WASSCE past question

Core Mathematics 2022

Core Mathematics Paper 1

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1. [1]

WASSCE 2022 · Paper 1

Find the number of even integers between 11 and 97.
2. [1]

WASSCE 2022 · Paper 1

Find the values of \(x\) for which \(\dfrac{1}{2x^{2}-13x+15}\) is not defined.
3. [1]

WASSCE 2022 · Paper 1

**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 \(\angle QPS\).
Diagram for question 3
4. [1]

WASSCE 2022 · Paper 1

The bearing of a point \(P\) from a point \(Q\) is \(065^\circ\). What is the bearing of \(Q\) from \(P\)?
5. [1]

WASSCE 2022 · Paper 1

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. \([Take\ \pi=\frac{22}{7}]\)
6. [1]

WASSCE 2022 · Paper 1

Find the truth set of \((3 + x)(1 - x) > 9 - x^{2}\).
7. [1]

WASSCE 2022 · Paper 1

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?
8. [1]

WASSCE 2022 · Paper 1

Simplify: \(\frac{1}{2}(x-1)-\frac{1}{3}\left(\frac{1}{2}x-1\right)\).
9. [1]

WASSCE 2022 · Paper 1

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?
10. [1]

WASSCE 2022 · Paper 1

Given that \(4x + 6y = 5\) and \(2x + 4y = 3\), find the value of \((x + 2y)\).
11. [1]

WASSCE 2022 · Paper 1

Simplify \(\dfrac{9-x^{2}}{3x-x^{2}}\), where \(x \ne 3\).
12. [1]

WASSCE 2022 · Paper 1

Given that \(P \propto v^{2}x\) and \(x \propto vt\), express \(P\) in terms of \(v\) and \(t\).
13. [1]

WASSCE 2022 · Paper 1

Express, correct to two significant figures \(\left(\frac{9}{28}-\frac{2}{7}\right)\).
14. [1]

WASSCE 2022 · Paper 1

**DIAGRAM WILL BE PROVIDED.** Find the value of \(y\) in the diagram.
Diagram for question 14
15. [1]

WASSCE 2022 · Paper 1

If \((23)_{x} = (1111)_{two}\), find the value of \(x\).
16. [1]

WASSCE 2022 · Paper 1

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?
17. [1]

WASSCE 2022 · Paper 1

If \(9^{\,y+1} = \left(\frac{1}{27}\right)^{\,y-2}\), find \(y\).
18. [1]

WASSCE 2022 · Paper 1

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?
19. [1]

WASSCE 2022 · Paper 1

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.
20. [1]

WASSCE 2022 · Paper 1

The interior angle of a regular polygon is twice the exterior angle. How many sides has the polygon?
21. [1]

WASSCE 2022 · Paper 1

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.
22. [1]

WASSCE 2022 · Paper 1

If \(A=\frac{1}{2}b(a + b)\), make \(a\) the subject of the relation.
23. [1]

WASSCE 2022 · Paper 1

Evaluate \(\dfrac{53,000,000 \times 0.002}{0.0004}\).
24. [1]

WASSCE 2022 · Paper 1

If \(\frac{x + y}{5} = \frac{x - y}{3}\), find \(x:y\).
25. [1]

WASSCE 2022 · Paper 1

Find the equation of the line passing through \(P(4,1)\) and parallel to \(2x + 5y = -10\).
26. [1]

WASSCE 2022 · Paper 1

The exterior angles of a quadrilateral are \(61^\circ,76^\circ,(x+10)^\circ\) and \((2x+45)^\circ\). Find the value of \(x\).
27. [1]

WASSCE 2022 · Paper 1

If \(17 \equiv 3 \pmod{x}\), find the least value of \(x\).
28. [1]

WASSCE 2022 · Paper 1

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.
29. [1]

WASSCE 2022 · Paper 1

Consider the following statements: M: Helena studies hard; N: Helena passes her examination. If \(M \Rightarrow N\)
30. [1]

WASSCE 2022 · Paper 1

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.
31. [1]

WASSCE 2022 · Paper 1

Given that \(6\log(x + 4) = \log 64\), find the value of \(x\).
32. [1]

WASSCE 2022 · Paper 1

A die is rolled once. Find the probability of obtaining a number less than 3.
33. [1]

WASSCE 2022 · Paper 1

**DIAGRAM WILL BE PROVIDED.** If the area of the trapezium \(MNOP\) is \(300\ \text{cm}^{2}\), find the value of \(x\).
Diagram for question 33
34. [1]

WASSCE 2022 · Paper 1

Find the 11th term of \(\frac{1}{4},\frac{5}{8},1,\frac{13}{8}, \ldots\).
35. [1]

WASSCE 2022 · Paper 1

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.
36. [1]

WASSCE 2022 · Paper 1

**DIAGRAM WILL BE PROVIDED.** In the diagram, \(MN // PQ\). Find the value of \((x + y)\).
Diagram for question 36
37. [1]

WASSCE 2022 · Paper 1

Simplify \(\dfrac{\sqrt{3}+\sqrt{48}}{\sqrt{6}}\).
38. [1]

WASSCE 2022 · Paper 1

The length of a rectangular lawn is 3 cm longer than the width. If the perimeter is 42 cm, find the width.
39. [1]

WASSCE 2022 · Paper 1

Given that \(p=x-\frac{1}{x}\) and \(q=x^{2}+\frac{1}{x^{2}}\), express \(q\) in terms of \(p\).
40. [1]

WASSCE 2022 · Paper 1

A car moves at an average speed of 30 kmh\(^{-1}\). How long does it take to cover 200 metres?
41. [1]

WASSCE 2022 · Paper 1

If \(y\) varies as the square of \(x\), \(y = 3\) when \(x = \sqrt{2}\), find the value of \(y\) when \(x = 2\).
42. [1]

WASSCE 2022 · Paper 1

**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 \(x\).
Diagram for question 42
43. [1]

WASSCE 2022 · Paper 1

The mass of some market women in kg are: 83, 47, 62, 49, 55, 72, 58 and 62. Find the range.
44. [1]

WASSCE 2022 · Paper 1

The mass of some market women in kg are: 83, 47, 62, 49, 55, 72, 58 and 62. Find the mean.
45. [1]

WASSCE 2022 · Paper 1

Evaluate \(\tan 30^\circ - 2\sin 60^\circ\).
46. [1]

WASSCE 2022 · Paper 1

Simplify: \(8\frac{1}{6}-\left(11\frac{2}{3}\div 2\frac{2}{3}\right)\).
47. [1]

WASSCE 2022 · Paper 1

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?
48. [1]

WASSCE 2022 · Paper 1

One side of a rectangle is 8 cm and the diagonal is 10 cm. Calculate the area of the rectangle.
49. [1]

WASSCE 2022 · Paper 1

**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 \(\angle FEP\).
Diagram for question 49
50. [1]

WASSCE 2022 · Paper 1

**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 \(\angle PRS\).
Diagram for question 50

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