WASSCE past question

Core Mathematics 2025

Core Mathematics Paper 1

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1. [1]

WASSCE 2025 · Paper 1

Given that log₁₀5 = x and log₁₀11 = y, express log₁₀275 in terms of x and y.
2. [1]

WASSCE 2025 · Paper 1

The sets P = {x:x = 3, 5, 6} and Q = {x: 2 ≤ x ≤ 5} are subsets of μ = {x: 1 ≤ x ≤ 10, where x is an integer}. Find P' ∩ Q.
3. [1]

WASSCE 2025 · Paper 1

A pyramid has a rectangular base of length 6.5 cm and width 4.2 cm. If the height of the pyramid is 12 cm, find the volume.
4. [1]

WASSCE 2025 · Paper 1

Given that \((1 \tfrac{2}{3})^{\tfrac{x}{2}} = (4 \tfrac{17}{27})\), find the value of \(x\).
5. [1]

WASSCE 2025 · Paper 1

The first 4 terms of an Arithmetic Progression (A.P) are 8, x , y and 17. Find the value of \((x + y)\).
6. [1]

WASSCE 2025 · Paper 1

In a test, the mean mark of 25 students in a class, P, is 72.2 and the mean mark of 20 students in another class, Q, is 65. Find the mean mark of all the students in P and Q.
7. [1]

WASSCE 2025 · Paper 1

Mr. Gyan bought a car for USD 16,800.00 and later sold it at 85 % of the original cost. He spent USD 3,930.75 from the money he received from the sale of the car and invested the remaining at 18 % per annum simple interest. How much interest did he earn in 9 years?
8. [1]

WASSCE 2025 · Paper 1

The mean and range of 1.20, 1.00, 0.90, 1.40, 0.80, 0.80, 1.20 and 1.10 are m and r respectively. Find the value of \((m + r)\)
9. [1]

WASSCE 2025 · Paper 1

Given that \(\dfrac{3}{x+y} - \dfrac{4}{x-y} = 0\), find the value of \(\dfrac{x}{y}\), where \(y \ne 0\).
10. [1]

WASSCE 2025 · Paper 1

The last term of the sequence: 7, 11, 15, ... is 115. Find the number of terms in the sequence.
11. [1]

WASSCE 2025 · Paper 1

Find the mean deviation of 2, 5, 7, 9 and 15.
12. [1]

WASSCE 2025 · Paper 1

The locus, L is such that \(|PM| = |PN|\). Which of the following best describes L?
13. [1]

WASSCE 2025 · Paper 1

A train is moving at 60 miles per hour. If it passes a sign post in 15 seconds, find, in yards, the length of the train. [Take 1 mile = 1760 yards]
14. [1]

WASSCE 2025 · Paper 1

Kwaku is 2 years older than Atanga and 6 years younger than Esi. The sum of their ages is 70. If they decide to share USD 153.00 in the ratio of their ages, how much will the eldest person receive?
15. [1]

WASSCE 2025 · Paper 1

Solve: \(\dfrac{\log_{3}(2x - 1)}{\log_{3}243} = \dfrac{2}{5}\).
16. [1]

WASSCE 2025 · Paper 1

The sum of the ages of Esi and Amina is 24 years and the difference in their ages is 6 years. If Amina is older than Esi, find Esi's age.
17. [1]

WASSCE 2025 · Paper 1

Solve: \(4x + 1 \equiv 3(\text{mod }11)\).
18. [1]

WASSCE 2025 · Paper 1

Diagram will be provided In the diagram, \(|PQ| = 6.7\) cm, \(|QR| = 5.5\) cm and \(|RT| = 3.3\) cm. Find the area.
Diagram for question 18
19. [1]

WASSCE 2025 · Paper 1

Diagram will be provided In the diagram, \(\triangle OMN\) is similar to \(\triangle OPQ\). Find \(|MQ|\).
Diagram for question 19
20. [1]

WASSCE 2025 · Paper 1

A scientific sensor records air pollution levels in base 3. If the highest recorded pollution level for a week was \(2120_3\), what is the decimal equivalent?
21. [1]

WASSCE 2025 · Paper 1

Factorize: \(5p^2 + 4pq - 15pr - 12qr\).
22. [1]

WASSCE 2025 · Paper 1

A school has a total population of 1,800 students. Out of this number \(\frac{4}{9}\) are in SHS 1, \(\frac{13}{36}\) are in SHS 2 and the rest are in SHS 3. Calculate the number of students in SHS 3.
23. [1]

WASSCE 2025 · Paper 1

The straight line \(3y + bx - 6 = 0\) passes through (3, 4). Find the value of \(b\).
24. [1]

WASSCE 2025 · Paper 1

A function is defined by \(g:x \rightarrow \dfrac{2x - 1}{3x - 2}\). For what value of x is g not defined?
25. [1]

WASSCE 2025 · Paper 1

Diagram will be provided In the diagram \(\angle QPR = 90^\circ\). If \(q^2 = 25 - r^2\), find the value of \(p\).
Diagram for question 25
26. [1]

WASSCE 2025 · Paper 1

Diagram will be provided In the diagram \(PQRST\) is a trapezium. \(|ST| = 3\) cm, \(|RS| = y\) cm and \(|PS| = 4\) cm. For what values of \(y\) will the area of the trapezium \(PQRST\) be less than or equal to \(10\text{ cm}^2\)?
Diagram for question 26
27. [1]

