WAEC Mathematics Past Questions & Answers - Page 90

446.

A man's eye level is 1.7m above the horizontal ground and 13m from a vertical pole. If the pole is 8.3m high, calculate, correct to the nearest degree, the angle of elevation of the top of the pole from his eyes.

A.

33o

B.

32o

C.

27o

D.

26o

Correct answer is C

tan \(\theta = \frac{opp}{adj} = \frac{6.6}{13}\)

tan \(\theta = 0.5077\)

\(\theta\) = tan-1 0.5077

\(\theta = 27^o\)

447.

Subtract \(\frac{1}{2}\)(a - b - c) from the sum of \(\frac{1}{2}\)(a - b + c) and \(\frac{1}{2}\)
(a + b - c)

A.

\(\frac{1}{2}\) (a + b + c)

B.

\(\frac{1}{2}\) (a - b - c)

C.

\(\frac{1}{2}\) (a - b + c)

D.

\(\frac{1}{2}\) (a + b - c)

Correct answer is A

\(\frac{1}{2}\)(a - b + c) + \(\frac{1}{2}\)(a + b - c) - [\(\frac{1}{2}\) (a - b - c)]

\(\frac{1}{2}a - \frac{1}{2}b + \frac{1}{2}c + \frac{1}{2}a + \frac{1}{2}b - \frac{1}{2}c - \frac{1}{2}a + \frac{1}{2}b + \frac{1}{2}c\)

= \(\frac{1}{2}a + \frac{1}{2}b + \frac{1}{2}c\)

= \(\frac{1}{2}(a + b + c)\)

448.

If \(\frac{2}{x - 3} - \frac{3}{x - 2}\) is equal to \(\frac{p}{(x - 3)(x - 2)}\), find p

A.

-x - 5

B.

-(x + 3)

C.

5x - 13

D.

5 - x

Correct answer is D

\(\frac{2}{x - 3} - \frac{3}{x - 2}\) = \(\frac{p}{(x - 3)(x - 2)}\)

\(\frac{2(x - 2) - 3(x - 3)}{(x - 3)(x - 2)}\) = \(\frac{p}{(x - 3)(x - 2)}\)

= \(\frac{2x - 4 - 3x + 9}{(x - 3)(x - 2)}\) = \(\frac{p}{(x - 3)(x - 2)}\)

\(\frac{-x + 5}{(x - 3)(x - 2)} = \frac{p}{(x - 3)(x - 2)}\)

p(x - 3)(x - 2) = -x + 5(x - 3)(x - 2)

p = -x + 5 or p = 5 - x

449.

Simplify \(\frac{\sqrt{8^2 \times 4^{n + 1}}}{2^{2n} \times 16}\)

A.

16

B.

8

C.

4

D.

1

Correct answer is C

\(\frac{\sqrt{8^2 \times 4^{n + 1}}}{2^{2n} \times 16}\)

= \(\frac{\sqrt{2^{3(2)} \times 2^{2(n + 1)}}}{2^{2n} \times 2^4}\)

= \(\frac{\sqrt{2^6 \times 2^{2n + 2)}}}{2^{2n} + 4}\)

= \(\frac{\sqrt{2^6 + 2^{2n + 2)}}}{2^{2n} + 4}\)

= \(\frac{\sqrt{2^{2n + 8}}}{2^{2n} + 4}\)

= \(\sqrt{2^{2n + 8} \div 2^{2n} + 4}\)

= \(\sqrt{2^{2n - 2n} + 8 - 4}\)

= \(\sqrt{2^4}\)

= \(\sqrt{16}\)

= 4

450.

Approximate 0.0033780 to 3 significant figures

A.

338

B.

0.338

C.

0.00338

D.

0.003

Correct answer is C

No explanation has been provided for this answer.