ECZ 2022 · GCE Paper 2 · Question 12 — Graphs of Functions
Question from ECZ 2022 · GCE Paper 2 · Question 12
(a) Find the equation of the tangent to the curve y = 1 + 3x - 3x2 at the point (1, 1).[3]
Verified working — step 1
dydx = 3 - 6x; at x = 1 the tangent gradient is 3 - 6 = -3.(b) The following diagram shows the graph of y = 27x - x3.
(b(i)) Use the graph to solve the equations
(b(i)(a)) 27x - x3 = 0,[2]
Verified working — step 1
27x - x3 = 0 is the curve at y = 0.(b(i)(b)) 27x - x3 = 5x + 10.[3]
Verified working — step 1
The equation says curve = line, so draw y = 5x + 10 through (0, 10) and (2, 20).(b(ii)) Calculate an estimate of the
(b(ii)(a)) gradient of the curve at the point where x = 2,[2]
Verified working — step 1
At x = 2 the curve passes through (2, 46).(b(ii)(b)) area bounded by the curve, x-axis and x = 3.[2]
Verified working — step 1
Estimate the area between the curve and the x-axis from x = 0 to x = 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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