ECZ 2025 · O-Level Paper 2 · Question 9 — Graphs of Functions
Question from ECZ 2025 · O-Level Paper 2 · Question 9
(a) The diagram shows the graph of y = x3 - 2x2 - 11x + 12.
(a(i)) Use the graph to solve the equations
(a(i)(a)) x3 - 2x2 - 11x + 12 = 0,[2]
Verified working — step 1
The solutions are where the curve meets y = 0 — read the three x-intercepts off the drawn graph.(a(i)(b)) x3 - 2x2 - 11x + 12 = 4x + 10.[2]
Verified working — step 1
Curve = line: the equation rearranges to x3 - 2x2 - 11x + 12 = 4x + 10.(a(ii)) Find the gradient of the curve at the point where x = -2.[2]
Verified working — step 1
Differentiate: dydx = 3x2 - 4x - 11(a(iii)) Calculate the area bounded by the curve, x = -3, x = 0 and y = 0.[3]
Verified working — step 1
Area under the curve from x = -3 to x = 0, by integration:(b) Express 33p - 5 + 7p + 1 as a single fraction in its lowest terms.[3]
Verified working — step 1
Put both fractions over the common denominator (3p - 5)(p + 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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