WAEC Mathematics Past Questions & Answers - Page 123

611.

In the diagram, < WOX = 60o, < YOE = 50o and < OXY = 30o. What is the bearing of x from y?

A.

300o

B.

240o

C.

190o

D.

150o

Correct answer is A

The bearing of x from y = 270o + \(\theta\)

where \(\theta\) + 50o = y

in \(\bigtriangleup\) OXY

O + X + Y = 180o

Where O = 40o + 30o = 70o

70o + 30o + y = 180o

y + 100o = 180o

y = 180o - 100o = 30o

\(\theta\) + 50o = 80o

80o - 50o = 30o

The bearing of x from y = 270o + 30o = 300o

612.

In the diagram, 0 is the centre of the circle. Find the value x

A.

34

B.

29

C.

17

D.

14

Correct answer is D

POQ in a straight line

Hence, < POQ + < QOR = 180o

56o + < QOR = 180o

< QOR = 180o - 56o

= 124o

Now, in \(\bigtriangleup\) QOR OR = OQ = Radius

< ORQ = < OQR = 2x (Base angles of an Isosceles \(\bigtriangleup\))

2x + 124 + 2x = 180o

4x + 124 = 180

4x = 180 - 124

4x = 56

x = \(\frac{56}{4}\)

x = 14o

613.

The diagram shows a rectangular cardboard from which a semi-circle is cut off. Calculate the area of the remaining part

A.

44cm2

B.

99cm2

C.

154cm2

D.

165cm2

Correct answer is B

Area of remaining = Area of rectangle = Area of semi-circle

22 x 8 - \(\frac{1}{2}\)xar2

ehere r - \(\frac{14}{2}\)cm = 7cm

Area of remaining = 176 - \(\frac{1}{2}\) x \(\frac{22}{4}\) x 7 x 7

= 176 - 77

= 99cm2

614.

The diagram is a net right rectangular pyramid. Calculate the total surface area

A.

208cm2

B.

112cm2

C.

92cm2

D.

76cm2

Correct answer is C

Total surface area = sum of the area of the \(\bigtriangleup\) S + Area of the rectangle

= 2 x Area of \(\bigtriangleup\) PTQ + 2 x Area of \(\bigtriangleup\) QUR + Area of rectangle PQRS

2 x \(\frac{1}{2}\)(8 x 4) + 2 x \(\frac{1}{2}\)(5 x 4) + 8 x 5

= 32 + 20 + 40

= 92cm2

615.

In the diagram, GI is a tangent to the circle at H. If EF//GI, calculate the size of < EHF

A.

126o

B.

72o

C.

64cmo

D.

32cmo

Correct answer is B

F = 54o (Alternate triangle angles)

< GHE = F = 54o(Angle between a chord and a tangent = angles in the alternate segment)

Now, < GHE + < EHF + < IHF = 180o(Angles on a straight line)

54o + < EHF + 54o = 180o

< EHF = 180o - 108o

= 72o