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.
9\(ms^{-1}\)
9.49\(ms^{-1}\)
13.42\(ms^{-1}\)
18.97\(ms^{-1}\)
Correct answer is D
Due to conservation of energy, K.E = P.E
\(\frac{1}{2}mv^{2} = mgh\)
\(\implies m \times 10 \times 18 = \frac{1}{2}mv^{2}\)
\(v^{2} = 2 \times 10 \times 18 = 360\)
\(v = \sqrt{360} = 18.97ms^{-1}\)
760N
800N
805N
840N
Correct answer is D
\(\text{Net force = Upward force - weight}\)
\(ma = F - mg \implies F = ma + mg \)
\(F = (80 \times 10) + (80 \times 0.5) = 800 + 40 = 840N\)
\((3 + 3\sqrt{3})N\)
\((-3 + 5\sqrt{3})N\)
\((5 + 3\sqrt{3})N\)
\((5 + 5\sqrt{3})N\)
Correct answer is B
\(F = F\cos \theta + F\sin \theta\) (Resolving into its components)
\(10N = 10 \cos 60, 10 \sin 60\)
\(6N = 6 \cos 330, 6 \sin 330\)
\(R = F_{1} + F_{2} = (10 \cos 60, 10 \sin 60) + (6 \cos 330, 6 \sin 330)\)
The y- component : \(10 \sin 60 + 6 \sin 330 = 10 \times \frac{\sqrt{3}}{2} + 6 \times \frac{-1}{2}\)
= \((5\sqrt{3} - 3)N\)
3.2
5.3
7.0
8.0
Correct answer is A
Momentum of bodies with common velocity = \(m_{1}v_{1} + m_{2}v_{2} = (m_{1} + m_{2})v\)
\((10 \times 5) + (15 \times 2) = (10 + 15)v\)
\(50 + 30 = 25v \implies v = \frac{80}{25} = 3.2ms^{-1}\)
Find the unit vector in the direction of \(-2i + 5j\).
\(\frac{1}{\sqrt{29}}(2i + 5j)\)
\(\frac{1}{\sqrt{29}}(-2i + 5j)\)
\(\frac{1}{29}(2i - 5j)\)
\(\frac{1}{29}(-2i - 5j)\)
Correct answer is B
The unit vector, \(\hat{n}\) is given by \(\hat{n} = \frac{\overrightarrow{r}}{|\overrightarrow{r}|}\)
= \(\frac{(-2i + 5j)}{\sqrt{(-2)^{2} + 5^{2}}} = \frac{(-2i + 5j)}{\sqrt{29}}\)
= \(\frac{1}{\sqrt{29}}(-2i + 5j)\)