WASSCE past question

Core Mathematics 2021

Core Mathematics Paper 1

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1. [1]

WASSCE 2021 · Paper 1

Correct 0.00798516 to three significant figures.
2. [1]

WASSCE 2021 · Paper 1

Simplify: \((11)_2\)^2
3. [1]

WASSCE 2021 · Paper 1

Solve: \(2^{\sqrt{2x + 1}} = 32\)
4. [1]

WASSCE 2021 · Paper 1

If \(\log_{10} 2 = m\) and \(\log_{10} 3 = n\), find \(\log_{10} 24\) in terms of m and n.
5. [1]

WASSCE 2021 · Paper 1

Find the 5th term of the sequence 2, 5, 10, 17....?
6. [1]

WASSCE 2021 · Paper 1

If \(P = \{-3 < x < 1\}\) and \(Q = \{-1 < x < 3\}\), where x is a real number, find \(P \cap Q\).
7. [1]

WASSCE 2021 · Paper 1

Factorize \(6pq - 3rs - 3ps + 6qr\).
8. [1]

WASSCE 2021 · Paper 1

What number should be subtracted from the sum of \(2\frac{1}{6}\) and \(2\frac{7}{12}\) to give \(3\frac{1}{4}\)?
9. [1]

WASSCE 2021 · Paper 1

Mensah is 5 years old and Joyce is thrice as old as Mensah. In how many years will Joyce be twice as old as Mensah?
10. [1]

WASSCE 2021 · Paper 1

If \(16 \times 2^{(x + 1)} = 4^{x} \times 8^{(1 − x)}\), find the value of x.
11. [1]

WASSCE 2021 · Paper 1

The circumference of a circular track is 9 km. A cyclist rides round it a number of times and stops after covering a distance of 302 km. How far is the cyclist from the starting point?
12. [1]

WASSCE 2021 · Paper 1

Simplify \(2\sqrt{7} - \frac{14}{\sqrt{7}} + \frac{7}{\sqrt{21}}\)
13. [1]

WASSCE 2021 · Paper 1

If \(4x + 2y = 16\) and \(6x - 2y = 4\), find the value of \((y - x)\).
14. [1]

WASSCE 2021 · Paper 1

Given that R is directly proportional to L and inversely proportional to P, R = 3 when L = 9 and P = 0.8, find R when L = 15 and P = 1.8.
15. [1]

WASSCE 2021 · Paper 1

**DIAGRAM WILL BE PROVIDED.** In the diagram, \(\angle ABC\) and \(\angle BCD\) are right angles, \(\angle BAD = t\) and \(\angle EDF = 70^\circ\). Find the value of t.
Diagram for question 15
16. [1]

WASSCE 2021 · Paper 1

The sum of the interior angles of a regular polygon with k sides is (3k - 10) right angles. Find the size of the exterior angle.
17. [1]

WASSCE 2021 · Paper 1

Make U the subject of the relation: \(x = \frac{2U - 3}{3U + 2}\).
18. [1]

WASSCE 2021 · Paper 1

A trader paid import duty of 38 kobo in the naira on the cost of an engine. If a total of ₦ 22,800.00 was paid as import duty, calculate the cost of the engine.
19. [1]

WASSCE 2021 · Paper 1

The height of an equilateral triangle is \(10\sqrt{3}\) cm. Calculate its perimeter.
20. [1]

WASSCE 2021 · Paper 1

In a \(\triangle LMN\), \(|LM| = 6\) cm, \(\angle LMN = 90^\circ\), \(\angle LNM = x\) and \(\sin x = \frac{3}{5}\). Find the area of \(\triangle LMN\).
21. [1]

WASSCE 2021 · Paper 1

**DIAGRAM WILL BE PROVIDED.** Consider the statements: P: = All students offering Literature(L) also offer History(H); Q: = Students offering History(H) do not offer Geography(G). Which of the Venn diagram correctly illustrate the two statements?
22. [1]

WASSCE 2021 · Paper 1

Find The quadratic Equation whose roots are \(-2q\) And \(5q\).
23. [1]

WASSCE 2021 · Paper 1

If \(\tan \theta = \frac{3}{4}\), \(180^\circ < \theta < 270^\circ\), find the value of \(\cos \theta\).
24. [1]

WASSCE 2021 · Paper 1

If \(\frac{2}{(x - 3)} - \frac{3}{(x - 2)} = \frac{p}{(x - 3)(x - 2)}\), find p.
25. [1]

WASSCE 2021 · Paper 1

The diagonal of a rhombus are 12 cm and 5 cm. Calculate its perimeter.
26. [1]

WASSCE 2021 · Paper 1

**DIAGRAM WILL BE PROVIDED.** In the diagram, \(\triangle XYZ\) is produced to T. If \(|XY| = |ZY|\) and \(\angle XYT = 40^\circ\), find \(\angle XZT\).
Diagram for question 26
27. [1]

