ECZ 2019 · GCE Paper 2 · Question 12 — Graphs of Functions
Answer this part of the question on a sheet of graph paper. The values of x and y are connected by the equation y = x3 - 5x + 3. Some corresponding values of x and y are given in the table below. x-3-2-10123yk573-1115
(a(i)) Calculate the value of k.[1]
Verified working — step 1
k is the y-value at x = -3 on y = x3 - 5x + 3.(a(ii)) Using a scale of 2 cm to 1 unit on the x-axis for -3 ≤ x ≤ 3 and 2 cm to represent 5 units on the y-axis for -10 ≤ y ≤ 20, draw the graph of y = x3 - 5x + 3.[3]
Verified working — step 1
Build a table for -3 ≤ x ≤ 3: (-3, -9), (-2, 5), (-1, 7), (0, 3), (1, -1), (2, 1), (3, 15).(a(iii)) Use your graph to
(a(iii)(a)) solve the equation x3 - 5x = 0,[2]
Verified working — step 1
x3 - 5x = 0 rearranges to x3 - 5x + 3 = 3, matching the drawn curve.(a(iii)(b)) estimate the area bounded by the curve, y = 3 and x = -2.[3]
Verified working — step 1
Shade the region between the curve, the line y = 3 and x = -2 (from x = -2 to x = 0).(b) Find the equation of the tangent to the curve y = (2x + 3)3 at the point where x = -1.[3]
Verified working — step 1
Chain rule: dydx = 3(2x + 3)2 × 2 = 6(2x + 3)2.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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