ECZ 2017 · O-Level Paper 2 · Question 2 — Vectors In Two Dimensions
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. In the diagram, OP = 2p, OQ = 4q and PX : XQ = 1 : 2.
(a(i)) A box of chalk contains 5 white, 4 blue and 3 yellow pieces. A piece is selected at random and not replaced, then a second piece is selected. Draw a tree diagram to show all the possible outcomes.[2]
Verified working — step 1
There are 12 pieces at the first draw and only 11 at…(a(ii)) Find the probability of selecting pieces of chalk of the same colour.[3]
Verified working — step 1
P(same) = P(WW) + P(BB) + P(YY)(b(i)(a)) In the diagram, OP = 2p, OQ = 4q and PX : XQ = 1 : 2. Express PQ in terms of p andorq.[1]
Verified working — step 1
PQ = OQ - OP = …(b(i)(b)) Express PX in terms of p andorq.[1]
Verified working — step 1
Since PX : XQ = 1 : 2, PX = …(b(i)(c)) Express OX in terms of p andorq.[1]
Verified working — step 1
OX = OP + PX = 2p + (43)q - (23)p(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)qThe 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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