ECZ 2021 · GCE Paper 2 · Question 8 — Graphs of Functions

Question from ECZ 2021 · GCE Paper 2 · Question 8

(a) The following diagram shows the graph of y = -(15)x(12 - x²).

(a(i)) Use the graph to solve the equations

(a(i)(a)) -(15)x(12 - x²) = 1,[2]

Verified working — step 1

The solutions are where the curve meets the line y = 1.

(a(i)(b)) -(15)x(12 - x²) = -2.[2]

Verified working — step 1

Draw the horizontal line y = -2 across the graph.

(a(ii)) Calculate an estimate of the

(a(ii)(a)) area bounded by the curve and the lines y = 0, x = -3 and x = -1,[3]

Verified working — step 1

Estimate the area under the curve from x = -3 to x = -1.

(a(ii)(b)) gradient of the curve at the point (3, -1.8).[2]

Verified working — step 1

At (3, -1.8) draw a tangent and pick two wel…

(b) Find the equation of the curve for which dydx = 2x - 3 where x = y = 3.[3]

Verified working — step 1

Integrate the gradient to recover the curve:

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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