Mathematics questions and answers

Mathematics Questions and Answers

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.

1,916.

If sin \(\theta\) = \(\frac{m - n}{m + n}\); Find the value of 1 + tan2\(\theta\)

A.

\(\frac{(m^2 + n^2)}{m + n}\)

B.

\(\frac{(m^2 + n^2 + 2mn)}{4mn}\)

C.

\(\frac{2(m^2 + n^2 + mn)}{m + n}\)

D.

\(\frac{(m^2 + n^2 + mn)}{m + n}\)

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\(\theta\)

= \(\frac{1}{cos^2\theta}\)

\(\cos \theta = \frac{2\sqrt{mn}}{(m + n)}\)

\(\frac{1}{\cos \theta} = \frac{(m + n)}{2\sqrt{mn}}\)

\(\sec^{2} \theta = \frac{(m + n)^{2}}{4mn}\)

= \(\frac{(m^2 + n^2 + 2mn)}{4mn}\)

1,917.

Given that p:q = \(\frac{1}{3}\):\(\frac{1}{2}\) and q:r = \(\frac{2}{5}\), find p:r

A.

4:105

B.

7:15

C.

20:21

D.

2:35

E.

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) : \(2q = 3p \)

\(10q = 15p\)

\(\implies 15p = 7r\)

\(\therefore \frac{p}{r} = \frac{7}{15}\)

\(p : r = 7 : 15\)

1,918.

A sector of a circle is bounded by two radii 7cm long and an arc length 6cm. Find the area of the sector.

A.

42cm2

B.

3cm2

C.

21cm2

D.

24cm2

E.

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

1,919.

If f(x - 2) = 3x2 + 4x + 1. Find the area of the sector

A.

8

B.

40

C.

7

D.

24

E.

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

1,920.

Find the median of the set of numbers 110, 116, 113, 119, 118, 127, 118, 117, 113

A.

117.5

B.

118

C.

117

D.

116

E.

113

Correct answer is C

Re-arrange in ascending order: 110, 113, 113, 116, |117|, 118, 119, 127 a= 117