Year : 
1999
Title : 
Mathematics (Core)
Exam : 
WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

1 - 10 of 43 Questions

# Question Ans
1.

The side of a rhombus is 10cm long, correct to the nearest whole number. Between what limits should the perimeter P lie?

A. 39cm ≤ P ≤41cm

B. 38cm ≤ P < 42cm

C. 38.5 ≤ P ≤ 41.5cm

D. 38.5 ≤ P ≤ 40cm

Detailed Solution

If the side = 10 cm, correct to the nearest whole number, then
The side ranges from 9.5 cm to 10.5 cm. (9.5 \(\leq\) s < 10.5)
Perimeter of a rhombus = 4 x side
\(\therefore\) 4 x 9.5 \(\leq\) perimeter < 4 x 10.5
= 38 cm \(\leq\) P < 42 cm
2.

Simplify log\(_7\) 8 - log\(_7\) 2 + log\(_7\) 4.

A. 0

B. \(2log_7 2\)

C. \(3log_7 2\)

D. \(4log_7 2\)

Detailed Solution

log\(_7\) 8 - log\(_7\) 2 + log\(_7\) 4
= log\(_7\) (8/2 x 4)
= log\(_7\) 16
= 4 log\(_7\) 2
3.

If \(K\sqrt{28}+\sqrt{63}-\sqrt{7}=0\), find K.

A. -2

B. -1

C. 1

D. 2

Detailed Solution

\(K\sqrt{28}+\sqrt{63}-\sqrt{7}=0\\
2K\sqrt{7}+3\sqrt{7}-\sqrt{7}=0\\
2K\sqrt{7}=-2\sqrt{7}\\
K=\frac{-2\sqrt{7}}{2\sqrt{7}}\\
K=-1\)
4.

From a set \(A = [3, \sqrt{2}, 2\sqrt{3}, \sqrt{9}, \sqrt{7}]\), a number is selected at random. Find the probability that is a rational number

A. \(\frac{1}{5}\)

B. \(\frac{2}{5}\)

C. \(\frac{3}{5}\)

D. \(\frac{4}{5}\)

Detailed Solution

\(A = {3, \sqrt{2}, 2\sqrt{3}, \sqrt{9}, \sqrt{7}}\)
n(A) = 5
Let the rational nos = R
n(R) = 2 (3, \(\sqrt{9}\))
P(R) = 2/5
5.

The pie chart illustrate the amount of private time a student spends in a week studying various subjects. use it to answer the question below
Find the value of K

A. 15o

B. 30o

C. 60o

D. 90o

Detailed Solution

Total angle in a circle = 360°
\(\therefore\) 105 + 75 + 2k + k + 3k = 360°
6k = 360 - 180 = 180
k = 180/6 = 30°
6.

The pie chart illustrate the amount of private time a student spends in a week studying various subjects. use it to answer the question below

If he sends \(2\frac{1}{2}\) hours week on science, find the total number of hours he studies in a week

A. \(3\frac{1}{3}\) hours

B. 5 hours

C. 8 hours

D. 12 hours

Detailed Solution

Let x represent the total number of hours spent per week
\(∴ \frac{75}{360} \times x = \frac{5}{2}\\
∴ x = \frac{360 \times 5}{725 \times 2}=12 hours\)
7.

A group of 11 people can speak either English or French or Both. Seven can speak English and six can speak French. What is the probability that a person chosen at random can speak both English and French?

A. \(\frac{2}{11}\)

B. \(\frac{4}{11}\)

C. \(\frac{5}{11}\)

D. \(\frac{11}{13}\)

Detailed Solution

Let the number of people that speak both English and French = x
Then (7 - x) + x + (6 - x) = 11
13 - x = 11 \(\implies\) x = 2.
\(\therefore\) P(picking a person that speaks both languages) = 2/11
8.

The interior angle of a regular polygon is twice the exterior angle. How many sides has the polygon?

A. 5

B. 6

C. 8

D. 9

Detailed Solution

Let the exterior angle = d
Note: Exterior angle + Interior angle = 180°
\(\implies\) d + 2d = 180°
3d = 180° \(\implies\) d = 60°
Recall, exterior angle = \(\frac{360}{\text{no of sides}}\)
\(\therefore \text{No of sides} = \frac{360}{60}\)
= 6 sides
9.

Which of the following figures have one line of symmetry only? I. Isosceles triangle II. Rhombus III. Kite

A. I and II only

B. II and III only

C. I and III only

D. I, II, and III

Detailed Solution

Isosceles triangle and Kite shapes have 1 line of symmetry each while the rhombus has 2 lines of symmetry.
10.

In the diagram above, |XR| = |RY| = |YZ| and ∠XRY = ∠YRZ = 62o, Calculate ∠XYZ

A. 50o

B. 62o

C. 112o

D. 115o

Detailed Solution

In triangle RXY, < RXY = < RYX (base angles of an isosceles triangle)
\(\implies\) 180° - 62° = 2 < RYX
118° = 2 < RYX \(\implies\) < RYX = 59°
In triangle RYZ, < RZY = 62° (base angles of an isosceles triangle)
\(\therefore\) < RYZ = 180° - (62° + 62°)
= 180° - 124° = 56°
\(\therefore\) < XYZ = 56° + 59°
= 115°
1.

