ECZ 2017 · GCE Paper 2 · Question 9 — Graphs of Functions
Question from ECZ 2017 · GCE Paper 2 · Question 9
(a) The diagram below shows the graph of y = x3 + x2 - 5x + 3. Use the graph
(a(i)) to calculate an estimate of the gradient of the curve at the point (2, 5).[2]
Verified working — step 1
Draw the tangent touching the curve at (2, 5).(a(ii)) to solve the equations
(a(ii)(a)) x3 + x2 - 5x + 3 = 0,[2]
Verified working — step 1
The solutions are where the curve meets the x-axis (y = 0).(a(ii)(b)) x3 + x2 - 5x + 3 = 5x.[3]
Verified working — step 1
The solutions are where the curve meets the line y = 5x.(a(iii)) to calculate an estimate of the area bounded by the curve, x = 0, y = 0 and x = -2.[2]
Verified working — step 1
The region lies between the curve and the x-axis, from x = -2 to x = 0, where the curve is above the axis.(b) Find the equation of the tangent to the curve y = x2 - 3x - 4 at the point where x = 2.[3]
Verified working — step 1
dydx = 2x - 3, so at x = 2 the gradient is 2(2) - 3 = 1.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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