Download 2023 WASSCE Core Mathematics Questions & Answers (PDF)

1. [1]

WASSCE 2023 · Paper 1

A point on the ground is 5 m away from the foot of a vertical wall 12 m high. Calculate, correct to the nearest degree, the angle of depression of the point from the top of the wall.

2. [1]

WASSCE 2023 · Paper 1

The gradient of the line passing through the points (3, 6) and (x, 4) is (-\frac{2}{5}). Find the value of x.

3. [1]

WASSCE 2023 · Paper 1

A woman pours 85 litres of kerosene into a cylindrical container with radius 7 cm. Calculate, correct to the nearest cm, the depth of the kerosene in the container. [\text{Take } \pi = \frac{22}{7}]

4. [1]

WASSCE 2023 · Paper 1

Given that (x^2 - 11x + m) is a perfect square, find the value of m.

5. [1]

WASSCE 2023 · Paper 1

The sides of a scalene triangle are 4 cm, 9 cm and 11 cm. Calculate, correct to the nearest whole number, the area of the triangle.

6. [1]

WASSCE 2023 · Paper 1

In a hall, there are 175 persons. 12% are children, 56 are men and the rest are women. If one person is selected at random from the hall, find the probability that a woman is selected.

7. [1]

WASSCE 2023 · Paper 1

A student measured the length of a classroom and obtained 3.99 m which is less than the actual length. If the percentage error was 5%, what was the actual length?

8. [1]

WASSCE 2023 · Paper 1

A car covers the first 80 km of a journey in 2 hours and completes the journey by travelling further 2.5 hours at 50 km/h. What is the average speed of the entire journey?

9. [1]

WASSCE 2023 · Paper 1

If (\log x = 2 - 3\log 2), find the value of x.

10. [1]

WASSCE 2023 · Paper 1

The graph of (y = x^2 - 5x + k) passes through the point (3, 1). Find the value of k.

11. [1]

WASSCE 2023 · Paper 1

Diagram will be provided Find the value of x in the diagram.

12. [1]

WASSCE 2023 · Paper 1

Diagram will be provided In the diagram, (p + q = 250^\circ). Find the angle marked s.

13. [1]

WASSCE 2023 · Paper 1

If (x : y : z = 2 : 3 : 4), evaluate (\dfrac{9x + 3y}{6z - 2y}).

14. [1]

WASSCE 2023 · Paper 1

Find the mean of ((x + y)), ((2x + 3y)), ((2x - 2y)) and ((3x - 2y)).

15. [1]

WASSCE 2023 · Paper 1

A box contains 2 red, 6 white and 5 black balls, all of the same size. If a ball is selected at random, what is the probability that it is black?

16. [1]

WASSCE 2023 · Paper 1

Diagram will be provided In the diagram, MNPQ is a circle, centre O. (\angle MQN = 43^\circ) and (\angle QNP = 57^\circ). Find the value of y.

17. [1]

WASSCE 2023 · Paper 1

Diagram will be provided Describe the locus, l in the diagram.

18. [1]

WASSCE 2023 · Paper 1

The base radius and slant height of a solid cone are 8 cm and 14 cm respectively. Calculate, correct to two decimal places, its volume. [\text{Take } \pi = \frac{22}{7}]

19. [1]

WASSCE 2023 · Paper 1

Abudu can do a piece of work in 6 days and Efah can do the same work in 3 days. What fraction of the work can both do together in a day?

20. [1]

WASSCE 2023 · Paper 1

If (P = {x: 1 \le x \le 6}) and (Q = {x: 2 < x < 9}) where (x \in R), find (P \cap Q).

21. [1]

WASSCE 2023 · Paper 1

Given that (p^2 + q^2 + r^2 = 50), (p = 5) and (\sqrt{q} = 2), find the positive value of r.

22. [1]

WASSCE 2023 · Paper 1

If (\frac{1}{2}) and -3 are the roots of (px^2 + qx + r = 0), find the values of p, q and r.

23. [1]

WASSCE 2023 · Paper 1

A cylindrical container closed at both ends has radius 5 cm and height 10 cm. Calculate to two decimal places, the total surface area. [\text{Take } \pi = \frac{22}{7}]

24. [1]

WASSCE 2023 · Paper 1

Badu is four times as old as Juliet. In 10 years Badu will be twice as old as Juliet. Find Juliet's age.

25. [1]

WASSCE 2023 · Paper 1

When the point (4, 5) is rotated through an angle in the anticlockwise direction about the origin, its image is (-5, 4). What is the angle of rotation?

26. [1]

WASSCE 2023 · Paper 1

Diagram will be provided Find the value of x in the diagram.

