Ama's share?

Question 17

If \(9^{\,y+1} = \left(\frac{1}{27}\right)^{\,y-2}\), find \(y\).

Question 18

A market woman demands GH₵ 15.00 for a tin of local rice. After some bargaining with a customer, she sells 5 tins for GH₵ 66.00. By what percentage did she reduce her original price?

Question 19

The graph of \(y = x^{2} + 4x - 6\) is drawn and a linear graph is drawn on the axes such that the intersection of the two graphs gives the solution to the equation \(x^{2} + 4x - 7 = 0\). Find the equation for the linear graph.

Question 20

The interior angle of a regular polygon is twice the exterior angle. How many sides has the polygon?

Question 21

Metuh is nine times as old as his cousin, Fafa. In six years time, he will be five times as old as Fafa. Find Fafa's present age.

Question 22

If \(A=\frac{1}{2}b(a + b)\), make \(a\) the subject of the relation.

Question 23

Evaluate \(\dfrac{53,000,000 \times 0.002}{0.0004}\).

Question 24

If \(\frac{x + y}{5} = \frac{x - y}{3}\), find \(x:y\).

Question 25

Find the equation of the line passing through \(P(4,1)\) and parallel to \(2x + 5y = -10\).

Question 26

The exterior angles of a quadrilateral are \(61^\circ,76^\circ,(x+10)^\circ\) and \((2x+45)^\circ\). Find the value of \(x\).

Question 27

If \(17 \equiv 3 \pmod{x}\), find the least value of \(x\).

Question 28

The shadow of a vertical pole is 50 cm. If the height of the pole is 2 m, find, correct to the nearest degree, the angle of elevation of the sun from the ground level.

Question 29

Consider the following statements: M: Helena studies hard; N: Helena passes her examination. If \(M \Rightarrow N\)

Question 30

The area of a sector of a circle is \(40\ \text{cm}^{2}\). If the sector subtends an angle of \(140^\circ\) at the centre, find the area of the circle.

Question 31

Given that \(6\log(x + 4) = \log 64\), find the value of \(x\).

Question 32

A die is rolled once. Find the probability of obtaining a number less than 3.

Question 33

**DIAGRAM WILL BE PROVIDED.** If the area of the trapezium \(MNOP\) is \(300\ \text{cm}^{2}\), find the value of \(x\).

Question 34

Find the 11th term of \(\frac{1}{4},\frac{5}{8},1,\frac{13}{8}, \ldots\).

Question 35

In a class of 30 students, 18 takes Mathematics, 5 take both Mathematics and Biology and 8 take neither Mathematics nor Biology. Find the number of students that take Biology.

Question 36

**DIAGRAM WILL BE PROVIDED.** In the diagram, \(MN // PQ\). Find the value of \((x + y)\).

Question 37

Simplify \(\dfrac{\sqrt{3}+\sqrt{48}}{\sqrt{6}}\).

Question 38

The length of a rectangular lawn is 3 cm longer than the width. If the perimeter is 42 cm, find the width.

Question 39

Given that \(p=x-\frac{1}{x}\) and \(q=x^{2}+\frac{1}{x^{2}}\), express \(q\) in terms of \(p\).

Question 40

A car moves at an average speed of 30 kmh\(^{-1}\). How long does it take to cover 200 metres?

Question 41

If \(y\) varies as the square of \(x\), \(y = 3\) when \(x = \sqrt{2}\), find the value of \(y\) when \(x = 2\).

Question 42

**DIAGRAM WILL BE PROVIDED.** In the diagram, \(O\) is the centre of the circle \(PQR\), \(|PS| = |PQ|\) and \(\angle RQS = 23^\circ\). Find the value of \(x\).

Question 43

The mass of some market women in kg are: 83, 47, 62, 49, 55, 72, 58 and 62. Find the range.

Question 44

The mass of some market women in kg are: 83, 47, 62, 49, 55, 72, 58 and 62. Find the mean.

Question 45

Evaluate \(\tan 30^\circ - 2\sin 60^\circ\).

Question 46

Simplify: \(8\frac{1}{6}-\left(11\frac{2}{3}\div 2\frac{2}{3}\right)\).

Question 47

The probabilities of three independent events \(X, Y\) and \(Z\) occurring are \(\frac{1}{2}, \frac{2}{3}\) and \(\frac{1}{4}\) respectively. What is the probability that only events \(X\) and \(Z\) are occurring?

Question 48

One side of a rectangle is 8 cm and the diagonal is 10 cm. Calculate the area of the rectangle.

Question 49

**DIAGRAM WILL BE PROVIDED.** In the diagram, \(EFGH\) are points on a circle centre \(P\). If \(\angle EFG = 142^\circ\) and \(\angle FGP = 63^\circ\), find \(\angle FEP\).

Question 50

**DIAGRAM WILL BE PROVIDED.** In the diagram \(PQ\) is the diameter of circle \(PQR\) with centre \(O\) and \(RS\) meets \(PQ\) at \(S\). If \(\angle RQP = 64^\circ\) and \(\angle RSQ = 36^\circ\), find \(\angle PRS\).