ECZ 2024 · O-Level Paper 2 · Question 11 — Graphs of Functions
Question from ECZ 2024 · O-Level Paper 2 · Question 11
(a) The values of x and y are connected by the equation y = x3 - 6x + 2. Some corresponding values of x and y are given in the table below. x-3-2-10123y-7672-3-2k
(a(i)) Calculate the value of k.[1]
Verified working — step 1
k is the curve's y-value at x = …(a(ii)) Using a scale of 2 cm to represent 1 unit on the x-axis for -3 ≤ x ≤ 3 and 2 cm to represent 5 units on the y-axis for -10 ≤ y ≤ 15, draw the graph of y = x3 - 6x + 2.[3]
Verified working — step 1
Plot the table's points: (-3, -7), (-2, 6),…(a(iii)) Use your graph to solve the equations
(a(iii)(a)) x3 - 6x + 2 = 0,[2]
Verified working — step 1
The solutions of x3 - 6x + 2 = …(a(iii)(b)) x3 - 6x = 2.[3]
Verified working — step 1
x3 - 6x = 2 rearranges to x3 - 6x + 2 = 4 — the curve at y = 4.(b) Find the equation of the normal to the curve y = x3 + 3x2 + 2 at the point (-1, 4).[3]
Verified working — step 1
dydx = 3x2 + 6x; at x = -1 the tangent gradient is 3 - 6 = -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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