ECZ 2026 · GCE Paper 2 · Question 5 — Vectors In Two Dimensions
Question from ECZ 2026 · GCE Paper 2 · Question 5
(a) In the diagram, OA = 2a, AB = 2b, M is the midpoint of OA and AN = 2NB. Express in terms of a and/or b
(a(i)) OB,[1]
Verified working — step 1
Go O to A, …(a(ii)) MB,[1]
Verified working — step 1
M is the midpoint of OA, so MA = (12)OA = …(a(iii)) ON,[1]
Verified working — step 1
AN = 2NB splits AB in the ratio 2 : 1, so AN = (23)AB = (23)(2b) = …(a(iv)) MN.[2]
Verified working — step 1
MA = a and AN = (43)b from the parts above.(b) Solve the equation x2 + 6x + 1 = 0, giving your answers correct to 2 decimal places.[5]
Verified working — step 1
a = 1, b = 6, c = 1 in the quadratic formula.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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