Year : 
2003
Title : 
Mathematics (Core)
Exam : 
WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

21 - 30 of 46 Questions

# Question Ans
21.

What is the size of angle x in the diagram

A. 15o

B. 30o

C. 45o

D. 60o

Detailed Solution

\(Sin\theta^{\circ} = \frac{opp}{hyp}\\
Sin X^{\circ}=\frac{5}{10}=0.5000\\SinX^{\circ}\\
X^{\circ} = sin^{-1}0.5000\\
X^{\circ}=30^{\circ}\)
22.

The four interior angles of a quadrilateral are (x + 20) o, (x+ 10) o (2x - 45) o and (x - 25) o. Find the value of x

A. 60

B. 80

C. 100

D. 360

Detailed Solution

Sum of interior angles in a quadrilateral is 360
(x + 20)o + (x+ 10)o + (2x - 45)o + (x - 25)o = 360o
5xo - 40o = 360o
x = 400/5 = 80o
23.

Calculate the value of y in the diagram

A. 17

B. 34

C. 44

D. 45

Detailed Solution

Sum of interior angle of the diagram equals 360o
180o - 5yo + 136o + 180o + 180o - 3yo = 360o
-8yo + 136o = 0
-8yo = -136; y = 17
24.

Out of 60 members of an Association, 15 are Doctors and 9 are Lawyers. If a member is selected at random from the Association, what is the probability that the member is neither a Doctor Nor a Lawyer

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

B. \(\frac{9}{10}\)

C. \(\frac{3}{20}\)

D. \(\frac{1}{4}\)

Detailed Solution

Member that are neither doctors nor lawyers = 60-(15+9)=36
Probability (Not doctors ad not lawyers) \(=\frac{36}{60}\\
=\frac{6}{10}=\frac{3}{5}\)
25.

Find the values of x for which \( \frac{1}{2x^2 - 13x +15} \) is not defined,

A. 5 or \( \frac{3}{2} \)

B. 1 or \( \frac{15}{13} \)

C. 2 or 15

D. 13 or 15

Detailed Solution

The fraction is undefined when the denominator is equal to zero
\(2x^2 - 13x + 15 = 0\\
2x^2 - 3x - 10x + 15\\
x(2x-3)-5(2x-3) = 0\\
(2x-3)(x-5)=0\\
x = \frac{3}{2} or x = 5\)
26.

In the diagram, \(P\hat{Q}S = 65^o, R\hat{P}S = 40^2\hspace{1mm}and\hspace{1mm}Q\hat{S}R=20^o\hspace{1mm}P\hat{S}Q\)

A. 85o

B. 60o

C. 55o

D. 45o

Detailed Solution

< QPS = < PRS = 65° (angles in the same segment)
< PSR + 40° + 65° = 180°
< PSR + 105° = 180°
< PSR = 75°
< PSR = < PSQ + < QSR
75° = < PSQ + 20° \(\implies\) < PSQ = 75° - 20° = 55°
27.

Evaluate \((111_{two})^2 - (101_{two})^2\)

A. 10two

B. 100two

C. 1100two

D. 11000two

Detailed Solution

\((111_{2})^2 - (101_{2})^2\)
Difference of two squares
\((111 - 101)(111 + 101)\)
= \((10)(1100)\)
= \(11000_{2}\)
28.

Given that x ≅ 0.0102 correct to 3 significant figures, which of the following cannot be the actual value of x?

A. 0.01014

B. 0.01021

C. 0.01015

D. 0.01016

A
29.

If \(\frac{3^{(1-n)}}{9^{-2n}}=\frac{1}{9}\) find n

A. \(-\frac{3}{2}\)

B. \(\frac{1}{3}\)

C. -1

D. -3

Detailed Solution

\(\frac{3^{(1-n)}}{9^{-2n}}=\frac{1}{9}\\
3^{1-n}\times 3^{-2(-2n)} = 3^{-2}\\
1-n-2(-2n)= -2\\
1-n+4n=-2\\
n=-1\)
30.

Which of the following is/are not the interior angle(s) of a regular polygon? I.108° II. 116° III. 120°

A. I only

B. II only

C. III only

D. I and III only

Detailed Solution

Using the formula, \((n - 2) \times 180°\) to get the sum of the interior angles. Then we can have
\((n - 2) \times 180° = 108n\) ... (1)
\((n - 2) \times 180° = 116n\) ... (2)
\((n - 2) \times 180° = 120n\) ... (3)
Solving the above given equations, where n is not a positive integer then that angle is not the interior for a regular polygon.
(1): \(180n - 360 = 108n \implies 72n = 360\)
\(n = 5\) (regular pentagon)
(2): \(180n - 360 = 116n \implies 64n = 360\)
\(n = 5.625\)
(3): \(180n - 360 = 120n \implies 60n = 360\)
\(n = 6\) (regular hexagon)
Hence, 116° is not an angle of a regular polygon.
21.

