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.

31.

The radius of a sphere is 3 cm. Find, in terms of π, its volume.

A.

\(30\pi cm^3\)

B.

\(108\pi cm^3\)

C.

\(27\pi cm^3\)

D.

\(36\pi cm^3\)

Correct answer is D

Given that radius = 3cm.

volume of sphere = \(\frac{4}{3}\times\pi\times r^3\)

= \(\frac{4}{3}\times\pi\times 3^3\)

= \(\frac{4}{3}\times\pi\times 27\)

= \(4\times\pi\times9\)

= \(36\pi cm^3\)

32.

The radius and height of a solid cylinder is 8 cm and 14 cm respectively. Find, correct to two d.p the total surface area.
(Take \(\pi = \frac{22}{7})\)

A.

\(1,106.29cm^2\)

B.

\(1,016.29cm^2\)

C.

\(1,106.89cm^2\)

D.

\(1,206.27cm^2\)

Correct answer is A

radius = 8cm , height = 14cm  and \(\pi = \frac{22}{7}\)

total surface area of a solid cylinder =\( 2πrh+2πr^2\) = 2πr( h + r )

 \( 2 \times \frac{22}{7} \times 8( 8 + 14)\)

 \( 2 \times \frac{22}{7} \times 8 \times 22\)

\(\frac{7744}{7}\)

= \(1,106.29cm^2\)

33.

A student measured the height of a pole as 5.98 m which is less than the actual height. If the percentage error is 5%, find correct to two d.p the actual height of the pole.

A.

6.29m

B.

7.67m

C.

7.18m

D.

6.65m

Correct answer is A

%error=5%, measured height = 5.98m

let the actual height = y 

error=x - 5.98 (since 'y' is more than 5.98)

%error = \(\frac{error}{actual height}\times 100%\)

5% =  \(\frac{y - 5.98}{y}\times 100%\)

\(\frac{5}{100} = \frac{y - 5.98}{y}\)

5y = 100(y - 5.98)

5y = 100y - 598

5y - 100y = - 598

-95y = - 598

y = \(\frac{-598}{-95}\)

y = 6.29m( to 2 d.p).

34.

Find the roots of the equations: \(3m^2 - 2m - 65 = 0\)

A.

\(( -5, \frac{-13}{3})\)

B.

\(( 5, \frac{-13}{3})\)

C.

\(( 5, \frac{13}{3})\)

D.

\(( -5, \frac{13}{3})\)

Correct answer is B

Find the roots of the equations: \(3m^2 - 2m - 65 = 0\)

= \( m^2 - 15m + 13m - 65 = 0\)

= 3m(m - 5) + 13( m - 5) = 0

( m - 5)(3m + 13) = 0 

m-5 = 0 or 3m + 13 = 0

therefore, m = 5 or \(\frac{-13}{3}\)

therefore the roots of the quadratic equation = ( 5, \(\frac{-13}{3})\)

35.

If \(log_a 3\) = m and \(log_a 5\) = p, find \(log_a 75\)

A.

\(m^2 + p \)

B.

2m + p

C.

m + 2p

D.

\(m + p^2\)

Correct answer is C

Given: \(log_a 3\) = m and \(log_a 5\) = p
\(log_a 75\) = \(log_a (3 × 25)\)
= \(log_a (3 × 5^2)\)
= \(log_a 3 + log_a 5^2\)
= \(log_a 3 + 2log_a 5\)
Since \(log_a 3\) = m and \(log_a 5\) = p
∴ \(log_a 75\) = m + 2p