WASSCE past question

Core Mathematics 2026

Core Mathematics Paper 1

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Objective Test — instructions

Answer all the questions. Mathematical tables may be used in any question. The use of non-programmable, silent and cordless calculator is allowed. Each question is followed by four options lettered A to D. Find the correct option for each question and shade in pencil, on your answer sheet, the answer space which bears the same letter as the option you have chosen. Give only one answer to each question.

1. [1]

WASSCE 2026 · Paper 1

A cylindrical flask of radius 6 cm and height 12 cm has a hemispherical cover. What is the total volume of the flask.
2. [1]

WASSCE 2026 · Paper 1

The sum of three consecutive positive integers is 87. Find the largest of the integers.
3. [1]

WASSCE 2026 · Paper 1

Given that \(\dfrac{p}{k} = \dfrac{dt}{r+k}\), make \(k\) the subject.
4. [1]

WASSCE 2026 · Paper 1

The exterior angles of a polygon are \((2x)^\circ, (3x)^\circ, (3x)^\circ, (2x)^\circ\) and \((5x)^\circ\). Find the value of \(x\).
5. [1]

WASSCE 2026 · Paper 1

The mean of six children whose ages are 4, 6, 7, x, 10 and 12 is 8 years. Find the standard deviation.
6. [1]

WASSCE 2026 · Paper 1

The pie chart shows the distribution of the favourite meal of 600 students in a school. The sectors are: Rice \(45^\circ\), Banku \(85^\circ\), Yam \(60^\circ\), Konkonte \(160^\circ\), Plantain \(50^\circ\). Use the information to answer the question. How many students has Konkonte as their favourite meal?
Diagram for question 6
7. [1]

WASSCE 2026 · Paper 1

The pie chart shows the distribution of the favourite meal of 600 students in a school. The sectors are: Rice \(45^\circ\), Banku \(85^\circ\), Yam \(60^\circ\), Konkonte \(160^\circ\), Plantain \(50^\circ\). Use the information to answer the question. What percentage of the students has rice as their favourite meal?
Diagram for question 7
8. [1]

WASSCE 2026 · Paper 1

Alieu, Bonsu and Charles share USD 170.00 in the ratio 19 : 27 : 37 respectively. How much more does Bonsu get than Alieu?
9. [1]

WASSCE 2026 · Paper 1

Evaluate: 92 (modulo 5).
10. [1]

WASSCE 2026 · Paper 1

Form the quadratic equation whose roots are -8 and 7.
11. [1]

WASSCE 2026 · Paper 1

If \(\log_2(5x-2) - \log_2(2x-5) = 2\), find the value of \(x\).
12. [1]

WASSCE 2026 · Paper 1

In the diagram \(PQR\) is a triangle with \(\overline{ST} \parallel \overline{PQ}\), \(\angle RQP = 80^\circ\) and \(\angle QRP = 70^\circ\). Find \(\angle RST\).
Diagram for question 12
13. [1]

WASSCE 2026 · Paper 1

Arrange \(\dfrac{1}{4}, \dfrac{2}{3}, \dfrac{5}{6}, \dfrac{3}{5}\) in ascending order.
14. [1]

WASSCE 2026 · Paper 1

Which of the following is not a measure of central tendency?
15. [1]

WASSCE 2026 · Paper 1

A man walks 8 km due North and then 6 km due East. Find the bearing of his final position from his starting point.
16. [1]

WASSCE 2026 · Paper 1

If \(\overrightarrow{PQ} = \begin{pmatrix} 3 \\ -4 \end{pmatrix}\) and \(\overrightarrow{QR} = \begin{pmatrix} -1 \\ 2 \end{pmatrix}\), find \(|\overrightarrow{PR}|\).
17. [1]

WASSCE 2026 · Paper 1

Evaluate \(\log_{10} 8 + \log_{10} 125\).
18. [1]

WASSCE 2026 · Paper 1

The gradient of a line passing through the points \(M(p, 3)\) and \(N(p-2, 1)\) is
19. [1]

WASSCE 2026 · Paper 1

From the top of a building 125 m high, the angle of depression of an object is \(22^\circ\). The foot of the building and the object are on the same horizontal. Find, correct to the nearest whole number, the distance of the object from the foot of the building.
20. [1]

WASSCE 2026 · Paper 1

Given that \(\cos k = \dfrac{4}{5}\), where \(k\) is acute, find the value of \((\tan k - \sin k)\).
21. [1]

WASSCE 2026 · Paper 1

It takes 3 technicians 8 days to install 36 solar panels in a factory. How many working days will it take 4 technicians to install the same number of solar panels in the same factory, working at the same rate?
22. [1]

WASSCE 2026 · Paper 1

Consider the statements: p: There is no Chief who is not wise; q: Every Baba is a chief. Which of the following statements is a valid conclusion from p and q?
23. [1]

WASSCE 2026 · Paper 1

Find the interior angle of a 12-sided regular polygon.
24. [1]

WASSCE 2026 · Paper 1

Solve: \(\dfrac{x-1}{2} + 3x = 10\).
25. [1]

