ECZ 2022 · GCE Paper 2 · Question 12 — Graphs of Functions
The graph of y = 27x - x3 is given printed on the paper.
(a) Find the equation of the tangent to the curve y = 1 + 3x - 3x2 at the point (1, 1).[3]
Verified working — step 1
y = 1 + 3x - 3x2(b(i)(a)) Use the graph to solve 27x - x3 = 0.[2]
Verified working — step 1
On the graph of y = 27x - x3, the solutions of 27x - x3 = 0 are the x-values where the curve crosses the x-axis (y = …(b(i)(b)) Use the graph to solve 27x - x3 = 5x + 10.[3]
Verified working — step 1
Draw the line y = 5x + 10 on the same axes (using two points, e.g. (0,10) and (2,20)).(b(ii)(a)) Calculate an estimate of the gradient of the curve at the point where x = 2.[2]
Verified working — step 1
At x = 2, y = 27(2) - 23 = 54 - 8 = 46, so the point is (2, 46).(b(ii)(b)) Calculate an estimate of the area bounded by the curve, x-axis and x = 3.[2]
Verified working — step 1
The area required is the region between the curve, the x-axis and the line x = 3 (from x = 0 to x = 3).The full step-by-step working and final answer are included with Premium — checked against ECZ marking standards.
Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.
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