WAEC Mathematics Past Questions & Answers - Page 205

1,021.

The angle of depression of a point Q from a vertical tower PR, 30m high, is 40°. If the foot P of the tower is on the same horizontal level as Q, find, correct to 2 decimal places, |PQ|.

A.

35.75m

B.

25.00m

C.

22.98m

D.

19.28

Correct answer is A

\(\tan 40° = \frac{30}{|PQ|}\)

\(|PQ| = \frac{30}{\tan 40°} = \frac{30}{0.839}\)

= 35.75m

1,022.

In the diagram, |SR| = |RQ| and ∠PRQ = 58o ∠VQT = 19o, PQT, SQV and PSR are straight lines. Find ∠QPS

A.

42o

B.

39o

C.

38o

D.

30o

Correct answer is A

No explanation has been provided for this answer.

1,023.

Simplify \(\frac{2^{\frac{1}{2}}\times 8^{\frac{1}{2}}}{4}\)

A.

1

B.

2

C.

4

D.

16

Correct answer is A

\(\frac{2^{\frac{1}{2}}\times 8^{\frac{1}{2}}}{4}\\=\frac{2^{\frac{1}{2}}\times 2^{\frac{3}{2}}}{2^2}\\=2^{\frac{1}{2}}+2^{\frac{3}{2}}-2=2^0 = 1\)

1,024.

In the diagram O is the centre of the circle. Which of the following is/are not true?

I. a = b
II. b + c = 180o
III. a + b = c

A.

I and II only

B.

II and III only

C.

II only

D.

III only

Correct answer is A

No explanation has been provided for this answer.

1,025.

In the diagram O and O' are the centres of the circles radii 15cm and 8cm respectively. If PQ = 12cm, find |OO'|.

A.

8.46cm

B.

19.04cm

C.

20.81cm

D.

26.16cm

Correct answer is B

 In \(\Delta\) POQ, 

\(12^2 = 15^2 + 15^2 - 2(15)(15) \cos < POQ\)

\(144 = 450 - 450\cos < POQ\)

\(450 \cos < POQ = 450 - 144 = 306\)

\(\cos <POQ = \frac{306}{450} = 0.68\)

\(< POQ = 47.2°\)

In \(\Delta\) PO'Q, 

\(12^2 = 8^2 + 8^2 - 2(8)(8) \cos <PO'Q\)

\(144 - 128 = -128 \cos < PO'Q\)

\(\cos < PO'Q = - 0.125\)

\(< PO'Q = 97.2°\)

In \(\Delta\) POQ,

\(\cos 23.6 = \frac{x}{15}\)

\(x = 15 \times \cos 23.6\)

= 13.75 cm

In \(\Delta\) PO'Q, 

\(\cos 48.6 = \frac{y}{8}\)

\(y = 8 \times \cos 48.6\)

= 5.29 cm

\(\therefore\) OO' = x + y = 13.75 + 5.29

= 19.04 cm