WAEC Further Mathematics Past Questions & Answers - Page 35

171.

The function f : x \(\to\) x\(^2\) + px + q has turning point when x = -3 and remainder of -6 when divided by (x + 2). Find the value of q.

A.

6

B.

2

C.

-2

D.

-8

Correct answer is B

f (x) = x\(^2\) + px + q

\(\frac{dy}{dx}\) = 2x + p

2x + p = 0

2(-3) + p = 0

p = +6

f(-2) = -2\(^2\) + p(-2) + q

= -6 2p + q = -10

-2(-16) + q = -10

-12 + q = -10 

q = -10 + 12 

= 2

172.

Evaluate \(\int^0_0 \sqrt{x} dx\)

A.

3

B.

9

C.

18

D.

27

Correct answer is C

\(\int^0_0 \sqrt{x} dx\)

\(\frac{x^{\frac{1}{2}} + 1}{\frac{1}{2} + 1}\) |\(^9_0\)

\(\frac{2x^{\frac{3}{2}}}{3}\)|\(^9_0\)

= \(\frac{2(9)^{\frac{3}{2}}}{3}\)

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

= \(\frac{2 \times 27}{3}\)

= 2 x 9

= 18

173.

Find the coordinates of the centre of the circle 3x\(^2\) + 3y\(^2\) - 6x + 9y - 5 = 0

A.

(-3. \(\frac{9}{2}\))

B.

(-1. \(\frac{3}{2}\))

C.

(1, - \(\frac{3}{2}\))

D.

(3. -\(\frac{9}{2}\))

Correct answer is C

\(\frac{3x^2}{3} + \frac{3y^2}{3} - \frac{6x}{3} + \frac{9y}{3} - \frac{5}{3}\) = 0

2gx = -2x, 2 fy = 3y 

g = -1, f = \(\frac{3}{2}\)

Centre (1, - \(\frac{3}{2}\)) 

174.

Find the coefficient of the term in the binomial expansion of [2x + \(\frac{3y}{4}\)]\(^3\) in descending powers of x.

A.

\(\frac{27}{64}\)y\(^2\)

B.

\(\frac{27}{8}\)y\(^2\)

C.

8y\(^2\)

D.

9y\(^2\)

Correct answer is B

(2x + \(\frac{3y}{4}\))\(^3\)

= 3(2x) (\(\frac{3y}{4}\))\(^2\)

= \(\frac{27}{8}\)y\(^2\)

175.

Given that P and Q are non-empty subsets of the universal set, U. Find P \(\cap\) (Q U Q`).

A.

p

B.

P`

C.

Q

D.

Q`

Correct answer is A

P \(\cap\) (Q U Q`)

P \(\cap\) U = P