ECZ 2025 · GCE Paper 2 · Question 10 — Graphs of Functions
The values of x and y are connected by y = x3 - 6x2 + 9x. Some corresponding values of x and y are given in the table below, correct to 1 decimal place where appropriate. x-1.5-10123455.5y-30.4p042042034.4
(a(i)) Calculate the value of p.[1]
Verified working — step 1
p = y(-1) = (-1)3 - 6(-1)2 + 9(-1) = -1 - 6 - 9 = …(a(ii)) Using the given scale of 2cm to represent 1 unit on the x-axis for -2 ≤ x ≤ 6 and 2cm 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
Using axes: x-axis from -2 to 6 at 2cm per 1 unit, y-axis from -40 to 40 at 2cm per 10 units, plot the points:(a(iii)(a)) Use your graph to solve the equation x3 - 6x2 + 9x = 0.[2]
Verified working — step 1
The equation x3 - 6x2 + 9x = 0 corresponds to y = …(a(iii)(b)) Use your graph to solve the equation x3 - 6x2 + 9x = 5x - 10.[3]
Verified working — step 1
Rearrange: x3 - 6x2 + 9x = 5x - 10 means the curve y = x3-6x2+9x meets the line y = 5x - 10.(b) Evaluate the integral of (5 + 4x - x2) dx from x = 1 to x = 4.[3]
Verified working — step 1
∫(5 + 4x - x2) dx from 1 to 4The 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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