ECZ 2019 · GCE Paper 2 · Question 12 — Graphs of Functions
The values of x and y are connected by the equation y = x3 - 5x + 3. Some corresponding values are given in the table below. x-3-2-10123yk573-1115
(a(i)) Calculate the value of k.[1]
Verified working — step 1
Substitute x = -3 into y = x3 - 5x + 3:(a(ii)) Draw the graph of y = x3 - 5x + 3 (2cm to 1 unit on x, 2cm to 5 units on y).[3]
Verified working — step 1
Using the scale 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, plot the points:(a(iii)(a)) Use your graph to solve the equation x3 - 5x = 0.[2]
Verified working — step 1
x3 - 5x = 0 can be written as x3 - 5x + 3 = 3, so we need the x-values where the curve y = x3 - 5x + 3 meets the line y = 3.(a(iii)(b)) Use your graph to estimate the area bounded by the curve, y = 3 and x = -2.[3]
Verified working — step 1
On the graph, shade the region enclosed between the curve, the line y = 3, and the vertical line x = -2 (this lies between x = -2 and x = 0, where the curve is above the line y = 3).(b) Find the equation of the tangent to the curve y = (2x + 3)3 at the point where x = -1.[3]
Verified working — step 1
y = (2x + 3)3The 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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