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Mathematics
WAEC / WASSCE 2008
Number and Numeration
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
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option C.
Source: Myschool Past Questions Archive (Record #36367)
Mathematics
WAEC / WASSCE 2008
Number and Numeration
Solution
Simplify \(\frac{\log \sqrt{8}}{\log 4 - \log 2}\)
A
\(\frac{2}{3}\)
B
\(\frac{1}{2} \log 2\)
C
\(\frac{3}{2}\)
D
\(\log 2\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{\log\sqrt{8}}{\log 4 - \log 2} = \frac{\log 8\frac{1}{2}}{\log (\frac{4}{2})}\)
= \(\frac{8 \frac{1}{2}}{\log (\frac{4}{2})}\)
= \(\frac{\frac{1}{2} \log 2^3}{\log 2}\)
= \(\frac{3}{2} \frac{\log 2}{\log 2}\)
= \(\frac{3}{2}\)
Source: Myschool Past Questions Archive (Record #36368)
Mathematics
WAEC / WASSCE 2008
Number and Numeration
Solution
What is the length of an edge of a cube whose total surface area is X cm\(^2\) and whose volume is \(\frac{X}{2}\)cm\(^3\)?
A
3
B
6
C
9
D
12
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Total surface area of cube = 6s\(^2\)
6s\(^2\) = x
s\(^2\) = x = \(\frac{x}{6}\).....(1)
volume of a cube = s\(^2\) = \(\frac{x}{2}\)
s\(^2\) = \(\frac{x}{2}\)......(2)
put(1) into (2)
s(\(\frac{x}{6}\)) = \(\frac{x}{2}\)
s = \(\frac{x}{2} \times \frac{6}{x}\)
= 3cm
Source: Myschool Past Questions Archive (Record #36383)
Mathematics
WAEC / WASSCE 2008
Number and Numeration
Solution
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\(\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
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\(\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #36392)
Mathematics
WAEC / WASSCE 2008
Number and Numeration
Solution
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
\(\frac{1}{4}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
A = [2, 4, 6, 8}
B = {2, 3, 5, 9}
Pr = (Prime in B) = \(\frac{3}{4}\)
Source: Myschool Past Questions Archive (Record #36398)
Mathematics
WAEC / WASSCE 2008
Number and Numeration
Solution
Given the sets A = [2, 4, 6, 8] and B = [2, 3, 5, 9]. If a number is picked at random from each of the two sets, what is the probability that their product is odd?
A
1
B
\(\frac{3}{4}\)
C
\(\frac{1}{4}\)
D
zero
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\begin{array}{c|c} x & 2 & 3 & 5 & 9 \\ \hline 2 & 4 & 6 & 10 & 18 \\ \hline 4 & 8 & 12 & 20 & 36 \\ \hline 6 & 12 & 18 & 30 & 54 \\ \hline 8 & 16 & 24 & 40 & 72 \end{array}\)
Note: A {vertical}
B {horizontal}
Pr (Odd Product) = \(\frac{0}{16}\)
= 0
Source: Myschool Past Questions Archive (Record #36399)
Mathematics
WAEC / WASSCE 2008
Number and Numeration
Solution
Given the sets A = [2, 4, 6, 8] and B = [2, 3, 5, 9]. If a number is picked at random from each of the two sets, what is the probability that their difference is 6 or 7?
A
\(\frac{1}{256}\)
B
\(\frac{1}{16}\)
C
\(\frac{1}{8}\)
D
\(\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\begin{array}{c|c} - & 2 & 3 & 5 & 9 \\ \hline 2 & 0 & 1 & 3 & 7 \\ \hline 4 & 2 & 1 & 1 & 5\\ \hline 6 & 4 & 3 & 1 & 3 \\ \hline 8 & 6 &5 & 3 & 1 \end{array}\)
Note: A {horizontal}
B {vertical}
Pr(Difference of 6 or 7) = \(\frac{2}{16} = \frac{1}{8}\)
Source: Myschool Past Questions Archive (Record #36400)
Mathematics
WAEC / WASSCE 2008
Number and Numeration
Diagram
Solution
In the diagram, o. If q2 = 25 - r2. Find the value of p
Attached Figure / Diagram
A
3
B
4
C
5
D
6
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Given q2 = 25 - r2.....(1)
from Pythagoras theorem
p2 = q2 + r2....(2)
put(1) into (2)
p2 = 25 - r2 + r2
p2 = 25
p = \(\sqrt{25}\)
Source: Myschool Past Questions Archive (Record #36405)
Mathematics
WAEC / WASSCE 2008
Number and Numeration
Diagram
Solution
In the figure shown, PQs is a straight line. What is the value of < PRQ?
