WAEC Further Mathematics Past Questions & Answers - Page 27

132.

Calculate the variance of \(\sqrt{2}\), (1 + \(\sqrt{2}\)) and (2 + \(\sqrt{2}\)) 

A.

0

B.

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

C.

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

D.

2

Correct answer is C

x (x - \(\bar{x}\)) (x - \(\bar{x}\))

\(\sqrt{2}\)

1 + \(\sqrt{2}\)

2 + \(\sqrt{2}\) 

-1

0

1

1

0

1

\(\overline{2}\)

 

variance = \(\frac{\sum(x - \bar{x})^2}{n}\)

= \(\frac{2}{3}\) 

133.

A force of 230N acts in its direction 065\(^o\). Find its horizontal component.

A.

208.5N

B.

197.2N

C.

118.5N

D.

97.2

Correct answer is D

Horizontal component = 230 cos 64 

= 97.2N 

134.

In what interval is the function f : x -> 2x - x\(^2\) increasing? 

A.

x = 1

B.

x < 1

C.

x > 1

D.

0 < x < 1

Correct answer is C

2x - x\(^2\) > 0

0 > x\(^2\) - 2x

x\(^2\) - 2x < 0

x(x - 2) < 0 

x > 1

135.

A function f defined by f : x -> x\(^2\) + px + q is such that f(3) = 6 and f(3) = 0. Find the value of q.

A.

-9

B.

-6

C.

15

D.

21

Correct answer is C

f(x) = x\(^3\) + px + q

f(3) 3\(^2\) + 3pf + q = 6

f\(^{1}\)(x) = 2x + p

f\(^1\)(3) = 2(3) + p = 0

p = -6

from 9 + 3p + q = 6

9 + 3(-6) + q = 6

9 - 18 + q = 6

-9 + q = 6

Q = 6 + 9

= 15