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.

2,007.

Two points X and Y both on latitude 60oS have longitude147oE and 153oW respectively. Find to the nearest kilometer the distance between X and Y measured along the parallel of latitude(Take 2\(\pi\)R = 4 x 104km, where R is the radius of the earth)

A.

16667km

B.

28850km

C.

8333km

D.

2233km

Correct answer is A

Length of an area = \(\frac{\theta}{360}\) x 2\(\pi\)r

Longitude difference = 147 + 153 = 30NoN

distance between xy = \(\frac{\theta}{360}\) x 2\(\pi\)R cos60o

= \(\frac{300}{360}\) x 4 x 104 x \(\frac{1}{2}\)

= 1.667 x 104km(1667 km)

2,008.

A bag contains 4 white balls and 6 red balls. Two balls are taken from the bag without replacement. What is the probability that they are both red?

A.

\(\frac{2}{3}\)

B.

\(\frac{2}{15}\)

C.

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

D.

\(\frac{1}{3}\)

Correct answer is D

P(R1) = \(\frac{6}{10}\)

= \(\frac{2}{3}\)

P(R1 n R11) = P(both red)

\(\frac{3}{5}\) x \(\frac{5}{9}\)

= \(\frac{1}{3}\)

2,009.

PRSQ is a trapezium of area 14cm2 in which PQ||RS. If PQ = 4cm and SR = 3cm, Find the area of SQR in cm2

A.

7.0

B.

6.0

C.

5.2

D.

5.0

Correct answer is B

Area of trapezium = 14cm2

Area of trapezium = \(\frac{1}{2}\)(a + b)h

14 = \(\frac{1}{2}\)(4 + 3)h

14 = \(\frac{7}{2}\)h

h = \(\frac{14 \times 2}{7}\)

= 4

Area of SQR = \(\frac{1}{2}\)(3 x 4)

= \(\frac{12}{2}\)

= 6.0

2,010.

A solid sphere of radius 4cm has a mass of 64kg. What will be the mass of a shell of the same metal whose internal and external radii are 2cm and 3cm respectively?

A.

5kg

B.

16kg

C.

19kg

D.

6kg

Correct answer is A

\(\frac{1\sqrt{3}}{(\frac{1}{2})^2}\)

= \(\frac{4}{\sqrt{3}}\)

= \(\frac{\sqrt{3}}{\sqrt{3}}\)

= \(\frac{4\sqrt{3}}{\sqrt{3}}\)

m = 64kg, V = \(\frac{4\pi r^3}{3}\)

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

= \(\frac{256\pi}{3}\) x 10-6m3

density(P) = \(\frac{\text{Mass}}{\text{Volume}}\)

= \(\frac{64}{\frac{256\pi}{3 \times 10^{-6}}}\)

= \(\frac{64 \times 3 \times 10^{-6}}{256}\)

= \(\frac{3}{4 \times 10^{-6}}\)

m = PV = \(\frac{3}{4 \pi \times 10^{-6}}\) x \(\frac{4}{3}\) \(\pi\)[32 - 22] x 10-6

\(\frac{3}{4 \times 10^{-6}}\) x \(\frac{4}{3}\) x 5 x 10-6

= 5kg