27. [1]

WASSCE 2023 · Paper 1

A woman bought a washing machine for USD 18,000.00. If the exchange rate is USD 0.045 to ₦1.00, find in ₦, the cost of the machine.

28. [1]

WASSCE 2023 · Paper 1

Determine the least value of x such that (7 + x \equiv 3 \pmod{8}).

29. [1]

WASSCE 2023 · Paper 1

If (\dfrac{4m + 3n}{4m - 3n} = \frac{5}{2}), find the ratio of m : n.

30. [1]

WASSCE 2023 · Paper 1

Yakubu received (12\frac{1}{2}%) of the sales made in a certain mouth. If the amount he received was USD 35,000.00, what was the total sales made?

31. [1]

WASSCE 2023 · Paper 1

The angle of elevation of the top of a vertical pole from a point, P on a level ground is 60°. The distance from P to the foot of the pole is 55 m. Find the height of the pole.

32. [1]

WASSCE 2023 · Paper 1

The ratio of girls to boys in a certain committee is 5 : 2. If there are 35 members in the committee, how many more boys must be added to the committee to have the ratio of girls to boys as 5 : 4?

33. [1]

WASSCE 2023 · Paper 1

Find the values of x for which (\dfrac{x + 1}{3x^2 - 12}) is not defined.

34. [1]

WASSCE 2023 · Paper 1

Given that (\tan x = \frac{12}{5}), find the value of ((\sin x \cos x))

35. [1]

WASSCE 2023 · Paper 1

Consider these two statements: P: N is an odd number Q: N is a prime number greater than 2. Express "If N is not an odd number then N is not a prime number greater than 2" in symbolic form.

36. [1]

WASSCE 2023 · Paper 1

A sector which subtends an angle 150° is cut from a circular plate of radius 14 cm. Find, correct to one decimal place, the perimeter of the remaining plate. [\text{Take } \pi = \frac{22}{7}]

37. [1]

WASSCE 2023 · Paper 1

One side of a gutter is 15 cm lower than the other side. A plank of wood, which is laid across the gutter to form a bridge, slopes at an angle of 35° to the horizontal. How wide is the gutter?

38. [1]

WASSCE 2023 · Paper 1

Diagram will be provided In the diagram, MOP is the diameter of the circle MNP centre O. (\angle NMP = (2x)^\circ) and (\angle EPM = (5x + 18)^\circ). Find the value of x.

39. [1]

WASSCE 2023 · Paper 1

The height of a square base pyramid is thrice the length of a side of its base. If the base area is 324 cm², find the volume of the pyramid.

40. [1]

WASSCE 2023 · Paper 1

If (4^x = \frac{1}{1024}), find the value of x

41. [1]

WASSCE 2023 · Paper 1

"Diagram will be provided" In the diagram, O is the centre of the circle WXY. (|WX| = |XZ|) and (\angle ZXY = 26^\circ). Find (\angle XYZ).

42. [1]

WASSCE 2023 · Paper 1

Evaluate (141_6 + 233_6 - 102_6)

43. [1]

WASSCE 2023 · Paper 1

In the first year, Mr. Kwakye's annual salary was USD 1,560.00. His salary was increased each year by a constant value, y until it was USD 13,980.00 in the 13th year. Calculate the value of y.

44. [1]

WASSCE 2023 · Paper 1

Given that (\frac{16}{9}, x, 1, y) is a Geometric Progression (G.P), find the value of xy.

45. [1]

WASSCE 2023 · Paper 1

A chord of a circle, 12 cm long subtends an angle of 150° at the centre of the circle. Find the radius of the circle.

46. [1]

WASSCE 2023 · Paper 1

The lines (3x + 2y = 4) and (y = 2x - 5) intersect at a point P(x, y). Find the coordinates of P.

47. [1]

WASSCE 2023 · Paper 1

Make u the subject of the relation (\dfrac{t}{s+u} = \dfrac{s}{t-u}).

48. [1]

WASSCE 2023 · Paper 1

"Table will be provided"The table shows the number of subjects registered by a class of students for an examination. Use the information to answer the question below Calculate the mean of the distribution.

49. [1]

WASSCE 2023 · Paper 1

"Table will be provided" The table shows the number of subjects registered by a class of students for an examination. Use the information to answer the question below Find the median.

50. [1]

WASSCE 2023 · Paper 1

A rectangular tank of sides 4 m by 8 m by 11 m has the same volume as a cylindrical tank of height 7 m. Calculate the base radius of the cylindrical tank. [\text{Take } \pi = \frac{22}{7}]

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