WAEC Further Mathematics Past Questions & Answers - Page 39

191.

Given that \(\frac{1}{x^2 - 4} = \frac{p}{(x + 2)} + \frac{Q}{(x - 2})\)

x \(\neq \pm 2\)

Find the value of (P + Q)

A.

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

B.

1

C.

\(\frac{1}{2}\)

D.

0

Correct answer is D

\(\frac{1}{x^2 - 4} = \frac{P}{(x + 2)} + \frac{Q}{(x - 2)}\)

I = p(x - 2) + Q(x + 2)

Let x = 2

I = P(2 - 2) + Q(2+ 2)

I = -4Q 

Q = \(\frac{1}{4}\) 

Let x = -2

I = P(-2  - 2) + Q(-2 + 2)

I = -4p 

P = \(\frac{1}{-4}\) 

PQQ = - \(\frac{1}{4} + \frac{1}{4}\)

= 0

192.

Consider the following statements:

p: Birds fly

q: The sky is blue

r: The grass is green
What is the symbolic representation of "If the grass is green and the sky is not blue, then the birds do not fly"?

A.

A. (r ^ p) \(\to\) q

B.

(r ^~ p) \(\to\) q

C.

(r ^ q) \(\to\) p

D.

(r ~ ^ p) \(\to\) q

Correct answer is A

No explanation has been provided for this answer.

193.

If g : r \(\to\) 5 - 2r, r is a real number, find the image of -3

A.

13

B.

11

C.

-1

D.

-9

Correct answer is B

g(-3) = 5 - 2(-3)

= 5 + 6 = 11

194.

A linear transformation is defined by T: (x, y) \(\to\) (-x + y, -4y). Find the image, Q`, of Q(-3, 2) under T

A.

Q`(5, -8)

B.

Q`(-8, 5)

C.

Q`(5, -3)

D.

Q`(-5, -8)

Correct answer is A

Q(3 -3, 2) = [-(-3) + 2, -4(2)]

= (3 + 2, -8) 

= (5, -8) 

195.

Given that g ; x \(\to\) 3x and f ; x \(\to\) cos x. Find the value of g\(^o\) f(20\(^o\)) 

A.

0.50

B.

0.94

C.

2.60

D.

2.82

Correct answer is D

f(20\(^o\)) = cos 20\(^o\) = 0.9397

g(0.9397) = 3(0.9397)

= 2.82