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Mathematics
UTME / JAMB 2012
Number and Numeration
Solution
Convert 112\(_6\) to a number in base three
A
2211
B
2121
C
1212
D
1122
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
First, convert to base 10
112\(_6\) = (1 x 6\(^2\)) + (1 x 6\(^1\)) + (2 x 6\(^0\))
= 36 + 6 + 2
= 44\(_{10}\)
\(\begin{array}{c|c} 3 & 44 \\ \hline 3 & 14 & r 2 \\ \hline 3 & 4 & r 2 \\ \hline 3 & 1 & r 1 \\ \hline 3 & 0 & r 1 \end{array}\)
Ans = 1122 = D
Source: Myschool Past Questions Archive (Record #27186)
Mathematics
UTME / JAMB 2012
Number and Numeration
Solution
Simply \(\frac{2\frac{2}{3} \times 1\frac{1}{2}}{4\frac{4}{5}}\)
A
\(1\frac{1}{4}\)
B
\(1\frac{1}{6}\)
C
\(\frac{5}{6}\)
D
\(\frac{4}{5}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{2\frac{2}{3} \times 1\frac{1}{2}}{4\frac{4}{5}}\)
\(\frac{8}{3} \times \frac{3}{2} \div \frac{24}{5}\)
\(\frac{8}{3} \times \frac{3}{2} \times \frac{5}{24}\)
\(\frac{5}{6}\)
Source: Myschool Past Questions Archive (Record #27189)
Mathematics
UTME / JAMB 2012
Number and Numeration
Solution
Evaluate \(\frac{21}{9}\) to 3 significant figures
A
2.30
B
2.31
C
2.32
D
2.33
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{21}{9} = \frac{7}{3}\)
= 2.33 (to 3 sig. figs)
Source: Myschool Past Questions Archive (Record #27190)
Mathematics
UTME / JAMB 2012
Number and Numeration
Solution
A man earns N3,500 per month out of which he spends 15% on his children's education. If he spends additional N1,950 on food, how much does he have left?
A
N525
B
N1,025
C
N1,950
D
N2,975
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Amount spent on children = \(\frac{15}{100} \times 3500 = N525\)
Amount spent = Amount on children + Additional amount on food
Amount Spent = N525 + N1950 = N2475
Therefore amount left = N3,500 - N2,475 = N1,025
Source: Myschool Past Questions Archive (Record #27191)
Mathematics
UTME / JAMB 2012
Number and Numeration
Solution
If 27\(^{x + 2}\) \(\div\) 9\(^{x + 1}\) = 3\(^{2x}\), find x.
A
3
B
4
C
5
D
6
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(27^{x + 2} \div 9^{x + 1} = 3^{2x}\)
\(3^{3(x + 2)} \div 3^{2(x + 1)} = 3^{2x}\)
\(3^{3x + 6} \div 3^{2x + 2} = 3^{2x}\)
\(\therefore (3x + 6) - (2x + 2) = 2x\)
\(x + 4 = 2x \implies x = 4\)
Source: Myschool Past Questions Archive (Record #27192)
Mathematics
UTME / JAMB 2012
Number and Numeration
Solution
If log3x2 = -8, what is x?
A
\(\frac{1}{3}\)
B
\(\frac{1}{9}\)
C
\(\frac{1}{27}\)
D
\(\frac{1}{81}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
log3x2 = -8
x2 = 3-8
x = \(3^{-8 \times \frac{1}{2}}\)
x = 3-4
x = \(\frac{1}{3^4}\)
x = \(\frac{1}{81}\)
Source: Myschool Past Questions Archive (Record #27194)
Mathematics
UTME / JAMB 2012
Number and Numeration
Solution
Simplify \((\sqrt{6} + 2)^2 - (\sqrt{6} - 2)^2\)
A
\(2\sqrt{6}\)
B
\(4\sqrt{6}\)
C
\(8\sqrt{6}\)
D
\(16\sqrt{6}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\((\sqrt{6} + 2)^2 - (\sqrt{6} - 2)^2\)
= \([(\sqrt{6} + 2) + (\sqrt{6} - 2)][(\sqrt{6} + 2) - (\sqrt{6} - 2)]\)
= \((\sqrt{6} + 2 + \sqrt{6} - 2)(\sqrt{6} + 2 - \sqrt{6} + 2)]\)
= \((2\sqrt{6})(4)\)
= \(8\sqrt{6}\)
Source: Myschool Past Questions Archive (Record #27200)
Mathematics
UTME / JAMB 2012
Number and Numeration
Solution
If P is a set of all prime factors of 30 and Q is a set of all factors of 18 less than 10, find P \(\cap\) Q
A
{3}
B
{2,3}
C
{2,3,5}
D
{1,2}
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
P = {2,3,5}
Q = {2,3,6,9}
P \(\cap\) Q = {2,3}
Source: Myschool Past Questions Archive (Record #27202)
Mathematics
UTME / JAMB 2012
Number and Numeration
Solution
In a class of 46 students, 22 play football and 26 play volleyball. If 3 students play both games, how many play neither?
