WAEC Past Questions and Answers - Page 1101

5,502.

The binary operation * is defined on the set of R, of real numbers by \(x * y = 3x + 3y - xy, \forall x, y \in R\). Determine, in terms of x, the identity element of the operation.

A.

\(\frac{2x}{x - 3}, x \neq 3\)

B.

\(\frac{2x}{x + 3}, x \neq -3\)

C.

\(\frac{3x}{x - 3}, x \neq 3\)

D.

\(\frac{3x}{x + 3}, x \neq -3\)

Correct answer is A

From the rules of binary operation, \(x * e = x\)

\(\implies x * e = 3x + 3e - xe = x\)

\(3e - xe = x - 3x = -2x\)

\(e = \frac{2x}{x - 3}, x \neq 3\)

5,503.

Simplify \(\frac{\tan 80° - \tan 20°}{1 + \tan 80° \tan 20°}\)

A.

\(3\sqrt{2}\)

B.

\(2\sqrt{3}\)

C.

\(\sqrt{3}\)

D.

\(\sqrt{2}\)

Correct answer is C

\(\tan (x - y) = \frac{\tan x - \tan y}{1 + \tan x \tan y}\)

\(\implies \frac{\tan 80 - \tan 20}{1 + \tan 80 \tan 20} = \tan (80 - 20) = \tan 60°\)

\(\tan 60 = \frac{\sin 60}{\cos 60} = \frac{\sqrt{3}}{2} ÷ \frac{1}{2}\)

= \(\sqrt{3}\)

5,504.

Simplify \(\frac{\sqrt{3}}{\sqrt{3} - 1} + \frac{\sqrt{3}}{\sqrt{3} +1}\)

A.

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

B.

\(\frac{1}{2}\sqrt{3}\)

C.

\(3\)

D.

\(2\sqrt{3}\)

Correct answer is C

\(\frac{\sqrt{3}}{\sqrt{3} - 1} + \frac{\sqrt{3}}{\sqrt{3} + 1}\)

= \(\frac{\sqrt{3}(\sqrt{3} + 1) + \sqrt{3}(\sqrt{3} - 1)}{(\sqrt{3} - 1)(\sqrt{3} + 1)}\)

= \(\frac{6}{3 - 1} \)

= 3