WAEC Mathematics Past Questions & Answers - Page 89

442.

In parallelogram PQRS, QR is produced to M such that |QR| = |RM|. What fraction of the area of PQMS is the area of PRMS?

A.

\(\frac{1}{4}\)

B.

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

C.

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

D.

\(\frac{3}{4}\)

Correct answer is C

There are 3 triangles: \(\bigtriangleup\)MRS, \(\bigtriangleup\) and \(\bigtriangleup\) PRQ

Area PRMS has 2 triangles: \(\bigtriangleup\) MRS and \(\bigtriangleup\) RSP

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

443.

A chord subtends an angle of 120o at the centre of a circle of radius 3.5cm. Find the perimeter of the minor sector containing the chord, [Take \(\pi = \frac{22}{7}\)]

A.

14\(\frac{1}{3}\)cm

B.

12\(\frac{5}{6}\)cm

C.

8\(\frac{1}{7}\)cm

D.

7\(\frac{1}{3}\)cm

Correct answer is A

perimeter of minor sector

2r + \(\frac{\theta}{360} \times 2 \pi r\)

= 2 x 3.5 + \(\frac{120^o}{360^o} \times 2 \frac{22}{7} \times 3.5\)

= 7 + \(\frac{154}{21}\)

= 7 + 7.33

= 14.33

= 14\(\frac{1}{3}\)cm

444.

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

\(\theta = 27^o\)

445.

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)]

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

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

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