ECZ 2021 · GCE Paper 2 · Question 4 — Sets
Question from ECZ 2021 · GCE Paper 2 · Question 4
(a) In a group of 60 football fans, 37 support Team A, 28 support Team B and 29 support Team C. 2 support Team A and Team C only, 5 support Team B and Team C only, 7 support Team A and Team B only, 18 support Team A only and 10 support all the three teams.
(a(i)) Illustrate this information in a Venn diagram.[2]
Verified working — step 1
Fill the given regions, then find the two unknowns.(a(ii)) Find
(a(ii)(a)) n(B)',[1]
Verified working — step 1
n(B)' is everyone outside B, …(a(ii)(b)) n(A ∩ B)',[1]
Verified working — step 1
n(A∩B) = A∩B only + all three = 7 + 10 = …(a(ii)(c)) n(A ∪ B)'.[1]
Verified working — step 1
n(A∪B) = n(A) + n(B) - n(A∩B) = 37 + 28 - 17 = …(b) Given that the determinant of the matrix A = 2x - 114-2 is -10, find
(b(i)) the value of x,[2]
Verified working — step 1
det A = (2x - 1)(-2) - (1)(4) = -4x + 2 - 4 = -4x - 2(b(ii)) the inverse of matrix A.[2]
Verified working — step 1
With x = 2: A = 314-2 and det A = -10.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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