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WAEC Further Mathematics Past Questions & Answers - Page 27

131.

A three-digit odd number less than 500 is to be formed from 1,2,3,4 and 5. If repetition of digits is allowed, in how many ways can this be done?

A.

125

B.

75

C.

60

D.

36

View answer & explanation

Correct answer is B

No. of ways = 3 x 5 x 5

= 75

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

View answer & explanation

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

View answer & explanation

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

View answer & explanation

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

View answer & explanation

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

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