Explanation

(a)Ecosystem;is defined as the relationship between the living things and the non-living things in a community. The living things are referred to as the biotic factors while the non-living things are the abiotic factors. Examples of biotic factors are plants and animals which can be producers or consumers, while the abiotic factors include temperature, wind, rainfall, sunlight, etc. Food chain refers to the linear feeding relationships among certain species of a community. Food chain can lead to energy transfer from one organism to another. Examples of a food chain is

Grass →Grasshoppers →Toads→ Hawks

Grass is the producer while grasshopper, toad and hawks are consumers

(b) The interdependence of the biotic and abiotic components of the environment;

(i) Plants (biotic) depend on oxygen (abiotic) for respiration

(ii) Plants (biotic) also depend on carbon dioxide (non biotic) for photosynthesis

(iii) Plants (biotic) also depend on water (abiotic) for nutrition and other uses

(iv) Plants also require sunlight for photosynthesis

(v) Abiotic factors like oxygen, carbon dioxide are produced by plants and animals during photosynthesis and respiration respectively.

Correct Answer: A) Z only

Correct Answer: C. seasonal pattern of rainfall

Correct Answer: C) Extinct

Correct Answer: C. the emergence of educated elite

Correct Answer: B. Maize grain

Correct Answer: B. QWERTY

Correct Answer: B. 25

Explanation

(a) \(2Ax - Kx^{2}\)

When x = 1, \(2A(1) - K(1^{2}) = 7\)

\(2A - K = 7 ... (1)\)

When x = 2, \(2A(2) - K(2^{2}) = 4\)

\(4A - 4K = 4 \implies A - K = 1 ... (2)\)

From (2), \(A = 1 + K\)

(1) becomes : \(2(1 + K) - K = 7\)

\(2 + 2K - K = 7 \implies 2 + K = 7\)

\(\therefore K = 5\)

\(A = 1 + K = 1 + 5 = 6\)

\(A, K = 6, 5\)

(b) \(x^{2} - 3x - 1 = 0\)

\(a = 1, b = -3, c = -1\)

Using the quadratic formula,

\(x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}\)

\(x = \frac{-(-3) \pm \sqrt{(-3)^{2} - 4(1)(-3)}}{2(1)}\)

\(x = \frac{3 \pm \sqrt{9 + 12}}{2}\)

\(x = \frac{3 \pm \sqrt{21}}{2} = \frac{3 \pm 4.583}{2}\)

\(x = \frac{3 + 4.583}{2} ; x = \frac{3 - 4.583}{2}\)

\(x = \frac{7.583}{2} = 3.7915 \approxeq 3.8\) (to 1 d.p)

\(x = \frac{-1.583}{2} = -0.7915 \approxeq -0.8\) (to 1 d.p)

Correct Answer: A. Troposphere