1.
Matrices
Find the determinant of the matrix (-3 -1; 3 -5).
Answer: D. Determinant = ad − bc = (-3)(-5) − (-1)(3) = 18.
WAEC GCE Further Mathematics practice questions
Try 10 free Further Mathematics questions below, each with the answer explained. When you are ready, practise all 954 on a timed CBT screen.
The GCE is the version of the school-leaving exam for private candidates, usually held towards the end of the year. It follows the same syllabus as the May/June exam, with objective and theory papers.
- 954 questions in our bank
- 15 topics
- Every answer explained
10 free sample questions
Tap an answer to check it and see the explanation.
2.
Mechanics
A body of mass 7 kg moving at 17 m/s collides with a stationary body of mass 9 kg and they move off together. Find their common velocity.
Answer: C. Momentum is conserved: 7 × 17 = (7 + 9)v, so v = 7.44 m/s.
3.
Statistics
Calculate the variance of: 2, 3, 10, 2.
Answer: C. Mean = 4.25. Variance = Σ(x − mean)² ÷ n = 11.19.
4.
Sequences and series
Find the sum to infinity of a geometric progression with first term 12 and common ratio 3/4.
Answer: D. S∞ = a ÷ (1 − r) = 12 ÷ (1 − (3/4)) = 48.
5.
Limits
Evaluate the limit as x → 8 of (x² − 15x + 56) ÷ (x − 8).
Answer: A. Factorise the numerator: (x − 8)(x − 7). Cancel (x − 8) and substitute x = 8: 1.
6.
Integration
Evaluate ∫ from 1 to 4 of (12x² − 10x) dx.
Answer: C. The integral is 4x³ − 5x². Evaluate at 4 and 1 and subtract: 177.
7.
Coordinate geometry
Find the radius of the circle x² + y² − 12x + 35 = 0.
Answer: A. Centre (6, 0); r² = 6² + 0² − (35) = 1, so r = 1.
8.
Polynomials
Find the remainder when x³ − 4x² − 5x + 4 is divided by (x − 2).
Answer: C. By the remainder theorem, the remainder is f(2) = -14.
9.
Permutation and combination
In how many ways can a committee of 4 be chosen from 12 people?
Answer: D. Order does not matter, so use combinations: ⁿCᵣ = 12!/(4!(8)!) = 495.
10.
Binomial theorem
Find the coefficient of x² in the expansion of (1 + 3x)⁵.
Answer: C. The term is 10 × (3x)², so the coefficient is 10 × 3² = 90.
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Questions in the MyGradePrep bank for each topic.
| Topic | Questions |
|---|---|
| Matrices | 121 |
| Vectors | 93 |
| Mechanics | 78 |
| Differentiation | 64 |
| Integration | 62 |
| Sequences and series | 62 |
| Coordinate geometry | 62 |
| Limits | 61 |
| Polynomials | 61 |
| Statistics | 61 |
| Probability | 61 |
| Quadratic equations | 60 |
| Permutation and combination | 59 |
| Binomial theorem | 24 |
| Logarithms | 20 |