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Mathematics
WAEC / WASSCE 2007
Number and Numeration
Solution
Simplify \(\frac{3x^3}{(3x)^3}\)
A
1
B
\(\frac{1}{3}\)
C
\(\frac{1}{9}\)
D
\(\frac{1}{27}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{3x^3}{(3x)^3}\) = \(\frac{3 \times x^3}{3^3 \times x^3}\)
= \(\frac{3 \times x^3}{3 \times 3 \times 3 \times x^3}\)
= \(\frac{1}{3^2}\)
= \(\frac{1}{9}\)
Source: Myschool Past Questions Archive (Record #36235)
Mathematics
WAEC / WASSCE 2007
Number and Numeration
Solution
N140,000 is shared between Abu, Kayode and Uche. Abu has twice as much as Kayode and Kayode has twice as much as Uche. What is Kayode'sshare?
A
N80,000
B
N40,000
C
N2,000
D
10,000
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Let Abu's share = 2x;
Kayode's = x
Uche's share = \(\frac{x}{2}\)
Total: 2x + x + \(\frac{x}{2}\) = N140,000
\(\frac{7x}{2}\) = N140,000
x = \(\frac{280,000}{7}\) = N40,000
Kayode's share = N40,000
Source: Myschool Past Questions Archive (Record #36236)
Mathematics
WAEC / WASSCE 2007
Number and Numeration
Solution
I am x years old and my brother is 3 years older. How old was my brother last year?
A
(x - 4)years
B
(x + 2) years
C
(3x - 10years
D
(3x + 1)years
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
I am x years old; My brother = 3 + x; My brother
last year = (3 + x) - 1 = x + 3 - 1
= (x + 2) years
Source: Myschool Past Questions Archive (Record #36237)
Mathematics
WAEC / WASSCE 2007
Number and Numeration
Solution
For what value of x is the expression \(\frac{2x - 1}{x + 3}\) not defined?
A
3
B
2
C
\(\frac{1}{2}\)
D
-3
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{2x - 1}{x + 3}\) not defined
x + 3 = 0
x = -3
Source: Myschool Past Questions Archive (Record #36238)
Mathematics
WAEC / WASSCE 2007
Number and Numeration
Solution
If x = 3, Y = 2 and z = 4, what is the value of 3x2 - 2y + z?
A
17
B
27
C
35
D
71
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
x = 3, y = 2, z = 4
3x2 - 2y + z
= 3(3)2 - 2(2) + 4
3(9) - 4 + 4 = 27
Source: Myschool Past Questions Archive (Record #36241)
Mathematics
WAEC / WASSCE 2007
Number and Numeration
Solution
If 8x-1 = \(\frac{1}{4}\), find x
A
-\(\frac{-5}{3}\)
B
-1
C
-\(\frac{1}{3}\)
D
\(\frac{1}{3}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
8x-1 = \(\frac{1}{4}\)
23(x - 1 = 2-2
3x - 3 = -2
3x = -2 + 3
3x = 1
x = \(\frac{1}{3}\)
Source: Myschool Past Questions Archive (Record #36244)
Mathematics
WAEC / WASSCE 2007
Number and Numeration
Solution
A sector of a circle of radius 14cm containing an angle 60o is folded to form a cone. Calculate the radius of the base of the cone
A
5\(\frac{1}{2}cm\)
B
4\(\frac{2}{3}cm\)
C
3\(\frac{1}{2}cm\)
D
2\(\frac{1}{3}cm\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Length of arc = circumference of the base of the
cone \(\frac{\theta}{360} \times 2\pi R = 2 \pi r\)
\(\frac{\theta R}{360}\) = r
r = \(\frac{60 \times 14}{360}\)
= \(\frac{7}{3} = 2\frac{1}{3}\)cm
Source: Myschool Past Questions Archive (Record #36268)
Mathematics
WAEC / WASSCE 2007
Number and Numeration
Solution
Find the volume of a solid cylinder with base radius 10cm and height 14cm.
