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.
Tap an answer to check it and see the explanation.
Evaluate the determinant of the 3 × 3 matrix (3 0 3; -2 -1 1; 1 -3 0).
Answer: B. Expanding along the first row with alternating signs (+ − +): determinant = 30.
A body of mass 5 kg moving at 8 m/s collides with a stationary body of mass 2 kg and they move off together. Find their common velocity.
Answer: A. Momentum is conserved: 5 × 8 = (5 + 2)v, so v = 5.71 m/s.
Calculate the variance of: 9, 9, 1, 11, 4, 5.
Answer: B. Mean = 6.5. Variance = Σ(x − mean)² ÷ n = 11.92.
Find the sum to infinity of a geometric progression with first term 51 and common ratio 3/4.
Answer: A. S∞ = a ÷ (1 − r) = 51 ÷ (1 − (3/4)) = 204.
Evaluate the limit as x → 1 of (x² + 2x − 3) ÷ (x − 1).
Answer: B. Factorise the numerator: (x − 1)(x + 3). Cancel (x − 1) and substitute x = 1: 4.
Evaluate ∫ from 1 to 4 of (3x² + 4x) dx.
Answer: A. The integral is 1x³ + 2x². Evaluate at 4 and 1 and subtract: 93.
Find the radius of the circle x² + y² + 4x − 12y − 41 = 0.
Answer: B. Centre (-2, 6); r² = -2² + 6² − (-41) = 81, so r = 9.
Find the remainder when x³ − 3x² − 2x + 3 is divided by (x + 3).
Answer: B. By the remainder theorem, the remainder is f(-3) = -45.
In how many ways can a president, a secretary and a treasurer be chosen from 5 candidates?
Answer: C. Order matters, so use permutations: ⁿPᵣ = 5!/(2)! = 60.
Find the coefficient of x³ in the expansion of (1 + 3x)⁷.
Answer: D. The term is 35 × (3x)³, so the coefficient is 35 × 3³ = 945.
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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 |