ECZ 2025 · GCE Paper 2 · Question 4 — Sets
At Kamulima Farming Community, 33 farmers planted sorghum (S), 25 planted groundnuts (G), 38 planted maize (M), 15 planted both sorghum and groundnuts, 14 planted both sorghum and maize, 13 planted both groundnuts and maize and 6 planted all three types of crops.
(a) Solve the equation 2x2 = 7 - 10x, giving your answers correct to 2 decimal places.[5]
Verified working — step 1
Rearrange: 2x2 = 7 - 10x → 2x2 + 10x - 7 = 0(b(i)) Illustrate this information on a Venn diagram.[2]
Verified working — step 1
Let the three circles represent S, G, M inside a rectangle (universal set).(b(ii)(a)) How many farmers were in this community altogether?[1]
Verified working — step 1
Total farmers = sum of all regions = 10+9+3+8+6+7+17 = …(b(ii)(b)) How many farmers planted one type of crop only?[1]
Verified working — step 1
Farmers planting one crop only = S only + G only + M only = 10 + 3 + 17 = …(b(ii)(c)) How many farmers planted two different types of crops only?[1]
Verified working — step 1
Farmers planting exactly two crops = (S∩G only) + (S∩M only) + (G∩M only) = 9 + 8 + 7 = …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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