WAEC / WASSCE
WASSCE 2025 Maths Theory: Practice Questions and Solutions
The WASSCE 2025 core mathematics theory paper had 13 questions: five compulsory in Section A worth 40 marks, then five from eight in Section B worth 60 marks, in 2 hours 30 minutes. Candidates reported questions on average speed, simple interest, mensuration, trigonometry and coordinate geometry. Below is that structure explained, plus original practice questions solved in full.
I should be upfront: I sit Cambridge exams, not WASSCE, so nothing on this page is exam-hall memory. I built it from what candidates and prep sites reported about the 2025 core mathematics theory paper, then wrote original practice questions matching that style and difficulty. The real past questions belong to WAEC and I do not copy them. What you get instead are questions testing the same topics the 2025 paper is reported to have tested, solved line by line the way an examiner wants to see working. Read the structure notes first, then attempt each question before opening the solution.
What the 2025 theory paper reportedly covered
WAEC does not publish a topic list, so this comes from candidate discussions and prep sites such as Kuulchat that walk through each paper after the sitting. For 2025, the compulsory Section A is reported to have tested an average speed word problem, simple interest on an investment, the volume of a hemisphere, an angle of depression problem, and coordinate geometry using midpoint and distance. Reported Section B questions include ratio with percentage increase, areas and perimeters of triangles, work rates, and a distance question using latitude and longitude. The usual WAEC staples, statistics, probability, bearings and circle geometry, fill out the choice section in most years. One caution: Ghana and Nigeria sit different series of the WASSCE, and first and second series papers differ too, so treat any reported list as a guide rather than a guarantee.
Paper structure, marks and timing
The theory paper, Paper 2, lasts 2 hours 30 minutes and carries 100 marks. There are 13 questions in two sections. Section A has five shorter compulsory questions worth 40 marks in total, roughly 8 marks each. Section B has eight longer questions of about 12 marks each, and you answer any five of them for 60 marks. So you answer ten questions in 150 minutes. A workable budget is about 10 minutes per Section A question and 18 to 20 minutes per Section B question, which leaves a few minutes to read all of Section B before choosing. Choosing well is a skill: pick the five topics you have actually drilled, not the five questions that look shortest on the page.
How WAEC marks theory answers
WAEC marking schemes award M marks for method, A marks for accuracy and B marks for independent correct statements. An A mark usually cannot be earned without the M mark before it, which is why a bare answer with no working can score almost nothing even when it is right. The flip side is generous: a wrong final answer with correct method keeps most of the marks, and many schemes allow follow-through, so an early slip is not fatal if your later working stays consistent. Give answers to the accuracy asked for, often three significant figures, use the value of pi the paper tells you to use, and always write units. These are small habits that are worth real marks over ten questions.
Worked questions, step by step
A lorry travels the first 100 km of a journey at an average speed of 50 km/h and the remaining 120 km at an average speed of 40 km/h. Calculate the average speed for the whole journey.
- Time for the first stage: 100 divided by 50 equals 2 hours.
- Time for the second stage: 120 divided by 40 equals 3 hours.
- Total distance is 100 plus 120 equals 220 km, and total time is 2 plus 3 equals 5 hours.
- Average speed equals total distance over total time: 220 divided by 5 equals 44 km/h.
Answer: 44 km/h
Where marks slip: Section A style, about 8 marks: M1 for each stage time, M1 for total distance over total time, A1 for 44 km/h with units. Averaging the two speeds to get 45 km/h is the classic error and loses the final marks.
Try one yourself: A cyclist covers 120 km at 40 km/h and then 60 km at 60 km/h. Find the average speed for the whole journey. [Answer: 45 km/h]
Efua invests GHc 8,000 in an account paying simple interest. After 3 years the amount in the account is GHc 9,440. Find (a) the rate of interest per annum, (b) how many years in total the money must stay invested for the amount to reach GHc 10,400 at the same rate.
- Interest earned in 3 years: 9,440 minus 8,000 equals GHc 1,440.
- Interest per year: 1,440 divided by 3 equals GHc 480.
