Year : 
1989
Title : 
Mathematics (Core)
Exam : 
WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

11 - 20 of 48 Questions

# Question Ans
11.

Instead of recording the number 1.23cm of the radius of a tube, a student recorded 1.32cm. Find the percentage of error, correct to one decimal place.

A. 6.8%

B. 7.3%

C. 9.6%

D. 14.4%

E. 15.4%

Detailed Solution

% error =
error/exact
x
100/1



=
0.09/1.23
x
12.

In the diagram above, ∠SPR = P and ∠SQR = 2x. Find x in terms of P

A. x = p + 2

B. x = p - 2

C. x = p2

D. x = p/2

E. x = 2p

Detailed Solution

P = 2x (angle in the same segment);

x = p/2
13.

In the diagram above ABDE and FCDE are parallelograms. If |FC| = 12.2cm and the height |PC| = 4.0cm, calculate the area of the parallelogram ABDE.

A. 3.05cm2

B. 8.20cm2

C. 16.20cm2

D. 24.40cm2

E. 48.8cm2

Detailed Solution

Area of ABDE = b x h

12.2 x 4 = 48.8cm 2
14.

Using the above graph, if 10o < x < 60o, what is the value of x for which sin x = cos x?

A. 0o

B. 20o

C. 30o

D. 45o

E. 50o

Detailed Solution

From the graph; when sin x = cos x

x = 45 0
15.

The venn diagram below shows the number of students who studied Physics, Chemistry, and Mathematics in a certain school. How many students took at least two of the three subjects?

A. 165

B. 160

C. 155

D. 135

E. 85

Detailed Solution

At least 2 subjects = 30 + 45 + 75 + 10 = 160 students
16.

An arc of a circle radius 7cm is 14cm long. What angle does the arc subtend at the center of circle?
[Take π = 22/7]

A. 25.7o

B. 44o

C. 51.43o

D. 98o

E. 114.55o

Detailed Solution

L = 14cm, r = 7cm; \(\theta\)= ?
L = \(\frac{\theta}{360}\) x 2πr
14= \(\frac{\theta\}{360}\) x 2π(7)
\(\theta = \frac{360 \times 14}{44}\)
=114.55°
17.

If twice a certain integer is subtracted from 5 times the integer, the result is 63. Find the integer.

A. 21

B. 9

C. 7

D. 4

E. 3

Detailed Solution

Let the integer = y
\(\therefore\) 5y - 2y = 63
3y = 63 \(\implies\) y = 21
18.

If 3\(^y\) = 243, find the value of y.

A. 2

B. 3

C. 4

D. 5

E. 6

Detailed Solution

3\(^y\) = 243;
3\(^y\) = 3\(^5\)
y = 5
19.

Points X and Y are respectively 20km North and 9km East of a point O. What is the bearing of Y from X? Correct to the nearest degree

A. 024o

B. 114o

C. 156o

D. 204o

E. 336o

Detailed Solution

tan\(\theta\) = 9/20 = 0.45

\(\theta\) = tan\(^{-1}\) 0.45 = 24.2°

the bearing of y from x = 180 0 - 0 = 180° - 24.2°

the bearing = 155.8°

\(\approxeq\) 156°
20.

In the diagram above, O is the center of the circle. Calculate the length of the chord AB if |OA| = 5cm, |OD| = 3cm and ∠AOD = ∠BOD

A. 3cm

B. 4cm

C. 5cm

D. 8cm

E. 15cm

Detailed Solution

In \(\Delta DOB\), let < DOB = \(\alpha\)
In \(\Delta DOB\), \(5^2 = 3^2 + s^2\)
\(s^2 = 25 - 9 = 16\)
\(s = 4cm\)
\(\sin \alpha = \frac{4}{5}\)
\(\alpha = \frac{< AOB}{2}\)
Length of chord = \(2r \sin (\frac{\theta}{2})\)
|OB| = r = 5cm
L = \(2(5)(\frac{4}{5})\)
= 8 cm
11.

