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.

1,661.

PMN and PQR are two secants of the circle MQTRN and PT is a tangent. If PM = 5cm, PN = 12cm and PQ = 4.8cm, calculate the respective lengths of PR and PT in centimeters

A.

7.3, 5.9

B.

7.7, 12.5

C.

12.5, 7.7

D.

5.9, 7.3

Correct answer is C

\(\frac{PQ}{PN} = \frac{PM}{PR} = \frac{QM}{NR}\)

\(\frac{4.8}{12} = \frac{5}{PR}\)

PR = \(\frac{5 \times 12}{4.8} = \frac{50}{4}\)

= 12.5

\(\frac{PQ}{PN} = \frac{PM}{PT} = \frac{TM}{NT}\)

\(\frac{PT}{12} = \frac{5}{PR}\)

PT2 = 60

PT = \(\sqrt{60}\)

= 7.746

= 7.7

1,662.

In the figure above, Find the value of x

A.

130o

B.

110o

C.

100o

D.

90o

Correct answer is A

No explanation has been provided for this answer.

1,663.

Find the curved surface area of the frustrum in the figure

A.

16\(\pi \sqrt{10}\)cm2

B.

20\(\pi \sqrt{10}\)cm2

C.

24\(\pi \sqrt{10}\)cm2

D.

36\(\pi \sqrt{10}\)cm2

Correct answer is B

\(\frac{x}{4} = \frac{6 + x}{6}\)

6x = 4(6 + x) = 24 + 4x

x = 12cm 

 CSA = \(\pi RL - \pi rl\)

= \(\pi (6) \sqrt{{18^2} + 6^2} - \pi \times 4 \times \sqrt{{12^2} + 4^2}\)

= 6\(\pi \sqrt{360} - 4 \pi \sqrt{160}\)

= 36\(\pi \sqrt{10} - 16 \pi \sqrt{10}\)

= 20\(\pi \sqrt{10}\)cm2

1,664.

In the figure, PQR is a semicircle. Calculate the area of the shaded region

A.

125\(\frac{2}{7}\)2

B.

149\(\frac{2}{7}\)cm2

C.

234\(\frac{1}{7}\)cm2

D.

267\(\frac{1}{2}\)cm2

Correct answer is A

No explanation has been provided for this answer.

1,665.

In the figure, YXZ = 30o, XYZ = 105o and XY = 8cm. Calculate YZ

A.

16\(\sqrt{2}\)cm

B.

8\(\sqrt{2}\)cm

C.

4\(\sqrt{2}\)cm

D.

22cm

Correct answer is C

yzx + 105o + 30o = 180o

yzx = 180 - 155 = 45o

\(\frac{yz}{sin 30^o} = \frac{8}{sin 45^o}\)

yz = \(\frac{8 \sin 30}{sin 45}\)

= 8(\(\frac{1}{2}) = \frac{8}{1} \times \frac{1}{2} \times \frac{\sqrt{2}}{1}\)

= 4 \(\div\) \(\frac{1}{\sqrt{2}}\)

= 4\(\sqrt{2}\)cm