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.

1,746.

Find x in the diagram below.

A.

3\(\sqrt{3}\)

B.

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

C.

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

D.

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

Correct answer is B

\(\frac{x + 3}{sin 60^o}\) = \(\frac{x}{sin 306o}\)

3sin 30o = x sin 60o - x sin 30o

= x(sin 60o - sin 30o)

but sin 30o = \(\frac{1}{2}\)

sin 60o = \(\frac{3}{2}\) = \(\frac{3(\sqrt{3} - 1)}{\sqrt{3} + 1}\)

1,747.

PQ is parallel to RS. Calculate the value of x.

A.

20o

B.

40o

C.

60o

D.

80o

E.

100o

Correct answer is B

< D = 180o - 100v

= 80o (< on a str. line)

< s = 60o - alternate angle

x = 180o - (80o + 60o)

180o - 140o = 40o

1,748.

In the parallelogram PQRS, PE is perpendicular to QR. Find the area of the parallelogram.

A.

60cm2

B.

65cm2

C.

72cm2

D.

132cm2

E.

156cm2

Correct answer is D

By Pythagoras, PE\(^2\) = 12\(^2\) - 5\(^2\)

= 144 - 25 = 119

h = PE\(^2\) = √119 = 10.9 ≈ 11cm,

Area of 11gm = b x h

QR = b =(5 + 7)cm = 12cm

area = 12 x 11

= 132cm\(^2\)

 

1,749.

(Numbers indicate the lengths of the sides of the triangles) If the area of \(\bigtriangleup\) PQR is k2sq. units what is the area of the shades portion?

A.

\(\frac{5}{9}\)k2 sq. units

B.

\(\frac{1}{3}\)k2 sq. units

C.

\(\frac{8}{9}\)k2 sq. units

D.

\(\frac{7}{9}\)k2 sq. units

E.

\(\frac{2}{3}\)k2 sq. u

Correct answer is A

Area of shaded portion = Area of triangle PQR - Area of inner triangle

Area of triangle given 3 sides a, b, c = \(\sqrt{s(s - a)(s - b)(s - c)}\)

where \(s = \frac{a + b + c}{2} \)

Area of PQR :

\(s = \frac{3 + 5 + 6}{2} = \frac{14}{2} = 7\)

Area = \(\sqrt{7(7 - 3)(7 - 5)(7 - 6)}\)

= \(\sqrt{7(4)(2)(1)} = \sqrt{56}\)

\(\implies K^{2} = \sqrt{56}\)

Area of inner triangle :

\(s = \frac{2 + 4 + \frac{10}{3}}{2} = \frac{14}{3}\)

Area = \(\sqrt{\frac{14}{3} (\frac{14}{3} - 2)(\frac{14}{3} - 4)(\frac{14}{3} - \frac{10}{3})}\)

= \(\sqrt{\frac{14}{3} (\frac{8}{3})(\frac{2}{3})(\frac{4}{3})}\)

= \(\sqrt{\frac{896}{81}}\)

= \(\sqrt{\frac{16}{81}} \times \sqrt{56}\)

= \(\frac{4}{9} K^{2}\)

\(\therefore \text{The area of the shaded portion} = K^{2} - \frac{4}{9}K^{2} = \frac{5}{9}K^{2}\)

1,750.

In the figure, PQ is parallel to SQ ; QS bisets < PSQ, < PQS is 65o and < RPS is 20o. What is the size of < PRS?

A.

45o

B.

35o

C.

40o

D.

30o

E.

42o

Correct answer is D

PSR = 65o x 2

= 130o

PRS = 180o - (130o + 20o)

= 30o