ECZ 2013 · O-Level Paper 2 · Question 5 — Vectors In Two Dimensions

Question from ECZ 2013 · O-Level Paper 2 · Question 5

(a) In triangle OPR below, the line OX produced, meets PR at Y. PQ and OY meet at X such that XQ = (13)PQ. OP = p, OQ = q and OQ = QR.

(a(i)) Express each of the following as simply as possible in terms of p and/or q

(a(i)(a)) PQ,[1]

Verified working — step 1

Route P to Q through O.

(a(i)(b)) OX.[2]

Verified working — step 1

XQ = (13)PQ, so PX is the other two thirds.

(a(ii)) Given that OY = hOX, show that PY = ((13)h - 1)p + (23)hq.[2]

Verified working — step 1

OY = h OX = h((13)p + (23)q) = (13)hp + (23)hq.

(b) Three liquids A, B and C are mixed in the ratio 1 : 2 : 3 to make a solution called elixir. Given that liquid B is 72 litres, find

(b(i)) the total number of litres for the solution elixir,[2]

Verified working — step 1

B is 2 parts and equals 72 litres, so 1 part = 36 litres.

(b(ii)) the difference in litres between liquid A and liquid B.[2]

Verified working — step 1

A = 1 part = 36 litres and B = 2 parts = 72 litres.

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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