Correct Answer: A. spread of Islam

Correct Answer: B. oxygenated blood from lungs to the left auricle

Correct Answer: B. comic relief

Explanation

\(h = 20t - \frac{3}{2}t^{2} - \frac{2}{3}t^{3}\)

Velocity, \(\frac{\mathrm d h}{\mathrm d t} = 20 - 3t - 2t^{2}\)

At point of rest, v = 0

\(2t^{2} + 3t - 20 = 0\)

\(\implies 2t^{2} - 5t + 8t - 20 = 0\)

\(t(2t - 5) + 4(2t - 5) = 0 \implies t = \frac{5}{2}; -4\)

The value of time cannot be negative hence \(t = \frac{5}{2}secs\)

(b) Maximum height, \(h_{m}\) is at time \(t = \frac{5}{2}s\).

\(h_{m} = 20(\frac{5}{2}) - \frac{3}{2}(\frac{5}{2})^{2} - \frac{2}{3}(\frac{5}{2})^{3}\)

= \(50 - \frac{75}{8} - \frac{250}{16} = \frac{400}{16} = 25 m\)

Correct Answer: B. 6.5

Explanation

\(f(x) = (x^{2} + 3)^{2}\)

Using the chain rule, \(\frac{\mathrm d y}{\mathrm d x} = \frac{\mathrm d y}{\mathrm d u} \times \frac{\mathrm d u}{\mathrm d x}\)

Let \(u = x^{2} + 3\) so that \(y = u^{2}\)

\(\frac{\mathrm d y}{\mathrm d u} = 2u\)

\(\frac{\mathrm d u}{\mathrm d x} = 2x\)

\(\therefore \frac{\mathrm d y}{\mathrm d x} = 2u(2x) = 4xu\)

But \(u = x^{2} + 3\),

\(\frac{\mathrm d y}{\mathrm d x} = 4x(x^{2} + 3)\)

At \(x = \frac{1}{2}, \frac{\mathrm d y}{\mathrm d x} = 4(\frac{1}{2})((\frac{1}{2})^{2} + 3)\)

= \(2 \times \frac{13}{4} = \frac{13}{2} = 6.5\)

Correct Answer: A. Most parts of Africa lies within the tropics

Explanation

(a) (i) Definition of Death rate: Death rate simply refers to the number of deaths in a year per 1000 of a given population in a country.

(ii) Definition of population explosion: This refers to the rapid increase in the population of a place over a short period of time.

(b) Factors that influence death rate in Tropical Africa: (o and insufficient food. (ii) Education and illiteracy.

(iii) Natural disaster. (iv) Family planning. (v) Frequent accidents. (vi) Improvement in health care. (vii) Wars and conflicts.

(viii) Diseases and epidemics. (ix) Improved sanitation and hygiene. (x) Improved standard of living. (xi) Improvement in food production. (xii) Level of economic development.

(c) Effects of a growing population in Tropical Africa: (i) Social unrest. (ii) Food shortage. (iii) Large supply of labour.

(iv) High demand for goods. (v) High cost of living. (vi) Increase in crime rate.

(vii) Traffic congestion. (viii) Inadequate housing. (ix) Large market. (x) Pressure on social amenities.

(xi) High rate of savings.

(xii) Easy spread of diseases. (xiii) Increase in productivity. (xiv) Increase in tax revenue.

(xv) Unemployment and underemployment.

(xvi) Environmental pollution. (xvii) Increase in government expenditure. (xviii) Increase in social vices.

(xix) Development of slums and ghetto. (xx) Poor waste management. (xxi) Pressure on natural resources.

Correct Answer: A. Rights issue

Correct Answer: D. 200000

Correct Answer: A. Deceptive advertising.