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.

46.

There are 30 students in a class. 15 study woodwork and 13 study metal work. 6 study neither of the 2 subjects. How many student study woodwork but not metal work?

A.

13

B.

11

C.

5

D.

9

Correct answer is B

Using the venn diagram above

μ = 30
n(W) = 15
n(M) = 13
\(n(W ∪ M)^1 = 6\)
Let x = number of students that study both woodwork and metalwork
i.e. n(W ∩ M) = x
Number of students that study only woodwork,\(n(W ∩ M^1)\) = \(15 - x\)
Number of students that study only metalwork, \(n(W^1 ∩ M)\) = \(13 - x \)
Bringing all together,
\(n(W ∩ M^1)\) +\( n(W^1 ∩ M)\) + \(n(W ∩ M)\) + \(n(W ∪ M)^1\) = \(μ\)
∴ (15 - x) + (13 - x) + x + 6 = 30
⇒ 34 - x = 30
⇒ 34 - 30 = x
∴ x = 4
\(n(W ∩ M^1)\) = \(15 - 4 = 11\)
∴ The number of students that study woodwork but not metalwork is 11.

47.

The angle of a sector of a circle of radius 3.4 cm is 115°. Find the area of the sector.

\((Take \pi = \frac{22}{7})\)

A.

\(11.6cm^2\)

B.

\(12.7cm^2\)

C.

\(10.2cm^2\)

D.

\(9.4cm^2\)

Correct answer is A

\(\theta = 115° , radius = 3.4cm^2\)

Area of a sector = \(\frac{\theta}{360} \times \pi r^2\)

= \(\frac{115}{360} \times \frac{22}{7} \times 3.4\times 3.4\)

= \(\frac{29246.4}{2520}\)

= \(11.6cm^2\)

48.

Solve  \(1 + \sqrt[3]{ x - 3} = 4\)

A.

30

B.

6

C.

12

D.

66

Correct answer is A

\(1 + \sqrt [3]{x-3} = 4\)

= \(\sqrt[3]{x - 3} = 4 - 1\)

\(\sqrt[3]{x - 3} = 3 \)

take the cube of both sides

= x - 3 = 27
 x = 27 + 3
∴ x = 30

49.

In the diagram, O is the center of the circle QRS and ∠SQR = 28°. Find ∠ORS.

A.

\(56^0\)

B.

\(28^0\)

C.

\(76^0\)

D.

\(62^0\)

Correct answer is D

∠SOR = 2 × 28° = 56° (angle at the centre is twice the angle at the circumference)
From ∆SOR
|OS| = |OR| (radii)
So, ∆SOR is isosceles.

ORS = \(\frac{180^0 -  56^0}{2} = \frac{124^0}{2}\)    ( base angles of isosceles triangle are equal)

∴ ∠ORS = 62°

50.

It takes 12 men 8 hours a day to finish a piece of work in 4 days. In how many days will it take 4 men working 16 hours a day to complete the same piece of work?

A.

6 days

B.

8 days

C.

10 days

D.

12 days

Correct answer is A

12 men working 8 hours a day can complete the work in 4 days

12 men working 1 hour a day will complete the same work in (8 x 4) days [working less hours a day means they have to work for more days]


1 man working 1 hour a day will complete same work in (8 x 4 x 12) days [fewer number of men working means the remaining ones will have to work for more days ]

So, it will take 1 man working 1 hour a day to complete a piece of work in (8 x 4 x 12) days = 384 days

Now,

1 man working 16 hours a day will complete the piece of work in (384/16) days = 24 days [working more hours a day means less days to complete the work]

4 men working 16 hours a day will complete the piece of work in (24/4) days = 6 days [more men working means fewer days to complete the work]

ALTERNATIVELY

12 x 8 x 4 = 4 x 16 x d

⇒ d = \(\frac{12 \times 8 \times 4}{4 \times 16}\)

⇒ d = \(\frac{384}{64}\)

⇒ d = 6

∴ 4 men working 16 hours a day will complete the piece of work in 6 days