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.

2,736.

If \(y \alpha \frac{1}{x^2}\) and \(y = 1\frac{1}{4}\) when x = 4, find the value of y when \(x = \frac{1}{2}\)

A.

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

B.

5

C.

10

D.

80

Correct answer is D

\(y \propto \frac{1}{x^2} \Rightarrow y = \frac{k}{x^2} \Rightarrow k = yx^2\\
k = 1\frac{1}{4} \times 4^2 \Rightarrow k=\frac{5}{4}\times \frac{16}{1}=20\\
∴y = 20 \div \left(\frac{1}{2}\right)^2=20\times \frac{4}{1}=80\)

2,737.

A rectangular packet has inner dimension 16cm by 12cm by 6cm. How many cubes of sugar of side 2cm can be neatly packed into the packet?

A.

90

B.

144

C.

150

D.

288

Correct answer is B

Volume of rectangular packet = (16 x 12 x 6)cm3 = 1152cm3. Volume of cube of sugar = 2 x 2 x 2 = 8cm
∴ The number of cubes f sugar \(=\frac{1152}{8}=144\)

2,738.

XOY is a real sector of a circle center O of radius 3.5cm which subtends an angle of 144o at the center. Calculate, in term of ϖ, the area of the sector

A.

1.4ϖcm2

B.

2.8ϖcm2

C.

4.9ϖcm2

D.

9.8ϖcm2

Correct answer is C

Area of a sector \(=\frac{\theta}{360}\times \pi r^2\\
\left(\frac{144}{360}\times \pi \times \frac{3.5}{1} \times 3.5\right)cm^2 = 4.9\pi cm^2\)

2,739.

The angle of elevation of the top of a cliff 15 meters high from a landmark is 60°. How far is the landmark from the foot of the cliff? Leave your answer in surd form

A.

\(15\sqrt{3}m\)

B.

\(15\sqrt{2}m\)

C.

\(10\sqrt{3}m\)

D.

\(5\sqrt{3}m\)

Correct answer is A

Tan 60º = \(\frac{15}{x}\)

cross multiply:

x = \(\frac{15}{\sqrt3}\) = 5\(\sqrt3\)m

2,740.

In the diagram PQRS is a circle, |PT| = |QT| and ∠QPT = 70o what is the size of ∠PRS?

A.

40o

B.

70o

C.

80o

D.

140o

Correct answer is B

∠QPT = ∠QTP = 70o. Since ∠QTR = 140o
∠PRS = TSR = 1/2(180-40) = 70o