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 \(x^{2} - kx + 9 = 0\) has equal roots, find the values of k.
3, 4
±3
±5
±6
Correct answer is D
For equal roots, we have that \(b^{2} = 4ac\), so, given a=1, b = -k and c = 9,
\((-k)^{2} = 4\times1\times9 \implies k^{2} = 36\)
\(k = \sqrt{36} = \pm6\)
Simplify \(\frac{1}{(1-\sqrt{3})^{2}}\)
\(1- \frac{1}{2}\sqrt{3}\)
\(1+ \frac{1}{2}\sqrt{3}\)
\(\sqrt{3}\)
\(1+\sqrt{3}\)
Correct answer is B
\(\frac{1}{(1-\sqrt{3})^{2}}\)
\((1-\sqrt{3})^{2} = (1-\sqrt{3})(1-\sqrt{3})\)
\(1 - 2\sqrt{3} + 3 = 4 - 2\sqrt{3}\)
\(\frac{1}{4-2\sqrt{3}}\)
After rationalising (multiplying the denominator and numerator with \(4+2\sqrt{3}\), we have
\(\frac{4+2\sqrt{3}}{4} = 1 + \frac{1}{2}\sqrt{3}\)
\(-4\sqrt{3}\)
\(\frac{-4\sqrt{3}}{3}\)
\(\frac{-3\sqrt{3}}{4}\)
\(\frac{-3\sqrt{3}}{4}\)
Correct answer is B
\(a \Delta b\) = \(\frac{a+b}{\sqrt{ab}}\)
\(-3\Delta -1\) = \(\frac{-3 + -1}{\sqrt{-3\times -1}}\)
\(\frac{-4}{\sqrt{3}}\), rationalising, we have
\(\frac{-4 \times \sqrt{3}}{\sqrt{3}\times \sqrt{3}} = \frac{-4\sqrt{3}}{3}\)
If \(log_{y}\frac{1}{8}\) = 3, find the value of y.
-2
-\(\frac{1}{2}\)
\(\frac{1}{2}\)
2
Correct answer is C
\(log_{y}\frac{1}{8} = 3 \implies y^{3} = \frac{1}{8}\) (Laws of logarithm)
\(y^{3} = \frac{1}{2^{3}} = (\frac{1}{2})^{3}\)
Equating both sides, we have
\(y = \frac{1}{2}\)