ECZ 2024 · GCE Paper 2 · Question 10 — Graphs of Functions
The values of x and y are connected by the equation y = -x3 + x2 + 6x. Some corresponding values are given in the table below. x-3-2-101234y180-40680q
(a(i)) Calculate the value of q.[1]
Verified working — step 1
Substitute x = 4 into y = -x3 + x2 + 6x:(a(ii)) Using a scale of 2cm to represent 1 unit on the x-axis for -3 ≤ x ≤ 4 and 2cm 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
Draw axes: x-axis from -3 to 4 using 2cm per unit, y-axis from -30 to 20 using 2cm per 10 units.(a(iii)(a)) Use your graph to solve the equation -x3 + x2 + 5x = 4 - x.[3]
Verified working — step 1
Rearrange -x3 + x2 + 5x = 4 - x as -x3 + x2 + 6x = 4 (adding x to both sides).(a(iii)(b)) Use your graph to estimate the gradient of the curve at the point where x = 1.[2]
Verified working — step 1
At x = 1, the point on the curve is (1, 6) (since y(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
y = x2 + x + 2The 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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