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.
If \(f(x) = x^{2}\) and \(g(x) = \sin x\), find g o f.
\(\sin^{2} x\)
\(\sin x^{2}\)
\((\sin x)x^{2}\)
\(x \sin x\)
Correct answer is B
\(f(x) = x^{2}, g(x) = \sin x\)
\(g \circ f = g(x^{2}) = \sin x^{2}\)
Express \(\log \frac{1}{8} + \log \frac{1}{2}\) in terms of \(\log 2\)
3 log 2
4 log 2
-3 log 2
-4 log 2
Correct answer is D
\(\log \frac{1}{8} + \log \frac{1}{2} = \log 8^{-1} + \log 2^{-1}\)
= \(\log 2^{-3} + \log 2^{-1}\)
= \(-3 \log 2 - 1 \log 2 = -4 \log 2\)
Given that \(a^{\frac{5}{6}} \times a^{\frac{-1}{n}} = 1\), solve for n
-6.00
-1.20
0.83
1.20
Correct answer is D
\(a^{\frac{5}{6}} \times a^{\frac{-1}{n}} = 1\)
\(\implies a^{\frac{5}{6} + \frac{-1}{n}} = a^{0}\)
Equating bases, we have
\(\frac{5}{6} - \frac{1}{n} = 0\)
\(\frac{5n - 6}{6n} = 0\)
\(5n - 6 = 0 \implies 5n = 6\)
\(n = \frac{6}{5} = 1.20\)
Solve: \(\sin \theta = \tan \theta\)
200°
90°
60°
0°
Correct answer is D
\(\sin \theta = \tan \theta \implies \frac{\sin \theta}{1} = \frac{\sin \theta}{\cos \theta}\)
Equating, we have
\(\cos \theta = 1 \implies \theta = \cos^{-1} 1\)
= \(0°\)
\(\frac{-x}{1 - x}, x \neq 1\)
\(\frac{1}{1 - x}, x \neq 1\)
\(\frac{-1}{1 - x}, x \neq 1\)
\(\frac{x}{1 - x}, x \neq 1\)
Correct answer is A
\(x * y = x + y - xy\)
Let \(x^{-1}\) be the inverse of x, so that
\(x * x^{-1} = x + x^{-1} - x(x^{-1}) = 0\)
\(x + x^{-1} - x(x^{-1}) = 0 \implies x(x^{-1}) - x^{-1} = x\)
\(x^{-1}(x - 1) = x \implies x^{-1} = \frac{x}{x - 1}\)
= \(\frac{x}{-(1 - x)} = \frac{-x}{1 - x}, x \neq 1\)