Question Library

3\(^{n - 1}\) \times \(\frac{27^{n + 1}}{81^n}\) = 3\(^{n - 1}\) \times \(\frac{3^{3(n + 1)}}{3^{4n}}\) = 3\(^{n - 1 + 3n + 3 − 4n}\) = 3\(^{4n − 4n − 1 + 3}\) = \(3^{2}\) = 9

The operation was performed in base 2 because when counting in base 2, there are only two possible digits: 0 and 1.

when x=2, we have \(2 + 2(2^{2})\) = \(2 + 8 = 10\)

Capacity = Volume = 3080m3 base diameter = 14m radius = \(\frac{\text{diameter}}{2}\) = 7m Volume of Cylidner = Capacity of cylinder πr2h = 3080 \(\frac{22}{7}\) × 7 × 7 × h = 3080 h = \(\frac{3080}{22 \times 7}\) h = 20m

4\(\sqrt{27}\) + 5\(\sqrt{12}\) − 3\(\sqrt{75}\) = 4\(\sqrt{3}\) × 9 + 5\(\sqrt{3}\) × 4 − 3\(\sqrt{3}\) × 25 = 4 × 3\(\sqrt{3}\) + 5 × 2\(\sqrt{3}\) − 3 × 5\(\sqrt{3}\) = 12\(\sqrt{3}\) + 10\(\sqrt{3}\) − 15\(\sqrt{3}\) = (12 + 10 − 15)\(\sqrt{3}\) = 7\(\sqrt{3}\)

by method of long division, we get the answer.

Total Cost Price = N(250,000 + 70,000) = N 320,000 Selling Price = N 400,000(Given) Gain = Selling Price - Cost Price = 400,000 - 320,000 = 80,000 % gain = \(\frac{\text{Gain}}{\text{Cost Price}}\) \times 100 = \(\frac{80,000}{320,000}\) \times 100 Gain % = 25%

Actual measurement = 10cm approximated value of measurement = 10.5cm % error = \(\frac{\text{Actual measurement − Approximated}}{\text{Actual measure}}\) × 100 = \(\frac{10 − 10.5}{10}\) × 100 = \(\frac{-0.5}{10}\) × 100 ignore -sign i.e take absolute value = \(\frac{0.5}{10}\) × 100 = 5 %

Principal = P, Simple Interest = I, Amount = A Amount = Principal + Simple Interest I = \(\frac{PRT}{100}\) R = rate, T = time I = \(\frac{P \times 5 \times 2}{100}\) I = \(\frac{10P}{100}\) I = \(\frac{P}{10}\) Amount A = P + I 5500 = P + \(\frac{P}{10}\) Multiply through by 100 5500 = 10P + P 5500 = 11P p = \(\frac{5500}{11}\) p = ₦5000

MATHEMATICS is an eleven-letter word = 11! There are 2Ms and 2As and 2Ts Divide the number of repeating letters = \(\frac{11!}{2!2!2!}\)

\(x^{2} + 2xy + y^{2} + 3x + 3y - 18\) \(x^{2} + 2xy + 3x + y^{2} + 3y -18\) \(x^{2} + 2xy - 3x + 6x + y^{2} -3y + 6y -18\) \(x^{2} + 2xy -3x + y^{2} -3y + 6x + 6y -18\) \(x^{2} + xy -3x + xy + y^{2} - 3y + 6x + 6y -18\) x(x + y - 3) + y(x + y - 3) + 6(x + y - 3) = (x + y - 3)(x + y + 6) = (x + y + 6)(x + y -3)

p = s + \(\frac{sm^2}{nr}\) p = s + ( 1 + \(\frac{m^2}{nr}\)) p = s (1 + \(\frac{nr + m^2}{nr}\)) nr \times p = s (nr + m2) s = \(\frac{nrp}{nr + m^2}\)

x * y is an operation on 3x + 2y − 1 Find 3A − 1 x = 3, y = −1 3 * − 1 on 3x + 2y − 1 3(3) + 2(−1) −1 = 9 − 2 − 1 = 6

(\(\sqrt[3]{64a^3})^{-1}\) \(\frac{1}{(\sqrt[3]{64a^3})}\) = \(\frac{1}{4a}\)

\(\frac{2 \sqrt{3} - \sqrt{2}}{\sqrt{3} + 2 \sqrt{2}}\)= m + n√6 \(\frac{2 \sqrt{3} - \sqrt{2}}{\sqrt{3} + 2 \sqrt{2}}\) x \(\frac{\sqrt{3} - 2 \sqrt{2}}{\sqrt{3} - \sqrt{2}}\) \(\frac{2 \sqrt{3} (\sqrt{3} - 2 \sqrt{2}) - \sqrt{2}(\sqrt{3} - 2 \sqrt{2})}{\sqrt{3}(\sqrt{3} - 2 \sqrt{2}) + 2 \sqrt{2}(\sqrt{3} - 2 \sqrt{2})}\) \(\frac{2 \times 3 - 4\sqrt{6} - 6 + 2 \times 2}{3 - 2 \sqrt{6} + 2 \sqrt{6} - 4 \times 2}\) = \(\frac{6 - 4 \sqrt{6} - \sqrt{6} + 4}{3 - 8}\) = \(\frac{0 - 4 \sqrt{6} - 6}{5}\) = \(\frac{10 - 5 \sqrt{6}}{5}\) = − 2 + √6 ∴ m + n\(\sqrt{6}\) = − 2 + √6 m = − 2, n = 1