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.

2,486.

\(\frac{d}{dx}\) cos(3x\(^2\) - 2x) is equal to

A.

-sin(6x - 2)

B.

-sin(3x2 - 2x)dx

C.

(6x - 2) sin(3x2 - 2x)

D.

-(6x - 2)sin(3x2 - 2x)

Correct answer is D

Let \(3x^{2} - 2x = u\)

\(y = \cos u \implies \frac{\mathrm d y}{\mathrm d u} = - \sin u\)

\(\frac{\mathrm d u}{\mathrm d x} = 6x - 2\)

\(\therefore \frac{\mathrm d y}{\mathrm d x} = (6x - 2) . - \sin u\)

= \(- (6x - 2) \sin (3x^{2} - 2x)\)

2,487.

Differentiate \(\frac{6x^3 - 5x^2 + 1}{3x^2}\) with respect to x

A.

\(\frac{2 + 2}{3x^3}\)

B.

2 + \(\frac{1}{6x}\)

C.

2 - \(\frac{2}{3x^3}\)

D.

\(\frac{1}{5}\)

Correct answer is C

\(\frac{6x^3 - 5x^2 + 1}{3x^2}\)

let y = 3x2

y = \(\frac{6x^3}{3x^2}\) - \(\frac{6x^2}{3x^2}\) + \(\frac{1}{3x^2}\)

Y = 2x - \(\frac{5}{3}\) + \(\frac{1}{3x^2}\)

\(\frac{dy}{dx}\) = 2 + \(\frac{1}{3}\)(-2)x-3

= 2 - \(\frac{2}{3x^3}\)

2,488.

In a triangle XYZ, if < ZYZ is 60, XY = 3cm and YZ = 4cm, calculate the length of the sides XZ.

A.

√23cm

B.

√13cm

C.

2√5cm

D.

2√3cm

Correct answer is B

(XZ)2 = 32 + 42 - 2 x 3 x 4 cos60o

= 25 - 24\(\frac{1}{2}\)

XZ = √13cm

2,489.

The angle of elevation of a building from a measuring instrument placed on the ground is 30°. If the building is 40m high, how far is the instrument from the foot of the building?

A.

\(\frac{20}{√3}\)m

B.

\(\frac{40}{√3}\)m

C.

20√3m

D.

40√3m

Correct answer is D

\(\frac{40}{x}\) = tan 30°

x = \(\frac{40}{tan 30}\)

= \(\frac{40}{1\sqrt{3}}\)

= 40√3m

2,490.

Find the distance between the point Q (4,3) and the point common to the lines 2x - y = 4 and x + y = 2

A.

3√10

B.

3√5

C.

√26

D.

√13

Correct answer is D

2x - y .....(i)

x + y.....(ii)

from (i) y = 2x - 4

from (ii) y = -x + 2

2x - 4 = -x + 2

x = 2

y = -x + 2

= -2 + 2

= 0

\(x_1\) = 2

\(y_1\) = 0

\(x_2\) = 4

\(y_2\) = 3

Hence, dist. = \(\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}\)

= \(\sqrt{(3 - 0)^2 + (4 - 2)^2}\)

= \(\sqrt{3^2 + 2^2}\)

= \(\sqrt{13}\)