ECZ 2013 · O-Level Paper 2 · Question 7 — Graphs of Functions
Question from ECZ 2013 · O-Level Paper 2 · Question 7
(a) The diagram shows the graph of y = 2 + x - x2.
(a(i)) Use the graph to find the solutions of the equations
(a(i)(a)) 0 = 2 + x - x2,[2]
Verified working — step 1
Set y = 0 and read where the curve crosses the x-axis.(a(i)(b)) x - x2 = -1.[2]
Verified working — step 1
Add 2 to both sides so the left matches the drawn curve.(a(ii)) Calculate an estimate of
(a(ii)(a)) the gradient of the curve at the point (1, 2),[2]
Verified working — step 1
Draw the tangent touching the curve at (1, 2).(a(ii)(b)) the area bounded by the curve, y = 1, x = 0 and x = 1.[3]
Verified working — step 1
The gap between curve and line is (2 + x - x2) - 1 = 1 + x - x2.(b) Solve 3(x5 - 4) = 6 - 3x.[3]
Verified working — step 1
Expand: 3x5 - 12 = 6 - 3x.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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