ECZ 2023 · O-Level Paper 2 · Question 10 — Graphs of Functions
Question from ECZ 2023 · O-Level Paper 2 · Question 10
(a) The values of x and y are connected by the equation y = x3 - 9x + 5. Some of the corresponding values of x and y are given in the table below. x-3.5-3-2-10122.533.5y-6.45q135-3-5-1.9516.4
(a(i)) Calculate the value of q.[1]
Verified working — step 1
q is the curve's y-value at x = -2:(a(ii)) Using a scale of 2 cm to represent 1 unit on the x-axis and 2 cm to represent 5 units on the y-axis for -4 ≤ x ≤ 4 and -10 ≤ y ≤ 20, draw the graph of y = x3 - 9x + 5.[3]
Verified working — step 1
Plot the table's points: (-3, 5), (-2, 15), (-1, 13), …(a(iii)) Use your graph to find the solutions of the equations
(a(iii)(a)) x3 - 9x + 5 = 0,[2]
Verified working — step 1
The solutions of x3 - 9x + 5 = …(a(iii)(b)) x3 - 9x + 5 = -3x + 6.[3]
Verified working — step 1
The equation says curve = line, so draw y = -3x + 6 through (0, 6) and (2, 0).(b) Evaluate ∫2-1 (3x2 - 2x + 1) dx.[3]
Verified working — step 1
Integrate term by term: antiderivative x3 - x2 + x.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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