ECZ 2020 · GCE Paper 2 · Question 11 — Graphs of Functions
The values of x and y are connected by the equation y = 3 - 5x + x2 + x3. Some corresponding values are given in the table below. x-3-2-10123y09r30524
(a(i)) Calculate the value of r.[1]
Verified working — step 1
r is the value of y when x = -1.(a(ii)) Taking 2cm to represent 1 unit on the x-axis for -3 ≤ x ≤ 3, and 2cm to represent 10 units on the y-axis for 0 ≤ y ≤ 30, draw the graph of y = 3 - 5x + x2 + x3.[3]
Verified working — step 1
Using the scale 2cm = 1 unit on the x-axis (for -3 ≤ x ≤ 3) and 2cm = 10 units on the y-axis (for 0 ≤ y ≤ 30), plot the points:(a(iii)(a)) Use your graph to calculate an estimate of the gradient of the curve at the point where x = 2.[2]
Verified working — step 1
At x = 2, draw a tangent line to the curve on your graph (touching the curve at (2, 5)).(a(iii)(b)) Use your graph to calculate an estimate of the area bounded by the curve, x = -3 and x = -2.[3]
Verified working — step 1
The area between the curve, the x-axis, x = -3 and x = -2 is estimated using the trapeziumcounting-squares method on the graph.(b) Find the coordinates of the stationary points on the curve y = 2x3 - 3x2 - 12x + 4.[3]
Verified working — step 1
y = 2x3 - 3x2 - 12x + 4The 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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