WAEC Mathematics Past Questions & Answers - Page 72

356.

If cos \(\theta\) = x and sin 60o = x + 0.5 0o < \(\theta\) < 90o, find, correct to the nearest degree, the value of \(\theta\)

A.

32o

B.

40o

C.

60o

D.

69o

Correct answer is D

sin 60o = x + 0.5 0o(given)

0.8660 = x + 0.5

0.8660 - 0.5 = x

x = 0.3660

cos\(\theta\) = x(given)

cos\(\theta\) = 0.3660

Hence, \(\theta\) = cos-1(0.3660)

= 68.53o

= 69o (nearest degree)

357.

A straight line passes through the point P(1,2) and Q
(5,8). Calculate the length PQ

A.

\(4\sqrt{11}\)

B.

\(4\sqrt{10}\)

C.

\(2\sqrt{17}\)

D.

\(2\sqrt{13}\)

Correct answer is D

|PQ| = \(\sqrt{(x_2 - X- 1) + (y_2 - y_1)^2}\)

= \(\sqrt{(5 - 1)^2 + (8 - 2)^2}\)

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

= \(\sqrt{16 + 36}\)

= \(\sqrt{52}\)

= 2\(\sqrt{13}\)

358.

A straight line passes through the points P(1,2) and Q(5,8). Calculate the gradient of the line PQ

A.

\(\frac{3}{5}\)

B.

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

C.

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

D.

\(\frac{5}{3}\)

Correct answer is C

Let: (x1, y1) = (1, 2)

(x2, y2) = (5, 8)

The gradient m of \(\bar{PQ}\) is given by

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

= \(\frac{8 - 2}{5 - 1}\)

= \(\frac{6}{4}\)

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

359.

The volume of a pyramid with height 15cm is 90cm3. If its base is a rectangle with dimension xcm by 6cm, find the value of x

A.

3

B.

5

C.

6

D.

8

Correct answer is A

Volume of pyramid = \(\frac{1}{3}\)lbh

90 = \(\frac{1}{3} \times x \times 6 \times 15\)

x = \(\frac{90 \times 33}{6 \times 15}\)

= 3

360.

The curve surface area of a cylinder, 5cm high is 110cm 2. Find the radius of its base. [Take \(\pi = \frac{22}{7}\)]

A.

2.6cm

B.

3.5cm

C.

3.6cm

D.

7.0cm

Correct answer is B

Curved surface area of cylinder = 2\(\pi\)rh

110 = 2 x \(\frac{22}{7}\) x r x 5

r = \(\frac{110 \times 7}{44 \times 5}\)

= 3.5cm