ECZ 2019 · O-Level Paper 2 · Question 6 — Vectors In Two Dimensions
Question from ECZ 2019 · O-Level Paper 2 · Question 6
(a) In the diagram below, OB = 4OA and AC = 5AX. M is the midpoint of BC, OA = a and BM = b.
(a(i)) Express in terms of a and/or b.
(a(i)(a)) AB,[1]
Verified working — step 1
OB = 4OA = …(a(i)(b)) AC,[1]
Verified working — step 1
M is the midpoint of BC, so BC = 2BM = …(a(i)(c)) OM.[1]
Verified working — step 1
OM = OB + BM = …(a(ii)) Show that OX = (25)(4a + b).[2]
Verified working — step 1
AC = 5AX, so AX = (15)AC = (15)(3a + 2b).(b) Find the equation of the normal to the curve y = 5x3 - 6x2 + 2x + 5 at the point (1, 2).[3]
Verified working — step 1
dydx = 15x2 - 12x + 2; at x = 1 the tangent gradient is 15 - 12 + 2 = 5.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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