ECZ 2021 · O-Level Paper 2 · Question 4 — Vectors In Two Dimensions
In the diagram, OA = 4a, OB = 3b, M is the midpoint of AB and OB = 3BD.
(a) Solve the equation 2x2 - 13x + 14 = 0, giving your answers correct to 2 decimal places.[5]
Verified working — step 1
a = 2, b = -13, c = 14(b(i)) In the diagram, OA = 4a, OB = 3b, M is the midpoint of AB and OB = 3BD. Express AB in terms of a andorb.[1]
Verified working — step 1
AB = OB - OA = …(b(ii)) Express OM in terms of a andorb.[1]
Verified working — step 1
M is the midpoint of AB, so OM = …(b(iii)) Express AD in terms of a andorb.[1]
Verified working — step 1
OB = 3BD gives BD = (13)OB = b, so OD = OB + BD = 3b + b = …(b(iv)) Express MD in terms of a andorb.[2]
Verified working — step 1
MD = OD - OM = …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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