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.
Given that \(2^{x} = 0.125\), find the value of x.
0
-1
-2
-3
Correct answer is D
\(2^{x} = 0.125 = \frac{125}{1000}\)
\(2^{x} = \frac{1}{8} = 8^{-1}\)
\(2^{x} = 2^{-3}\)
\(x = -3\)
\(\frac{25}{4} - m\)
\(\frac{25}{4} - 2m\)
\(\frac{25}{4} + m\)
\(\frac{25}{4} + 2m\)
Correct answer is A
\(2x^{2} - 5x + m = 0\)
\(a = 2, b = -5, c = m\)
\(\alpha + \beta = \frac{-b}{a} = \frac{5}{2}\)
\(\alpha \beta = \frac{c}{a} = \frac{m}{2}\)
\(\alpha^{2} + \beta^{2} = (\alpha + \beta)^{2} - 2\alpha\beta\)
= \((\frac{5}{2})^{2} - 2(\frac{m}{2}) \)
= \(\frac{25}{4} - m\)
Express \(\frac{2}{3 - \sqrt{7}} \text{ in the form} a + \sqrt{b}\), where a and b are integers.
\(6 + \sqrt{7}\)
\(3 + \sqrt{7}\)
\(3 - \sqrt{7}\)
\(6 - \sqrt{7}\)
Correct answer is B
Rationalizing \(\frac{2}{3 - \sqrt{7}}\) by multiplying through with \(3 + \sqrt{7}\),
\(\frac{2}{3 - \sqrt{7}} \frac{(3 + \sqrt{7})}{(3 + \sqrt{7})} = \frac{6 + 2\sqrt{7}}{9 - 7}\)
= \(\frac{6 + 2\sqrt{7}}{2} = 3 + \sqrt{7}\)
Which of the following binary operations is not commutative?
\(a * b = \frac{1}{a} + \frac{1}{b}\)
\(a * b = a + b - ab\)
\(a * b = 2a + 2b + ab\)
\(a * b = a - b + ab\)
Correct answer is D
All other options given are commutative i.e. \(a * b = b * a\), except option D.
\(a * b = a - b + ab\)
\(b * a = b - a + ba\)
\(a - b = -(b - a) \neq b - a\)
Find the coefficient of \(x^{4}\) in the binomial expansion of \((2 + x)^{6}\)
120
80
60
15
Correct answer is C
\((2 + x)^{6} \)
\(x^{4} = ^{6}C_{2}(2^{2})(x^{4}) = 15 \times 4 = 60\)