ECZ 2018 · O-Level Paper 2 · Question 7 — Graphs of Functions
Question from ECZ 2018 · O-Level Paper 2 · Question 7
(a) The values of x and y are connected by the equation y = 2x3 - 3x2 + 5. Some corresponding values of x and y are given in the table below. x-2-1.5-1-0.500.511.52yp-8.50454.5459
(a(i)) Calculate the value of p.[1]
Verified working — step 1
p is the y-value at x = -2 on y = 2x3 - 3x2 + 5.(a(ii)) Using a scale of 4 cm to represent 1 unit on the x-axis for -2 ≤ x ≤ 2 and 2 cm to represent 5 units on the y-axis for -25 ≤ y ≤ 10, draw the graph of y = 2x3 - 3x2 + 5.[3]
Verified working — step 1
Scale: x-axis 4 cm to 1 unit (-2 to 2), y-axis 2 cm to 5 units (-25 to 10).(a(iii)) Use your graph to solve the equation 2x3 - 3x2 + 5 = x.[3]
Verified working — step 1
The solutions are where the curve meets the line y = x.(a(iv)) Calculate an estimate of the gradient of the curve at the point where x = 1.5.[2]
Verified working — step 1
Draw the tangent to the curve at x = 1.5.(b) Express 3x + 1 - 2x - 1 as a single fraction in its lowest terms.[3]
Verified working — step 1
Common denominator (x + 1)(x - 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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