ECZ 2023 · O-Level Paper 2 · Question 6 — Vectors In Two Dimensions
Question from ECZ 2023 · O-Level Paper 2 · Question 6
(a) 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. Find the probability that the pens picked are
(a(i)) both blue,[2]
Verified working — step 1
9 pens: 5 blue and 4 black, drawn WITHOUT replacement.(a(ii)) of the same colour.[3]
Verified working — step 1
"Same colour" is both blue or both black:(b) The diagram shows a trapezium OABC in which OA = 2a, OC = 3c, AB = 3OC and D is the midpoint of AC. Express in terms of a and/or c
(b(i)) AC,[1]
Verified working — step 1
Head minus tail: AC = …(b(ii)) OD,[1]
Verified working — step 1
D is the midpoint of AC, so OD = OA + (12)AC.(b(iii)) OB,[1]
Verified working — step 1
AB = 3OC = …(b(iv)) BD.[2]
Verified working — step 1
BD = OD - OB = (a + (32)c) - (2a + 9c)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.
Have a different question?
Search it — if it is from a past paper or a school mock, chances are we have it worked out, or one that uses the same method.
Search any past-paper question