WASSCE 2021 · Paper 1

A solid brass cube is melted and recast as a solid cone of height h and base radius r. If the height of the cube is h, find r in terms of h.
28. [1]

WASSCE 2021 · Paper 1

Which of the following is not an exterior angle of a regular polygon?
29. [1]

WASSCE 2021 · Paper 1

From a point T, a man moves 12 km due West and then moves 12 km due South to another point Q. Calculate the bearing of T from Q.
30. [1]

WASSCE 2021 · Paper 1

**DIAGRAM WILL BE PROVIDED.** In the diagram, O is the centre of the circle PQRS, \(\angle PQR = 72^\circ\) and \(OR\parallel PS\). Find \(\angle OPS\).
Diagram for question 30
31. [1]

WASSCE 2021 · Paper 1

A trapezium of parallel sides 10 cm and 21 cm and height 8 cm is inscribed in a circle of radius 7 cm. Calculate the area of the region not covered by the trapezium. [Take \(\pi = \frac{22}{7}\)]
32. [1]

WASSCE 2021 · Paper 1

Find correct to two decimal places the mean of \(1\frac{1}{2},\;2\frac{2}{3},\;3\frac{3}{4},\;4\frac{4}{5}\) and \(5\frac{5}{6}\).
33. [1]

WASSCE 2021 · Paper 1

A cyclist moved at a speed of X km/h for 2 hours. He then increased his speed by 2 km/h for the next 3 hours. If the total distance covered is 36 km, calculate his initials speed.
34. [1]

WASSCE 2021 · Paper 1

**DIAGRAM WILL BE PROVIDED.** Find the value of \((x + y)\) in the diagram.
Diagram for question 34
35. [1]

WASSCE 2021 · Paper 1

**DIAGRAM WILL BE PROVIDED.** In the diagram, MP is a tangent to the circle NQR, \(\angle PNQ = 64^\circ\) and \(|RQ| = |RN|\). Find the angle marked t.
Diagram for question 35
36. [1]

WASSCE 2021 · Paper 1

Find the first quartile of 7, 8, 7, 9, 11, 8, 7, 9, 6 and 8.
37. [1]

WASSCE 2021 · Paper 1

**DIAGRAM WILL BE PROVIDED.** In the diagram, PQRS is a circle. find the value of x.
Diagram for question 37
38. [1]

WASSCE 2021 · Paper 1

A cone has a base radius of 8 cm and height 11 cm. Calculate, correct to two decimal places, the curved surface area. [Take \(\pi = \frac{22}{7}\)]
39. [1]

WASSCE 2021 · Paper 1

Given that \(\sin x = \frac{3}{5}\), \(0^\circ \le x \le 90^\circ\), evaluate \((\tan x + 2\cos x)\).
40. [1]

WASSCE 2021 · Paper 1

**DIAGRAM WILL BE PROVIDED.** In the diagram \(EC\) is a diameter of circle ABCDE. If \(\angle ABC = 158^\circ\), find \(\angle ADE\).
Diagram for question 40
41. [1]

WASSCE 2021 · Paper 1

**TABLE WILL BE PROVIDED.** The table shows the heights of thirty-seven players of a basketball team. Calculate, correct to one decimal place, the mean height of the players.
Diagram for question 41
42. [1]

WASSCE 2021 · Paper 1

XY is a line segment with the coordinates X(-8, -12) and Y(p, q). If the midpoint of XY is (-4, -2), find the coordinates of Y.
43. [1]

WASSCE 2021 · Paper 1

Five hundred tickets were sold for a concert. Tickets for adults and children were sold at USD 4.50 and USD 3.00, respectively. If the total receipts for the concerts was USD 1987.50, how many tickets for adults were sold?
44. [1]

WASSCE 2021 · Paper 1

The distance (d) between two villages is more than 18 km but not more than 23 km. Which of these inequalities represents the statements?
45. [1]

WASSCE 2021 · Paper 1

**DIAGRAM WILL BE PROVIDED.** The pie chart represents the distribution of fruits on display in a shop. If there are 60 apples on display, how many oranges are there?
Diagram for question 45
46. [1]

WASSCE 2021 · Paper 1

A box contains 40 identical balls of which 10 are red and 12 are blue. If a ball is selected at random from the box, what is the probability that it is neither red nor blue?
47. [1]

WASSCE 2021 · Paper 1

A fair die is tossed twice. What is the probability of getting a sum of at least 10?
48. [1]

WASSCE 2021 · Paper 1

A man will be (x + 10) years old in 8 years time. If 2 years ago he was 63 years, find the value of x
49. [1]

WASSCE 2021 · Paper 1

The equation of a line is given as 3x - 5y = 7. Find its gradient (slope).
50. [1]

WASSCE 2021 · Paper 1

For what value of x is \(4 - \frac{2x}{x + 1}\) undefined?

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