The side of a rhombus is 10cm long, correct to the nearest whole number. Between what limits should the perimeter P lie?

A. 39cm ≤ P ≤41cm

B. 38cm ≤ P < 42cm

C. 38.5 ≤ P ≤ 41.5cm

D. 38.5 ≤ P ≤ 40cm

Detailed Solution

If the side = 10 cm, correct to the nearest whole number, then
The side ranges from 9.5 cm to 10.5 cm. (9.5 \(\leq\) s < 10.5)
Perimeter of a rhombus = 4 x side
\(\therefore\) 4 x 9.5 \(\leq\) perimeter < 4 x 10.5
= 38 cm \(\leq\) P < 42 cm
2.

Simplify log\(_7\) 8 - log\(_7\) 2 + log\(_7\) 4.

A. 0

B. \(2log_7 2\)

C. \(3log_7 2\)

D. \(4log_7 2\)

Detailed Solution

log\(_7\) 8 - log\(_7\) 2 + log\(_7\) 4
= log\(_7\) (8/2 x 4)
= log\(_7\) 16
= 4 log\(_7\) 2
3.

If \(K\sqrt{28}+\sqrt{63}-\sqrt{7}=0\), find K.

A. -2

B. -1

C. 1

D. 2

Detailed Solution

\(K\sqrt{28}+\sqrt{63}-\sqrt{7}=0\\
2K\sqrt{7}+3\sqrt{7}-\sqrt{7}=0\\
2K\sqrt{7}=-2\sqrt{7}\\
K=\frac{-2\sqrt{7}}{2\sqrt{7}}\\
K=-1\)
4.

From a set \(A = [3, \sqrt{2}, 2\sqrt{3}, \sqrt{9}, \sqrt{7}]\), a number is selected at random. Find the probability that is a rational number

A. \(\frac{1}{5}\)

B. \(\frac{2}{5}\)

C. \(\frac{3}{5}\)

D. \(\frac{4}{5}\)

Detailed Solution

\(A = {3, \sqrt{2}, 2\sqrt{3}, \sqrt{9}, \sqrt{7}}\)
n(A) = 5
Let the rational nos = R
n(R) = 2 (3, \(\sqrt{9}\))
P(R) = 2/5
5.

The pie chart illustrate the amount of private time a student spends in a week studying various subjects. use it to answer the question below
Find the value of K

A. 15o

B. 30o

C. 60o

D. 90o

Detailed Solution

Total angle in a circle = 360°
\(\therefore\) 105 + 75 + 2k + k + 3k = 360°
6k = 360 - 180 = 180
k = 180/6 = 30°
6.

The pie chart illustrate the amount of private time a student spends in a week studying various subjects. use it to answer the question below

If he sends \(2\frac{1}{2}\) hours week on science, find the total number of hours he studies in a week

A. \(3\frac{1}{3}\) hours

B. 5 hours

C. 8 hours

D. 12 hours

Detailed Solution

Let x represent the total number of hours spent per week
\(∴ \frac{75}{360} \times x = \frac{5}{2}\\
∴ x = \frac{360 \times 5}{725 \times 2}=12 hours\)
7.

A group of 11 people can speak either English or French or Both. Seven can speak English and six can speak French. What is the probability that a person chosen at random can speak both English and French?

A. \(\frac{2}{11}\)

B. \(\frac{4}{11}\)

C. \(\frac{5}{11}\)

D. \(\frac{11}{13}\)

Detailed Solution

Let the number of people that speak both English and French = x
Then (7 - x) + x + (6 - x) = 11
13 - x = 11 \(\implies\) x = 2.
\(\therefore\) P(picking a person that speaks both languages) = 2/11
8.

The interior angle of a regular polygon is twice the exterior angle. How many sides has the polygon?

A. 5

B. 6

C. 8

D. 9

Detailed Solution

Let the exterior angle = d
Note: Exterior angle + Interior angle = 180°
\(\implies\) d + 2d = 180°
3d = 180° \(\implies\) d = 60°
Recall, exterior angle = \(\frac{360}{\text{no of sides}}\)
\(\therefore \text{No of sides} = \frac{360}{60}\)
= 6 sides
9.

Which of the following figures have one line of symmetry only? I. Isosceles triangle II. Rhombus III. Kite

A. I and II only

B. II and III only

C. I and III only

D. I, II, and III

Detailed Solution

Isosceles triangle and Kite shapes have 1 line of symmetry each while the rhombus has 2 lines of symmetry.
10.

In the diagram above, |XR| = |RY| = |YZ| and ∠XRY = ∠YRZ = 62o, Calculate ∠XYZ

A. 50o

B. 62o

C. 112o

D. 115o

Detailed Solution

In triangle RXY, < RXY = < RYX (base angles of an isosceles triangle)
\(\implies\) 180° - 62° = 2 < RYX
118° = 2 < RYX \(\implies\) < RYX = 59°
In triangle RYZ, < RZY = 62° (base angles of an isosceles triangle)
\(\therefore\) < RYZ = 180° - (62° + 62°)
= 180° - 124° = 56°
\(\therefore\) < XYZ = 56° + 59°
= 115°