WASSCE 2025 · Paper 1

A town \(P\) is due south of town \(Q\) and town \(R\) is on a bearing of \(125^\circ\) from \(Q\). If town \(R\) is 20 km due east of \(P\), find \(|PQ|\).
28. [1]

WASSCE 2025 · Paper 1

Diagram will be provided The diagram shows a sector of a circle of radius 42 cm. If the sector is folded to form a right circular cone, find the surface area of the cone. [Take \(\pi = \frac{22}{7}\) ]
Diagram for question 28
29. [1]

WASSCE 2025 · Paper 1

Diagram will be provided In the diagram, P, Q, R and S are points on the circle centre O and \(\angle PQR = 104^\circ\). Find the angle marked y.
Diagram for question 29
30. [1]

WASSCE 2025 · Paper 1

Diagram will be provided In the diagram \(\overline{TX}\) and \(\overline{TY}\) are tangents to the circle \(XYZ\) at \(X\) and \(Y\) respectively, \(\overline{TX} \parallel \overline{YZ}\) and \(\angle XTY = 100^\circ\). Find \(\angle ZXY\).
Diagram for question 30
31. [1]

WASSCE 2025 · Paper 1

The radius of a circle is 4 times the radius of another circle. What is the relationship between their areas?
32. [1]

WASSCE 2025 · Paper 1

Diagram will be provided In the diagram, \(\angle QMP = 40^\circ\) and \(\angle RPM = 30^\circ\). Find the value of x.
Diagram for question 32
33. [1]

WASSCE 2025 · Paper 1

Some of the interior angles of a pentagon are 111°, 131° and 79°. The remaining angles are x and y in the ratio 2 : 3 respectively. Find, correct to the nearest whole number, the value of x.
34. [1]

WASSCE 2025 · Paper 1

Diagram will be provided In the diagram, P, Q, R and S are points on the circle centre O. \(\overline{QS}\) is a diameter and \(\angle ORQ = 41^\circ\). Find \(\angle QSR\).
Diagram for question 34
35. [1]

WASSCE 2025 · Paper 1

Diagram will be provided In the diagram, O is the centre of the circle and \(\angle OXZ = 19^\circ\). Find \(\angle XYZ\).
Diagram for question 35
36. [1]

WASSCE 2025 · Paper 1

A car consumes 36 gallons of fuel over a distance of 2,268 km. Find, in km per litre, the fuel consumption. [Take 1 gallon = 4.5 litres]
37. [1]

WASSCE 2025 · Paper 1

Make \(w\) the subject of the relation \(\dfrac{1}{w} = (h - 1)\left(\dfrac{1}{m} - \dfrac{1}{n}\right)\).
38. [1]

WASSCE 2025 · Paper 1

The inverse of the sum of −3 and twice a certain number is \(\dfrac{1}{5}\). Find the number.
39. [1]

WASSCE 2025 · Paper 1

Diagram will be provided In the diagram, \(O\) is the centre of the circle, \(\angle KLM = x\) and \(|OM| = |ML| = |LK| = |KO|\). Find \(\angle OKL\).
Diagram for question 39
40. [1]

WASSCE 2025 · Paper 1

Diagram will be provided The diagram shows a field \(MNPQRST\), where \(MTS\) is a semicircle. Find the area of the field. [Take \(\pi = \dfrac{22}{7}\) ]
Diagram for question 40
41. [1]

WASSCE 2025 · Paper 1

A box contains 12 red, 8 yellow and 10 green pebbles, all of the same size. If two pebbles are selected at random one after the other, with replacement, find the probability that the first is green and the second is not a red pebble.
42. [1]

WASSCE 2025 · Paper 1

Find the coefficient of \(x^2\) in the expansion of \((4x + 5)(3 - 2x)\).
43. [1]

WASSCE 2025 · Paper 1

Gifty is 19 years younger than her mother. In three years time the sum of their ages will be 67 years. Find the sum of their ages now.
44. [1]

WASSCE 2025 · Paper 1

A fair dice is thrown once. What is the probability of obtaining a 3 or 5?
45. [1]

WASSCE 2025 · Paper 1

The mean of \(a, b, c, d\) and \(e\) is 15. Calculate the mean of \((a + 1)\), \((b + 3)\), \((c + 5)\), \((d + 7)\) and \((e + 9)\).
46. [1]

WASSCE 2025 · Paper 1

If \(V = \pi r^2h\) and \(S = 2\pi rh\), express \(V\) in terms of \(r\) and \(S\).
47. [1]

WASSCE 2025 · Paper 1

A man cycles a distance of (3a) km at \(V\) km/h and then walks a distance of \(a\) km at \((V - 7)\) km/h. Find the total number of hours he spent travelling.
48. [1]

WASSCE 2025 · Paper 1

Peter is in the East of Tom and Tom is in the North of John. If Mike is in the South of John, in which direction of Peter is Mike?
49. [1]

WASSCE 2025 · Paper 1

Simplify: \(\dfrac{25p^{2}-q^{2}}{5p^{2}+6pq+q^{2}}\).
50. [1]

WASSCE 2025 · Paper 1

Correct. 5.40514 to three significant figures.

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