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.

2,451.

The derivative of cosec x is

A.

tan x cosec x

B.

-cot x cosec x

C.

tan x sec x

D.

-cot x sec x

Correct answer is B

\(\csc x = \frac{1}{\sin x}\)

Using the quotient rule,

\(\frac{\mathrm d y}{\mathrm d x} = \frac{vdu - udv}{v^{2}}\)

= \(\frac{\sin x (0) - 1 (\cos x)}{(\sin x)^{2}}\)

= \(\frac{- \cos x}{\sin^{2} x}\)

= \((\frac{- \cos x}{\sin x}) (\frac{1}{\sin x})\)

= \(- \cot x \csc x\)

2,453.

P is on the locus of points equidiatant from two given points X and Y. UV is a straight line throuh Y parallel to the locus. If < PYU is 40°, find < XPY.

A.

100o

B.

80 o

C.

50 o

D.

40 o

Correct answer is B

< PYU = < YPQ = 40°(Alternative) = PQ\(\parallel\)UV

< XPQ = < YPQ = 40°, Since QX = QY

therefore < XPY = 80°

2,454.

Two perpendicular lines PQ and QR intersect at (1, -1). If the equation of PQ is x - 2y + 4 = 0, find the equation of QR

A.

x + 2y - 1= -0

B.

2x + y - 3 = 0

C.

x - 2y - 3 = 0

D.

2x + y - 1 = 0

Correct answer is D

Line PQ : x - 2y + 4 = 0

2y = x + 4 \(\implies y = \frac{x}{2} + 2 \)

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

Slope of the perpendicular line QR: \(\frac{-1}{\frac{1}{2}} = -2\)

Line QR: \(y = mx + b\)

\(y = -2x + b\) 

Point of intersection: (1, -1)

\(-1 = -2(1) + b \implies b = -1 + 2 = 1\)

\(y = -2x + 1 \implies y + 2x - 1 = 0\)

\(QR: 2x + y - 1 = 0\)

2,455.

Find the distance between two towns P(45°N, 30°W) and Q(15°S, 30°W) if the radius of the earth is 7000km. [\(\pi = \frac{22}{7}\)]

A.

\(\frac{1100}{3}\)km

B.

\(\frac{2200}{3}\)km

C.

\(\frac{22000}{3}\)km

D.

\(\frac{1100}{3}\)km

Correct answer is C

Angular difference = 45° + 15° = 60°.

\(D = \frac{60°}{360°} \times 2 \times \frac{22}{7} \times 7000\)

= \(\frac{22000}{3} km\)