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Mathematics
WAEC / WASSCE 2008
Number and Numeration
Solution
If x% of 240 equals 12, find x
A
x = 1
B
x = 3
C
x = 5
D
x = 7
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
x% of 240 = 12
\(\frac{x}{100} \times 240 = 12\)
x = \(\frac{12 \times 100}{240}\)
x = 5
Source: Myschool Past Questions Archive (Record #36318)
Mathematics
WAEC / WASSCE 2008
Number and Numeration
Solution
Evaluate \(\frac{(3.2)^2 - (4.8)^2}{3.2 + 4.8}\)
A
-0.08
B
-1.60
C
-10.24
D
-12.80
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{(3.2)^2 - (4.8)^2}{3.2 + 1.8} = \frac{(3.2 - 4.8)(3.2 + 4.8)}{(3.2 + 4.8)}\)
= 3.2 - 4.8
= -1.60
Source: Myschool Past Questions Archive (Record #36323)
Mathematics
WAEC / WASSCE 2008
Number and Numeration
Solution
Simplify \(\sqrt{50} + \frac{10}{\sqrt{2}}\)
A
10
B
10\(\sqrt{2}\)
C
20
D
20\(\sqrt{2}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\sqrt{50} + \frac{10}}{\sqrt{2}} = \(\frac{\sqrt{50}}{1} + \sqrt{10}{\sqrt{2}}\)
= \(\frac{\sqrt{50 \times 2} + 10}{\sqrt{2}}\)
= \(\frac{\sqrt{100} + 10}{\sqrt{2}}\)
= \(\frac{10 + 10}{\sqrt{2} = \frac{20}{\sqrt{2}}\)
= \(\frac{20}{\sqrt{2}}\) \times \frac{\sqrt{2}}{\sqrt{2}}\)
= \(\frac{20\sqrt{2}}{2}\)
= 10\(\sqrt{2}\)
Source: Myschool Past Questions Archive (Record #36326)
Mathematics
WAEC / WASSCE 2008
Number and Numeration
Solution
P naira invested for 4 years invested for 4 years at r% simple interest per annum yields 0.36 p naira interest. Find the value of r
A
1\(\frac{1}{9}\)
B
1\(\frac{4}{9}\)
C
9
D
11
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
I = \(\frac{PRT}{100}\)
where r = r% p.a; I = 0.36p
0.36p = \(\frac{P \times r \times 4}{100}\)
\(\frac{0.36 \times 100}{4}\) = r
r = 9
Source: Myschool Past Questions Archive (Record #36327)
Mathematics
WAEC / WASSCE 2008
Number and Numeration
Solution
If p-2g + 1 = g + 3p and p - 2 = 0, find g
A
-2
B
-1
C
1
D
2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
p - 2g + 1 = g + 3p.........(1)
p - 2 = 0 .........(2)
From (2), p = 2; put p = 2 into (1);
2 - 2g + 1 = g + 3(2)
3 - 2g = g + 6
-2g - g = 6 - 3
-3g = 3
g = \(\frac{3}{-3}\)
g = -1
Source: Myschool Past Questions Archive (Record #36335)
Mathematics
WAEC / WASSCE 2008
Number and Numeration
Solution
Simplify \(\frac{\frac{1}{x} + \frac{1}{y}}{x + y}\)
A
\(\frac{1}{x + y}\)
B
\(\frac{1}{xy}\)
C
x + y
D
xy
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{\frac{1}{x} + \frac{1}{y}}{x + y}\) = \(\frac{\frac{y + x}{xy}}{x + y}\)
= \(\frac{x + y}{xy}\)
= \(\frac{x + y}{xy} \times \frac{1}{x + y}\)
= \(\frac{1}{xy}\)
Source: Myschool Past Questions Archive (Record #36336)
Mathematics
WAEC / WASSCE 2008
Number and Numeration
Solution
Simplify 3\(\sqrt{27x^3y^9}\)
A
9xy3
B
3xy6
C
3xy3
D
9y3
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
3\(\sqrt{27x^3y^9}\) = 3\(\sqrt{27} \times 3\sqrt{3^3} \times 3\sqrt{y^9}\)
= 3 \(\times x \times y^3\)
= 3xy3
Source: Myschool Past Questions Archive (Record #36340)
Mathematics
WAEC / WASSCE 2008
Number and Numeration
Solution
Given that x = 2 and y = -\(\frac{1}{4}\), evaluate \(\frac{x^2y - 2xy}{5}\)
A
zero
B
\(\frac{1}{5}\)
C
1
D
2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Given; x = 2; y = \(\frac{-1}{4}\)
= \(\frac{x^2y - 2xy}{5}\)
= \(\frac{2^2(\frac{-1}{4}) - 2(2)(\frac{-1}{4})}{5}\)
= \(\frac{4(\frac{-1}{4}) + 4(\frac{-1}{4})}{5}\)
= \(\frac{1 + 1}{5}\)
= \(\frac{0}{5}\)
= 0
Source: Myschool Past Questions Archive (Record #36341)
Mathematics
WAEC / WASSCE 2008
Number and Numeration
Solution
Factorize 5y2 + 2ay - 3a2
A
(a - y)(5y - 3a)
B
(y - a)(5y - 3a)
C
(y - a)(5y + 3a)
D
(y + a)(5y - 3a)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
5y2 + 2ay - 3a2 = 5y2 + 5ay - 3a2
= 5y(y + a) - 3a(y + a)
= (y + a)(5y - 3a)
Source: Myschool Past Questions Archive (Record #36343)
Mathematics
WAEC / WASSCE 2008
Number and Numeration
Solution
If 4y is 9 greater than the sum of y and 3x, by how much is y greater than x?
