ECZ 2019 · O-Level Paper 2 · Question 3 — Sets
The Venn diagram shows the number of elements in sets A, B and C: A only 7, A and B 8, B only x - 4, B and C 5, C only 2y, and 10 outside all three sets.
(a) Solve the equation p2 - p = 4, giving your answers correct to 2 decimal places.[5]
Verified working — step 1
p2 - p - 4 = 0, so a = 1, b = -1, c = -4.(b(i)) From the Venn diagram, find x, such that n(B) = n(B union C)'.[2]
Verified working — step 1
n(B) = 8 + (x - 4) + 5 = x + 9(b(ii)) Find y, such that n(C) = n(A).[1]
Verified working — step 1
n(C) = 5 + 2y and n(A) = 7 + 8 = 15.(b(iii)) Find n(E).[1]
Verified working — step 1
With x = 8 and y = …(b(iv)) Find n(B').[1]
Verified working — step 1
n(B) = 8 + 4 + 5 = …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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