Classroom

Further Mathematics Past Questions

Study and practice Further Mathematics past questions with answers and detailed explanations. Then test your knowledge using our interactive CBT practice platform and prepare confidently for your upcoming examinations.

40 questions JAMB 2 WAEC 795 CUSTOM 2

Select subject

Download PHP app Ask a Question Check Syllabus Past Question Videos Topic Video Lessons

Take a test

Custom CBT

Create and set up a CBT environment with your preferred subjects.

JAMB CBT Simulator

Practice JAMB CBT with real UTME past questions in CBT format.

WAEC CBT Practice 2026 Simulator

CB-WASSCE styled past question practice.

NECO CBT Practice 2026 Simulator

SSCE & GCE styled past question practice.

Past Questions

40 questions

Question 1 of 20 40 total questions

Question 11

waec 2016

If \(P = \begin{pmatrix} 1 & 2 \\ 5 & 1 \end{pmatrix}\) and \(Q = \begin{pmatrix} 0 & 1 \\ 1 & 3 \end{pmatrix}\), find PQ.

A\(\begin{pmatrix} 5 & 1 \\ 16 & 5 \end{pmatrix}\)

B\(\begin{pmatrix} 2 & 16 \\ 1 & 10 \end{pmatrix}\)

C\(\begin{pmatrix} 2 & 7 \\ 1 & 8 \end{pmatrix}\)

D\(\begin{pmatrix} 2 & 5 \\ -1 & -8 \end{pmatrix}\)

View Explanation & Discuss

Question 12

waec 2016

If \(\begin{vmatrix} m-2 & m+1 \\ m+4 & m-2 \end{vmatrix} = -27\), find the value of m.

A\(3\frac{8}{9}\)

B\(3\)

C\(2\frac{1}{2}\)

D\(2\)

View Explanation & Discuss

Question 13

waec 2016

Given that \(-6, -2\frac{1}{2}, ..., 71\) is a linear sequence , calculate the number of terms in the sequence.

A20

B21

C22

D23

View Explanation & Discuss

Question 14

waec 2016

The 3rd and 6th terms of a geometric progression (G.P.) are \(\frac{8}{3}\) and \(\frac{64}{81}\) respectively, find the common ratio.

A\(\frac{1}{3}\)

B\(\frac{2}{3}\)

C\(\frac{3}{4}\)

D\(\frac{4}{3}\)

View Explanation & Discuss

Question 15

waec 2016

Find the fourth term in the expansion of \((3x - y)^{6}\).

A\(-540x^{3}y^{3}\)

B\(-540x^{4}y^{2}\)

C\(-27x^{3}y^{3}\)

D\(540x^{4}y^{2}\)

View Explanation & Discuss

Question 16

waec 2016

Find the coefficient of \(x^{3}\) in the expansion of \([\frac{1}{3}(2 + x)]^{6}\).

A\(\frac{135}{729}\)

B\(\frac{149}{729}\)

C\(\frac{152}{729}\)

D\(\frac{160}{729}\)

View Explanation & Discuss

Question 17

waec 2016

Given n = 3, evaluate \(\frac{1}{(n-1)!} - \frac{1}{(n+1)!}\)

A\(12\)

B\(2\frac{1}{2}\)

C\(2\)

D\(\frac{11}{24}\)

View Explanation & Discuss

Question 18

waec 2016

Simplify \(\frac{^{n}P_{5}}{^{n}C_{5}}\).

A80

B90

C110

D120

View Explanation & Discuss

Question 19

waec 2016

If \(\log_{10}y + 3\log_{10}x \geq \log_{10}x\), express y in terms of x.

A\(y \geq \frac{1}{x}\)

B\(y \leq \frac{1}{x}\)

C\(y \leq \frac{1}{x^{2}}\)

D\(y \geq \frac{1}{x^{2}}\)

View Explanation & Discuss

Question 20

waec 2016

Solve for x in the equation \(5^{x} \times 5^{x + 1} = 25\).

