Year : 
2001
Title : 
Mathematics (Core)
Exam : 
WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

31 - 40 of 49 Questions

# Question Ans
31.

If the probability that an event will occur is p and the probability that it will not occur is q, which of the following is true?

A. p-q=1

B. q-p=0

C. p+q=1

D. p+q=0

C
32.

What is the range of their age?

A. 14 years

B. 20 years

C. 30.5 years

D. 31 years

Detailed Solution

Range = 30.5 - 10.5
= 20 years
33.

What is the mode?

A. 22.5 years

B. 23.0 years

C. 24.0 years

D. 27.5 years

B
34.

How many students are there in the group?

A. 25

B. 30

C. 52

D. 55

Detailed Solution

Total number of students = 20 + 16 + 10 + 6
= 52 students
35.

Which of the following is not the the size of an exterior angle of a regular polygon?

A. 15o

B. 18o

C. 20o

D. 21o

Detailed Solution

The size of an exterior angle = \(\frac{360}{n}\)
From the options, all options can perfectly divide 360°, except 21°.
36.

In the diagram, PQR is a triangle.|PQ| = |PR|, |PS| = |SQ| and PRS = 50°. What is the size of ∠PSQ?

A. 75o

B. 80o

C. 85o

D. 95o

Detailed Solution

< PQS = 50° (PQ = PR)
< PQS = < SPQ = 50° (QS = PS)
In triangle PSQ, < PQS + < QPS + < PSQ = 180°
50° + 50° + < PSQ = 180°
< PSQ = 180° - 100° = 80°
37.

PQRS is a rhombus of side 16cm. The diagonal |QS| = 20cm. Calculate, correct to the nearest degree, ∠PQR

A. 51o

B. 64o

C. 77o

D. 103o

Detailed Solution

cos\(\alpha\) = \(\frac{10}{16}\) = 0.625

\(\alpha\) = cos-1(0.625)

= 51.3o

∠PQR = 2\(\alpha\)

= 2(51.3o)

= 102.6

= 103o
38.

In the diagram, PQ is a diameter of the circle and ∠PRS = 58°. Find ∠STQ.

A. 29o

B. 32o

C. 42o

D. 53o

Detailed Solution

In \(\Delta\) PRQ, < SRQ = 90° - 58°
< SRQ = < QTS = x (angles in the segment)
\(\therefore\) x = 32°
39.

A chord of length 30cm is 8cm away from the center of the circle. What is the radius of the circle. What is the perimeter of the sector? Take \(\pi =\frac{22}{7}\)

A. 16cm

B. 17cm

C. 18cm

D. 20cm

Detailed Solution

From the diagram
\(r^2 = B^2 + 15^2\\
= 64 + 225\\
r = \sqrt{289} = 17cm\)
40.

A sector of a circle radius 14 cm subtends an angle 135° at the center of the circle. What is the perimeter of the sector? Take \(\pi = \frac{22}{7}\)

A. 47cm

B. 61cm

C. 88cm

D. 231cm

Detailed Solution

Perimeter of the sector = \(2r + \frac{\theta}{360} \times 2\pi r\)
= \(2(14) + \frac{135}{360} \times 2 \times \frac{22}{7} \times 14\)
= \(28 + 33\)
= 61 cm
31.

If the probability that an event will occur is p and the probability that it will not occur is q, which of the following is true?

A. p-q=1

B. q-p=0

C. p+q=1

D. p+q=0

C
32.

What is the range of their age?

A. 14 years

B. 20 years

C. 30.5 years

D. 31 years

Detailed Solution

Range = 30.5 - 10.5
= 20 years
33.

What is the mode?

A. 22.5 years

B. 23.0 years

C. 24.0 years

D. 27.5 years

B
34.

How many students are there in the group?

A. 25

B. 30

C. 52

D. 55

Detailed Solution

Total number of students = 20 + 16 + 10 + 6
= 52 students
35.

Which of the following is not the the size of an exterior angle of a regular polygon?

A. 15o

B. 18o

C. 20o

D. 21o

Detailed Solution

The size of an exterior angle = \(\frac{360}{n}\)
From the options, all options can perfectly divide 360°, except 21°.
36.

In the diagram, PQR is a triangle.|PQ| = |PR|, |PS| = |SQ| and PRS = 50°. What is the size of ∠PSQ?

A. 75o

B. 80o

C. 85o

D. 95o

Detailed Solution

< PQS = 50° (PQ = PR)
< PQS = < SPQ = 50° (QS = PS)
In triangle PSQ, < PQS + < QPS + < PSQ = 180°
50° + 50° + < PSQ = 180°
< PSQ = 180° - 100° = 80°
37.

PQRS is a rhombus of side 16cm. The diagonal |QS| = 20cm. Calculate, correct to the nearest degree, ∠PQR

A. 51o

B. 64o

C. 77o

D. 103o

Detailed Solution

cos\(\alpha\) = \(\frac{10}{16}\) = 0.625

\(\alpha\) = cos-1(0.625)

= 51.3o

∠PQR = 2\(\alpha\)

= 2(51.3o)

= 102.6

= 103o
38.

In the diagram, PQ is a diameter of the circle and ∠PRS = 58°. Find ∠STQ.

A. 29o

B. 32o

C. 42o

D. 53o

Detailed Solution

In \(\Delta\) PRQ, < SRQ = 90° - 58°
< SRQ = < QTS = x (angles in the segment)
\(\therefore\) x = 32°
39.

A chord of length 30cm is 8cm away from the center of the circle. What is the radius of the circle. What is the perimeter of the sector? Take \(\pi =\frac{22}{7}\)

A. 16cm

B. 17cm

C. 18cm

D. 20cm

Detailed Solution

From the diagram
\(r^2 = B^2 + 15^2\\
= 64 + 225\\
r = \sqrt{289} = 17cm\)
40.

A sector of a circle radius 14 cm subtends an angle 135° at the center of the circle. What is the perimeter of the sector? Take \(\pi = \frac{22}{7}\)

A. 47cm

B. 61cm

C. 88cm

D. 231cm

Detailed Solution

Perimeter of the sector = \(2r + \frac{\theta}{360} \times 2\pi r\)
= \(2(14) + \frac{135}{360} \times 2 \times \frac{22}{7} \times 14\)
= \(28 + 33\)
= 61 cm