WASSCE 2026 · Paper 1

The bearing of \(P\) from \(Q\) is \(162^\circ\). What is the bearing of \(Q\) from \(P\)?
26. [1]

WASSCE 2026 · Paper 1

A bag contains 5 red, 3 green and 2 blue balls all of the same size. If a ball is picked at random, what is the probability that it is either red or blue?
27. [1]

WASSCE 2026 · Paper 1

A learner compares two data sets i.e. X and Y, both having the same mean. X has a standard deviation 0.95 and Y has a standard deviation 0.55. What does this imply about the distribution of X and Y?
28. [1]

WASSCE 2026 · Paper 1

A variable \(F\) varies directly as the square root of \(L\) and inversely as the square root of \(T\). Given that \(F = 2.1\) when \(L = 9\) and \(T = 25\), express \(L\) in terms of \(F\) and \(T\).
29. [1]

WASSCE 2026 · Paper 1

A car depreciates in value at a rate of 20% each year. If the value of the car is USD 25,000.00, find the value after 3 years.
30. [1]

WASSCE 2026 · Paper 1

By how much is the sum of \(3x\), \((6x - 5)\), \(9x\) and \((4x + 1)\) less than \(30x\)?
31. [1]

WASSCE 2026 · Paper 1

In the diagram, \(|PQ|=|QR|\), \(\angle PQR = 50^\circ\) and \(\angle PRN = (4x-5)^\circ\). Find the value of \(x\).
Diagram for question 31
32. [1]

WASSCE 2026 · Paper 1

Given that \(4x - 2y = 1\) and \(3x - 4y = -0.5\), find the value of \((x + y)\).
33. [1]

WASSCE 2026 · Paper 1

In the diagram, \(PQRS\) is a circle, centre \(O\) and \(\angle RQS = 40^\circ\). Find \(\angle PRS\).
Diagram for question 33
34. [1]

WASSCE 2026 · Paper 1

In a class, there are 20 boys and 15 girls. Two are selected at random one after the other without replacement from the class. What is the probability that they are both boys or both girls?
35. [1]

WASSCE 2026 · Paper 1

The height of an equilateral triangle is \(\sqrt{3}\) cm. Find the perimeter of the triangle.
36. [1]

WASSCE 2026 · Paper 1

When the sum of 84 and a certain number is divided by 3, the result is five times the number. Find the number.
37. [1]

WASSCE 2026 · Paper 1

In the diagram, \(\overline{PR}\) is a tangent to the circle at \(Q\), \(\angle TQS = 49^\circ\) and \(\angle TSQ = 52^\circ\). Find \(\angle SQR\).
Diagram for question 37
38. [1]

WASSCE 2026 · Paper 1

The fifth term of a Geometric Progression is 16 times the third term. Find the positive value of the common ratio.
39. [1]

WASSCE 2026 · Paper 1

Find the distance between \(P(6, -5)\) and \(Q(-2, 1)\).
40. [1]

WASSCE 2026 · Paper 1

In an examination, 32 candidates passed Economics while 36 passed Government. If 18 candidates passed both subjects and 10 failed both subjects, how many candidates sat for the examination?
41. [1]

WASSCE 2026 · Paper 1

Find the value(s) of \(x\) for which \(\dfrac{2+x}{x-3}\) is not defined.
42. [1]

WASSCE 2026 · Paper 1

Factorize: \(35 - 2b - b^2\).
43. [1]

WASSCE 2026 · Paper 1

The scores obtained by some learners are: 23, 27, 27, 32, 35, 36 and 52. Find the range.
44. [1]

WASSCE 2026 · Paper 1

A man gives USD 7,800.00 to be shared among his three sons and two daughters. The sons receives equal share of the amount and each daughter receives two-thirds of what a son received. How much did each son receive?
45. [1]

WASSCE 2026 · Paper 1

In the diagram, \(|PS| = 20\) cm, \(|PQ| = 6\) cm, \(|QR| = x\) cm and \(\angle SPR = 60^\circ\). Use this information to answer questions 45 and 46. Find the value of \(x\).
Diagram for question 45
46. [1]

WASSCE 2026 · Paper 1

In the diagram, \(|PS| = 20\) cm, \(|PQ| = 6\) cm, \(|QR| = x\) cm and \(\angle SPR = 60^\circ\). Use this information to answer questions 45 and 46. Find \(|SR|\).
Diagram for question 46
47. [1]

WASSCE 2026 · Paper 1

Simplify \(\dfrac{4-x^2}{2x-x^2}\), where \(x \neq 0, 2\).
48. [1]

WASSCE 2026 · Paper 1

Solve: \(53_x = 1121_{\text{three}}\).
49. [1]

WASSCE 2026 · Paper 1

A rectangle 10 cm by 9 cm is equal in area to a triangle. If the height of the triangle is 15 cm, find the length of the base.
50. [1]

WASSCE 2026 · Paper 1

Find the truth set of \(\dfrac{1}{2}(3x-5) < 3x+2\).

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