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.

2,531.

If y = 243(4x + 5)-2, find \(\frac{dy}{dx}\) when x = 1

A.

\(\frac{-8}{3}\)

B.

\(\frac{3}{8}\)

C.

\(\frac{9}{8}\)

D.

-\(\frac{8}{9}\)

Correct answer is A

y = 243(4x + 5)-2, find \(\frac{dy}{dx}\)

= -1944(4x + 5)-3

= 1944(9)-3

\(\frac{dy}{dx}\) when x = 1

= -\(\frac{1944}{9^3}\)

= -\(\frac{1944}{729}\)

= \(\frac{-8}{3}\)

2,532.

From the top of a vertical mast 150m high., two huts on the same ground level are observed. One due east and the other due west of the mast. Their angles of depression are 60° and 45° respectively. Find the distance between the huts

A.

150(1 + \(\sqrt{3}\))m

B.

50( \(\sqrt{3}\) - \(\sqrt{3}\))m

C.

150 \(\sqrt{3}\)m

D.

\(\frac{50}{\sqrt{3}}\)m

Correct answer is B

\(\frac{150}{Z}\) = tan 60o,

Z = \(\frac{150}{tan 60^o}\)

= \(\frac{150}{3}\)

= 50\(\sqrt{3}\)cm

\(\frac{150}{X x Z}\) = tan45o = 1

X + Z = 150

X = 150 - Z

= 150 - 50\(\sqrt{3}\)

= 50( \(\sqrt{3}\) - \(\sqrt{3}\))m

2,533.

solve the equation cos x + sin x \(\frac{1}{cos x - sinx}\) for values of such that 0 \(\leq\) x < 2\(\pi\)

A.

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

B.

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

C.

0, \(\frac{\pi}{3}\)

D.

0, \(\pi\)

Correct answer is D

cos x + sin x \(\frac{1}{cos x - sinx}\)

= (cosx + sinx)(cosx - sinx) = 1

= cos2x + sin2x = 1

cos2x - (1 - cos2x) = 1

= 2cos2x = 2

cos2x = 1

= cosx = \(\pm\)1 = x

= cos-1x (\(\pm\), 1)

= 0, \(\pi\) \(\frac{3}{2}\pi\), 2\(\pi\)

(possible solution)

2,534.

The midpoint of the segment of the line y = 4x + 3 which lies between the x-ax 1 is and the y-ax 1 is

A.

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

B.

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

C.

(\(\frac{3}{8}\), \(\frac{3}{2}\))

D.

(-\(\frac{3}{8}\), \(\frac{3}{2}\))

Correct answer is D

y = 4x + 3

when x = 0, y = 3 \(\to\) (0, 3)

when y = 0, x = -\(\frac{3}{4}\) \(\to\) (\(\frac{3}{4}\), 0)

mid-point \(\frac{0 + (-{\frac{3}{4}})}{2}\), \(\frac{3 + 0}{4}\)

-\(\frac{3}{8}\), \(\frac{3}{2}\)

2,535.

If the distance between the points (x, 3) and (-x, 2) is 5. Find x

A.

6.0

B.

2.5

C.

\(\sqrt{6}\)

D.

\(\sqrt{3}\)

Correct answer is C

d2 = (y - y)2 + (x - x)2

5 = 4x2 + 1 = 25= 4x2 + 1

= 4x2 = 25 - 1= 24

x2 = \(\frac{24}{4}\)

x = \(\sqrt{6}\)