ECZ 2010 · O-Level Paper 2 · Question 6 — Vectors In Two Dimensions
Question from ECZ 2010 · O-Level Paper 2 · Question 6
(a) The diagram below shows a trapezium in which OA = a, OC = c and CB is parallel to OA. CB is twice OA, the points D and E are midpoints of AB and CB respectively. Express in terms of a and/or c the following vectors
(a(i)) CA,[1]
Verified working — step 1
Route C to A through O.(a(ii)) AB,[1]
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Route A to B through O and C.(a(iii)) EB,[2]
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E is the midpoint of CB, and CB = 2a.(a(iv)) OD,[2]
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D is the midpoint of AB, so OD = OA + (12)AB.(a(v)) BO.[1]
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OB = OA + AB = a + (a + c) = 2a + c.(b) At one college, a group of 25 students were asked which Cell Phone service providers they subscribed to. The results are shown in the Venn diagram below.
(b(i)) Calculate the value of x.[1]
Verified working — step 1
All the Venn regions add to 25.(b(ii)) Given that G = {Glo}, R = {Rodgers} and D = {Du}, find,
(b(ii)(a)) n(G ∩ R)[1]
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n(G intersect R) is the overlap of the Glo and Rodgers circles.(b(ii)(b)) n(D ∪ G').[2]
Verified working — step 1
G holds 10 + 3 = 13 students, so G' holds 25 - 13 = 12.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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