WAEC Mathematics Past Questions & Answers - Page 58

286.

The diagram shows a trapezium inscribed in a semi-circle. If O is the mid-point of WZ and |WX| = |XY| = |YZ|, calculate the value of m

A.

90\(^o\)

B.

60\(^o\)

C.

45\(^o\)

D.

30\(^o\)

Correct answer is B

In the diagram, < WOZ = 180\(^o\) (angle on a straight line)

< WOX = < XOY = < YOZ

(|WX| = |XY| = |YZ|)

\(\frac{180^o}{3}\) = 60\(^o\)

= 60\(^o\)

M + m =2m (base angles of isosceles \(\bigtriangleup\), |OY| and |OZ| are radii)

< YOZ + 2m (base angles of a \(\bigtriangleup\))

60\(^o\) + 2m = 180\(^o\) (sum of a \(\bigtriangleup\))

60\(^o\) + 2m = 180\(^o\)

2m = 180\(^o\) - 60\(^o\)

2m = 120\(^o\)

m = \(\frac{120^o}{2}\)

= 60\(^o\)

 

287.

The solution of x + 2 \(\geq\) 2x + 1 is illustrated

A.

i

B.

ii

C.

iii

D.

iv

Correct answer is A

x + 2 \(\geq\) 2x + 1

x - 2x \(\geq\) 1 - 2

-x \(\geq\) -1

\(\frac{-x}{-1}\) \(\geq\) \(\frac{-1}{-1}\)

x \(\leq\) 1

288.

In the diagram, WXYZ is a rectangle with diamension 8cm by 6cm. P, Q, R and S are the midpoints of the rectangle as shown. Using this information calculate the area of the part of the rectangle that is not shaded

A.

25cm\(^2\)

B.

24cm\(^2\)

C.

16cm\(^2\)

D.

12cm\(^2\)

Correct answer is B

Area of shaded part = 2 x area of \(\bigtriangleup\)SPQ

= 2 x \(\frac{1}{2}\) 8 x 3 =24cm

Hence, area of the unshaded part of the rectangle = area of rectangle - area of shaded part

= 8 x 6 - 24

= 48 - 24

= 24 cm\(^2\)

289.

In the diagram, PS and RS are tangents to the circle centre O. ∠PSR = 70°, ∠POR = m, and ∠PSR =n. Find ( m + n ).

A.

110\(^o\)

B.

135\(^o\)

C.

165\(^o\)

D.

225\(^o\)

Correct answer is C

In the diagram,

 

Thus, m = 2 x 55\(^o\) (is a bisector of obtuse

m = 110\(^o\)

n = \(\frac{1}{2}\) x 110\(^o\) (angle at centre = 2 x angle at circum)

n = 55\(^o\)

m + n =  110 + 55 = 165\(^o\)