ECZ 2020 · O-Level Paper 2 · Question 2 — Vectors In Two Dimensions
Question from ECZ 2020 · O-Level Paper 2 · Question 2
(a) Of the 115 students who attended an end of year party, 74 took fanta, 93 took sprite, 87 took coke, 61 took fanta and sprite, 71 took sprite and coke, 60 took fanta and coke and 50 took all the three drinks.
(a(i)) Illustrate this information on a Venn diagram.[2]
Verified working — step 1
Fill from the CENTRE outwards: all three = 50.(a(ii)) How many students took
(a(ii)(a)) none of the drinks,[1]
Verified working — step 1
112 students took at least one d…(a(ii)(b)) fanta and sprite but not coke,[1]
Verified working — step 1
"Fanta and sprite but not coke…(a(ii)(c)) at least two different drinks?[1]
Verified working — step 1
"At least two drinks" is the three…(b) In the diagram below, AVC is a straight line, AB = 8p, AC = 4p + 9q, BV = -6p + kq and AM = MB.
(b(i)) Express in terms of p, q and/or k
(b(i)(a)) AM,[1]
Verified working — step 1
M is the midpoint of AB (AM = MB), so AM = …(b(i)(b)) AV.[1]
Verified working — step 1
AV = AB + BV = …(b(ii)) Given that AV = hAC, by forming an equation involving p, q, h and k or otherwise, find the numerical values of h and k.[3]
Verified working — step 1
AV = hAC gives 2p + kq = h(4p + 9q) = 4hp + 9hq.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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