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

Paper 1 | Objectives

21 - 30 of 48 Questions

# Question Ans
21.

Calculate the surface area of a hallow cylinder which is closed at one end, if the base radius is 3.5cm and the height 8cm.[take π = 22/7]

A. 126.5cm2

B. 165cm2

C. 176cm2

D. 214.5cm2

E. 253.5cm2

Detailed Solution

since it is an open cylinder; r= 3.5cm = 7/2cm
h= 8cm;
S.A = 2πrh + πr 2

= πr(2h + r)
(16 + 3.5); 11 x 19.5 = 214.5cm2
22.

Solve the following equation: 6x\(^2\) - 7x - 5 = 0

A. x = 1/2 or x = -21/2

B. x = 1/3 or x = 21/2

C. x = 1 2/3 or x = -1/2

D. x = 12/3 or x = 1/2

E. x = 5/6 or x = -1

Detailed Solution

6x\(^2\) - 7x - 5 = 0
6x\(^2\) - 10x + 3x - 5 = 0
2x(3x - 5) + 1(3x - 5) = 0
(2x + 1)(3x - 5) = 0
x = \(\frac{5}{3}\) or x = \(-\frac{1}{2}\)
23.

What angle represents grown up girls ? Correct to one decimal place

A. 37.5o

B. 26.7o

C. 25.7o

D. 20o

E. 3.75o

Detailed Solution

Total population = 1400 + 550 + 200 + 150 + 400 = 2700

grown up girls = 200

= \(\frac {200}{2700}\) x \(\frac {360}{1}\)

=80/3 = 26.7°
24.

What percentage of the population are married? correct to one decimal place

A. 14.8%

B. 20.4%

C. 30.5%

D. 35.2%

E. 36.5%

Detailed Solution

Married = 550 + 400 = 950

Married% = \(\frac {950}{2700}\) x \(\frac {100}{1}\)

=35.2%
25.

If A = {a,b,c}, B = {a,b,c,d,e} and C = {a,b,c,d,e,f}. Find (A∪B)∩(A∪C)

A. {a,b,c,d}

B. {a,b,c,d,e}

C. {a,b,c,d,e,f}

D. {a,b,c}

E. Φ

Detailed Solution

A = {a, b, c}; B = {a, b, c, d, e}; C = {a, b, c, d, e, f}
(A \(\cup\) B) = {a, b, c, d, e}
(A \(\cup\) C) = {a, b, c, d, e, f}
(A \(\cup\) B) \(\cap\) (A \(\cup\) C) = {a, b, c, d, e}

For a class of 30 students, the scores in a Mathematics test out of 10 marks were as follows;

4,5,7,2,3,6,5,5,8,9,5,4,2,3,7,9,8,7,7,7,3,4,5,5,2,3,6,7,7,2
26.

What is the mode of the score

A. 3

B. 4

C. 5

D. 6

E. 7

E
27.

What is the median score?

A. 2

B. 7

C. 8

D. 9

E. 10

C
28.

What is the range of the distribution?

A. 2

B. 7

C. 8

D. 9

E. 10

B
29.

In the diagram above O is the center of the circle, if ∠PAQ = 75o, what is the value of ∠PBQ?

A. 15o

B. 75o

C. 105o

D. 150o

E. 210o

Detailed Solution

< PBQ = 180° - 75° (opp angles of a cyclic quadrilateral)
= 105°
30.

Simplify \(\frac{9^{-\frac{1}{2}}}{27^{\frac{2}{3}}}\)

A. 1

B. 1/3

C. 1/9

D. 1/18

E. 1/27

Detailed Solution

\(\frac{9^{-\frac{1}{2}}}{27^{\frac{2}{3}}}\)
=\(\frac{3^{-1}}{3^2}\) = \(\frac{1}{27}\)
21.

Calculate the surface area of a hallow cylinder which is closed at one end, if the base radius is 3.5cm and the height 8cm.[take π = 22/7]

A. 126.5cm2

B. 165cm2

C. 176cm2

D. 214.5cm2

E. 253.5cm2

Detailed Solution

since it is an open cylinder; r= 3.5cm = 7/2cm
h= 8cm;
S.A = 2πrh + πr 2

= πr(2h + r)
(16 + 3.5); 11 x 19.5 = 214.5cm2
22.

Solve the following equation: 6x\(^2\) - 7x - 5 = 0

A. x = 1/2 or x = -21/2

B. x = 1/3 or x = 21/2

C. x = 1 2/3 or x = -1/2

D. x = 12/3 or x = 1/2

E. x = 5/6 or x = -1

Detailed Solution

6x\(^2\) - 7x - 5 = 0
6x\(^2\) - 10x + 3x - 5 = 0
2x(3x - 5) + 1(3x - 5) = 0
(2x + 1)(3x - 5) = 0
x = \(\frac{5}{3}\) or x = \(-\frac{1}{2}\)
23.

What angle represents grown up girls ? Correct to one decimal place

A. 37.5o

B. 26.7o

C. 25.7o

D. 20o

E. 3.75o

Detailed Solution

Total population = 1400 + 550 + 200 + 150 + 400 = 2700

grown up girls = 200

= \(\frac {200}{2700}\) x \(\frac {360}{1}\)

=80/3 = 26.7°
24.

What percentage of the population are married? correct to one decimal place

A. 14.8%

B. 20.4%

C. 30.5%

D. 35.2%

E. 36.5%

Detailed Solution

Married = 550 + 400 = 950

Married% = \(\frac {950}{2700}\) x \(\frac {100}{1}\)

=35.2%
25.

If A = {a,b,c}, B = {a,b,c,d,e} and C = {a,b,c,d,e,f}. Find (A∪B)∩(A∪C)

A. {a,b,c,d}

B. {a,b,c,d,e}

C. {a,b,c,d,e,f}

D. {a,b,c}

E. Φ

Detailed Solution

A = {a, b, c}; B = {a, b, c, d, e}; C = {a, b, c, d, e, f}
(A \(\cup\) B) = {a, b, c, d, e}
(A \(\cup\) C) = {a, b, c, d, e, f}
(A \(\cup\) B) \(\cap\) (A \(\cup\) C) = {a, b, c, d, e}

For a class of 30 students, the scores in a Mathematics test out of 10 marks were as follows;

4,5,7,2,3,6,5,5,8,9,5,4,2,3,7,9,8,7,7,7,3,4,5,5,2,3,6,7,7,2
26.

What is the mode of the score

A. 3

B. 4

C. 5

D. 6

E. 7

E
27.

What is the median score?

A. 2

B. 7

C. 8

D. 9

E. 10

C
28.

What is the range of the distribution?

A. 2

B. 7

C. 8

D. 9

E. 10

B
29.

In the diagram above O is the center of the circle, if ∠PAQ = 75o, what is the value of ∠PBQ?

A. 15o

B. 75o

C. 105o

D. 150o

E. 210o

Detailed Solution

< PBQ = 180° - 75° (opp angles of a cyclic quadrilateral)
= 105°
30.

Simplify \(\frac{9^{-\frac{1}{2}}}{27^{\frac{2}{3}}}\)

A. 1

B. 1/3

C. 1/9

D. 1/18

E. 1/27

Detailed Solution

\(\frac{9^{-\frac{1}{2}}}{27^{\frac{2}{3}}}\)
=\(\frac{3^{-1}}{3^2}\) = \(\frac{1}{27}\)