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).

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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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