ECZ 2019 · O-Level Paper 2 · Question 10 — Graphs of Functions
The diagram shows part of the graphs of y = x3 + 2x - 1 and y = 10x.
(a(i)(a)) Use the graphs to solve the equation x3 + 2x = 6.[2]
Verified working — step 1
Rewrite so the left side matches the drawn curve:(a(i)(b)) Use the graphs to solve the equation x3 + 2x - 1 = 10x.[2]
Verified working — step 1
The solutions are where the curve y = x3 + 2x - 1 meets the line y = …(a(ii)(a)) Calculate an estimate of the gradient of the curve at the point (2, 11).[2]
Verified working — step 1
Draw the tangent at (2, 11) and take two points on it, for example (1.5, 4) and (2.5, 18).(a(ii)(b)) Calculate an estimate of the area bounded by the curve, y = 10x, y = 0 and x = 2.[3]
Verified working — step 1
The region lies between the line y = 10x and the curve y = x3 + 2x - 1, from the y-axis across to x = 2, bounded below by y = …(b) Evaluate the integral from 1 to 3 of (3x2 + 4x) dx.[3]
Verified working — step 1
Integral of (3x2 + 4x) dx = x3 + 2x2.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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