ECZ 2021 · GCE Paper 2 · Question 4 — Sets

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

Use the given data to fill each region of a three-circle Venn diagram (A, B, C) inside a rectangle of 60 fans.

(a(ii)(a)) Find n(B)'.[1]

Verified working — step 1

n(B) = 28, total = …

(a(ii)(b)) Find n(A ∩ B)'.[1]

Verified working — step 1

n(A∩B) = A∩B only + all three = 7 + 10 = …

(a(ii)(c)) Find n(A ∪ B)'.[1]

Verified working — step 1

n(A∪B) = n(A) + n(B) - n(A∩B) = 37 + 28 - 17 = …

(b(i)) Given that the determinant of the matrix A = 2x-114-2 is -10, find the value of x.[2]

Verified working — step 1

For A = [ (2x-1, 1), (4, -2) ], det(A) = (2x-1)(-2) - (1)(4)

(b(ii)) Find the inverse of matrix A.[2]

Verified working — step 1

With x = 2, A = [ (3, 1), (4, -2) ], 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.

Have a different question?

Search it — if it is from a past paper or a school mock, chances are we have it worked out, or one that uses the same method.