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.

2,011.

If cos \(\theta\) = \(\frac{\sqrt{3}}{2}\) and \(\theta\) is less than 90o. Calculate \(\frac{\cot(90 - \theta)}{sin^2\theta}\)

A.

\(\frac{4}{\sqrt{3}}\)

B.

\(4 \sqrt{3}\)

C.

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

D.

\(\frac{1}{\sqrt{3}}\)

E.

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

Correct answer is A

\(\frac{\cot (90 - \theta)}{sin^2\theta}\)

\(\cot (90 - \theta) = \tan \theta\)

\(\therefore \frac{\cot (90 - \theta)}{\sin^{2} \theta} = \frac{\tan \theta}{\sin^{2} \theta}\)

\(\tan \theta = \frac{\sqrt{3}}{3}\)

\(\sin \theta = \frac{1}{2} \implies \sin^{2} \theta = \frac{1}{4}\)

\(\frac{\cot(90 - \theta)}{\sin^{2} \theta} = \frac{\sqrt{3}}{3}\div\frac{1}{4}\)

= \(\frac{4}{\sqrt{3}}\)

2,012.

Find the area of a regular hexagon inscribed in a circle of radius 8cm

A.

16\(\sqrt{3}\) cm3

B.

96\(\sqrt{3}\) cm3

C.

192\(\sqrt{3}\) cm3

D.

16\(\sqrt{3}\) cm2

E.

33cm2

Correct answer is B

Area of a regular hexagon = 8 x 8 x sin 60o

= 32 x \(\frac{\sqrt{3}}{2}\) 

Area = 16\(\sqrt{3}\) x 6 = 96 \(\sqrt{3}\)cm2

2,013.

What is the probability that a number chosen at random from the intergers between 1 and 10 inclusive is either a prime or a multiple of 3?

A.

\(\frac{7}{10}\)

B.

\(\frac{3}{5}\)

C.

\(\frac{4}{5}\)

D.

\(\frac{3}{10}\)

Correct answer is B

Simple Space: (1, 2, 3, 4, 5, 6, 7, 8, 9, 10 = 10)

Prime: (2, 3, 5, 7)

multiples of 3: (3, 6, 9)

Prime or multiples of 3: (2, 3, 5, 6, 7, 9 = 6)

Probability = \(\frac{6}{10}\)

= \(\frac{3}{5}\)

2,014.

Without using table, calculate the value of 1 + sec2 30o

A.

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

B.

\(\frac{2}{15}\)

C.

\(\frac{5}{3}\)

D.

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

Correct answer is A

1 + sec2 30o = sec 30o

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

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

= \(\frac{4}{3}\)

1 + sec2 30o = sec 30o

= 1 + \(\frac{4}{3}\)

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

2,015.

The bearing of a bird on a tree from a hunter on the ground is N72oE. What is the bearing of the hunter from the birds?

A.

S 18o W

B.

S 72o W

C.

S 72o E

D.

S 27o E

E.

S 27o W

Correct answer is B

B = Bird ; H = Hunter.

Bearing of the hunter from the bird = S 72° W.