ECZ 2026 · GCE Paper 2 · Question 2 — Sets
Question from ECZ 2026 · GCE Paper 2 · Question 2
(a) In a group of 40 girls, 25 like mangoes, 20 like bananas, 15 like guavas, 9 like mangoes and bananas, 10 like mangoes and guavas, 7 like bananas and guavas and 4 like all the three types of fruits.
(a(i)) Illustrate this information in a Venn diagram.[2]
Verified working — step 1
Fill the Venn diagram from the CENTRE outwards.(a(ii)) How many girls
(a(ii)(a)) like guavas only,[1]
Verified working — step 1
"Guavas only" is the pa…(a(ii)(b)) like two types of fruits,[1]
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Exactly two fruits = …(a(ii)(c)) do not like bananas?[1]
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Everyone outside the banana circle:(b) Given that the determinant of matrix M = x - 3-1x + 23 is 5, find the
(b(i)) value of x,[2]
Verified working — step 1
The determinant of abcd is ad - bc.(b(ii)) inverse of matrix M.[2]
Verified working — step 1
With x = 3: M = 0-153, and det M = 5 as given.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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