WAEC Mathematics Past Questions & Answers - Page 57

281.

If tan x = \(\frac{4}{3}\), 0\(^o\) < x < 90\(^o\), find the value of sin x - cos x

A.

\(\frac{1}{10}\)

B.

\(\frac{1}{5}\)

C.

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

D.

1\(\frac{2}{5}\)

Correct answer is B

From the diagram,

h\(^2\) = 4\(^2\) + 3\(^2\) (pythagoras')

h\(^2\) = 16 + 9 = 25

h = \(\sqrt{25}\) = 5

Hence, sin x - cos x

= \(\frac{4}{5} - \frac{3}{5}\)

= \(\frac{1}{5}\)

282.

A piece of thread of length 21.4cm is used to form a sector of a circle of radius 4.2cm on a piece of cloth. Calculate, correct to the nearest degree, the angle of the sector. [Take \(\pi = \frac{22}{7}\)]

A.

170\(^o\)

B.

192\(^o\)

C.

177\(^o\)

D.

182\(^o\)

Correct answer is B

Length of arc, L = 21.4 - 2 x 4.2cm

= 21.4 - 8.4

= 13cm

But L = \(\frac{\theta}{360^o}\) x 2\(\pi r\)

i.e 13 = \(\frac{\theta}{360^o}\)  x 2 x \(\frac{22}{7}\) x 4.2

= 13 x 360\(^o\) x 7

= \(\theta\) x 2 x 22 x 4.2

\(\theta\) = \(\frac{13 \times 360^o \times 7}{44 \times 4.2}\)

= \(\approx\) 177.27\(^o\)

\(\approx\) 177\(^o\) (to the nearest degree)

283.

Donations during the launching of a church project were sent in sealed envolopes. The table shows the distribution of the amount of money in the envelope. How much was the donation?

A.

N26,792.00

B.

N26,972.00

C.

N62.792.00

D.

N62,972.00

Correct answer is D

Total donation = 4 x 500 + 7 x 2000 + 20 x 1000 + 9 x 700 + 4 x 500 + 5 x 100 + 3 x 50 + 1 x 2 + 2 x 10 = 20000 + 14000 + 20000 + 6300 + 2000 + 500 + 150 + 2 + 20 = N62,972

284.

In the diagram, PQ is a straight line, (m + n) = 110\(^o\) and (n + r) = 130\(^o\) and (m + r) = 120\(^o\). Find the ratio of m : n : r

A.

2 : 3 : 4

B.

3 : 4 : 5

C.

4 : 5 : 6

D.

5 : 6 : 7

Correct answer is D

m + n = 110\(^o\), (n + r) = 130\(^o\)

(m + n) = 120\(^o\)

then, r = 130\(^o\) - n

and;

m + (130^o - n) = 120\(^o\)

m - n = -10\(^o\)

2m + (n + r) = 110 + 120 = 230

2m + 130 = 230

2m = 230 - 130

m = \(\frac{100}{2}\) = 50\(^o\)

n = 110\(^o\) - 50\(^o\)

= 60\(^o\)

r = 130\(^o\) - 60\(^o\) = 70\(^o\)

Hence, the ratio m : n : r

= 50 : 60 : 70

= 5 : 6 : 7

285.

In the diagram, PQ//RS. Find x in terms of y and z

A.

x = 240\(^o\) - y - z

B.

x = 180\(^o\) - y - z

C.

x = 360\(^o\) + y -z

D.

x = 360\(^o\) - y - z

Correct answer is D

In the diagram,

a = z (alternate angles)

b = 180\(^o\) - a (angles on a straight line)

b = 180\(^o\) - z

c = 180\(^o\) - x (angles on a straight line)

y = b + c (sum of oposite interior angles)

y = 180\(^o\) - z + 180\(^o\) - x

y = 360\(^o\) - z - x

x = 360\(^o\) - y - z