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.
Find the equation of the line passing through (0, -1) and parallel to the y- axis.
y = -1
y = 0
x = 0
x = -1
Correct answer is C
No explanation has been provided for this answer.
Find the coefficient of \(x^{4}\) in the binomial expansion of \((1 - 2x)^{6}\).
320
240
-320
-240
Correct answer is B
\((1 - 2x)^{6} = ^{6}C_{0}(1^{6}) + ^{6}C_{1}(1^{5})(-2x^{1}) + ^{6}C_{2}(1^{4})(-2x^{2}) + ^{6}C_{3}(1^{3})(-2x^{3}) + ^{6}C_{4}(1^{2})(-2x^{4}) + ...\)
\(\text{The coefficient of} x^{4} = 15 \times 16 = 240\)
If \(f(x) = \frac{1}{2 - x}, x \neq 2\), find \(f^{-1}(-\frac{1}{2})\).
4
0
-2
-4
Correct answer is A
\(f(x) = \frac{1}{2 - x}, x \neq 2\)
\(f(y) = \frac{1}{2 - y}\)
\(x = \frac{1}{2 - y}\) (Let x = f(y))
\(2x - xy = 1 \implies y = \frac{2x - 1}{x}\)
\(\therefore f^{-1}(x) = \frac{2x - 1}{x}\)
\(f^{-1}(-\frac{1}{2}) = \frac{2(-\frac{1}{2}) - 1}{-\frac{1}{2}}\)
= \(-2 \times -2 = 4\)
Given that \((\sqrt{3} - 5\sqrt{2})(\sqrt{3} + \sqrt{2}) = p + q\sqrt{6}\), find q.
4
-4
-5
-7
Correct answer is B
\((\sqrt{3} - 5\sqrt{2})(\sqrt{3} + \sqrt{2}) = 3 + \sqrt{6} - 5\sqrt{6} - 10\)
= \(-7 - 4\sqrt{6} = p + q\sqrt{6}\)
\(\therefore q = -4\)
Given that \(\frac{1}{8^{2y - 3y}} = 2^{y + 2}\).
\(\frac{1}{5}\)
\(\frac{7}{8}\)
1
\(1\frac{1}{5}\)
Correct answer is C
\(\frac{1}{8^{2y - 3y}} = \frac{1}{8^{-y}} = 8^{y}\)
\(8^{y} = 2^{y + 2} \implies (2^{3})^{y} = 2^{y + 2}\)
\(3y = y + 2 \implies 2y = 2\)
\(y = 1\)