ECZ 2023 · GCE Paper 2 · Question 12 — Graphs of Functions
The diagram shows the graph of y = x3 - x2 - 5x - 3 (printed on the paper).
(a) Evaluate the integral of (-1 - 3x2) dx from x = -1 to x = 1.[3]
Verified working — step 1
Integral of (-1 - 3x2) dx = -x - x3 + C(b(i)(a)) Use the graph to find the solution of the equation x3 - x2 - 5x - 3 = 0.[2]
Verified working — step 1
On the graph, the curve crosses the x-axis (y=0) at the points where x3 - x2 - 5x - 3 = 0.(b(i)(b)) Use the graph to find the solution of the equation x3 - x2 - 5x = x - 3.[3]
Verified working — step 1
Rearrange x3 - x2 - 5x = x - 3 by subtracting 3 from both sides:(b(ii)(a)) Find the gradient of the curve at the point (-2, -5).[2]
Verified working — step 1
Draw a tangent to the curve at the point (-2, -5) (check: y(-2) = -8-4+10-3 = -5, correct point on curve).(b(ii)(b)) Find the area bounded by the curve, x = 1, y = 0 and x = 3.[2]
Verified working — step 1
Area = ∫ from 1 to 3 of (x3 - x2 - 5x - 3) dxThe 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.
Have a different question?
Search it — if it is from a past paper or a school mock, chances are we have it worked out, or one that uses the same method.
Search any past-paper question