ECZ 2016 · GCE Paper 2 · Question 5 — Sets
Venn diagram of a Mayuka clinic survey: W = body weakness, H = headache, F = fever (regions 18, 13, 14, 6, 5).
(a(i)(a)) Number who complained of body weakness only.[1]
Verified working — step 1
Body weakness only = region inside W but outside H and F = …(a(i)(b)) Number who complained of body weakness and fever only.[1]
Verified working — step 1
Body weakness and fever only (W∩F but not H) = …(a(i)(c)) Number who complained of headache.[1]
Verified working — step 1
Headache (set H) = the two H regions = 14 + 6 = …(a(ii)) Calculate the percentage of those who complained of all three ailments.[2]
Verified working — step 1
Total surveyed = 18+13+14+6+5 = 56(b) Solve the inequality (32)n + 5 < 14.[2]
Verified working — step 1
(32)n + 5 < 14(c) Given that 4% of bricks get damaged, how many bricks should a builder order if 4 800 are needed?[2]
Verified working — step 1
Let total bricks ordered = x. Undamaged = 96% of x = 4800.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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