ECZ 2012 · O-Level Paper 2 · Question 5 — Sets
Question from ECZ 2012 · O-Level Paper 2 · Question 5
(a) A class of 41 girls takes History (H), Commerce (C) and Geography (G) as optional subjects. The Venn diagram below shows their choice distribution.
(a(i)) Calculate the value of x.[2]
Verified working — step 1
All the Venn regions add to 41.(a(ii)) Find
(a(ii)(a)) n(H ∪ G),[1]
Verified working — step 1
H holds 2x = 10, and G holds x + (x + 15) = 5 + 20 = 25.(a(ii)(b)) n(G' ∩ H').[1]
Verified working — step 1
G' intersect H' is everything OUTSIDE both G and H, which is the x + 1 region.(b) Express 3 25 % as a decimal.[1]
Verified working — step 1
First turn the mixed number into a decimal percentage.(c) The ratio of adults to children that bought tickets for a video show was 17:15 respectively. The total number of tickets sold for the video show was 4 704.
(c(i)) How many more adults than children attended the video show?[2]
Verified working — step 1
Total parts = 17 + 15 = 32, so one part = 470432 = 147.(c(ii)) If the tickets for adults were sold at K12 500 each and the tickets for children were sold at K8 500 each, calculate the total amount realised from the sell of tickets.[2]
Verified working — step 1
Adults = 17 × 147 = 2 499 and children = 15 × 147 = 2 205.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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