- Rate: 480 divided by 8,000, times 100, equals 6 percent per annum.
- For part (b), total interest needed: 10,400 minus 8,000 equals GHc 2,400.
- Time: 2,400 divided by 480 equals 5 years.
Answer: (a) 6 percent per annum (b) 5 years
Where marks slip: M1 for finding the interest, M1 for the rate formula, A1 for 6 percent; then M1 A1 for the time. If you misread amount as interest, the follow-through rule usually protects your part (b) method marks.
Try one yourself: N50,000 invested at simple interest amounts to N59,000 in 4 years. Find the rate per annum. [Answer: 4.5 percent]
The volume of a solid hemisphere is 2,425.5 cm^3. Taking pi as 22/7, calculate (a) the radius of the hemisphere, (b) its total surface area.
- Volume of a hemisphere is (2/3) pi r^3, so (2/3) times (22/7) times r^3 equals 2,425.5.
- Rearrange: r^3 equals 2,425.5 times 21 divided by 44 equals 1,157.625.
- Cube root: r equals 10.5 cm.
- Total surface area of a solid hemisphere is the curved surface plus the flat circular face: 2 pi r^2 plus pi r^2 equals 3 pi r^2.
- Substitute: 3 times (22/7) times 10.5^2 equals 3 times (22/7) times 110.25 equals 1,039.5 cm^2.
Answer: (a) 10.5 cm (b) 1,039.5 cm^2
Where marks slip: M1 for the volume formula, M1 for isolating r^3, A1 for 10.5 cm; then M1 for 3 pi r^2 and A1. Forgetting the flat face and giving 2 pi r^2 is the most common way to lose the last two marks.
Try one yourself: A solid hemisphere has radius 7 cm. Taking pi as 22/7, find its volume. [Answer: approximately 718.7 cm^3]
From the top of a vertical cliff 60 m high, the angle of depression of a boat at sea is 35 degrees. The boat sails on a straight line towards the foot of the cliff until the angle of depression becomes 55 degrees. Calculate, correct to three significant figures, the distance the boat sailed.
- The angle of depression from the top equals the angle of elevation from the boat, so each position forms a right triangle with the 60 m cliff.
- First distance from the cliff: 60 divided by tan 35 equals 60 divided by 0.7002 equals 85.7 m.
- Second distance: 60 divided by tan 55 equals 60 divided by 1.4281 equals 42.0 m.
- Distance sailed: 85.7 minus 42.0 equals 43.7 m.
Answer: 43.7 m (3 s.f.)
Where marks slip: B1 for a correct diagram with both angles marked at the boat positions, M1 A1 for each distance, A1 for the subtraction. Mixing up which distance is larger, or putting the angle at the top of the triangle, costs heavily, so draw first.
Try one yourself: From the top of a tower 45 m high, the angle of depression of a car is 40 degrees. How far is the car from the foot of the tower, to three significant figures? [Answer: 53.6 m]
Stuck on a different question?
Paste or photograph it and get the full working, free — no account needed.
Solve my question →Quiz me on this topicQuestions students ask
Are these the real WAEC 2025 theory questions?
No. WAEC past questions are copyrighted, so this site never reproduces them. These are original questions written in the same format and difficulty, based on the topics the 2025 paper is reported to have covered. For the official questions, use WAEC's own past question booklets or platforms.
How many questions do I answer in the WASSCE core maths theory paper?
Ten out of 13: all five compulsory questions in Section A, worth 40 marks, and any five of the eight questions in Section B, worth 60 marks. The paper lasts 2 hours 30 minutes and carries 100 marks.
Does WAEC give marks for working even if the final answer is wrong?
Yes. Marking schemes award M marks for correct method and A marks for accuracy, and many parts allow follow-through from an earlier slip. Showing every step protects most of the marks; a correct answer with no working can score very little.
Which topics should I revise first for the theory paper?
The recurring ones: algebra, mensuration, statistics, probability, bearings with trigonometry, and circle geometry. This site has a solved practice page for each of those topics written in the same WASSCE style as this one.