WAEC Mathematics Past Questions & Answers - Page 139

691.

In an examination, Kofi scored x% in Physics, 50% in Chemistry and 70% in Biology. If his mean score for the three subjects was 55%, find x

A.

40

B.

45

C.

55

D.

60

Correct answer is B

\(\frac{x + 50 + 70}{3} = 55\)

x + 120 = 3(55)

x + 120 = 165

= 165 - 120

x = 45%

692.

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

A.

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

B.

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

C.

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

D.

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

Correct answer is D

Sin 60 = \(\frac{\sqrt{3}}{2}\); cos 60o = \(\frac{1}{2}\)

= \(\frac{1 - \sin 60}{1 + \cos 60} = \frac{1 - \frac{\sqrt{3}}{2}}{1 + \frac{1}{2}}\)

= \(\frac{2 - \sqrt{3}}{3}{2}\div \frac{2 + 1}{2}\)

= \(\frac{2 - \sqrt{3}}{2} \times \frac{2}{3}\)

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

693.

If M and N are two fixed points in a plane. Find the locus L = [P : PM = PN]

A.

a line equal to MN

B.

line parallel to MN

C.

Perpendicular bisector of MN

D.

A circle centre P, radius MN

Correct answer is C

Locus L = (P : PM = Pn}

For M and N being two fixed points

Since PM = PN, P is equidistant from Mand N, So L must be the perpendicular bisector of the line MN

694.

The interior angles of a pentagon are (2x + 5)o, (x + 20)o, xo, (3x - 20)o and (x + 15)o. Find the value of x

A.

80o

B.

70o

C.

65o

D.

40o

Correct answer is C

(2x + 5)o + (xo + 20o) + x + (3x - 20)o + (x + 15)o = (n - 2) x 180

8n + 20 = (5 - 2) x 180

where n = 5(Pentagon)

8n + 20 = 3 x 180

8n + 20 = 540

8n = 540 - 20

8n = 520

x = 65o

695.

The diameter of a bicycle wheel is 42cm. If the wheel makes 16 complete revolution, what will be the total distance covered by the wheel? [Take \(\pi \frac{22}{7}\)

A.

672cm

B.

1056cm

C.

2112cm

D.

4224cm

Correct answer is C

d = 42cm

Circumference = \(\pi d = \frac{22}{7} \times 42cm\)

= 22 x 6cm = 132cm

Total distance covered = circumference x number of revolutions

= 132cm x 16 = 2112cm