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 P = \({n^{2} + 1: n = 0,2,3}\) and Q = \({n + 1: n = 2,3,5}\), find P\(\cap\) Q.
{5, 10}
{4, 6}
{1, 3}
{ }
Correct answer is D
\(P = {n^{2} + 1: n = 0,2,3} \therefore P = {1, 5,10}\)
\(Q = {n + 1: n = 2,3,5} \therefore Q = {3, 4, 6}\)
\(P \cap Q = { }\)
Given that \(f(x) = 2x^{2} - 3\) and \(g(x) = x + 1\) where \(x \in R\). Find g o f(x).
\(2(x^{2} - 1)\)
\(2x^{2} + 4x - 1\)
\(2x^{2} + 6x - 1\)
\(3(x^{2} - 1)\)
Correct answer is A
\(f(x) = 2x^{2} - 3; g(x) = x + 1\)
\(g o f(x) = g (2x^{2} - 3)\)
= \( 2x^{2} - 3 + 1 = 2x^{2} - 2 = 2(x^{2} - 1)\)
10\(ms^{-2}\)
12\(ms^{-2}\)
14\(ms^{-2}\)
17\(ms^{-2}\)
Correct answer is C
\(accl = \frac{\mathrm d V}{\mathrm d t}\)
\(V = 3t^{2} + 2t - 1 \therefore a = \frac{\mathrm d V}{\mathrm d t} = 6t + 2\)
\(a \text{(after 2 seconds)} = (6\times 2) + 2 = 12+2 = 14ms^{-2}\)
Find the magnitude and direction of the vector \(p = (5i - 12j)\)
(13, 113.38°)
(13, 067.38°)
(13, 025.38°)
(13, 157.38°)
Correct answer is D
\(p = (5i - 12j); |p| = \sqrt{5^{2} + (-12)^{2}}\)
= \(\sqrt{169} = 13\)
\(\tan\theta = \frac{-12}{5} = -2.4 \implies \theta = -67.38°\)
Direction = \(90° - (-67.38°) = 157.38°\)
Solve \(3^{2x} - 3^{x+2} = 3^{x+1} - 27\)
1 or 0
1 or 2
1 or -2
-1 or 2
Correct answer is B
\(3^{2x} - 3^{x+2} = 3^{x+1} - 27\)
= \((3^{x})^{2} - (3^{x}).(3^{2}) = (3^{x}).(3^{1}) - 27\)
Let \(3^{x}\) be B; we have
= \(B^{2} - 9B - 3B + 27 = B^{2} - 12B + 27 = 0\).
Solving the equation, we have B = 3 or 9.
\(3^{x} = 3\) or \(3^{x} = 9\)
\(3^{x} = 3^{1}\) or \(3^{x} = 3^{2}\)
Equating, we have x = 1 or 2.