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 21st term of the Arithmetic Progression (A.P.): -4, -1.5, 1, 3.5,...
43.5
46
48.5
51
Correct answer is B
\(T_{n} = a + (n-1)d\)
\( d = T_{2} - T_{1} = T_{3} - T_{2} = -1.5 - (-4) = 2.5\)
\(T_{21} = -4 + (21 - 1) \times 2.5 = -4 + (20\times 2.5) \)
= \(-4 + 50 = 46\)
Find the coefficient of \(x^{4}\) in the expansion of \((1-2x)^{6}\)
-320
-240
240
320
Correct answer is C
\(^{6}C_{4}(1)^{6-4}(-2x)^{4}\) = \(15\times1\times16x^{4} = 240x^{4}\)
The coefficient of \(x^{4}\)= 240
Given that \(\frac{6x+m}{2x^{2}+7x-15} \equiv \frac{4}{x+5} - \frac{2}{2x-3}\), find the value of m
20
12
-10
-22
Correct answer is D
Taking the LCM of the right hand side of the equation, we have
\(\frac{4(2x-3) - 2(x+5)}{(x+5)(2x-3)} = \frac{6x+m}{2x^{2}+7x-15}\)
Comparing the numerators, we have
\(4(2x-3) - 2(x+5) = 6x+m\)
\(8x-12-2x-10 = 6x -22 = 6x + m\)
\(\implies m = -22\)
Given that \(f(x) = \frac{x+1}{2}\), find \(f^{1}(-2)\).
-5
-3
\(-\frac{1}{2}\)
5
Correct answer is A
Let \(f(x) = y\), then we have
\(y = \frac{x+1}{2} \implies 2y = x+1; x = 2y-1\)
Let \(f^{1}(x) = x; x = 2y-1\), replacing y with x,
\(f^{1}(x) = 2x - 1 \implies f^{1}(-2) = 2(-2) -1= -5\)
\(x<2\)
\(x \leq 2\)
\(x = 2\)
\(x > -2\)
Correct answer is B
\(f : x \to \sqrt{4 -2x}\) defined on the set of real numbers, R, which has range from \((-\infty, \infty)\) but because of the root sign, it is defined from \([0, \infty)\).
This is because the root of numbers only has real number values from 0 and upwards.
\(\sqrt{4-2x} \geq 0 \implies 4-2x \geq 0\)
\(-2x \geq -4; x \leq 2\)