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.

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