ECZ 2014 · O-Level Paper 2 · Question 6 — Vectors In Two Dimensions
Question from ECZ 2014 · O-Level Paper 2 · Question 6
(a) In the diagram below, OP = 2p and OQ = 2q. X is a point on PQ such that PXPQ = 23.
(a(i)) Express 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)) QX.[1]
Verified working — step 1
PX:PQ = 2:3, so XQ is the remaining third of PQ.(a(ii)) Given also that OY = hOX, express OY in terms of p, q and h.[2]
Verified working — step 1
OX = OP + PX = 2p + (23)(2q - 2p).(b) The diagonals of a rhombus are 20 cm and 16 cm long. Calculate the length of the side of the rhombus, giving your answer correct to 2 decimal places.[2]
Verified working — step 1
The diagonals of a rhombus bisect each other at right angles.(c) Factorise completely 2xy + 8x - 3y - 12.[2]
Verified working — step 1
Group the terms in pairs.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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