2008 - WAEC Mathematics Past Questions and Answers - page 3
21
If x \(\alpha\) (45 + \(\frac{1}{2}y\)), which of the following is true>?
A
x varies directly as y
B
x varies inversely as y
C
x is partly constant and partly varies as y
D
x vries jointly as 45 and directly as y
correct option: c
Users' Answers & Comments22
Simplify \(\frac{\log \sqrt{8}}{\log 4 - \log 2}\)
A
\(\frac{2}{3}\)
B
\(\frac{1}{2} \log 2\)
C
\(\frac{3}{2}\)
D
\(\log 2\)
correct option: c
\(\frac{\log\sqrt{8}}{\log 4 - \log 2} = \frac{\log 8\frac{1}{2}}{\log (\frac{4}{2})}\)
= \(\frac{8 \frac{1}{2}}{\log (\frac{4}{2})}\)
= \(\frac{\frac{1}{2} \log 2^3}{\log 2}\)
= \(\frac{3}{2} \frac{\log 2}{\log 2}\)
= \(\frac{3}{2}\)
Users' Answers & Comments= \(\frac{8 \frac{1}{2}}{\log (\frac{4}{2})}\)
= \(\frac{\frac{1}{2} \log 2^3}{\log 2}\)
= \(\frac{3}{2} \frac{\log 2}{\log 2}\)
= \(\frac{3}{2}\)
23
A train travels 60km in M minutes. If its average speed is 400km per hour, find the value of M
A
15
B
12
C
10
D
9
correct option: d
Average speed = \(\frac{Distance}{Time}\)
\(\frac{400km}{hr} = \frac{60km}{Time}\)
Time = \(\frac{60km}{400 km/hr}\)
= \(\frac{60hr}{400}\)
M = \(\frac{60hr}{400} \times \frac{60min}{1hr}\)
= 9 minutes
Users' Answers & Comments\(\frac{400km}{hr} = \frac{60km}{Time}\)
Time = \(\frac{60km}{400 km/hr}\)
= \(\frac{60hr}{400}\)
M = \(\frac{60hr}{400} \times \frac{60min}{1hr}\)
= 9 minutes
24
An arc of a circle, radius 14cm, is 18.33cm long. Calculate to the nearest degree, the angle which the arc subtends at the centre of the circle. [T = \(\frac{22}{7}\)]
A
11o
B
20o
C
22o
D
75o
correct option: d
Length of an arc = \(\frac{\theta}{360} \times 2\pi r\)
18.33 = \(\frac{\theta}{360} \times 2 \times \frac{22}{7} \times 14\)
\(\theta = \frac{18.33 \times 360 \times 17}{2 \times 22 \times 14}\)
= 75o (approx.)
Users' Answers & Comments18.33 = \(\frac{\theta}{360} \times 2 \times \frac{22}{7} \times 14\)
\(\theta = \frac{18.33 \times 360 \times 17}{2 \times 22 \times 14}\)
= 75o (approx.)
25
What is the length of an edge of a cube whose total surface area is X cm2 and whose total surface area is \(\frac{X}{2}\)cm3?
