ECZ 2025 · GCE Paper 2 · Question 10 — Graphs of Functions
Question from ECZ 2025 · GCE Paper 2 · Question 10
(a) The values of x and y are connected by the equation y = x3 - 6x2 + 9x. Some corresponding values of x and y correct to 1 decimal place where appropriate are given in the table below. x-1.5-10123455.5y-30.4p042042034.4
(a(i)) Calculate the value of p.[1]
Verified working — step 1
p is the table's y-value at x = -1, so substitute into the curve:(a(ii)) Using a scale of 2 cm to represent 1 unit on the x-axis for -2 ≤ x ≤ 6 and 2 cm to represent 10 units on the y-axis for -40 ≤ y ≤ 40, draw the graph of y = x3 - 6x2 + 9x.[3]
Verified working — step 1
Plot the table's points, including (-1, -16), (…(a(iii)) Use your graph to solve the equations
(a(iii)(a)) x3 - 6x2 + 9x = 0,[2]
Verified working — step 1
x3 - 6x2 + 9x = 0 is the curve at y = …(a(iii)(b)) x3 - 6x2 + 9x = 5x - 10.[3]
Verified working — step 1
The equation says curve = line, so draw y = 5x - 10 through (0, -10) and (4, 10).(b) Evaluate ∫41 (5 + 4x - x2) dx.[3]
Verified working — step 1
Integrate term by term: the antiderivative of 5 + 4x - x2 is 5x + 2x2 - x3/3.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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