ECZ 2018 · O-Level Paper 2 · Question 7 — Graphs of Functions

The values of x and y are connected by the equation y = 2x3 - 3x2 + 5. Some corresponding values 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

Substitute x = -2 into y = …

(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

Plot the nine points from the completed tab…

(a(iii)) Use your graph to solve the equation 2x3 - 3x2 + 5 = x.[3]

Verified working — step 1

Draw the line y = …

(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 at x = …

(b) Express 3x + 1- 2x - 1as a single fraction in its lowest terms.[3]

Verified working — step 1

Common denominator (x + 1)(x - 1):

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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