A
3
B
6
C
9
D
12
correct option: a
Total surface area of cube = 6s2
6s2 = x
s2 = x = \(\frac{x}{6}\).....(1)
volume of a cube = s2 = \(\frac{x}{2}\)
s2 = \(\frac{x}{2}\)......(2)
put(1) into (2)
s(\(\frac{x}{6}\)) = \(\frac{x}{2}\)
s = \(\frac{x}{2} \times \frac{6}{x}\)
= 3cm
Users' Answers & Comments6s2 = x
s2 = x = \(\frac{x}{6}\).....(1)
volume of a cube = s2 = \(\frac{x}{2}\)
s2 = \(\frac{x}{2}\)......(2)
put(1) into (2)
s(\(\frac{x}{6}\)) = \(\frac{x}{2}\)
s = \(\frac{x}{2} \times \frac{6}{x}\)
= 3cm
26
XY is a chord of circle centre O and radius 7cm. The chord XY which is 8cm long subtends an angle of 120o at the centre of the circle. Calculate the perimeter of the minor segment. [Take \(\pi = \frac{22}{7}\)]
A
14.67cm
B
22.67cm
C
29.33cm
D
37.33cm
correct option: b
perimeter of minor segment = Length of arc xy + chord xy
where lxy = \(\frac{120}{360} \times 2x \times \frac{22}{7} \times 7\)
= 14.67cm
perimeter of minor segment = 14.67 + 8 = 22.67cm
Users' Answers & Commentswhere lxy = \(\frac{120}{360} \times 2x \times \frac{22}{7} \times 7\)
= 14.67cm
perimeter of minor segment = 14.67 + 8 = 22.67cm
27
If p = \(\frac{1}{2}\) and \(\frac{1}{p - 1} = \frac{2}{p + x}\), find the value of x
A
-2\(\frac{1}{2}\)
B
-1\(\frac{1}{2}\)
C
1\(\frac{1}{2}\)
D
2\(\frac{1}{2}\)
correct option: b
p = \(\frac{1}{2}; \frac{1}{p - 1} = \frac{2}{p + x}\)
\(\frac{1}{\frac{1}{2} - 1} = \frac{2}{\frac{1}{2} + x}\)
\(\frac{1}{\frac{1 - 2}{2}} = \frac{2}{\frac{1 + 2x}{2}}\)
\(\frac{1}{-\frac{1}{2}} = \frac{2}{\frac{1 + 2x}{2}}\)
-2 = \(\frac{4}{1 + 2x} -2(1 + 2x) = 4\)
1 + 2x = \(\frac{4}{-2}\)
1 + 2x = -2
2x = -2 - 1
2x = -3
x = -\(\frac{3}{2}\)
x = -1\(\frac{1}{2}\)
Users' Answers & Comments\(\frac{1}{\frac{1}{2} - 1} = \frac{2}{\frac{1}{2} + x}\)
\(\frac{1}{\frac{1 - 2}{2}} = \frac{2}{\frac{1 + 2x}{2}}\)
\(\frac{1}{-\frac{1}{2}} = \frac{2}{\frac{1 + 2x}{2}}\)
-2 = \(\frac{4}{1 + 2x} -2(1 + 2x) = 4\)
1 + 2x = \(\frac{4}{-2}\)
1 + 2x = -2
2x = -2 - 1
2x = -3
x = -\(\frac{3}{2}\)
x = -1\(\frac{1}{2}\)
28
Find the quadratic equation whose roots are c and -c
A
x2 - c2 = 0
B
x2 + 2cx = 0
C
x2 + 2cx + c2 = 0
D
x2 - 2cx + c2 = 0
correct option: a
Roots; x and -c
sum of roots = c + (-c) = 0
product of roots = c x -c = -c2
Equation; x2 - (sum of roots) x = product of roots = 0
x2 - (0)x + (-c2) = 0
x2 - c2 = 0
Users' Answers & Commentssum of roots = c + (-c) = 0
product of roots = c x -c = -c2
Equation; x2 - (sum of roots) x = product of roots = 0
x2 - (0)x + (-c2) = 0
x2 - c2 = 0
29
Solve the inequality 1 - 2x < - \(\frac{1}{3}\)
A
x < \(\frac{2}{3}\)
B
x < -\(\frac{2}{3}\)
C
x > \(\frac{2}{3}\)
D
x > -\(\frac{2}{3}\)
correct option: c
1 - 2x < - \(\frac{1}{3}\); -2x < -\(\frac{1}{3}\) - 1
-2x < - \(\frac{1- 3}{3}\)
-2x < - \(\frac{4}{-6}\)
3x -2x < -4; -8x < -4
x > -\(\frac{4}{-6}\) = x > \(\frac{2}{3}\)
Users' Answers & Comments-2x < - \(\frac{1- 3}{3}\)
-2x < - \(\frac{4}{-6}\)
3x -2x < -4; -8x < -4
x > -\(\frac{4}{-6}\) = x > \(\frac{2}{3}\)
30
Given the sets A = [2, 4, 6, 8] and B = [2, 3, 5, 9]. If a number is selected at random from set B, what is the probability that the number is prime?
A
1
B
\(\frac{3}{4}\)
C
\(\frac{1}{2}\)
D
\(\frac{1}{4}\)
correct option: b
A = [2, 4, 6, 8}
B = {2, 3, 5, 9}
Pr = (Prime in B) = \(\frac{3}{4}\)
Users' Answers & CommentsB = {2, 3, 5, 9}
Pr = (Prime in B) = \(\frac{3}{4}\)