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 WASSCE (May/June) is the West African Examinations Council's final exam for secondary school students. Each subject has an objective (multiple-choice) paper and a theory or essay paper.
Tap an answer to check it and see the explanation.
Evaluate the determinant of the 3 × 3 matrix (4 0 3; -1 4 -1; 1 -1 2).
Answer: A. Expanding along the first row with alternating signs (+ − +): determinant = 19.
A particle is projected with a speed of 70 m/s at 30° to the horizontal. Find its time of flight. (g = 10 m/s²)
Answer: B. T = 2u sin θ ÷ g = 2 × 70 × sin 30° ÷ 10 = 7 s.
Find the sum to infinity of a geometric progression with first term 51 and common ratio 2/3.
Answer: A. S∞ = a ÷ (1 − r) = 51 ÷ (1 − (2/3)) = 153.
Calculate the variance of: 10, 7, 12, 9, 7, 12.
Answer: B. Mean = 9.5. Variance = Σ(x − mean)² ÷ n = 4.25.
Evaluate the limit as x → 6 of (x² + 3x − 54) ÷ (x − 6).
Answer: D. Factorise the numerator: (x − 6)(x + 9). Cancel (x − 6) and substitute x = 6: 15.
Find the radius of the circle x² + y² − 6x − 72 = 0.
Answer: D. Centre (3, 0); r² = 3² + 0² − (-72) = 81, so r = 9.
Evaluate ∫ from 0 to 5 of (3x² + 12x) dx.
Answer: B. The integral is 1x³ + 6x². Evaluate at 5 and 0 and subtract: 275.
Find the remainder when x³ + 2x² − 6x − 2 is divided by (x − 1).
Answer: B. By the remainder theorem, the remainder is f(1) = -5.
In how many ways can a president, a secretary be chosen from 9 candidates?
Answer: A. Order matters, so use permutations: ⁿPᵣ = 9!/(7)! = 72.
Find the coefficient of x³ in the expansion of (1 + 2x)⁶.
Answer: A. The term is 20 × (2x)³, so the coefficient is 20 × 2³ = 160.
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Create a free accountQuestions 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 |