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Mathematics
UTME / JAMB 2006
Number and Numeration
Solution
The sum of the first n positive integers is
A
1/2 n(n-1)
B
n(n+1)
C
n(n-1)
D
1/2 n(n+1)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Let the positive integers be 1, 2, ,3, 4, .....n
∴ a = 1, d = 1 and n = n
Sn = n/2(2a + (n-1)d)
= n/2 (2 + n – 1)
= 1/2n(n + 1)
Source: Myschool Past Questions Archive (Record #9040)
Mathematics
UTME / JAMB 2006
Number and Numeration
Solution
If \(T = 2\pi \sqrt{\frac{l}{g}}\), make g the subject of the formula
A
(4π l2) / T
B
(4π2l) / T2
C
(4π2l2) / T2
D
(2π√l) / T
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(T = 2\pi \sqrt{\frac{l}{g}}\)
\(\frac{T}{2\pi} = \sqrt{\frac{l}{g}}\)
\((\frac{T}{2\pi})^{2} = \frac{l}{g}\)
\(\therefore g = \frac{4 \pi^{2} l}{T^{2}}\)
Source: Myschool Past Questions Archive (Record #9041)
Mathematics
UTME / JAMB 2006
Number and Numeration
Diagram
Solution
The response of 160 pupils in a school asked to indicate their favourite subjects is given in the bar chart above. What percentage of the pupils have English and Health education as the their favourite subjects?
Attached Figure / Diagram
A
55%
B
52%
C
36%
D
22%
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
English = 52 students
Health education = 36 students
Total = 88 students
= \(\frac{88}{160} \times 100%\)
= 55%
Source: Myschool Past Questions Archive (Record #33132)
Mathematics
WAEC / WASSCE 2006
Number and Numeration
Solution
Evaluate (0.13)\(^3\)correct to three significant figures
A
0.00219
B
0.00220
C
0.00300
D
0.00390
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
(0.13)\(^3\) = 0.13 x 0.13 x 0.13 = 0.002197
= 0.00220 (3 s.f)
Source: Myschool Past Questions Archive (Record #36156)
Mathematics
WAEC / WASSCE 2006
Number and Numeration
Solution
Simplify: 11011\(_2\) - 1101\(_2\)
A
101000\(_2\)
B
1100\(_2\)
C
1110\(_2\)
D
1011\(_2\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
11011\(_2\) - 1101\(_2\) = 1110\(_2\)
Source: Myschool Past Questions Archive (Record #36157)
Mathematics
WAEC / WASSCE 2006
Number and Numeration
Solution
Simplify \(\frac{25 ^\frac{2}{3} \div 25 ^\frac{1}{6}}{( \frac{1}{5})^{-\frac{7}{6}} \times ( \frac{1}{5})^{\frac{1}{6}}}\)
A
25
B
\(\frac{1}{5}\)
C
1
D
\(\frac{1}{25}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{25 \frac{2}{3} \div 25 \frac{1}{6}}{( \frac{1}{5})^{-\frac{7}{6}} \times ( \frac{1}{5})^{\frac{1}{6}}}\) = \(\frac{25^{4 - \frac{1}{6}}}{(\frac{1}{5})^{-7 + \frac{1}{6}}}\)
= \(\frac{25^{\frac{1}{2}}}{(\frac{1}{5})^{-1}}\)
= \(\frac{(5^2)^{\frac{1}{2}}}{(5^{-1})^{-1}}\)
= \(\frac{5}{5}\)
= 1
Source: Myschool Past Questions Archive (Record #36158)
Mathematics
WAEC / WASSCE 2006
Number and Numeration
Solution
Simplify \(\frac{x - 4}{4} - \frac{x - 3}{6}\)
A
\(\frac{x - 18}{12}\)
B
\(\frac{x - 6}{12}\)
C
\(\frac{x - 18}{24}\)
D
\(\frac{x - 6}{24}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{x - 4}{4} - \frac{x - 3}{6}\) = \(\frac{3(x - 4) - 2(x - 3)}{12}\)
= \(\frac{3x -12 - 2x + 6}{12}\)
= \(\frac{3x - 2x - 12 + 6}{12}\)
= \(\frac{x - 6}{12}\)
Source: Myschool Past Questions Archive (Record #36159)
Mathematics
WAEC / WASSCE 2006
Number and Numeration
Solution
Given that y = 1 - \(\frac{2x}{4x - 3}\), find the value of x for which y is undefined
A
3
B
\(\frac{3}{4}\)
C
\(\frac{-3}{4}\)
D
-3
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
for undefined expression, the denomination is zero 4x - 3 = 0
4x = 3; x = \(\frac{3}{4}\)
Source: Myschool Past Questions Archive (Record #36160)
Mathematics
WAEC / WASSCE 2006
Number and Numeration
Solution
If 30% of y is equal to x, what in terms of x, is 30% of 3y?
