2009 - JAMB Mathematics Past Questions and Answers - page 1

5*X¹ + 5*X^o + 5*X¹ + 2*X^o = 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

\(7\frac{1}{12}-4\frac{3}{4}+2\frac{1}{2}=5\left(\frac{1-9+6}{12}\right)\\ 5\left(\frac{-2}{12}\right)\\ =4\left(\frac{12-2}{12}\right)\)
(carry one from 5 and call it 12)
\(4\frac{10}{12}\\ =4\frac{5}{6}\)

\(\frac{81.81 + 99.44}{20.09 + 36.16}\\ =\frac{181.25}{56.25}\\ =\frac{18125}{5625}\\ \frac{29}{9}\\ =3\frac{2}{9}\\ ≅ 3.22\)

C.P = N34000 + N2000 = N36000
Gain = 100 + 15 = 115%
S.P = \(\frac{115}{100}\times \frac{N3600}{1}\)
= N41400

5^2(x-1) x 5^(x-1) = 0.04
5^2x-2 x 5^x-1 = ⁴/₁₀₀
5^{2x-2 + x-1} = ¹/₂₅
5^3x-1 = ¹/_5²
5^3x-1 = 5^-2 (Equating the indices)
3x-1 = -2
3x = -2+1
3x = -1
X = ^-1/₃

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

\(\frac{5+\sqrt{7}}{3+\sqrt{7}}=\frac{5+\sqrt{7}}{3+\sqrt{7}}\times \frac{3-\sqrt{7}}{3-\sqrt{7}}\\ =\frac{(5+\sqrt{7})(3-\sqrt{7})}{3^2 - \sqrt{7}^2}\\ =\frac{15-5\sqrt{7}+3\sqrt{7}-7}{9-7}\\ =\frac{8-2\sqrt{7}}{2}\)
Factorize then divide by 2
\(=\frac{2(4-\sqrt{7}}{2}\\ =4-\sqrt{7}\)

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}