ECZ 2017 · O-Level Paper 2 · Question 10 — Graphs of Functions
Question from ECZ 2017 · O-Level Paper 2 · Question 10
(a) The diagram below shows the graph of y = x3 + 3x2 - x - 3.
(a(i)) Use the graph to find the solutions of the equations
(a(i)(a)) x3 + 3x2 - x - 3 = 0,[2]
Verified working — step 1
The solutions are where the drawn curve cuts the x-axis (y = 0).(a(i)(b)) x3 + 3x2 - x = 5.[2]
Verified working — step 1
Rearrange so the left matches the drawn curve y = x3 + 3x2 - x - 3.(a(ii)) Calculate an estimate of
(a(ii)(a)) the gradient of the curve at the point (-3, 0),[2]
Verified working — step 1
Draw the tangent at (-3, 0) and pick a second point on it, e.g. (-2, 8).(a(ii)(b)) the area bounded by the curve, x = 0, y = 0 and y = 20.[3]
Verified working — step 1
The curve reaches y = 20 at about x = 2.2.(b) Express 1x - 4 - 25x - 1 as a single fraction in its lowest terms.[3]
Verified working — step 1
Common denominator (x - 4)(5x - 1).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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