ECZ 2021 · O-Level Paper 2 · Question 2 — Sets

At a certain secondary school, all the learners in Grade twelve take at least one of the following optional subjects: French (F), Home Economics (HE) and Geography (G). 20 learners take French only, 25 learners take Home Economics only and 22 learners take Geography only. Furthermore, 9 learners take French and Geography, 12 learners take French and Home Economics, 15 learners take Geography and Home Economics and 4 learners take all the three subjects.

(a) Evaluate the integral from -1 to 1 of (1 - 4x + 3x2) dx.[3]

Verified working — step 1

Integral of (1 - 4x + 3x2) dx = x - 2x2 + x3.

(b(i)) Illustrate the information about the optional subjects in a Venn diagram.[2]

Verified working — step 1

Centre first: n(all three) = 4.

(b(ii)(a)) How many Grade twelve learners are at this school?[1]

Verified working — step 1

Every learner takes at least one …

(b(ii)(b)) How many take Home Economics and Geography but not French?[1]

Verified working — step 1

Geography and Home Economics = 15, of whom 4 also take French, so 15 - 4 = …

(b(ii)(c)) How many take two optional subjects only?[1]

Verified working — step 1

Exactly two subjects = 5 + 8 + 11 = …

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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