WAEC Further Mathematics Past Questions & Answers - Page 33

161.

A binary operation * is defined on the set of real number, R, by x*y = x\(^2\) - y\(^2\) + xy, where x, \(\in\)  R. Evaluate (\(\sqrt{3}\))*(\(\sqrt{2}\))

 

\({\color{red}2x} \times 3\)

A.

1 - \(\sqrt{6}\)

B.

\(\sqrt{6}\) - 1

C.

\(\sqrt{6}\)

D.

1 + \(\sqrt{6}\)

Correct answer is D

x*y = x\(^2\) - y\(^2\) + xy

(\(\sqrt{3}\))*(\(\sqrt{2}\)) = (\(\sqrt{3}\))\(^2\) - (\(\sqrt{2}\))\(^2\) + \(\sqrt{3}\) x \(\sqrt{2}\) 

= 3 - 2 + \(\sqrt{6}\)

= 1 + \(\sqrt{6}\) 

162.

Evaluate: \(^{lim}_{x \to 1} \begin{pmatrix} \frac{1 - x}{x^2 - 3x + 2} \end {pmatrix}\)

A.

-1

B.

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

C.

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

D.

1

Correct answer is D

Lim(\(\frac{1 - x}{x^2 - 3x + 2}\))

= \(^{lim}_{x \to 1} \begin{pmatrix} \frac{1 - x}{x^2 - 3x + 2} \end {pmatrix}\)

= \(^{lim}_{x \to 1} \begin{pmatrix} \frac{x - 1}{(x - 2)(x + 1)} \end {pmatrix}\)

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

= \(\frac{-1}{-1}\) 

= 1

164.

Given that X and Y are independent events such that P(X) = 0.5, P(Y) = m and P(X U Y) = 0.75, find the value of m. 

A.

0.6

B.

0.5

C.

0.4

D.

0.3

Correct answer is C

P(X \(\cup\) Y) = P(X)P(Y) 

0.15 = 0.5m

m = \(\frac{0.015}{0.5}\)

= 0.3 

165.