WAEC Mathematics Past Questions & Answers - Page 52

256.

Given that cos 30\(^o\) = sin 60\(^o\) = \(\frac{3}{2}\) and sin 30\(^o\) = cos 60\(^o\) = \(\frac{1}{2}\), evaluate \(\frac{tan 60^o - q}{1 - tan 30^o}\)

A.

\(\sqrt{3 - 2}\)

B.

2 - \(\sqrt{3}\)

C.

\(\sqrt{3}\)

D.

-2

Correct answer is C

Tan 60 = 3; Tan 30 = 1

\(\frac{\tan 60^o - 1}{1 - tan 30^o}\)  = \(\frac{\sqrt{3 - 1}}{1 - \frac{1}{\sqrt{3}}}\) = \(\frac{\sqrt{3 - 1}}{\frac{3 - 1}{\sqrt{3}}}\)

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

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

= \(\sqrt{3}\)

257.

A bearing of 320\(^o\) expressed as a compass bearing is

A.

N 50\(^o\) W

B.

N 40\(^o\) W

C.

N 50\(^o\) E

D.

N 40\(^o\) E

Correct answer is B

No explanation has been provided for this answer.

258.

If P(2,3) and Q)2, 5) are points on a graph, calculate the length PQ

A.

6 units

B.

5 units

C.

4 units

D.

2 units

Correct answer is D

\(\sqrt{(x_2 - x_1)^2 + (y_2 - Y_1)^2}\)

= \(\sqrt{(2 - 2)^2 + (5 - 3)^2}\)

= \(\sqrt{0^2 + 2^2}\)

= \(\sqrt{4}\)

= 2 units

259.

Calculate the gradient (slope) of the joining points (-1, 1) and (2, -2)

A.

-1

B.

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

C.

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

D.

1

Correct answer is A

Gradient = m = \(\frac{y_2 - y_1}{x_2 - x_1}\)

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

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

= -1

260.

Which of the following is true about parallelogram?

A.

opposite angles are supplementary

B.

opposite angles are complementary

C.

opposite angles are equal

D.

opposite angles are reflex angles

Correct answer is C

No explanation has been provided for this answer.