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.

3,881.

If tan θ = 4/3, calculate sin\(^2\) θ - cos\(^2\) θ.

A.

16/25

B.

24/25

C.

7/25

D.

9/25

Correct answer is C

\(\tan \theta = \frac{opposite}{adjacent} = \frac{4}{3}\)

Hyp\(^2\) = 4\(^2\) + 3\(^2\)

Hyp = 5.

\(\sin \theta = \frac{4}{5}; \cos \theta = \frac{3}{5}\)

\(\sin^{2} \theta - \cos^{2} \theta = \frac{16}{25} - \frac{9}{25}\)

= \(\frac{7}{25}\)

3,882.

A chord of a circle subtends an angle of 120° degrees at the centre of a circle of diameter 4√3 cm. Calculate the area of the major sector.

A.

4π cm2

B.

32 π cm2

C.

16 π cm2

D.

8 π cm2

Correct answer is D

Diameter = 4\(\sqrt{3}\) cm<

radius = 2\(\sqrt{3}\) cm

Area of major sector = \(\frac{\theta}{360} \times \pi r^{2}\)

\(\theta = 360 - 120 = 240°\)

= \(\frac{240}{360} \times \pi \times 12\)

= \(8\pi cm^{2}\)

3,883.

If x varies directly as √n and x = 9 when n = 9, find x when n = (17/9)

A.

4

B.

27

C.

√3

D.

√17

Correct answer is D

\(x \propto \sqrt{n}\)

\(x = k \sqrt{n}\)

\(9 = k \sqrt{9} \implies 9 = 3k\)

\(k = 3\)

\(x = 3 \sqrt{n}\)

When n = 17/9,

\(x = 3 \times \sqrt{\frac{17}{9}} = \sqrt{17}\)

 

3,884.

The sum to infinity of the series: 1 + (1/3) + (1/9) + (1/27) + ... is

A.

11/3

B.

10/3

C.

5/2

D.

3/2

Correct answer is D

The series is geometric with common ratio \(\frac{1}{3}\).

\(S_{\infty} = \frac{a}{1 - r}\)

= \(\frac{1}{1 - \frac{1}{3}} \)

= \(\frac{1}{\frac{2}{3}}\)

= \(\frac{3}{2}\)

3,885.

The binary operation * is defined on the set of integers p and q by p*q = pq + p + q. Find 2 * (3 * 4).

A.

59

B.

19

C.

67

D.

38

Correct answer is A

\(p \ast q = pq + p + q\)

\(2 \ast (3 \ast 4) \)

\(3 \ast 4 = 12 + 3 + 4 = 19\)

\(2 \ast 19 = 38 + 2 + 19 = 59\)