ECZ 2020 · GCE Paper 2 · Question 11 — Graphs of Functions
Answer the whole of this question on a sheet of graph paper. The variables x and y are connected by the equation y = 3 - 5x + x2 + x3. Some of the corresponding values of x and y are given in the table below. x-3-2-10123y09r30524
(a(i)) Calculate value of r.[1]
Verified working — step 1
r is the curve's y-value at x = -1:(a(ii)) Taking 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 0 ≤ y ≤ 30, draw the graph of y = 3 - 5x + x2 + x3.[3]
Verified working — step 1
Plot the table's points: (-3, 0), (-2, 9),…(a(iii)) Use your graph to calculate an estimate of the
(a(iii)(a)) gradient of the curve at the point where x = 2,[2]
Verified working — step 1
At x = 2 the curve passes through (2, 5).(a(iii)(b)) area bounded by the curve, x = -3 and x = -2.[3]
Verified working — step 1
Estimate the area between the curve and the x-axis from x = -3 to x = -2.(b) Find the coordinates of the stationary points on the curve y = 2x3 - 3x2 - 12x + 4.[3]
Verified working — step 1
Stationary points occur where dydx = 0.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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