A\(-2\)

B\(\frac{-1}{2}\)

C\(\frac{1}{2}\)

D\(2\)

View Explanation & Discuss

Question 21

waec 2016

If (2t - 3s)(t - s) = 0, find \(\frac{t}{s}\).

A\(\frac{3}{2}\) or \(1\)

B\(\frac{3}{2}\) or \(-1\)

C\(\frac{-3}{2}\) or \(-1\)

D\(\frac{-3}{2}\) or \(1\)

View Explanation & Discuss

Question 22

waec 2016

The remainder when \(x^{3} - 2x + m\) is divided by \(x - 1\) is equal to the remainder when \(2x^{3} + x - m\) is divided by \(2x + 1\). Find the value of m.

A\(\frac{-7}{8}\)

B\(\frac{-3}{8}\)

C\(\frac{1}{8}\)

D\(\frac{5}{8}\)

View Explanation & Discuss

Question 23

waec 2016

If the solution set of \(x^{2} + kx - 5 = 0\) is (-1, 5), find the value of k.

A-6

B-4

View Explanation & Discuss

Question 24

waec 2016

Factorize completely: \(x^{2} + x^{2}y + 3x - 10y + 3xy - 10\).

A(x + 2)(x + 5)(y + 1)

B(x + 2)(x - 5)(y + 1)

C(x - 2)(x + 5)(y + 1)

D(x - 2)(x - 5)(y + 1)

View Explanation & Discuss

Question 25

waec 2016

If \(y = 4x - 1\), list the range of the domain \({-2 \leq x \leq 2}\), where x is an integer.

A{-9, -1, 2,3, 4}

B{-9, -2, 0, 1, 7}

C{-5, -4, -3, -2}

D{-9, -5, -1, 3, 7}

View Explanation & Discuss

Question 26

waec 2016

If \(f(x) = \frac{4}{x} - 1, x \neq 0\), find \(f^{-1}(7)\).

A\(\frac{-3}{7}\)

B\(0\)

C\(\frac{1}{2}\)

D\(4\)

View Explanation & Discuss

Question 27

waec 2016

Consider the statements:

p : Musa is short

q : Musa is brilliant

Which of the following represents the statement "Musa is short but not brilliant"?

A\(p \vee q\)

B\(p \vee \sim q\)

C\(p \wedge \sim q\)

D\(p \wedge q\)

View Explanation & Discuss

Question 28

waec 2016

An operation * is defined on the set, R, of real numbers by \(p * q = p + q + 2pq\). If the identity element is 0, find the value of p for which the operation has no inverse.

A\(\frac{-1}{2}\)

B\(0\)

C\(\frac{2}{3}\)

D\(2\)

View Explanation & Discuss

Question 29

waec 2016

Express \(\frac{8 - 3\sqrt{6}}{2\sqrt{3} + 3\sqrt{2}}\) in the form \(p\sqrt{3} + q\sqrt{2}\).

A\(7\sqrt{3} - \frac{17\sqrt{2}}{3}\)

B\(7\sqrt{2} - \frac{17\sqrt{3}}{3}\)

C\(-7\sqrt{2} + \frac{17\sqrt{3}}{3}\)

D\(-7\sqrt{3} - \frac{17\sqrt{2}}{3}\)

View Explanation & Discuss

Question 30

waec 2016

If \(P = {x : -2 < x < 5}\) and \(Q = {x : -5 < x < 2}\) are subsets of \(\mu = {x : -5 \leq x \leq 5}\), where x is a real number, find \((P \cup Q)\).

A\({x : -5 < x < 5}\)

B\({x : -5 \leq x \leq 5}\)

C\({x : -5 \leq x < 5}\)

D\({x : -5 < x \leq 5}\)

View Explanation & Discuss

Question Navigator

Current

Further Mathematics Past Questions

Take a test

Custom CBT

JAMB CBT Simulator

WAEC CBT Practice 2026 Simulator

NECO CBT Practice 2026 Simulator

Past Questions

Question Navigator

MathsFaculty