A
3
B
6
C
9
D
12
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
4y - 9 > y + 3x; 4y - y > 3x + 9
3y > 3(x + 3); y = > \(\frac{3(x + 3)}{3}\)
y > x + 3; y - 3 > x
y is greater than x by 3
Source: Myschool Past Questions Archive (Record #36353)
Mathematics
WAEC / WASSCE 2008
Number and Numeration
Solution
If p = \(\frac{3}{5} \sqrt{\frac{q}{r}}\), express q in terms of p and r
A
\(\frac{9}{25} pr^2\)
B
\(\frac{9}{25} p^2r\)
C
\(\frac{25}{9} p^2r\)
D
\(\frac{25}{9} pr^2\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
p = \(\frac{3}{5} \sqrt{\frac{q}{r}}; \frac{5p}{3} = \sqrt{\frac{q}{r}}\)
= (\(\frac{5}{3}p\))2
= \(\frac{q}{r}\)
= \(\frac{25p^2}{9} = \frac{q}{r}\)
q = \(\frac{25}{9} p^2 r\)
Source: Myschool Past Questions Archive (Record #36354)
Mathematics
WAEC / WASSCE 2008
Number and Numeration
Solution
Simplify: \(\frac{2x^2 - 5x - 12}{4x^2 - 9}\)
A
\(\frac{x + 4}{2x + 3}\)
B
\(\frac{x + 4}{2x - 3}\)
C
\(\frac{x - 4}{2x + 3}\)
D
\(\frac{x - 4}{2x - 3}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{2x^2 - 5x - 12}{4x^2 - 9}\) = \(\frac{2x^2 - 8x + 3x - 12}{(2x)^2 - 3^2}\)
= \(\frac{2x(x - 4) + 3(x - 4)}{(2x - 3)(2x + 3)} - \frac{(x - 4) + (2x + 3)}{(2x - 3) (2x + 3)}\)
= \(\frac{x - 4}{2x - 3}\)
Source: Myschool Past Questions Archive (Record #36355)
Mathematics
WAEC / WASSCE 2008
Number and Numeration
Solution
If the volume of a cube is 343cm3, find the length of its side
A
3cm
B
6cm
C
7cm
D
96cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Volume of a cube = (side)3
= (side)3
(side)3 = 343
side = 3\(\sqrt{343}\)
side = 7cm
Source: Myschool Past Questions Archive (Record #36359)
Mathematics
WAEC / WASSCE 2008
Number and Numeration
Solution
If tan x = 1, evaluate sin x + cos x, leaving your answer in the surd form
A
2\(\sqrt{2}\)
B
\(\frac{1}{2} \sqrt{2}\)
C
\(\sqrt{2}\)
D
2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
tan x = 1; x = tan-1(10 = 45o
sin x + cos x
= sin 45o + cos 45o
= \(\frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2}\)
= \(\frac{\sqrt{2} + \sqrt{2}}{2}\)
= \(\frac{2\sqrt{2}}{2}\)
= \(\sqrt{2}\)
Source: Myschool Past Questions Archive (Record #36363)
Mathematics
WAEC / WASSCE 2008
Number and Numeration
Solution
If \(2^n = 128\), find the value of \(2^{n - 1})(5^{n - 2})\)
A
5(106)
B
2(106)
C
5(105)
D
2(105)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(2^n\) = 128
\(2^n = 2^7\)
n = 7
(2\(^{n - 1}\))(5\(^{n - 2}\)), then, put n = 7
= (2\(^{7 - 1}\))(5\(^{7 - 2}\))
= (\(2^6\))(\(2^5\))
= \(2^1 \times 2^5 \times 2^5\)
= 2 x (\(2 \times 5)^5\)
= 2(\(10^5\))
Source: Myschool Past Questions Archive (Record #36366)