ECZ 2017 · O-Level Paper 2 · Question 10 — Graphs of Functions
The diagram shows the graph of y = x3 + 3x2 - x - 3.
(a(i)(a)) Use the graph to find the solutions of the equation x3 + 3x2 - x - 3 = 0.[2]
Verified working — step 1
The solutions are the x-intercepts of the drawn curve.(a(i)(b)) Use the graph to find the solutions of the equation x3 + 3x2 - x = 5.[2]
Verified working — step 1
Rewrite so the left side matches the drawn curve:(a(ii)(a)) Calculate an estimate of the gradient of the curve at the point (-3, 0).[2]
Verified working — step 1
Draw the tangent at (-3, 0) and take a second point on it, for example (-2, 8).(a(ii)(b)) Calculate an estimate of 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 - 1as 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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