Further Mathematics Questions and Answers
Test your knowledge of advanced level mathematics with this aptitude test. This test comprises Further Maths questions and answers from past JAMB and WAEC examinations.
Test your knowledge of advanced level mathematics with this aptitude test. This test comprises Further Maths questions and answers from past JAMB and WAEC examinations.
Simplify \(\frac{^{n}P_{3}}{^{n}C_{2}} + ^{n}P_{0}\)
n - 5
n - 3
2n - 1
2n - 3
Correct answer is D
\(\frac{^{n}P_{3}}{^{n}C_{2}} + ^{n}P_{0}\)
\(\frac{^{n}P_{3}}{^{n}C_{2}} = \frac{n!}{(n - 3)!} ÷ \frac{n!}{(n - 2)! 2!}\)
\(\frac{n!}{(n - 3)!} \times \frac{(n - 2)(n - 3)! 2!}{n!} = 2n - 4\)
\(^{n}P_{0} = \frac{n!}{(n - 0)!} = 1\)
\(\frac{^{n}P_{3}}{^{n}C_{2}} + ^{n}P_{0} = 2n - 4 + 1 = 2n - 3\)
\(3, (-1, 2)\)
\(2\sqrt{2}, (2, -1)\)
\(2\sqrt{2}, (2, 1)\)
\(9, (2, 1)\)
Correct answer is C
Equation of a circle with radius r and centre (a, b).
= \((x - a)^{2} + (y - b)^{2} = r^{2}\)
Expanding, we have
\(x^{2} - 2ax + a^{2} + y^{2} - 2by + b^{2} = r^{2}\)
Comparing, with \(x^{2} + y^{2} - 4x - 2y - 3 = 0\)
\(2a = 4 \implies a = 2\)
\(2b = 2 \implies b = 1\)
\(r^{2} - a^{2} - b^{2} = 3 \implies r^{2} = 3 + 2^{2} + 1^{2} = 8\)
\(r = 2\sqrt{2}\)
\(\begin{pmatrix} 16 & 36 \end{pmatrix}\)
\(\begin{pmatrix} 8 & 18 \end{pmatrix}\)
\(\begin{pmatrix} 8 & 0 \end{pmatrix}\)
\(\begin{pmatrix} 1 & 2 \end{pmatrix}\)
Correct answer is A
\(|Q| = \begin{vmatrix} -1 & -2 \\ 3 & 2 \end{vmatrix}\)
= \(-2 - (-6) = 4\)
\(4P = 4\begin{pmatrix} 4 & 9 \end{pmatrix}\)
= \(\begin{pmatrix} 16 & 36 \end{pmatrix}\)
\(QP\)
\(P^{2}\)
\(Q^{2}P\)
\(PQ\)
Correct answer is D
A \(1 \times 2\) matrix can be multiplied by \(2 \times 2\) matrix to give a \(1 \times 2\) matrix.
How many ways can 12 people be divided into three groups of 2, 7 and 3 in that order?
7920
792
187
42
Correct answer is A
= \(\frac{12!}{2! 3! 7!} \)
\(\frac{12 \times 11 \times 10 \times 9 \times 8 \times 7!}{2 \times 3 \times 2 \times 7!}\)
= \(7,920\)