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.

411.

The chord ST of a circle is equal to the radius r of the circle. Find the length of arc ST

A.

\(\frac{\pi r}{3}\)

B.

\(\frac{\pi r}{2}\)

C.

\(\frac{\pi r}{12}\)

D.

\(\frac{\pi r}{6}\)

Correct answer is A

\(\frac{ \frac{r}{2}}{r}\) Sin \(\theta\) = \(\frac{1}{2}\) 

\(\theta\) = sin\(^{-1}\) (\(\frac{1}{2}\)) = 30\(^o\) = 60\(^o\) 

Length of arc (minor)

ST = \(\frac{\theta}{360}\) x 2\(\pi r\) 

\(\frac{60}{360} \times 2 \pi \times r = \frac{\pi}{3}\) 

412.

A binary operation x is defined by a x b = a\(^b\). If a x 2 = 2 - a, find the possible values of a?

A.

1, -2

B.

2, -1

C.

2, -2

D.

1, -1

Correct answer is A

a = b = a\(^2\)

a + 2 = a\(^2\).....(i)

a + 2 = 2 - a..............(ii) 

a\(^2\) = 2 - a 

a\(^2\)+ a - 2 = a\(^2\) + a - 2 = 0

= (a + 2)(a - 1) = 0

a = 1 or - 2

413.

Find the value of x if \(\frac{\sqrt{2}}{x + \sqrt{2}}\) = \(\frac{1}{x - \sqrt{2}}\) 

A.

3\(\sqrt{2}\) + 4

B.

3\(\sqrt{2}\) - 4

C.

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

D.

4 + 2\(\sqrt{2}\)

Correct answer is A

\(\frac{\sqrt{2}}{x + 2}\) = x - \(\frac{1}{\sqrt{2}}\)

x\(\sqrt{2}\) (x - \(\sqrt{2}\)) = x + \(\sqrt{2}\) (cross multiply)

x\(\sqrt{2}\) - 2 = x + \(\sqrt{2}\) 

= x\(\sqrt{2}\) - x 

= 2 + \(\sqrt{2}\)

x (\(\sqrt{2}\) - 1) = 2 + \(\sqrt{2}\)

= \(\frac{2 + \sqrt{2}}{\sqrt{2} - 1} \times \frac{\sqrt{2} + 1}{\sqrt{2} + 1}\)

x = \(\frac{2 \sqrt{2} + 2 + 2 + \sqrt{2}}{2 - 1}\) 

= 3\(\sqrt{2}\) + 4 

414.

If x is positive real number, find the range of values for which \(\frac{1}{3x}\) + \(\frac{1}{2}\)x = \(\frac{2 + 3x}{6x}\) > \(\frac{1}{4x}\) 

A.

x > -\(\frac{1}{6}\)

B.

x > 0

C.

0 < x < 6

D.

0 < x <\(\frac{1}{6}\)

Correct answer is A

\(\frac{1}{3x}\) + \(\frac{1}{2}\)x = \(\frac{2 + 3x}{6x}\) > \(\frac{1}{4x}\) 

= 4(2 + 3x) > 6x = 12x\(^2\) - 2x = 0

= 2x(6x - 1) > 0 = x(6x - 1) > 0

Case 1 (-, -) = x < 0, 6x - 1 > 0

= x < 0, x < \(\frac{1}{6}\) (solution) 

Case 2 (+, +) = x > 0, 6x - 1 > 0 = x > 0

x > \(\frac{1}{6}\)

Combining solutions in cases (1) and (2) 

= x > 0, x < \(\frac{1}{6}\) = 0 < x < \(\frac{1}{6}\) 

415.

The pie chart shows the income of a civil servant in month. If his monthly income is N6,000. Find his monthly basic salary. 

A.

N2,050

B.

N2,600

C.

N3,100

D.

N3,450

Correct answer is A

360\(^o\) - (60\(^o\) + 60\(^o\) + 67 + 50 = 237\(^o\)) 

360\(^o\) - 237 = 130\(^o\) 

B. Salary = \(\frac{123}{360} X \frac{N6000}{1}\) 

= N2,050