A
2203
B
880cm3>
C
1400cm3
D
4400cm3
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
volume of a cylinder = \(\pi r^2h\)
r = 10cm
h = 14cm
= \(\frac{22}{7} \times 10 \times 10 \times 14\)
= 4400cm3
Source: Myschool Past Questions Archive (Record #36270)
Mathematics
WAEC / WASSCE 2007
Number and Numeration
Solution
Find the value of a if log\(_{10}\) a + log\(_{10}\)a\(^2\) = 0.9030
A
4.0
B
2.0
C
1.6
D
0.0
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
log\(_{10}\) a + log\(_{10}\)a\(^2\) = 0.9030
log (a x a\(^2\)) = 0.9030
log a\(^3\) = 0.9030
a\(^3\) = 10^.9030(antilogarithm table)
a\(^3\) = 7.998
a = 3\(\sqrt{7.998}\)
a = 1.9998 ≈ 2.0
Source: Myschool Past Questions Archive (Record #36283)
Mathematics
WAEC / WASSCE 2007
Number and Numeration
Solution
A messenger was paid N2.50 an hour during the normal working hours and 4.00 n hour during overtime. If he received N31.00 for 10 hours work, how many hours are for overtime?
A
2
B
3
C
4
D
6
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Let normal working hour = x
let overtime = y
after 10 hours = N31.00
1 x 2.50x + 4y = 31
4 x x + y = 10
2.50x + 4y = 31
- 4x + 4y = 30
----------------
-1.5x = -9
x = 6; x + y = 10
6 + y = 10
y = 10 - 4
y = 4hrs for over time
Source: Myschool Past Questions Archive (Record #36284)
Mathematics
WAEC / WASSCE 2007
Number and Numeration
Solution
At what rate per cent per annum will N520.00 yield a simple interest of N39.00 in three years?
A
4%
B
3\(\frac{1}{2}\)%
C
3%
D
2\(\frac{1}{2}\)%
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
SI = \(\frac{PRT}{100}\)
39 = \(\frac{520 \times R \times 3}{100}\)
1560R = 3900
R = \(\frac{3900}{1560}\)
= 2.5%
R = 2\(\frac{1}{2}\)%
Source: Myschool Past Questions Archive (Record #36286)
Mathematics
WAEC / WASSCE 2007
Number and Numeration
Solution
Which of the following is a factor of 2 - x - x2?
A
1 - x
B
1 + x
C
x - 1
D
2 - x
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
2 - x - x2; (2 - 2x) + (x - x2)
= 2(1 - x) + x(1 - x)
= (1 - x)(2 + x)
= 1 - x
Source: Myschool Past Questions Archive (Record #36288)
Mathematics
WAEC / WASSCE 2007
Number and Numeration
Solution
make w the subject of the relation \(\frac{a + bc}{wd + f}\) = g
A
\(\frac{a + bc - fg}{dg}\)
B
\(\frac{a - bc + fg}{dg}\)
C
\(\frac{a + bc - f}{dg}\)
D
\(\frac{a + bc - dg}{dg}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{a + bc}{wd + f}\) = g(cross multiply)
a = bc + wdg + fg
wdg = a + bc - fg
w = \(\frac{a + bc - fg}{dg}\)
Source: Myschool Past Questions Archive (Record #36289)
Mathematics
WAEC / WASSCE 2007
Number and Numeration
Solution
For what range of values of x is 4x - 3(2x - 1) > 1?
A
x > -1
B
x > 1
C
x < 1
D
x < -1
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
4x - 3(2x - 1) > 1
4x - 6x + 3 > 1
-2x > 1 - 3; 2x > -2
x < \(\frac{-2}{-2}\)
= x < 1
Source: Myschool Past Questions Archive (Record #36290)
Mathematics
WAEC / WASSCE 2007
Number and Numeration
Solution
Find the smallest value of k such that 2\(^2\) x 3\(^3\) x 5 x k is a perfect square.
A
3
B
5
C
15
D
30
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
2\(^2\) x 3\(^3\) x 5\(^1\) x k;
2\(^2\) x 3\(^2\) x 3 x 5 x k
2\(^2\) x 3\(^2\) x 15 x k
smallest value for k
2\(^2\) x 3\(^2\) x 15 = 2\(^2\) x 3\(^2\) x 15\(^2\)
k = 15
Source: Myschool Past Questions Archive (Record #36291)