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 unit vector in the direction of (-5i + 12j).
\(\frac{1}{13}(-5i - 12j)\)
\(\frac{1}{13}(5i - 12j)\)
\(\frac{1}{13}(-5i + 12j)\)
\(\frac{1}{13}(5i + 12j)\)
Correct answer is C
The unit vector \(\hat{n} = \frac{\overrightarrow{r}}{|r|}\)
\(\hat{n} = \frac{-5i + 12j}{\sqrt{(-5)^{2} + (12)^{2}} \)
= \(\frac{-5i + 12j}{13} \)
-8
-6
-4
-3
Correct answer is C
\(f : x \to x^{2} - x - 6\); \(g : x \to x - 1\)
\(g(3) = 3 - 1 = 2\)
\(f(g(3)) = f(2) = 2^{2} - 2 - 6 = 4 - 2 - 6 = -4\)
Given that \(q = 9i + 6j\) and \(r = 4i - 6j\), which of the following statements is true?
r and q are collinear
r and q are perpendicular
The magnitude of r is 52 units
The projection of r on q is \(\sqrt{117}\) units.
Correct answer is B
The dot product of two perpendicular forces = 0
\((9i + 6j).(4i - 6j) = 36 - 36 = 0\)
Hence, r and q are perpendicular.
\(4 ms^{-2}\)
\(6 ms^{-2}\)
\(8 ms^{-2}\)
\(10 ms^{-2}\)
Correct answer is D
\(v(t) = (3t^{2} - 2t) ms^{-1}\)
\(a(t) = \frac{\mathrm d v}{\mathrm d t} = (6t - 2) ms^{-2}\)
\(a(2) = 6(2) - 2 = 12 - 2 = 10 ms^{-2}\)
2m
4m
6m
8m
Correct answer is B
\(v(t) = (3t^{2} - 2t) ms^{-1}\)
\(s(t) = \int v(t) \mathrm {d} t\)
= \(\int (3t^{2} - 2t) \mathrm {d} t = t^{3} - t^{2}\)
\(s(2) = 2^{3} - 2^{2} = 8 - 4 = 4m\)