ECZ 2018 · GCE Paper 2 · Question 12 — Graphs of Functions
Question from ECZ 2018 · GCE Paper 2 · Question 12
(a) Express 32x - 5 - 4x - 3 as a single fraction in its lowest terms.[3]
Verified working — step 1
Common denominator (2x - 5)(x - 3).(b) The diagram below shows the graph of y = x3 + x2 - 12x.
(b(i)) Use the graph to solve the equations
(b(i)(a)) x3 + x2 - 12x = 0,[2]
Verified working — step 1
The solutions are where the curve crosses the x-axis (y = 0).(b(i)(b)) x3 + x2 - 12x = x + 10.[3]
Verified working — step 1
The solutions are where the curve meets the line y = x + 10.(b(ii)) Calculate an estimate of the
(b(ii)(a)) gradient of the curve at the point where x = -3,[2]
Verified working — step 1
The point is (-3, 18), since (-3)3 + (-3)2 - 12(-3) = 18.(b(ii)(b)) area bounded by the curve, x = -3, x = -1 and y = -10.[2]
Verified working — step 1
Measure each curve height ABOVE y = -10 (height = y + 10) at x = -3, -2.5, -2, -1.5, -1: 28, 30.6, 30, 26.9, 22.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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