Attached Figure / Diagram
A
128o
B
108o
C
98o
D
78o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
o + o - 70o
= 78o
Source: Myschool Past Questions Archive (Record #36408)
Mathematics
WAEC / WASSCE 2008
Number and Numeration
Diagram
Solution
In the figure /PX/ = /XQ/, PQ//YZ and XV//QR. What is the ratio of the area of XYZQ to the area of \(\bigtriangleup\)YZR?
Attached Figure / Diagram
A
1:2
B
2:1
C
1:3
D
3:1
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
From the diagram, XYZQ is a parallelogram. Thus, |YZ| = |XQ| = |PX|; \(\bigtriangleup\)PXY, Let the area of XYZQ = A1, the area of \(\bigtriangleup\)PXY
= Area of \(\bigtriangleup\)YZR = A2
Area of \(\bigtriangleup\)PQR = A = A1 + 2A2
But from similarity of triangles
\(\frac{\text{Area of PQR}}{\text{Area of PXY}} = (\frac{PQ}{PX})^2 = (\frac{QR}{XY})^2\)
\(\frac{A}{A_2} = (\frac{2}{1})^2 = \frac{2}{1}\)
A = 4A2 But, A = A1 + 2A
A1 = 4A2 - 2A2
A1 = 2A2
\(\frac{A_1}{A_2}\) = 2
A1:A2 = 2:1
Area of XYZQ:Area of \(\bigtriangleup\)YZR = 2:1
Source: Myschool Past Questions Archive (Record #36415)
Mathematics
WAEC / WASSCE 2008
Number and Numeration
Solution
Every staff in an office owns either a Mercedes and/or a Toyota car. 20 own Mercedes, 15 own Toyota and 5 own both. How many staff are there in the office?
A
25
B
30
C
35
D
45
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
M = Mercedez; T = Toyota
Number of staff = 0 + (20 - 5) + (15 - 5) + 5
0 + 15 + 10 + 5 = 30
Source: Myschool Past Questions Archive (Record #36427)
Mathematics
NECO SSCE 2008
Number and Numeration
Solution
x varies directly as y and inversely as z. when x = 5, y = 2 and z = 1. What is the value of x when y = 5 and z = 2?
A
2.5
B
5
C
6.25
D
6.52
E
7.5
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
x = \(\frac{ Ky}{z}\)
x = 5, y = 2 and z = 1
x = \(\frac{ Ky}{z}\)
5 = \(\frac{ K2}{1}\)
K = \(\frac{5}{2}\) = 2.5
find x when y = 5 and z = 2
x = \(\frac{2.5 \times5}{2}\)
x = \(\frac{12.5}{2}\) = 6.25.
Source: Myschool Past Questions Archive (Record #42514)
Mathematics
NECO SSCE 2008
Number and Numeration
Solution
The ratio of the base area of a hollow cone to that of its curved surface is 1:4. If its base radius is 7cm, calculate the slant height of the cone
A
7cm
B
22cm
C
28cm
D
49cm
E
154cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
The base of a cone is a circle, r = 7cm
Base area of a cone = \(\pi\)r\(^2\)
Curve surface area of a cone = \(\pi\)l
\(\pi\)r\(^2\) : \(\pi\)l = 1 : 4
\(\frac{\pi r^2}{\pi l}\) = \(\frac{1}{4}\)
\(\frac{r}{l} = \frac{1}{4}\)
\(\frac{7}{l} = \frac{1}{4}\)
cross multiplying
l = 4 x 7 = 28cm.
Source: Myschool Past Questions Archive (Record #42523)
Mathematics
NECO SSCE 2008
Number and Numeration
Solution
Increase 135 in the ratio 3:5
A
225
B
216
C
143
D
140
E
140
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
To increase 135 in the ratio 3:5
Simply divide 135 by 3 and then multiply the result by 5
= \(\frac{135}{3}\) = 45, 45 x 5 = 225
Source: Myschool Past Questions Archive (Record #42526)
Mathematics
NECO SSCE 2008
Number and Numeration
Solution
Simplify the expression: \(Log_{4}16\) + \(Log_{3}27\) + \(Log_{8}4096\)
A
-9
B
\(\frac{1}{3}\)
C
\(\frac{1}{9}\)
D
3
E
9
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
WHERE:
\(Log_{4}16\) = 2
\(Log_{3}27\) = 3
\(Log_{8}4096\) = 4
: 2 + 3 + 4 = 9
Source: Myschool Past Questions Archive (Record #42536)