Year : 
2009
Title : 
Mathematics (Core)
Exam : 
WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

21 - 30 of 46 Questions

# Question Ans
21.

An arc of a circle subtends an angle of 60o at the centre. If the radius of the circle is 3cm, find , in terms of \(\pi\), the length of the arc

A. \(\pi\)cm

B. 2\(\pi\)cm

C. 3\(\pi\)cm

D. 6\(\pi\)cm

Detailed Solution

Length of arc = \(\frac{\theta}{360} \times 2\pi r\)

= \(\frac{60}{360} \times 2\pi \times 3cm\)

= \(\pi\)cm
22.

Solve \(\frac{2x + 1}{6} - \frac{3x - 1}{4}\) = 0

A. 1

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

C. -\(\frac{1}{5}\)

D. -1

Detailed Solution

\(\frac{2x + 1}{6} - \frac{3x - 1}{4}\) = 0

\(\frac{4(2n + 1) - 6(3x - 1)}{24}\) = 0

-10x + 10 = 0

-10x = -10

x = \(\frac{-10}{-10}\)

x = 1
23.

If a positive integer, list the values of x which satisfy the equation 3x - 4 < 6 and x - 1 > 0

A. {1, 2, 3}

B. {2, 3}

C. {2, 3, 4}

D. {2, 3, 4, 5}

Detailed Solution

3x - 4 < 6 = 3x < 6 = 4

3x < 10

x < \(\frac{10}{3}\)

x < 3.33 and x - 1 = 0

n > 1 = 1< x; since x is an integer, and 1 < x3.33

x = {2, 3}
24.

If c and k are the roots of 6 - x - x2 = 0, find c + k

A. 2

B. 1

C. -1

D. -3

Detailed Solution

6 - x - x2 = 0

a = -1; b = -1; c = 6

Sum of roots = c + k = -\(\frac{-b}{a}\)

= \(\frac{-(-1)}{-1}\)

= -1
25.

Each of the interior angles of a regular polygon is 140o. Calculate the sum of all the interior angles of the polygon

A. 1080o

B. 1260o

C. 1800o

D. 2160o

Detailed Solution

Each interior angle = 140

\(\frac{(n - 2) \times 180}{n} = 140\)

(n - 2) x 180 = 140n

150 - 360 = 140n

180m - 140n = 360

40n - 360

n = \(\frac{360}{40}\)

n = 9

Sum of all interior angles = (n - 2) x 180

= (9 - 2) x 180

= 7 x 180

= 1260
26.

A bucket holds 10 litres of water. How many buckets of water will fill a reservoir of size 8m x 7m x 5m.(1 litre = 1000cm3)`

A. 28

B. 280

C. 2800

D. 28000

Detailed Solution

No. of buckets of water = \(\frac{\text{Capacity of reservoir}}{\text{Capacity of buckets}}\)

= \(\frac{800 \times 700 \times 500}{10 \times 1000}\)

= \(\frac{28000 0000}{10000}\)

= 28000
27.

A box contains black, white and red identical balls. The probability of picking a black ball at random from the box is \(\frac{3}{10}\) and the probability of picking a white ball at random is \(\frac{2}{5}\). If there are 30 balls in the box, how many of them are red?

A. 3

B. 7

C. 9

D. 12

Detailed Solution

Total no of balls = 30

Let x = no. of red balls

Pr(red) = \(\frac{x}{30}\)

Pr(black) = \(\frac{3}{10} = \frac{9}{30}\)

Pr(white) = \(\frac{2}{5} = \frac{12}{30}\)

No. of black balls = 9

No. of white balls = 12

9 = 12 + x = 30

x = 30 - 21

x = 9

No. of red balls = 9
28.

Simplify; \(\frac{1}{2}\sqrt{32} - \sqrt{18} \sqrt{2}\)

A. zero

B. \(\sqrt{2}\)

C. 2\(\sqrt{2}\)

D. 4\(\sqrt{2}\0

Detailed Solution

\(\frac{1}{2}\sqrt{32} - \sqrt{18} \sqrt{2}\) = \(\frac{1}{2} (4\sqrt{2}) - 3\sqrt{2} + \sqrt{2}\)

= 2\(\sqrt{2} - 3\sqrt{2} + \sqrt{2}\)

= 3\(\sqrt{2} - 3\sqrt{2} - 3\sqrt{2}\) = 0
29.

The angles of triangle are (x + 10)o, (2x - 40)o and (3x - 90)o. Which of the following accurately describes the triangle?

A. it is a scalene triangle

B. it is right angled isosceles triangle

C. t is an equilateral triangle

D. It is an isosceles triangle but not right angled

Detailed Solution

(x + 10)o + (2x - 40)o + (3x - 90)o = 180

6x - 120 = 180

6x = 180 + 120

6x = 300

x = \(\frac{300}{6}\)

x = 50

x + 10o = 50o + 10o = 60o

2x - 40 = 2(50o) - 40 = 60o

3x - 90 = 3(50o) - 90o = 60o

Hence, it is an equilateral triangle
30.

Simplify (x - 3y)2 - (x + 3y)2

A. 2(x + 3y)

B. (2x - 3y)

C. -12xy

D. 6xy

Detailed Solution

(x - 3y)2 - (x + 3y)2 = [(x - 3y) - (x + 3y)]

[(x + 3y + x + 3y)] = [-6y] [2x]

= -12xy
21.

