WAEC Mathematics Past Questions & Answers - Page 121

601.

The cross section section of a uniform prism is a right-angled triangle with sides 3cm. 4cm and 5cm. If its length is 10cm. Calculate the total surface area

A.

142cm2

B.

132cm2

C.

122cm2

D.

112cm2

Correct answer is B

A prism has 3 rectangular faces and 2 triangular faces and 2 rectangular faces = 10(3 + 4 + 5) = 120

Area of triangular faces = \(\sqrt{s(s - a) (s - b) (s - c)}\)

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

= \(\frac{3 + 4 + 5}{2}\)

= \(\frac{12}{2}\)

= 6

Area of \(\bigtriangleup\) = \(\sqrt{6(6 - 30(6 - 4)(6 - 5)}\)

= \(\sqrt{6 \times 3 \times 2 \times 1}\) = 6

Area of triangle faces = 2 x 6 = 12cm2

Total surface area = Area of rectangular face + Area of \(\bigtriangleup\) = 120 + 12

= 132cm2

602.

Esther was facing S 20° W. She turned 90° in the clock wise direction. What direction is she facing?

A.

N 70o W

B.

S 70o W

C.

N 20o W

D.

S 20o E

Correct answer is A

The bearing S 20° W is equivalent to a bearing of 200°.

Moving clockwise 90° ⇒ 200° + 90°

= 290°

This is equivalent to N 70° W.

603.

A regular polygon of n sides has each exterior angle to 45o. Find the value of n

A.

6

B.

8

C.

12

D.

15

Correct answer is B

Each interior angle = \(\frac{360^o}{n}\)

45o = \(\frac{360^o}{n}\)

45on = 360o

n = \(\frac{360^o}{45}\)

= 8

604.

A cylindrical container has a base radius of 14cm and height 18cm. How many litres of liquid can it hold? correct to the nearest litre [Take \(\pi = \frac{22}{7}\)]

A.

11

B.

14

C.

16

D.

18

Correct answer is A

Volume of cylinder = \(\pi r^2 h\)

= \(\frac{22}{7} \times 14^2\) x 14 x 18 = 22 x 28 x 18

= 11088cm3

1000cm3 = \(\frac{1}{1000}\) x 11088cm3

= 11.088

= 11

605.

One of the factors of (mn - nq - n2 + mq) is (m - n). The other factor is?

A.

(n - q)

B.

(q - n)

C.

(n + q)

D.

(q - m)

Correct answer is C

mn - nq - n\(^2\) + mq

mn - n\(^2\) - nq + mq

(mn - n\(^2\)) (mq - nq)

n(m - n) + q(m - n)

= (n +q) (m - n)