ECZ 2023 · GCE Paper 2 · Question 1 — Sets

Learners in a Grade 10 class were asked the types of drinks they liked. Venn diagram: Fanta only = 17, Fanta∩Coke only = x + 2, Coke only = 5, Fanta∩Sprite only = x, all three = x, Coke∩Sprite only = x - 2, Sprite only = 3, outside = 7.

(a) Simplify (13a³ / 28a² b²) ÷ (65a⁴ b56a² b⁴).[2]

Verified working — step 1

Change division to multiplication by the reciprocal:

(b(i)) Given that 40 learners liked Fanta, find the value of x.[2]

Verified working — step 1

Total who like Fanta = Fanta only + (Fanta∩Coke only) + (Fanta∩Sprite only) + (all three)

(b(ii)) Find the total number of learners in the class.[1]

Verified working — step 1

Substitute x = 7 into all regions:

(b(iii)(a)) How many learners did not like Fanta?[1]

Verified working — step 1

Learners who like Fanta = 40 (given)

(b(iii)(b)) How many learners liked two types of drinks only?[1]

Verified working — step 1

Learners liking exactly two drinks = (Fanta∩Coke only) + (Fanta∩Sprite only) + (Coke∩Sprite only)

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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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