A
\(\frac{x}{9}\)
B
\(\frac{x}{3}\)
C
x
D
3x
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
If 30% of y = x, then 30% of 3y = 3x
Source: Myschool Past Questions Archive (Record #36163)
Mathematics
WAEC / WASSCE 2006
Number and Numeration
Solution
A baker used 40% of a 50kg bag of flour. If \(\frac{1}{8}\) of the amount used was for the cake, how many kilogram of flour was used for the cake?
A
2\(\frac{1}{2}\)
B
6\(\frac{1}{2}\)
C
15\(\frac{3}{8}\)
D
17\(\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{40}{100} \times 50\)kg = 20kg
\(\frac{1}{8}\) of 20kg for cake; \(\frac{1}{8}\) x \(\frac{20}{1}\)
= 2\(\frac{1}{2}\)kg
Source: Myschool Past Questions Archive (Record #36164)
Mathematics
WAEC / WASSCE 2006
Number and Numeration
Solution
The ratio of boys to girls in a class is 5:3. Find the probability of selecting at random, a girl from the class
A
\(\frac{1}{8}\)
B
\(\frac{1}{3}\)
C
\(\frac{3}{8}\)
D
\(\frac{3}{5}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
ratio of boys to girls = 5:3
total = 5 + 3 = 8
Pr(girl) = \(\frac{3}{8}\)
Source: Myschool Past Questions Archive (Record #36166)
Mathematics
WAEC / WASSCE 2006
Number and Numeration
Solution
What must be added to x2 - 3x to make it a perfect square?
A
\(\frac{9}{4}\)
B
\(\frac{9}{2}\)
C
6
D
9
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
x2 - 3x + k(perfect square)
k = (-\(\frac{3}{2}\))2 ; k = \(\frac{9}{4}\)
Source: Myschool Past Questions Archive (Record #36169)
Mathematics
WAEC / WASSCE 2006
Number and Numeration
Solution
Given that (2x - 1)(x + 5) = 2x2 - mx - 5, what is the value of m
A
11
B
5
C
-9
D
-10
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
(2x - 1)(x + 5) = 2x2 - mx - 5
2x2 + 10x - x - 5
= 2x2 + 9x - 5 = 2x2 - mx - 5
comparing the co-efficient of x
-m = 9
m = -9
Source: Myschool Past Questions Archive (Record #36170)
Mathematics
WAEC / WASSCE 2006
Number and Numeration
Solution
What is the place value of 9 in the number 3.0492?
A
\(\frac{9}{10000}\)
B
\(\frac{9}{1000}\)
C
\(\frac{9}{100}\)
D
\(\frac{9}{10}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Place value of 9 in 3.0492
= 0.009
= \(\frac{9}{1000}\)
Source: Myschool Past Questions Archive (Record #36171)
Mathematics
WAEC / WASSCE 2006
Number and Numeration
Solution
If the simple interest on a sum of money invested at 3% per annum for 2\(\frac{1}{2}\) years is N123, find the principal.
A
N676.50
B
N820
C
N1,640
D
N4,920
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
I = N123; R = 3%' T = 2\(\frac{1}{2}\) yrs; P = \(\frac{100 \times 1}{RT}\)
P = \(\frac{100 \times 123}{3 \times 2.5}\)
principal(P) = N1640
Source: Myschool Past Questions Archive (Record #36172)