ECZ 2016 · O-Level Paper 2 · Question 12 — Graphs of Functions
Question from ECZ 2016 · O-Level Paper 2 · Question 12
(a) The values of x and y are connected by the equation y = x(x - 2)(x + 2). Some corresponding values of x and y are given in the table below. x-3-2-10123y-15030-30k
(a(i)) Calculate the value of k.[1]
Verified working — step 1
k is the y-value at x = 3 on y = x(x - 2)(x + 2).(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 -16 ≤ y ≤ 16, draw the graph of y = x(x - 2)(x + 2).[3]
Verified working — step 1
Scale: x-axis 2 cm to 1 unit (-3 to 3), y-axis 2 cm to 5 units (-16 to 16).(a(iii)) Use your graph to solve the equations
(a(iii)(a)) x(x - 2)(x + 2) = 0,[2]
Verified working — step 1
The solutions are where the curve cuts the x-axis (y = 0).(a(iii)(b)) x(x - 2)(x + 2) = x + 2.[3]
Verified working — step 1
The solutions are where the curve meets the line y = x + 2.(b) Express 22x - 1 - 13x + 1 as a single fraction in its simplest form.[3]
Verified working — step 1
Common denominator (2x - 1)(3x + 1).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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