ECZ 2024 · GCE Paper 2 · Question 10 — Graphs of Functions
Question from ECZ 2024 · GCE Paper 2 · Question 10
(a) Answer this part of the question on a sheet of graph paper. The values of x and y are connected by the equation y = -x3 + x2 + 6x. Some corresponding values of x and y are given in the table below. x-3-2-101234y180-40680q
(a(i)) Calculate the value of q.[1]
Verified working — step 1
q is the curve's y-value at x = 4:(a(ii)) Using a scale of 2 cm to represent 1 unit on the x-axis for -3 ≤ x ≤ 4 and 2 cm to represent 10 units on the y-axis for -30 ≤ y ≤ 20, draw the graph of y = -x3 + x2 + 6x.[3]
Verified working — step 1
Plot: (-3, 18), (-2, 0), (-1, -4), (0,…(a(iii)) Use your graph to
(a(iii)(a)) solve the equation -x3 + x2 + 5x = 4 - x,[3]
Verified working — step 1
Add x to both sides so the left matches the drawn curve:(a(iii)(b)) estimate the gradient of the curve at the point where x = 1.[2]
Verified working — step 1
At x = 1 the curve passes through (1, 6).(b) Find the equation of the normal to the curve y = x2 + x + 2 at the point (1, 4).[3]
Verified working — step 1
dydx = 2x + 1; 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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