Further Mathematics questions and answers

Further Mathematics Questions and Answers

Test your knowledge of advanced level mathematics with this aptitude test. This test comprises Further Maths questions and answers from past JAMB and WAEC examinations.

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