ECZ 2019 · GCE Paper 2 · Question 3 — Vectors In Two Dimensions
OA = a, OB = b and ACCB= 12(C divides BA with AC:CB = 1:2). M is the midpoint of OC.
(a) Express 6n - 3- 5n - 2as a single fraction in its simplest form.[3]
Verified working — step 1
Common denominator = (n-3)(n-2).(b(i)(a)) Express AB in terms of a andorb.[1]
Verified working — step 1
AB = AO + OB = -a + b = …(b(i)(b)) Express AC in terms of a andorb.[1]
Verified working — step 1
Since AC:CB = 1:2, C divides AB so that AC = …(b(i)(c)) Express OC in terms of a andorb.[1]
Verified working — step 1
OC = OA + AC = a + (13)(b - a) = a - (13)a + (13)b = …(b(ii)) Given that M is the midpoint of OC, show that AM = (16)(b - 4a).[2]
Verified working — step 1
M is the midpoint of OC, so OM = (12)OC = (12)[(23)a + (13)b] = (13)a + (16)b.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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