WAEC Mathematics Past Questions & Answers - Page 111

551.

If cos(x + 40)o = 0.0872, what is the value of x?

A.

85o

B.

75o

C.

65o

D.

45o

Correct answer is D

cos(x + 40)o = 0.0872

x + 40 = cos-10.0872

x + 40o = 84.99o

x = 84.99o - 40o

x = 44.99

x = 45o

552.

In \(\bigtriangleup\) XYZ, /XY/ = 8cm, /YZ/ = 10cm and /XZ/ = 6cm. Which of these relation is true?

A.

/XY/ + /YZ/ = /XZ/

B.

/XY/ - /YZ/ = /XZ/

C.

/XY/2 = /Y/2 - /XY/2

D.

/YZ/2 = /XZ/2 + /XY/2

Correct answer is D

No explanation has been provided for this answer.

553.

The lengths of the minor and major arcs 54cm and 126cm respectively. Calculate the angle of the major sector

A.

360o

B.

252o

C.

246o

D.

234o

Correct answer is B

Let 0 = angle of the minor sector

angle of the major sector = 360 - \(\theta\)(angle at a point)

2 \(\pi r\) = 54 + 126(i.e circumference of minor and major arc)

2\(\pi r = 180^o\)

r = \(\frac{180}{2\pi}\) = \(\frac{90}{\pi}\)

Lenght of ninor arc

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

54 = \(\frac{\theta}{360} \times 3 \pi r\)

\(\theta = \frac{360 \times 54}{2 \pi r}\)

but r = \(\frac{90}{\pi}\) substituting \(\frac{90}{\pi}\) for r

\(\theta = \frac{360 \times 54 \times \pi}{2 \times \pi \times 90}\)

\(\theta = 2 \times 54 = 108^o\)

angle of the major sector = 360 - 108o

= 252o

554.

The curved surface area of a cylindrical tin is 704cm2. If the radius of its base is 8cm, find the height. [Take \(\pi = \frac{22}{7}\)]`

A.

14cm

B.

9cm

C.

8cm

D.

7cm

Correct answer is A

Curved surface area = 2\(\pi h\)

704 = 2 x \(\frac{22}{7} \times 8 \times h\)

704 = \(\frac{352}{7}\)h

352h = 704 x 7

h = \(\frac{704 \times 7}{352}\)

= \(\frac{4928}{352}\)

h = 14cm

555.

Solve the inequality: \(\frac{-m}{2} - \frac{5}{4} \geq \frac{5m}{12} - \frac{7}{6}\)

A.

m \(\leq \frac{5}{4}\)

B.

m \(\geq \frac{5}{4}\)

C.

m \(\leq - \frac{1}{11}\)

D.

m \(\geq - \frac{1}{11}\)

Correct answer is C

\(\frac{-m}{2} - \frac{5}{4} \geq \frac{5m}{12} - \frac{7}{6}\)

= \(\frac{-2m - 5}{4} \geq \frac{5m - 14}{12}\)

12(-2m - 5) \(\geq\) 4(5m - 14)

-24m - 60 \(\geq\) 20m - 56

-24m - 20m \(\geq\) -56 + 60

44m \(\geq\) 4

m \(\leq \frac{4}{-44}\)

m \(\leq \frac{-1}{11}\)