An arc of a circle subtends an angle of 60o at the centre. If the radius of the circle is 3cm, find , in terms of \(\pi\), the length of the arc

A. \(\pi\)cm

B. 2\(\pi\)cm

C. 3\(\pi\)cm

D. 6\(\pi\)cm

Detailed Solution

Length of arc = \(\frac{\theta}{360} \times 2\pi r\)

= \(\frac{60}{360} \times 2\pi \times 3cm\)

= \(\pi\)cm
22.

Solve \(\frac{2x + 1}{6} - \frac{3x - 1}{4}\) = 0

A. 1

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

C. -\(\frac{1}{5}\)

D. -1

Detailed Solution

\(\frac{2x + 1}{6} - \frac{3x - 1}{4}\) = 0

\(\frac{4(2n + 1) - 6(3x - 1)}{24}\) = 0

-10x + 10 = 0

-10x = -10

x = \(\frac{-10}{-10}\)

x = 1
23.

If a positive integer, list the values of x which satisfy the equation 3x - 4 < 6 and x - 1 > 0

A. {1, 2, 3}

B. {2, 3}

C. {2, 3, 4}

D. {2, 3, 4, 5}

Detailed Solution

3x - 4 < 6 = 3x < 6 = 4

3x < 10

x < \(\frac{10}{3}\)

x < 3.33 and x - 1 = 0

n > 1 = 1< x; since x is an integer, and 1 < x3.33

x = {2, 3}
24.

If c and k are the roots of 6 - x - x2 = 0, find c + k

A. 2

B. 1

C. -1

D. -3

Detailed Solution

6 - x - x2 = 0

a = -1; b = -1; c = 6

Sum of roots = c + k = -\(\frac{-b}{a}\)

= \(\frac{-(-1)}{-1}\)

= -1
25.

Each of the interior angles of a regular polygon is 140o. Calculate the sum of all the interior angles of the polygon

A. 1080o

B. 1260o

C. 1800o

D. 2160o

Detailed Solution

Each interior angle = 140

\(\frac{(n - 2) \times 180}{n} = 140\)

(n - 2) x 180 = 140n

150 - 360 = 140n

180m - 140n = 360

40n - 360

n = \(\frac{360}{40}\)

n = 9

Sum of all interior angles = (n - 2) x 180

= (9 - 2) x 180

= 7 x 180

= 1260
26.

A bucket holds 10 litres of water. How many buckets of water will fill a reservoir of size 8m x 7m x 5m.(1 litre = 1000cm3)`

A. 28

B. 280

C. 2800

D. 28000

Detailed Solution

No. of buckets of water = \(\frac{\text{Capacity of reservoir}}{\text{Capacity of buckets}}\)

= \(\frac{800 \times 700 \times 500}{10 \times 1000}\)

= \(\frac{28000 0000}{10000}\)

= 28000
27.

A box contains black, white and red identical balls. The probability of picking a black ball at random from the box is \(\frac{3}{10}\) and the probability of picking a white ball at random is \(\frac{2}{5}\). If there are 30 balls in the box, how many of them are red?

A. 3

B. 7

C. 9

D. 12

Detailed Solution

Total no of balls = 30

Let x = no. of red balls

Pr(red) = \(\frac{x}{30}\)

Pr(black) = \(\frac{3}{10} = \frac{9}{30}\)

Pr(white) = \(\frac{2}{5} = \frac{12}{30}\)

No. of black balls = 9

No. of white balls = 12

9 = 12 + x = 30

x = 30 - 21

x = 9

No. of red balls = 9
28.

Simplify; \(\frac{1}{2}\sqrt{32} - \sqrt{18} \sqrt{2}\)

A. zero

B. \(\sqrt{2}\)

C. 2\(\sqrt{2}\)

D. 4\(\sqrt{2}\0

Detailed Solution

\(\frac{1}{2}\sqrt{32} - \sqrt{18} \sqrt{2}\) = \(\frac{1}{2} (4\sqrt{2}) - 3\sqrt{2} + \sqrt{2}\)

= 2\(\sqrt{2} - 3\sqrt{2} + \sqrt{2}\)

= 3\(\sqrt{2} - 3\sqrt{2} - 3\sqrt{2}\) = 0
29.

The angles of triangle are (x + 10)o, (2x - 40)o and (3x - 90)o. Which of the following accurately describes the triangle?

A. it is a scalene triangle

B. it is right angled isosceles triangle

C. t is an equilateral triangle

D. It is an isosceles triangle but not right angled

Detailed Solution

(x + 10)o + (2x - 40)o + (3x - 90)o = 180

6x - 120 = 180

6x = 180 + 120

6x = 300

x = \(\frac{300}{6}\)

x = 50

x + 10o = 50o + 10o = 60o

2x - 40 = 2(50o) - 40 = 60o

3x - 90 = 3(50o) - 90o = 60o

Hence, it is an equilateral triangle
30.

Simplify (x - 3y)2 - (x + 3y)2

A. 2(x + 3y)

B. (2x - 3y)

C. -12xy

D. 6xy

Detailed Solution

(x - 3y)2 - (x + 3y)2 = [(x - 3y) - (x + 3y)]

[(x + 3y + x + 3y)] = [-6y] [2x]

= -12xy