ECZ 2021 · O-Level Paper 2 · Question 11 — Graphs of Functions

Question from ECZ 2021 · O-Level Paper 2 · Question 11

(a) The values of x and y are connected by the equation y = x(x2 - 4). Some corresponding values of x and y are given in the table below. x-3-2-10123y-15r30-3015

(a(i)) Calculate the value of r.[1]

Verified working — step 1

r is the curve's y-value at x = -2:

(a(ii)) Using a scale of 2 cm to represent 1 unit on the x-axis for -3 ≤ x ≤ 3 and 2 cm to represent 10 units on the y-axis for -20 ≤ y ≤ 20, draw the graph of y = x(x2 - 4).[3]

Verified working — step 1

Plot the table's points: (-3, -15), (-2, 0)…

(a(iii)) Use your graph to solve the equations

(a(iii)(a)) x(x2 - 4) = 0,[2]

Verified working — step 1

x(x2 - 4) = 0 is the curve at y = …

(a(iii)(b)) x(x2 - 4) = 2.[3]

Verified working — step 1

The equation says curve = 2, so draw the horizontal line y = 2.

(b) Find the equation of the normal to the curve y = x2 - x + 4 at the point (-1, 6).[3]

Verified working — step 1

dydx = 2x - 1; at x = -1 the tangent gradient is -2 - 1 = -3.

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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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