ECZ 2021 · O-Level Paper 2 · Question 11 — Graphs of Functions
The values of x and y are connected by the equation y = x(x2 - 4). Some corresponding values are given in the table below. x-3-2-10123y-15r30-3015
(a(i)) Calculate the value of r.[1]
Verified working — step 1
Substitute x = -2 into y = x(x2 - 4):(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 seven points from the completed ta…(a(iii)(a)) Use your graph to solve the equation x(x2 - 4) = 0.[2]
Verified working — step 1
The solutions are the x-…(a(iii)(b)) Use your graph to solve the equation x(x2 - 4) = 2.[3]
Verified working — step 1
Draw the line y = …(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, so at x = -1 the tangent gradient is -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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