Correct Answer: A. 12x² + 11x + 2 = 0

Explanation

x = \(-\frac{2}{3}\) and \(-\frac{1}{4}\)

\(\implies (x + \frac{2}{3}) = 0; (x + \frac{1}{4}) = 0\)

\((x + \frac{2}{3})(x + \frac{1}{4}) = 0\)

\(x^{2} + \frac{1}{4}x + \frac{2}{3}x + \frac{1}{6} = 0\)

\(x^2 + \frac{11}{12}x + \frac{1}{6} = 0\)

\(12x^2 + 11x + 2 = 0\)

Correct Answer: A. A. (r ^ p) \(\to\) q

Correct Answer: A. 0.040

Correct Answer: C. -0.19

Explanation

\(\frac{5b+(a+b)^2}{(a-b)^2}\)

= \(\frac{5 * -7 +(3+ -7)^2}{(3- -7)^2}\)

= \(\frac{-35 + 16}{10^2}\)

= \(\frac{-19}{100}\) or -0.19

Correct Answer: B. 22\(cm^{2}s^{-1}\)

Explanation

With radius = 7cm, \(Area = \pi r^{2} = \frac{22}{7} \times 7^{2}\)

= \(154cm^{2}\)

The next second, radius = 7.5cm, \(Area = \pi r^{2} = \frac{22}{7} \times 7.5^{2}\)

= \(176cm^{2}\)

Change in area = \((176 - 154)cm^{2} = 22cm^{2}\)

\(\therefore\) The rate of increase = \(22cm^{2}s^{-1}\)

OR

\(Area (A) = \pi r^{2} \implies \frac{\mathrm d A}{\mathrm d r} = 2\pi r\)

Given \(\frac{\mathrm d r}{\mathrm d t} = 0.5\)

\(\frac{\mathrm d A}{\mathrm d r} \times \frac{\mathrm d r}{\mathrm d t} = \frac{\mathrm d A}{\mathrm d t}\)

\(\frac{\mathrm d A}{\mathrm d t} = 2\pi r \times 0.5 = 2 \times \frac{22}{7} \times 7 \times 0.5\)

= \(22cm^{2}s^{-1}\)

Correct Answer: D. (1, -4)

Explanation

Equate the equation of the curve and the line in order to find their point of intersection ie The values of y in both equations.

\(y + x = 1 \implies y = 1 - x\)

\(x^{2} + 2x - 3 = 1 - x\)

\(x^{2} + 2x + x - 3 - 1 = 0 \implies x^{2} + 3x - 4 = 0\)

\((x - 1)(x + 4) = 0\)

\(x = (1, -4)\)

Explanation

(a) Sheets expected from 5 packets = \(480 \times 5 = 2400\)

Actual sheet contained in the packets = \(435 + 420 + 405 + 415 + 440 = 2115\)

Error in supply = 2400 - 2115 = 285 sheets.

\(\therefore\) Percentage error = \(\frac{285}{2400} \times 100% = 11.875%\)

\(\approxeq 12%\)

(b) If 1 packet = 480 sheets cost N35.00

\(\therefore \text{2400 sheets cost } \frac{2400}{480} \times N35.00 = N175.00\)

Amount of buyer was cheated = \(\frac{Error \times N175}{\text{Expected no of sheets}}\)

\(\frac{N285 \times 175}{2400} = N20.78\)

The buyer was cheated by N21 to the nearest naira.

Correct Answer: C. 4 \( \frac{3}{8}\)

Correct Answer: D. \(-\frac{3}{2}\)

Explanation

\(\log_{0.25} 8 = x\)

\(8 = 0.25^{x}\)

\(2^{3} = (2^{-2})^{x} \implies 3 = -2x\)

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

Correct Answer: D. 100 km/hr