ECZ 2021 · GCE Paper 2 · Question 5 — Introduction To Calculus
Question from ECZ 2021 · GCE Paper 2 · Question 5
(a) Find the equation of a tangent to the curve y = 5x3 - 7x2 + 3x + 2 at the point (1, 3).[3]
Verified working — step 1
dydx = 15x2 - 14x + 3; at x = 1 the tangent gradient is 15 - 14 + 3 = 4.(b) In the diagram below OA = a, OB = b and X is the midpoint of AB.
(b(i)) Express in terms of a and/or b
(b(i)(a)) BA,[1]
Verified working — step 1
Head minus tail: BA = …(b(i)(b)) AX,[1]
Verified working — step 1
X is the midpoint of AB, so AX = (12)AB = (12)(-BA) = …(b(i)(c)) OX.[2]
Verified working — step 1
OX = OA + AX = a + (12)(b - a)(b(ii)) Given that OC = 3a, express BC in terms of a and b.[1]
Verified working — step 1
BC = OC - OB = …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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