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.
I only
II only
I and III only
II and III only
Correct answer is B
No explanation has been provided for this answer.
If \(^nC_2\) = 15, find the value of n
8
7
6
5
Correct answer is C
\(^nC_2\) = 15
\(\frac{n!}{(n - 3)! 2!}\) = 15
\(\frac{n(n - 1)(n - 2)!}{(n - 2)!2}\) = 15
n\(^2\) - n = 30
n\(^2\) - n - 30 = 0
(n - 6)(n + 5) = 0
n = 6 or n = -5
Rationalize; \(\frac{1}{\sqrt{2 + 1}}\)
\(\sqrt{2}\) - 1
1 - \(\sqrt{2}\)
\(\frac{\sqrt{2} - 1}{2}\)
\(\frac{1 - \sqrt{2}}{2}\)
Correct answer is A
\(\frac{1}{\sqrt{2} + 1}\) x \(\frac{\sqrt{2} - 1}{\sqrt{2} - 1}\)
= \(\frac{\sqrt{2} - 1}{2 - 1}\)
= \(\frac{\sqrt{2} - 1}{1} = \sqrt{2} - 1\)
Evaluate tan 75\(^o\); leaving the answer in surd form (radicals)
\(\sqrt{3 + 2}\)
\(\sqrt{3 + 1}\)
\(\sqrt{3 - 1}\)
\(\sqrt{3 - 2}\)
Correct answer is D
Tan 75\(^o\) = Tan (45\(^o\) + 30\(^o\))
= \(\frac{\tan 45^o + \tan 30^o}{1 - \tan 45^o \tan 30^o}\)
= \(\frac{\sqrt{3} + 1}{\sqrt{3} - 1}\)
RATIONALIZE THE DENOMINATOR
= \(\frac{\sqrt{3} + 1}{\sqrt{3} - 1}\) X \(\frac{\sqrt{3} + 1}{\sqrt{3} +1}\)
= \(\frac{4 + 2\sqrt{3}}{3 - 1}\)
= \(\frac{2(2 + \sqrt{3})}{2}\)
= 2 + \(\sqrt{3}\)
Solve; \(\frac{P}{2} + \frac{k}{3}\) = 5 and 2p = k = 6 simultaneously
p = -6, k = -6
p = -6, k = 6
p = 6, k = 6
p = 6, k = -6
Correct answer is C
\(\frac{P}{2} + \frac{k}{3}\) = 5
\(\frac{3p + 2k}{6}\) = 5
2p + 3k = 30
- 2p - k = 6
\(\overline{\frac{4k}{4} = \frac{24}{4}}\)
k = 6
From 2p - k = 6
2p - 6 = 6
\(\frac{2p}{2} = \frac{12}{2}\)
p = 6