ECZ 2023 · GCE Paper 2 · Question 12 — Graphs of Functions
Question from ECZ 2023 · GCE Paper 2 · Question 12
(a) Evaluate ∫1-1 (-1 - 3x2) dx.[3]
Verified working — step 1
Integrate term by term: antiderivative -x - x3.(b) The diagram shows the graph of y = x3 - x2 - 5x - 3.
(b(i)) Use the graph to find the solution of the equations
(b(i)(a)) x3 - x2 - 5x - 3 = 0,[2]
Verified working — step 1
x3 - x2 - 5x - 3 = 0 is the curve at y = 0.(b(i)(b)) x3 - x2 - 5x = x - 3.[3]
Verified working — step 1
Rearrange so the left matches the drawn curve: x3 - x2 - 5x - 3 = x - 6.(b(ii)) Find the
(b(ii)(a)) gradient of the curve at the point (-2, -5),[2]
Verified working — step 1
At (-2, -5) draw a tangent to the curve and pick two well-spaced points on it, e.g. (-3, -16) and (-1, 6).(b(ii)(b)) area bounded by the curve, x = 1, y = 0 and x = 3.[2]
Verified working — step 1
Area = ∫31 (x3 - x2 - 5x - 3) dx, antiderivative x4/4 - x3/3 - 5x2/2 - 3x.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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