What is the size of angle x in the diagram

A. 15o

B. 30o

C. 45o

D. 60o

Detailed Solution

\(Sin\theta^{\circ} = \frac{opp}{hyp}\\
Sin X^{\circ}=\frac{5}{10}=0.5000\\SinX^{\circ}\\
X^{\circ} = sin^{-1}0.5000\\
X^{\circ}=30^{\circ}\)
22.

The four interior angles of a quadrilateral are (x + 20) o, (x+ 10) o (2x - 45) o and (x - 25) o. Find the value of x

A. 60

B. 80

C. 100

D. 360

Detailed Solution

Sum of interior angles in a quadrilateral is 360
(x + 20)o + (x+ 10)o + (2x - 45)o + (x - 25)o = 360o
5xo - 40o = 360o
x = 400/5 = 80o
23.

Calculate the value of y in the diagram

A. 17

B. 34

C. 44

D. 45

Detailed Solution

Sum of interior angle of the diagram equals 360o
180o - 5yo + 136o + 180o + 180o - 3yo = 360o
-8yo + 136o = 0
-8yo = -136; y = 17
24.

Out of 60 members of an Association, 15 are Doctors and 9 are Lawyers. If a member is selected at random from the Association, what is the probability that the member is neither a Doctor Nor a Lawyer

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

B. \(\frac{9}{10}\)

C. \(\frac{3}{20}\)

D. \(\frac{1}{4}\)

Detailed Solution

Member that are neither doctors nor lawyers = 60-(15+9)=36
Probability (Not doctors ad not lawyers) \(=\frac{36}{60}\\
=\frac{6}{10}=\frac{3}{5}\)
25.

Find the values of x for which \( \frac{1}{2x^2 - 13x +15} \) is not defined,

A. 5 or \( \frac{3}{2} \)

B. 1 or \( \frac{15}{13} \)

C. 2 or 15

D. 13 or 15

Detailed Solution

The fraction is undefined when the denominator is equal to zero
\(2x^2 - 13x + 15 = 0\\
2x^2 - 3x - 10x + 15\\
x(2x-3)-5(2x-3) = 0\\
(2x-3)(x-5)=0\\
x = \frac{3}{2} or x = 5\)
26.

In the diagram, \(P\hat{Q}S = 65^o, R\hat{P}S = 40^2\hspace{1mm}and\hspace{1mm}Q\hat{S}R=20^o\hspace{1mm}P\hat{S}Q\)

A. 85o

B. 60o

C. 55o

D. 45o

Detailed Solution

< QPS = < PRS = 65° (angles in the same segment)
< PSR + 40° + 65° = 180°
< PSR + 105° = 180°
< PSR = 75°
< PSR = < PSQ + < QSR
75° = < PSQ + 20° \(\implies\) < PSQ = 75° - 20° = 55°
27.

Evaluate \((111_{two})^2 - (101_{two})^2\)

A. 10two

B. 100two

C. 1100two

D. 11000two

Detailed Solution

\((111_{2})^2 - (101_{2})^2\)
Difference of two squares
\((111 - 101)(111 + 101)\)
= \((10)(1100)\)
= \(11000_{2}\)
28.

Given that x ≅ 0.0102 correct to 3 significant figures, which of the following cannot be the actual value of x?

A. 0.01014

B. 0.01021

C. 0.01015

D. 0.01016

A
29.

If \(\frac{3^{(1-n)}}{9^{-2n}}=\frac{1}{9}\) find n

A. \(-\frac{3}{2}\)

B. \(\frac{1}{3}\)

C. -1

D. -3

Detailed Solution

\(\frac{3^{(1-n)}}{9^{-2n}}=\frac{1}{9}\\
3^{1-n}\times 3^{-2(-2n)} = 3^{-2}\\
1-n-2(-2n)= -2\\
1-n+4n=-2\\
n=-1\)
30.

Which of the following is/are not the interior angle(s) of a regular polygon? I.108° II. 116° III. 120°

A. I only

B. II only

C. III only

D. I and III only

Detailed Solution

Using the formula, \((n - 2) \times 180°\) to get the sum of the interior angles. Then we can have
\((n - 2) \times 180° = 108n\) ... (1)
\((n - 2) \times 180° = 116n\) ... (2)
\((n - 2) \times 180° = 120n\) ... (3)
Solving the above given equations, where n is not a positive integer then that angle is not the interior for a regular polygon.
(1): \(180n - 360 = 108n \implies 72n = 360\)
\(n = 5\) (regular pentagon)
(2): \(180n - 360 = 116n \implies 64n = 360\)
\(n = 5.625\)
(3): \(180n - 360 = 120n \implies 60n = 360\)
\(n = 6\) (regular hexagon)
Hence, 116° is not an angle of a regular polygon.