1.
Matrices
Find the determinant of the matrix (1 -5; -5 6).
Answer: B. Determinant = ad − bc = (1)(6) − (-5)(-5) = -19.
NECO SSCE 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 NECO SSCE (June/July) is the National Examinations Council's final exam for Nigerian secondary school students. Like WAEC, each subject has an objective paper and a theory paper, and the syllabus covers the same topics.
- 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 5 kg moving at 7 m/s collides with a stationary body of mass 7 kg and they move off together. Find their common velocity.
Answer: C. Momentum is conserved: 5 × 7 = (5 + 7)v, so v = 2.92 m/s.
3.
Sequences and series
Find the sum to infinity of a geometric progression with first term 24 and common ratio 3/4.
Answer: C. S∞ = a ÷ (1 − r) = 24 ÷ (1 − (3/4)) = 96.
4.
Statistics
Calculate the variance of: 6, 6, 2, 2, 3, 8.
Answer: C. Mean = 4.5. Variance = Σ(x − mean)² ÷ n = 5.25.
5.
Limits
Evaluate the limit as x → 4 of (x² + x − 20) ÷ (x − 4).
Answer: B. Factorise the numerator: (x − 4)(x + 5). Cancel (x − 4) and substitute x = 4: 9.
6.
Integration
Evaluate ∫ from 0 to 5 of (3x² − 10x) dx.
Answer: D. The integral is 1x³ − 5x². Evaluate at 5 and 0 and subtract: 0.
7.
Coordinate geometry
Find the radius of the circle x² + y² + 2y − 35 = 0.
Answer: D. Centre (0, -1); r² = 0² + -1² − (-35) = 36, so r = 6.
8.
Polynomials
Find the remainder when x³ + 4x² + 5x − 9 is divided by (x).
Answer: D. By the remainder theorem, the remainder is f(0) = -9.
9.
Permutation and combination
In how many ways can a committee of 3 be chosen from 5 people?
Answer: B. Order does not matter, so use combinations: ⁿCᵣ = 5!/(3!(2)!) = 10.
10.
Binomial theorem
Find the coefficient of x² in the expansion of (1 + 2x)⁶.
Answer: A. The term is 15 × (2x)², so the coefficient is 15 × 2² = 60.
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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 |