A
1
B
2
C
3
D
4
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
n(f \(\cap\) v) + n(f) + n(v) + n(f \(\cap\) v) = 46
3 + 19 + 23 + x = 46
22 + 23 + x = 46
45 + x = 46
x = 46 - 45
x = 1
Source: Myschool Past Questions Archive (Record #27203)
Mathematics
UTME / JAMB 2012
Number and Numeration
Solution
Make 'n' the subject of the formula if w = \(\frac{v(2 + cn)}{1 - cn}\)
A
\(\frac{1}{c}(\frac{w - 2v}{v + w})\)
B
\(\frac{1}{c}(\frac{w - 2v}{v - w})\)
C
\(\frac{1}{c}(\frac{w + 2v}{v - w})\)
D
\(\frac{1}{c}(\frac{w + 2v}{v + w})\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
w = \(\frac{v(2 + cn)}{1 - cn}\)
2v + cnv = w(1 - cn)
2v + cnv = w - cnw
2v - w = -cnv - cnw
Multiply through by negative sign
-2v + w = cnv + cnw
-2v + w = n(cv + cw)
n = \(\frac{-2v + w}{cv + cw}\)
n = \(\frac{1}{c}\frac{-2v + w}{v + w}\)
Re-arrange...
n = \(\frac{1}{c}\frac{w - 2v}{v + w}\)
Source: Myschool Past Questions Archive (Record #27219)
Mathematics
UTME / JAMB 2012
Number and Numeration
Solution
Find the remainder when 2x3 - 11x2 + 8x - 1 is divided by x + 3
A
-871
B
-781
C
-187
D
-178
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Hence f(x) = 2x3 - 11x2 + 8x - 1
f(-3) = 2(-3)3 - 11(-3)2 + 8(-3) - 1
= 2(-27) - 11(9) + 8(-3) - 1
= -54 - 99 - 24 - 1
= -178
Source: Myschool Past Questions Archive (Record #27220)
Mathematics
UTME / JAMB 2012
Number and Numeration
Solution
If y varies directly as \(\sqrt{n}\) and y = 4 when n = 4, find y when n = 1\(\frac{7}{9}\)
A
\(\sqrt{17}\)
B
\(\frac{4}{3}\)
C
\(\frac{8}{3}\)
D
\(\frac{2}{3}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
y \(\propto \sqrt{n}\)
y = k\(\sqrt{n}\)
when y = 4, n = 4
4 = k\(\sqrt{4}\)
4 = 2k
k = 2
Therefore,
y = 2\(\sqrt{n}\)
y = 2\(\sqrt{\frac{16}{9}}\)
y = 2\((\frac{4}{3})\)
y = \(\frac{8}{3}\)
Source: Myschool Past Questions Archive (Record #27222)
Mathematics
UTME / JAMB 2012
Number and Numeration
Solution
U is inversely proportional to the cube of V and U = 81 when V = 2. Find U when V = 3
A
24
B
27
C
32
D
36
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
U \(\propto \frac{1}{V^3}\)
U = \(\frac{k}{V^3}\)
k = UV\(^3\)
k = 81 x 2\(^3\) = 81 x 8
When V = 3,
U = \(\frac{k}{V^3}\)
U = \(\frac{81 \times 8}{3^3}\)
U = \(\frac{81 \times 8}{27}\) = 24
Source: Myschool Past Questions Archive (Record #27223)
Mathematics
UTME / JAMB 2012
Number and Numeration
Solution
The value of y for which \(\frac{1}{5}y + \frac{1}{5} < \frac{1}{2}y + \frac{2}{5}\) is
A
\(y > \frac{2}{3}\)
B
\(y < \frac{2}{3}\)
C
\(y > -\frac{2}{3}\)
D
\(y < -\frac{2}{3}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{1}{5}y + \frac{1}{5} < \frac{1}{2}y + \frac{2}{5}\)
Collect like terms
\(\frac{y}{5} - \frac{y}{2} < \frac{2}{5} - \frac{1}{5}\)
\(\frac{2y - 5y}{10} < \frac{2 - 1}{5}\)
\(\frac{-3y}{10} < \frac{1}{5}\)
\(y > \frac{-2}{3}\)
Source: Myschool Past Questions Archive (Record #27326)
Mathematics
UTME / JAMB 2012
Number and Numeration
Solution
Find the range of values of m which satisfy (m - 3)(m - 4) < 0
A
2 < m < 5
B
-3 < m < 4
C
3 < m < 4
D
-4 < m < 3
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
(m - 3)(m - 4) < 0
(m - 3) < 0 ; (m - 4) < 0
m < 3 ; m < 4
3 < m < 4
Source: Myschool Past Questions Archive (Record #27327)