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.
What is the angle between \(a = (3i - 4j)\) and \(b = (6i + 4j)\)?
13°
87°
100°
110°
Correct answer is B
\(a . b = |a||b| \cos \theta\)
\(a = 3i - 4j; b = 6i + 4j\)
\(18 - 16 = (\sqrt{3^{2} + (-4)^{2}})(\sqrt{6^{2} + 4^{2}}) \cos \theta\)
\(2 = 5\sqrt{52} \cos \theta\)
\(\cos \theta = \frac{2}{5\sqrt{52}} = 0.0555\)
\(\theta = 86.8° \approxeq 87°\)
Simplify \((1 + 2\sqrt{3})^{2} - (1 - 2\sqrt{3})^{2}\)
0
\(8\sqrt{3}\)
13
\(2 - 4\sqrt{3}\)
Correct answer is B
\((1 + 2\sqrt{3})^{2} = 1 + 4\sqrt{3} + 12 = 13 + 4\sqrt{3}\)
\((1 - 2\sqrt{3})^{2} = 1 - 4\sqrt{3} + 12 = 13 - 4\sqrt{3}\)
\(13 + 4\sqrt{3} - (13 - 4\sqrt{3}) = 13 + 4\sqrt{3} - 13 + 4\sqrt{3}\)
= \(8\sqrt{3}\)
Find the maximum value of \(2 + \sin (\theta + 25)\).
1
2
3
4
Correct answer is C
\(\sin \theta \leq 1\)
i.e Maximum value of \(\sin \theta \forall \theta = 1\).
Therefore, \(2 + \sin \theta \leq 2 + 1 = 3\)
\(\begin{pmatrix} -14 \\ 15 \end{pmatrix} ms^{-1}\)
\(\begin{pmatrix} -2 \\ 1 \end{pmatrix} ms^{-1}\)
\(\begin{pmatrix} 4 \\ -9 \end{pmatrix} ms^{-1}\)
\(\begin{pmatrix} 14 \\ -9 \end{pmatrix} ms^{-1}\)
Correct answer is C
\(u = \begin{pmatrix} -5 \\ 3 \end{pmatrix} ms^{-1}\)
\(a = \begin{pmatrix} 3 \\ -4 \end{pmatrix} ms^{-2}; t = 3 secs\)
\(v = u + at \implies v = \begin{pmatrix} -5 \\ 3 \end{pmatrix} + \begin{pmatrix} 3 \\ -4 \end{pmatrix} \times 3\)
= \(\begin{pmatrix} -5 \\ 3 \end{pmatrix} + \begin{pmatrix} 9 \\ -12 \end{pmatrix} = \begin{pmatrix} 4 \\ -9 \end{pmatrix} ms^{-1}\)\)
5
7
8
10
Correct answer is A
No explanation has been provided for this answer.