2009 - JAMB Mathematics Past Questions and Answers - page 1
2
If 55x + 52x = 7710 find X
A
5
B
6
C
7
D
10
correct option: c
5*X1 + 5*Xo + 5*X1 + 2*Xo = 77 (change to base 10)
5*X + 5*1 + 5*X + 2*1 = 77
5X + 5 + 5X + 2 = 77
10X + 7 = 77
10X = 77-7
10X = 70
X = 70/10
X = 7
Users' Answers & Comments5*X + 5*1 + 5*X + 2*1 = 77
5X + 5 + 5X + 2 = 77
10X + 7 = 77
10X = 77-7
10X = 70
X = 70/10
X = 7
3
Simplify \(7\frac{1}{12}-4\frac{3}{4}+2\frac{1}{2}\)
A
4
B
41/6
C
45/6
D
51/6
correct option: c
\(7\frac{1}{12}-4\frac{3}{4}+2\frac{1}{2}=5\left(\frac{1-9+6}{12}\right)\\
5\left(\frac{-2}{12}\right)\\
=4\left(\frac{12-2}{12}\right)\)
(carry one from 5 and call it 12)
\(4\frac{10}{12}\\ =4\frac{5}{6}\)
Users' Answers & Comments(carry one from 5 and call it 12)
\(4\frac{10}{12}\\ =4\frac{5}{6}\)
4
Evaluate \(\frac{81.81+99.44}{20.09+36.16}\) correct to 3 significant figures.
A
6.24
B
3.22
C
2.78
D
2.13
correct option: b
\(\frac{81.81 + 99.44}{20.09 + 36.16}\\
=\frac{181.25}{56.25}\\
=\frac{18125}{5625}\\
\frac{29}{9}\\
=3\frac{2}{9}\\
≅ 3.22\)
Users' Answers & Comments5
A man bought a second-hand photocopying machine for N34,000. He serviced is at a cost od N2,000 and then sold it i profit of 15%. What was the selling price?
A
N37,550
B
N40,400
C
N41,400
D
N42,400
correct option: c
C.P = N34000 + N2000 = N36000
Gain = 100 + 15 = 115%
S.P = \(\frac{115}{100}\times \frac{N3600}{1}\)
= N41400
Users' Answers & CommentsGain = 100 + 15 = 115%
S.P = \(\frac{115}{100}\times \frac{N3600}{1}\)
= N41400
6
A student spent 1/5of his allowance on books, 1/2 of remainder on food and kept the rest for contingencies. What fraction was kept?
A
7/15
B
8/15
C
2/5
D
4/5
correct option: c
Users' Answers & Comments7
Solve 52(x-1) x 5(x-1) = 0.04
A
1/3
B
1/6
C
-1/5
D
-1/3
correct option: d
52(x-1) x 5(x-1) = 0.04
52x-2 x 5x-1 = 4/100
52x-2 + x-1 = 1/25
53x-1 = 1/52
53x-1 = 5-2 (Equating the indices)
3x-1 = -2
3x = -2+1
3x = -1
X = -1/3
Users' Answers & Comments52x-2 x 5x-1 = 4/100
52x-2 + x-1 = 1/25
53x-1 = 1/52
53x-1 = 5-2 (Equating the indices)
3x-1 = -2
3x = -2+1
3x = -1
X = -1/3
8
If log102 = 0.3010 and log107 = 0.8451, evaluate log10280
A
3.4471
B
2.4471
C
1.4471
D
1.4071
correct option: b
Log 2 = 0.3010, Log 7 = 0.8451
∴Log 280 = Log 28 x 10
= Log 7x4x10
=Log7 + Log4 + Log10
= Log7 + Log22 + Log10
= Log7 + 2Log2 + Log10
= 0.8451 + 2(0.3010) + 1
= 0.8451 + 0.6020 + 1
= 2.4471
Users' Answers & Comments∴Log 280 = Log 28 x 10
= Log 7x4x10
=Log7 + Log4 + Log10
= Log7 + Log22 + Log10
= Log7 + 2Log2 + Log10
= 0.8451 + 2(0.3010) + 1
= 0.8451 + 0.6020 + 1
= 2.4471
9
Simplify \(\frac{5+\sqrt{7}}{3+\sqrt{7}}\)
A
17-√7
B
4-√7
C
15+√7
D
7-√7
correct option: b
\(\frac{5+\sqrt{7}}{3+\sqrt{7}}=\frac{5+\sqrt{7}}{3+\sqrt{7}}\times \frac{3-\sqrt{7}}{3-\sqrt{7}}\\
=\frac{(5+\sqrt{7})(3-\sqrt{7})}{3^2 - \sqrt{7}^2}\\
=\frac{15-5\sqrt{7}+3\sqrt{7}-7}{9-7}\\
=\frac{8-2\sqrt{7}}{2}\)
Factorize then divide by 2
\(=\frac{2(4-\sqrt{7}}{2}\\ =4-\sqrt{7}\)
Users' Answers & CommentsFactorize then divide by 2
\(=\frac{2(4-\sqrt{7}}{2}\\ =4-\sqrt{7}\)
10
If x = {n2+1:n is a positive integer and 1 \(\leq\) n \(\leq\) 5},
Y = {5n:n is a positive integer and 1 \(\leq\) n \(\leq\) 5}, find x \(\cap\) y.
Y = {5n:n is a positive integer and 1 \(\leq\) n \(\leq\) 5}, find x \(\cap\) y.
A
{5,10}
B
{5, 10, 15}
C
{2, 5, 10}
D
{5, 10, 15, 20}
correct option: a
X = {n2+1:n is a positive integer and 1 \(\leq\) n \(\leq\) 5}
Implies X = {2, 5, 10, 17, 26} i.e. put n= 1, 2, 3, 4 and 5
Y = {5n:n is a positive integer and 1 \(\leq\) n \(\leq\) 5}
Put X = 1, 2, 3, 4, and 5
Y = {5, 10, 15, 20, 25}
X \(\cap\) Y = {2, 5, 10, 17, 26} \(\cap\) {5, 10, 15, 20, 25}
= {5, 10}
Users' Answers & CommentsImplies X = {2, 5, 10, 17, 26} i.e. put n= 1, 2, 3, 4 and 5
Y = {5n:n is a positive integer and 1 \(\leq\) n \(\leq\) 5}
Put X = 1, 2, 3, 4, and 5
Y = {5, 10, 15, 20, 25}
X \(\cap\) Y = {2, 5, 10, 17, 26} \(\cap\) {5, 10, 15, 20, 25}
= {5, 10}