ECZ 2018 · GCE Paper 2 · Question 12 — Graphs of Functions
The graph of y = x3 + x2 - 12x is given.
(a) Express 32x - 5- 4x - 3as a single fraction in its lowest terms.[3]
Verified working — step 1
32x-5- 4x-3(b(i)(a)) Use the graph to solve x3 + x2 - 12x = 0.[2]
Verified working — step 1
The solutions of x3 + x2 - 12x = 0 are the x-values where the curve crosses the x-axis (y = 0).(b(i)(b)) Use the graph to solve x3 + x2 - 12x = x + 10.[3]
Verified working — step 1
Rewrite x3 + x2 - 12x = x + 10 as the intersection of y = x3 + x2 - 12x with the line y = x + 10.(b(ii)(a)) Calculate an estimate of the gradient of the curve at the point where x = -3.[2]
Verified working — step 1
Draw a tangent to the curve at the point where x = -3 (curve value y = (-3)3+(-3)2-12(-3) = -27+9+36 = 18, so the point is (-3,18)).(b(ii)(b)) Calculate an estimate of the area bounded by the curve, x = -3, x = -1 and y = -10.[2]
Verified working — step 1
The region is bounded above by the curve, below by y = -10, and by x = -3 and x = -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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