Year : 
1990
Title : 
Mathematics (Core)
Exam : 
WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

31 - 40 of 47 Questions

# Question Ans
31.

In the diagram above PS||RQ, |RQ| = 6.4cm and perpendicular PH = 3.2cm. Find the area of SQR

A. 5.12cm2

B. 9.60cm2

C. 10.24cm2

D. 20.48cm2

E. 40.96cm2

Detailed Solution

Area of a triangle = \(\frac{1}{2} \times b \times h\)
Area of \(\Delta\) SQR = \(\frac{1}{2} \times 6.4 \times 3.2\)
= 10.24 cm\(^2\)
32.

Which angle is equal to ∠VWZ?

A. ∠VXZ

B. ∠VYX

C. ∠XZW

D. ∠YXZ

E. ∠VYW

Detailed Solution

< VWZ = < VXZ (angles in the same segment)
33.

Which triangle is equal in area to ΔVWZ

A. ΔVXZ

B. ΔVYZ

C. ΔXYV

D. ΔWYV

E. ΔWYZ

Detailed Solution

Area of \(\Delta\) VYZ = Area of \(\Delta\) VWZ (same base and within same parallel)
34.

In the diagram above, PQRS s a cyclic quadrilateral, ∠PSR = 86o and ∠QPR = 38o. Calculate PRQ

A. 58o

B. 53o

C. 48o

D. 43o

E. 38o

Detailed Solution

PQR = 180o - 86o = 94o
∴PRQ = 180o - 94o - 36o = 48o
35.

In the diagram below, O is the center of the circle if ∠QOR = 290o, find the size ∠QPR

A. 110o

B. 70o

C. 55o

D. 35o

E. 20o

Detailed Solution

360o - 290o = 70o
70/2 = 35o
36.

In the diagram above, PQ is a tangent at T to the circle ABT. ABC is a straight line and TC bisects ∠BTO. Find x.

A. 20o

B. 30o

C. 35o

D. 40o

E. 50o

Detailed Solution

From the figure < TAB = < BTQ = 40° (alternate segment)
\(\therefore\)< ATB = 180° - (70° + 40°) = 70° (angle on a straight line)
< BTC = \(\frac{40°}{2} = \frac{< BTQ}{2}\)
\(\therefore < BTQ = 40°\)
x° = 180° - (40° + 70° + 20°)
= 50°
37.

Which of the sketches above gives a correct method for constructed an angle of 120o at the point P?

A. I only

B. II only

C. III only

D. I and II only

E. I, II and III

D

38.

Use mathematical table to evaluate (cos40° - sin30°)

A. -0.2660

B. -0.0266

C. 0.0266

D. 0.2660

E. 1.5320

Detailed Solution

(cos 40° - sin 30°)
= 0.7660 - 0.5
= 0.2660
39.

If the shadow of a pole 7m high is 1/2 its length what is the angle of elevation of the sun, correct to the nearest degree?

A. 90o

B. 63o

C. 60o

D. 26o

E. 0o

Detailed Solution

tan θ - 7/3.5 = 2
tan θ= 2.0000
θ = 63o
40.

From the top of a building 10m high, the angle of depression of a stone lying on the horizontal ground is 69o. Calculate ,correct to one decimal place, the distance of the stone from the foot of the building

A. 3.6m

B. 3.8m

C. 6.0m

D. 9.3m

E. 26.1m

Detailed Solution

tan21o =x/10
x = 10 tan 21o
= 3.3839 = 3.8m
31.

In the diagram above PS||RQ, |RQ| = 6.4cm and perpendicular PH = 3.2cm. Find the area of SQR

A. 5.12cm2

B. 9.60cm2

C. 10.24cm2

D. 20.48cm2

E. 40.96cm2

Detailed Solution

Area of a triangle = \(\frac{1}{2} \times b \times h\)
Area of \(\Delta\) SQR = \(\frac{1}{2} \times 6.4 \times 3.2\)
= 10.24 cm\(^2\)
32.

Which angle is equal to ∠VWZ?

A. ∠VXZ

B. ∠VYX

C. ∠XZW

D. ∠YXZ

E. ∠VYW

Detailed Solution

< VWZ = < VXZ (angles in the same segment)
33.

Which triangle is equal in area to ΔVWZ

A. ΔVXZ

B. ΔVYZ

C. ΔXYV

D. ΔWYV

E. ΔWYZ

Detailed Solution

Area of \(\Delta\) VYZ = Area of \(\Delta\) VWZ (same base and within same parallel)
34.

In the diagram above, PQRS s a cyclic quadrilateral, ∠PSR = 86o and ∠QPR = 38o. Calculate PRQ

A. 58o

B. 53o

C. 48o

D. 43o

E. 38o

Detailed Solution

PQR = 180o - 86o = 94o
∴PRQ = 180o - 94o - 36o = 48o
35.

In the diagram below, O is the center of the circle if ∠QOR = 290o, find the size ∠QPR

A. 110o

B. 70o

C. 55o

D. 35o

E. 20o

Detailed Solution

360o - 290o = 70o
70/2 = 35o
36.

In the diagram above, PQ is a tangent at T to the circle ABT. ABC is a straight line and TC bisects ∠BTO. Find x.

A. 20o

B. 30o

C. 35o

D. 40o

E. 50o

Detailed Solution

From the figure < TAB = < BTQ = 40° (alternate segment)
\(\therefore\)< ATB = 180° - (70° + 40°) = 70° (angle on a straight line)
< BTC = \(\frac{40°}{2} = \frac{< BTQ}{2}\)
\(\therefore < BTQ = 40°\)
x° = 180° - (40° + 70° + 20°)
= 50°
37.

Which of the sketches above gives a correct method for constructed an angle of 120o at the point P?

A. I only

B. II only

C. III only

D. I and II only

E. I, II and III

D

38.

Use mathematical table to evaluate (cos40° - sin30°)

A. -0.2660

B. -0.0266

C. 0.0266

D. 0.2660

E. 1.5320

Detailed Solution

(cos 40° - sin 30°)
= 0.7660 - 0.5
= 0.2660
39.

If the shadow of a pole 7m high is 1/2 its length what is the angle of elevation of the sun, correct to the nearest degree?

A. 90o

B. 63o

C. 60o

D. 26o

E. 0o

Detailed Solution

tan θ - 7/3.5 = 2
tan θ= 2.0000
θ = 63o
40.

From the top of a building 10m high, the angle of depression of a stone lying on the horizontal ground is 69o. Calculate ,correct to one decimal place, the distance of the stone from the foot of the building

A. 3.6m

B. 3.8m

C. 6.0m

D. 9.3m

E. 26.1m

Detailed Solution

tan21o =x/10
x = 10 tan 21o
= 3.3839 = 3.8m