ECZ 2017 · O-Level Paper 2 · Question 2 — Vectors In Two Dimensions
Question from ECZ 2017 · O-Level Paper 2 · Question 2
(a) A box of chalk contains 5 white, 4 blue and 3 yellow pieces of chalk. A piece of chalk is selected at random from the box and not replaced. A second piece of chalk is then selected.
(a(i)) Draw a tree diagram to show all the possible outcomes.[2]
Verified working — step 1
12 pieces at the first draw, and only 11 at the second because the first is not replaced.(a(ii)) Find the probability of selecting pieces of chalk of the same colour.[3]
Verified working — step 1
Same colour = both white, both blue, or both yellow.(b) In the diagram below, OP = 2p, OQ = 4q and PX : XQ = 1 : 2.
(b(i)) Express in terms of p and/or q
(b(i)(a)) PQ,[1]
Verified working — step 1
Route P to Q through O.(b(i)(b)) PX,[1]
Verified working — step 1
PX:XQ = 1:2, so PX is one third of PQ.(b(i)(c)) OX.[1]
Verified working — step 1
OX = OP + PX.(b(ii)) Given that OC = hOX, show that CQ = 4(1 - h3)q - (4h3)p.[2]
Verified working — step 1
OC = h OX = h((43)p + (43)q) = (4h3)p + (4h3)q.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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