How good are you with figures and formulas? Find out with these Mathematics past questions and answers. This Test is useful for both job aptitude test candidates and students preparing for JAMB, WAEC, NECO or Post UTME.
If sin \(\theta\) = \(\frac{m - n}{m + n}\); Find the value of 1 + tan2\(\theta\)
\(\frac{(m^2 + n^2)}{m + n}\)
\(\frac{(m^2 + n^2 + 2mn)}{4mn}\)
\(\frac{2(m^2 + n^2 + mn)}{m + n}\)
\(\frac{(m^2 + n^2 + mn)}{m + n}\)
Correct answer is B
\((m + n)^{2} = (m - n)^{2} + x^{2}\)
\(m^{2} + 2mn + n^{2} = m^{2} - 2mn + n^{2} + x^{2}\)
\(x^{2} = 4mn\)
\(x = \sqrt{4mn} = 2\sqrt{mn}\)
1 + tan2\(\theta\) = sec2\(\theta\)
= \(\frac{1}{cos^2\theta}\)
\(\cos \theta = \frac{2\sqrt{mn}}{(m + n)}\)
\(\frac{1}{\cos \theta} = \frac{(m + n)}{2\sqrt{mn}}\)
\(\sec^{2} \theta = \frac{(m + n)^{2}}{4mn}\)
= \(\frac{(m^2 + n^2 + 2mn)}{4mn}\)
Given that p:q = \(\frac{1}{3}\):\(\frac{1}{2}\) and q:r = \(\frac{2}{5}\), find p:r
4:105
7:15
20:21
2:35
3:20
Correct answer is B
\(p : q = \frac{1}{3} : \frac{1}{2}\)
\(\frac{p}{q} = \frac{2}{3}\)
\(2q = 3p ... (1)\)
\(q : r = \frac{2}{5} : \frac{4}{7}\)
\(\frac{q}{r} = \frac{2}{5} \times \frac{7}{4} = \frac{7}{10}\)
\(10q = 7r ... (2)\)
Eliminating q, we have
(1) : \(2q = 3p \)
\(10q = 15p\)
\(\implies 15p = 7r\)
\(\therefore \frac{p}{r} = \frac{7}{15}\)
\(p : r = 7 : 15\)
42cm2
3cm2
21cm2
24cm2
12cm2
Correct answer is C
Length of arc = \(\frac{\theta}{360}\) x 2\(\pi\)r = 6
\(\theta\) x 2\(\pi\)r = 360 x 6
\(\theta\) = \(\frac{360 \times 6}{2\pi r}\)
Area of the sector = \(\frac{\theta}{360}\) x \(\pi\)r2
\(\frac{360 \times 6}{2\pi r}\) x \(\frac{1}{360}\) x \(\pi\)r2 = r
= 3 x 7
= 21cm2
If f(x - 2) = 3x2 + 4x + 1. Find the area of the sector
8
40
7
24
32
Correct answer is B
f(x - 2) = 3x2 + 4x + 1
f(1) will be f(3 - 2)
When x = 3, f(1) = 3(3)2 + 4 x 3 = 1
27 + 12 +1 = 40
Find the median of the set of numbers 110, 116, 113, 119, 118, 127, 118, 117, 113
117.5
118
117
116
113
Correct answer is C
Re-arrange in ascending order: 110, 113, 113, 116, |117|, 118, 119, 127 a= 117