WAEC Past Questions and Answers - Page 1038

5,186.

If log 5(\(\frac{125x^3}{\sqrt[ 3 ] {y}}\) is expressed in the values of p, q and k respectively

A.

3, \(\frac{-1}{3}\), 5

B.

\(\frac{-1}{3}\), 3, 5

C.

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

D.

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

Correct answer is D

log\(_5\) (\(\frac{125x^3}{\sqrt[3] {y}}\))

= \(\log_5 125 x^3 - \log _1 x^3 - log_5 y\frac{1}{3}\)

= \(3 log_5 5 + 3 log_5 x - \frac{1}{3} log _5 y\)

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

5,187.

If the sum of the roots of 2x\(^2\) + 5mx + n = 0 is 5, find the value of m

A.

-2.5

B.

-2.0

C.

2.0

D.

2.5

Correct answer is B

Sum of roots = \(\frac{-a}{b}\) 

= \(\frac{-5m}{2}\) = 5

\(\frac{-5m}{m} = \frac{10}{-5}\)

m = -2

5,188.

Find the unit vector in the direction opposite to the resultant of forces.  F\(_1\) = (-2i - 3j) and F\(_2\) = (5i - j)

A.

\(\frac{1}{5}\)(-3i - 4j)

B.

\(\frac{1}{5}\)(-3i + 4j)

C.

\(\frac{1}{5}\)(3i - 4j)

D.

\(\frac{1}{5}\)(3i + 4j)

Correct answer is C

Resultant 

(- 2i - 3j) + (5i - j)

= 3i - 4j 

Unit vector 

= \(\frac{3i - 4j}{|3i - 4j|} = \frac{3i - 4j}{\sqrt{3i } + (-4)}\)

= \(\frac{3i - 4j}{\sqrt{25}}\) 

= \(\frac{3i - 4j}{5}\) 

5,189.

P(3,4) and Q(-3, -4) are two points in a plane. Find the gradient of the line that is normal to the line PQ. 

A.

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

B.

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

C.

\(\frac{-3}{4}\)

D.

\(\frac{-4}{3}\)

Correct answer is B

Gradient = \(\frac{-4 - 4}{-3 - 3}\)

= \(\frac{-8}{6}\)

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

Normal = -(\(\frac{1}{\frac{1}{4}}\))

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

5,190.

The distance(s) in metres covered by a particle in motion at any time, t seconds, is given by S =120t - 16t\(^2\). Find in metres, the distance covered by the body before coming to rest.

A.

220

B.

222

C.

223

D.

225

Correct answer is D

s = 120t - 16t\(^2\) - 16t\(^2\)

\(\frac{ds}{dt} = 120 - 32t\)

120 - 32t = 0

\(\frac{32t}{32}\) = \(\frac{120}{32}\)

t = 3.75

s = 120(3.75) - 16(3.75)\(^2\)

= 450 - 225 

= 225