ECZ 2016 · GCE Paper 2 · Question 6 — Vectors In Two Dimensions
Question from ECZ 2016 · GCE Paper 2 · Question 6
(a) In the diagram below, OA = a and OB = b. C on AB is such that AC:CB = 2 : 1 and B on OD is such that OB : OD = 1 : 2. Express as simply as possible in terms of a and/or b.
(a(i)) AB,[1]
Verified working — step 1
Route A to B through O.(a(ii)) AD,[1]
Verified working — step 1
OB:OD = 1:2, so OD = 2OB = 2b.(a(iii)) CD.[2]
Verified working — step 1
AC:CB = 2:1, so AC = (23)AB = (23)(b - a).(b) Tickets for a variety show held at Movi Secondary School were sold at K50.00 each. Half of the money collected at the show was donated to charity. If the charity received K2 500.00, how many tickets were sold?[3]
Verified working — step 1
Let n be the number of tickets; total collected = 50n.(c) 72 ladies were invited to a kitchen party. The ratio of those who took Fanta to those who did not was 13 : 5 respectively. Given that 18 others came in uninvited and 8 of these took Fanta, find the new ratio of those who took Fanta to those who did not.[3]
Verified working — step 1
13 + 5 = 18 parts share 72 ladies, so one part = 4.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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