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.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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