ECZ 2023 · O-Level Paper 2 · Question 6 — Vectors In Two Dimensions
A box contains 4 black and 5 blue identical pens. Two pens are picked from the box at random one after the other without replacement. The diagram shows a trapezium OABC in which OA = 2a, OC = 3c, AB = 3OC and D is the midpoint of AC.
(a(i)) A box contains 4 black and 5 blue identical pens. Two pens are picked at random one after the other without replacement. Find the probability that the pens picked are both blue.[2]
Verified working — step 1
There are 9 pens at the fir…(a(ii)) Find the probability that the pens picked are of the same colour.[3]
Verified working — step 1
P(both black) = (49)(38) = 1272(b(i)) The diagram shows a trapezium OABC in which OA = 2a, OC = 3c, AB = 3OC and D is the midpoint of AC. Express AC in terms of a andorc.[1]
Verified working — step 1
AC = OC - OA = …(b(ii)) Express OD in terms of a andorc.[1]
Verified working — step 1
D is the midpoint of AC, so OD = …(b(iii)) Express OB in terms of a andorc.[1]
Verified working — step 1
AB = 3OC = …(b(iv)) Express BD in terms of a andorc.[2]
Verified working — step 1
BD = OD - OB = …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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