1991 - JAMB Mathematics Past Questions and Answers - page 2

I = (\frac{PRT}{100})

= (\frac{10 \times 2 \times 4}{100})

= (\frac{4}{5})

= 0.8

Total amount = N10.80

He pays N8.00

Remainder = 10.80 - 8.00

= N2.80

% of water in the mixture

= (\frac{\text{Total Amount of water}}{\text{Total quantity of spirit}}) x (\frac{100}{1})

(\frac{3(\frac{20}{100}) + 5 (\frac{15}{100})}{3 + 5}) x (\frac{100}{1})

= (\frac{\frac{6}{10} + \frac{75}{100}}{8}) x (\frac{100}{1})

= (\frac{0.6 + 0.75}{8}) x (\frac{100}{1})

= (\frac{1.35}{8}) x (\frac{100}{1})

= (\frac{33.75}{2})

= 16.875

= 16(\frac{7}{8})

(\frac{27}{5^1})(3)^-3 x (\frac{(1)^{-1}}{5}) = (\frac{27}{5}) x (\frac{1}{3^3}) x (\frac{1}{\frac{1}{5}})

= (\frac{27}{5}) x (\frac{1}{27}) x (\frac{5}{1})

= 1

2log (\frac{2}{5}) - log(\frac{72}{125}) + log 9

[(\frac{2}{5}))² x 9] = log (\frac{4}{25}) x (\frac{9}{1}) x (\frac{125}{72})

= log (\frac{72}{125})

= log (\frac{5}{2})

= log (\frac{10}{4})

= log 10 - log 4

= log₁₀ 10 - log₁₀ 22

= 1 - 2 log2

(\frac{1}{1 + \sqrt{5}}) - (\frac{1}{1 - \sqrt{5}})

= (\frac{3 - \sqrt{5} - 3 - \sqrt{5}}{(3 + \sqrt{5}) (3 - \sqrt{5}})

= (\frac{-2\sqrt{5}}{9 - 5})

= (\frac{-2\sqrt{5}}{4})

= - (\frac{1}{2}\sqrt{5})

(\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}})

= (\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}}) x (\frac{3\sqrt{2} + 2 \sqrt{3}}{3\sqrt{2} - 2 \sqrt{3}})

(\frac{4(3) + 9(2) + 2(6) \sqrt{6}}{9(2) - 4(3)})

(\frac{12 + 18 + 12\sqrt{6}}{1`8 - 12})

= (\frac{30 + 12\sqrt{6}}{6})

= 5 + 2(\sqrt{6})

(x² - 3x + 1)(x - a) = x³ - 3x² + x - ax² + 3ax - a

= x³ - (3 + a) x² + (1 + 3a)x - a

(\frac{xy^2 - x^2y}{x^2 - xy^1})

= (\frac{(-2)(3)^2 - (-2)^2(3)}{(-2)^2 - (-2)(3)})

= -30

= -3

Average speed = (\frac{\text{total Distance}}{\text{Total Time})

from Calabar to Enugu in time t₁, hence

t₁ = (\frac{P}{U}) also from Enugu to Benin

t₂ (\frac{q}{w})

Av. speed = (\frac{p + q}{t_1 + t_2}

= (\frac{p + q}{\frac{p}{u} + \frac{q}{w})

= p + q x (\frac{uw}{pw + qu})

= (\frac{uw(p + q)}{pw + qu})

W (\alpha) (\frac{\frac{1}{uv}}{u + v})

∴ w = (\frac{\frac{k}{uv}}{u + v})

= (\frac{k(u + v)}{uv})

w = (\frac{k(u + v)}{uv})

w = 8, u = 2 and v = 6

8 = (\frac{k(2 + 6)}{2(6)})

= (\frac{k(8)}{12})

k = 12