2009 - WAEC Mathematics Past Questions and Answers - page 3
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
correct option: a
Length of arc = \(\frac{\theta}{360} \times 2\pi r\)
= \(\frac{60}{360} \times 2\pi \times 3cm\)
= \(\pi\)cm
Users' Answers & Comments= \(\frac{60}{360} \times 2\pi \times 3cm\)
= \(\pi\)cm
22
solve \(\frac{2x + 1}{6} - \frac{3x - 1}{4}\) = 0
A
1
B
\(\frac{1}{5}\)
C
-\(\frac{1}{5}\)
D
-1
correct option: a
\(\frac{2x + 1}{6} - \frac{3x - 1}{4}\) = 0
\(\frac{4(2n + 1) - 6(3x - 1)}{24}\) = 0
-10x + 10 = 0
-10x = -10
x = \(\frac{-10}{-10}\)
x = 1
Users' Answers & Comments\(\frac{4(2n + 1) - 6(3x - 1)}{24}\) = 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}
correct option: b
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}
Users' Answers & Comments3x < 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
correct option: c
6 - x - x2 = 0
a = -1; b = -1; c = 6
Sum of roots = c + k = -\(\frac{-b}{a}\)
= \(\frac{-(-1)}{-1}\)
= -1
Users' Answers & Commentsa = -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
correct option: b
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
Users' Answers & Comments\(\frac{(n - 2) \times 180}{n} = 140\)
(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
correct option: d
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
Users' Answers & Comments= \(\frac{800 \times 700 \times 500}{10 \times 1000}\)
= \(\frac{28000 0000}{10000}\)
= 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
correct option: c
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
Users' Answers & CommentsLet 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
correct option: a
\(\frac{1}{2}\sqrt{32} - \sqrt{18} \sqrt{2}\) = \(\frac{1}{2} (4\sqrt{2}) - 3\sqrt{2} + \sqrt{2}\)
= 2\(\sqrt{2} - 3\sqrt{2} + \sqrt{2}\)
= 3\(\sqrt{2} - 3\sqrt{2} - 3\sqrt{2}\) = 0
Users' Answers & Comments= 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
correct option: c
(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
Users' Answers & Comments6x - 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
correct option: c
(x - 3y)2 - (x + 3y)2 = [(x - 3y) - (x + 3y)]
[(x + 3y + x + 3y)] = [-6y] [2x]
= -12xy
Users' Answers & Comments[(x + 3y + x + 3y)] = [-6y] [2x]
= -12xy