ECZ 2017 · GCE Paper 2 · Question 9 — Graphs of Functions
The graph of y = x3 + x2 - 5x + 3 is given.
(a(i)) Use the graph to calculate an estimate of the gradient of the curve at the point (2, 5).[2]
Verified working — step 1
At the point (2,5), draw a tangent line to the curve touching it only at that point.(a(ii)(a)) Use the graph to solve x3 + x2 - 5x + 3 = 0.[2]
Verified working — step 1
x3+x2-5x+3 = 0 is solved by reading where the curve y = x3+x2-5x+3 crosses the x-axis (y=0).(a(ii)(b)) Use the graph to solve x3 + x2 - 5x + 3 = 5x.[3]
Verified working — step 1
Rearrange: x3+x2-5x+3 = 5x means we need points where the curve y = x3+x2-5x+3 meets the line y = 5x.(a(iii)) Use the graph to calculate an estimate of the area bounded by the curve, x = 0, y = 0 and x = -2.[2]
Verified working — step 1
The area between the curve, x=0, y=0 and x=-2 is found by counting squares under the curve from x=-2 to x=0 (curve is above the x-axis here).(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
y = x2-3x-4The 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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