2009 - JAMB Mathematics Past Questions and Answers - page 1

5X¹ + 5X^o + 5X¹ + 2X^o = 77 (change to base 10)

5X + 51 + 5X + 21 = 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}