Instead of recording the number 1.23cm of the radius of a tube, a student recorded 1.32cm. Find the percentage of error, correct to one decimal place.

A. 6.8%

B. 7.3%

C. 9.6%

D. 14.4%

E. 15.4%

Detailed Solution

% error =
error/exact
x
100/1



=
0.09/1.23
x
12.

In the diagram above, ∠SPR = P and ∠SQR = 2x. Find x in terms of P

A. x = p + 2

B. x = p - 2

C. x = p2

D. x = p/2

E. x = 2p

Detailed Solution

P = 2x (angle in the same segment);

x = p/2
13.

In the diagram above ABDE and FCDE are parallelograms. If |FC| = 12.2cm and the height |PC| = 4.0cm, calculate the area of the parallelogram ABDE.

A. 3.05cm2

B. 8.20cm2

C. 16.20cm2

D. 24.40cm2

E. 48.8cm2

Detailed Solution

Area of ABDE = b x h

12.2 x 4 = 48.8cm 2
14.

Using the above graph, if 10o < x < 60o, what is the value of x for which sin x = cos x?

A. 0o

B. 20o

C. 30o

D. 45o

E. 50o

Detailed Solution

From the graph; when sin x = cos x

x = 45 0
15.

The venn diagram below shows the number of students who studied Physics, Chemistry, and Mathematics in a certain school. How many students took at least two of the three subjects?

A. 165

B. 160

C. 155

D. 135

E. 85

Detailed Solution

At least 2 subjects = 30 + 45 + 75 + 10 = 160 students
16.

An arc of a circle radius 7cm is 14cm long. What angle does the arc subtend at the center of circle?
[Take π = 22/7]

A. 25.7o

B. 44o

C. 51.43o

D. 98o

E. 114.55o

Detailed Solution

L = 14cm, r = 7cm; \(\theta\)= ?
L = \(\frac{\theta}{360}\) x 2πr
14= \(\frac{\theta\}{360}\) x 2π(7)
\(\theta = \frac{360 \times 14}{44}\)
=114.55°
17.

If twice a certain integer is subtracted from 5 times the integer, the result is 63. Find the integer.

A. 21

B. 9

C. 7

D. 4

E. 3

Detailed Solution

Let the integer = y
\(\therefore\) 5y - 2y = 63
3y = 63 \(\implies\) y = 21
18.

If 3\(^y\) = 243, find the value of y.

A. 2

B. 3

C. 4

D. 5

E. 6

Detailed Solution

3\(^y\) = 243;
3\(^y\) = 3\(^5\)
y = 5
19.

Points X and Y are respectively 20km North and 9km East of a point O. What is the bearing of Y from X? Correct to the nearest degree

A. 024o

B. 114o

C. 156o

D. 204o

E. 336o

Detailed Solution

tan\(\theta\) = 9/20 = 0.45

\(\theta\) = tan\(^{-1}\) 0.45 = 24.2°

the bearing of y from x = 180 0 - 0 = 180° - 24.2°

the bearing = 155.8°

\(\approxeq\) 156°
20.

In the diagram above, O is the center of the circle. Calculate the length of the chord AB if |OA| = 5cm, |OD| = 3cm and ∠AOD = ∠BOD

A. 3cm

B. 4cm

C. 5cm

D. 8cm

E. 15cm

Detailed Solution

In \(\Delta DOB\), let < DOB = \(\alpha\)
In \(\Delta DOB\), \(5^2 = 3^2 + s^2\)
\(s^2 = 25 - 9 = 16\)
\(s = 4cm\)
\(\sin \alpha = \frac{4}{5}\)
\(\alpha = \frac{< AOB}{2}\)
Length of chord = \(2r \sin (\frac{\theta}{2})\)
|OB| = r = 5cm
L = \(2(5)(\frac{4}{5})\)
= 8 cm