ECZ 2024 · GCE Paper 2 · Question 3 — Vectors In Two Dimensions
In the diagram, OA = a, OB = b and AX : AB = 2 : 3, with Y on OX produced.
(a) Express 2x + 2- 53x - 1as a single fraction in its simplest form.[3]
Verified working — step 1
Common denominator = (x+2)(3x-1).(b(i)(a)) Express AB in terms of a andorb.[1]
Verified working — step 1
AB = AO + OB = -a + b = …(b(i)(b)) Express XB in terms of a andorb.[1]
Verified working — step 1
Since AX:AB = 2:3, X divides AB so that AX = (23)AB, hence XB = (13)AB = …(b(i)(c)) Express XO in terms of a andorb.[1]
Verified working — step 1
XO = XA + AO = -(23)(b-a) - a(b(ii)) Given also that OY = 3OX, show that BY = a + b.[2]
Verified working — step 1
OX = -XO = (13)a + (23)bThe 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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