ECZ 2022 · O-Level Paper 2 · Question 8 — Graphs of Functions
Question from ECZ 2022 · O-Level Paper 2 · Question 8
(a) The variables x and y are connected by the equation y = (x - 3)(x - 5)(x + 2). Some corresponding values of x and y are shown in the table below. x-2-10123456y0243024120-60k
(a(i)) Calculate the value of k.[1]
Verified working — step 1
k is the curve's y-value at x = 6:(a(ii)) Using a scale of 2 cm to represent 1 unit on the x axis for -2 ≤ x ≤ 6 and a scale of 2 cm to represent 10 units on the y axis for -10 ≤ y ≤ 40, draw the graph of y = (x - 3)(x - 5)(x + 2).[3]
Verified working — step 1
Plot the table's points: (-2, 0), (-1, 24), (0, 30),…(a(iii)) Use your graph to estimate the
(a(iii)(a)) gradient of the curve at the point (-1, 24),[2]
Verified working — step 1
Draw a tangent to the curve at (-1, 24) and read its gradient from two well-spaced points.(a(iii)(b)) area bounded by the curve, x = -1, x = 2 and y = 0.[3]
Verified working — step 1
Estimate the area between the curve and the x-axis from x = -1 to x = 2 by counting squares.(b) Express 2x + 5 + 53x - 4 as a single fraction in its simplest form.[3]
Verified working — step 1
Common denominator (x + 5)(3x - 4):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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