ECZ 2016 · O-Level Paper 2 · Question 12 — Graphs of Functions
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
Substitute x = 3 into 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
Plot the seven points from the completed table and join them with a smooth cubic curve, showing the maximum near x = -1.15 and the minimum near x = …(a(iii)(a)) Use your graph to solve the equation x(x - 2)(x + 2) = 0.[2]
Verified working — step 1
The solutions are the x-…(a(iii)(b)) Use your graph to solve the equation x(x - 2)(x + 2) = x + 2.[3]
Verified working — step 1
Draw the line y = x + 2 on the same axes and read the x-coordinates where it cuts the curve.(b) Express 22x - 1- 13x + 1as 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.
Have a different question?
Search it — if it is from a past paper or a school mock, chances are we have it worked out, or one that uses the same method.
Search any past-paper question