2012 - JAMB Mathematics Past Questions and Answers - page 1
1
Convert 726 to a number in base three
A
2211
B
2121
C
1212
D
1122
correct option: d
First, convert to base 10
726 = (7 x 61) + (2 x 60)
= 42 + 2
= 4410
\(\begin{array}{c|c} 3 & 44 \ \hline 3 & 14 & r 2 \ \hline 3 & 4 & r 2 \ \hline 3 & 1 & r 1 \ \hline 3 & 0 & r 1 \end{array}\)
Ans = 1122 = D
Users' Answers & Comments726 = (7 x 61) + (2 x 60)
= 42 + 2
= 4410
\(\begin{array}{c|c} 3 & 44 \ \hline 3 & 14 & r 2 \ \hline 3 & 4 & r 2 \ \hline 3 & 1 & r 1 \ \hline 3 & 0 & r 1 \end{array}\)
Ans = 1122 = D
2
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
\(\frac{4}{5}\)
correct option: c
\(\frac{2\frac{2}{3} \times 1\frac{1}{2}}{4\frac{4}{5}}\)
\(\frac{8}{3} \times \frac{3}{2} \div \frac{24}{5}\)
\(\frac{8}{3} \times \frac{3}{2} \times \frac{5}{24}\)
\(\frac{5}{6}\)
Users' Answers & Comments\(\frac{8}{3} \times \frac{3}{2} \div \frac{24}{5}\)
\(\frac{8}{3} \times \frac{3}{2} \times \frac{5}{24}\)
\(\frac{5}{6}\)
3
Evaluate \(\frac{21}{9}\) to 3 significant figures
A
2.30
B
2.31
C
2.32
D
2.33
correct option: d
Users' Answers & Comments4
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
correct option: b
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
Users' Answers & CommentsAmount spent = Amount on children + Additional amount on food
Amount Spent = N525 + N1950 = N2475
Therefore amount left = N3,500 - N2,475 = N1,025
6
If log3x2 = -8, what is x?
A
\(\frac{1}{3}\)
B
\(\frac{1}{9}\)
C
\(\frac{1}{27}\)
D
\(\frac{1}{81}\)
7
Simplify \((\sqrt{6} + 2)^2 - (\sqrt{6} - 2)^2\)
A
\(2\sqrt{6}\)
B
\(4\sqrt{6}\)
C
\(8\sqrt{6}\)
D
\(16\sqrt{6}\)
correct option: c
\((\sqrt{6} + 2)^2 - (\sqrt{6} - 2)^2\)
= \([(\sqrt{6} + 2) + (\sqrt{6} - 2)][(\sqrt{6} + 2) - (\sqrt{6} - 2)]\)
= \((\sqrt{6} + 2 + \sqrt{6} - 2)(\sqrt{6} + 2 - \sqrt{6} + 2)]\)
= \((2\sqrt{6})(4)\)
= \(8\sqrt{6}\)
Users' Answers & Comments= \([(\sqrt{6} + 2) + (\sqrt{6} - 2)][(\sqrt{6} + 2) - (\sqrt{6} - 2)]\)
= \((\sqrt{6} + 2 + \sqrt{6} - 2)(\sqrt{6} + 2 - \sqrt{6} + 2)]\)
= \((2\sqrt{6})(4)\)
= \(8\sqrt{6}\)
8
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}
9
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
correct option: a
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
Users' Answers & Comments3 + 19 + 23 + x = 46
22 + 23 + x = 46
45 + x = 46
x = 46 - 45
x = 1
10
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
\(\frac{1}{c}(\frac{w + 2v}{v + w})\)
correct option: a
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 = \(\frac{1}{c}\frac{w - 2v}{v + w}\)
Users' Answers & Comments2v + 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 = \(\frac{1}{c}\frac{w - 2v}{v + w}\)