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 \(\frac{\log_{5} 8}{\log_{5} \sqrt{8}}\).
-2
\(\frac{-1}{2}\)
\(\frac{1}{2}\)
2
Correct answer is D
\(\frac{\log_{5} 8}{\log_{5} \sqrt{8}} = \frac{\log_{5} 8}{\log_{5} 8^{\frac{1}{2}}}\)
= \(\frac{\log_{5} 8}{\frac{1}{2}\log_{5} 8}\)
= \(\frac{1}{\frac{1}{2}} \)
= 2
If \(16^{3x} = \frac{1}{4}(32^{x - 1})\), find the value of x.
\(-1\)
\(\frac{-1}{3}\)
\(\frac{-3}{7}\)
\(\frac{-5}{19}\)
Correct answer is A
\(16^{3x} = \frac{1}{4}(32^{x - 1})\)
\((2^{4})^{3x} = (2^{-2})((2^{5})^{x - 1})\)
\(2^{12x} = 2^{-2 + 5x - 5}\)
\(12x = -7 + 5x\)
\(7x = -7 \implies x = -1\)
If \(\frac{5}{\sqrt{2}} - \frac{\sqrt{8}}{8} = m\sqrt{2}\), where m is a constant. Find m.
\(1\frac{1}{2}\)
\(1\frac{1}{4}\)
\(2\frac{1}{4}\)
\(2\frac{1}{2}\)
Correct answer is C
\(\frac{5}{\sqrt{2}} = \frac{5 \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}} = \frac{5\sqrt{2}}{2}\)
\(\frac{\sqrt{8}}{8} = \frac{2\sqrt{2}}{8} = \frac{\sqrt{2}}{4}\)
\(\frac{5}{\sqrt{2}} - \frac{\sqrt{8}}{8} = (\frac{5}{2} - \frac{1}{4})\sqrt{2}\)
= \(\frac{9}{4}\sqrt{2} \)
= \(2\frac{1}{4}\sqrt{2}\)
Find the value of \(\cos(60° + 45°)\) leaving your answer in surd form
\(\frac{6 + \sqrt{2}}{4}\)
\(\frac{3 + \sqrt{6}}{4}\)
\(\frac{\sqrt{2} - \sqrt{6}}{4}\)
\(\frac{3 - \sqrt{6}}{4}\)
Correct answer is C
\(\cos (x + y) = \cos x \cos y - \sin x \sin y \)
\(\cos (60 + 45) = \cos 60 \cos 45 - \sin 60 \sin 45\)
= \(\frac{1}{2} \times \frac{\sqrt{2}}{2} - \frac{\sqrt{3}}{2} \times \frac{\sqrt{2}}{2}\)
= \(\frac{\sqrt{2} - \sqrt{6}}{4}\)
Find the domain of \(f(x) = \frac{x}{3 - x}, x \in R\), the set of real numbers.
\({x : x \in R, x \neq 3}\)
\({x : x \in R, x \neq 1}\)
\({x : x \in R, x \neq 0}\)
\({x : x \in R, x\neq -3}\)
Correct answer is A
\(f(x) = \frac{x}{3 - x} \)
f(x) has a defined value except at x = 3 where the function is undefined.