ECZ 2023 · O-Level Paper 2 · Question 2 — Sets
Matrix K = 89x1x. A survey carried out in a certain district showed that out of 215 teachers, 170 taught Mathematics, 100 taught Additional Mathematics, 41 taught Computer Studies, 65 taught Mathematics and Additional Mathematics, 30 taught Additional Mathematics and Computer Studies, 26 taught Computer Studies and Mathematics and 21 taught all the three subjects.
(a(i)) Given that matrix K = 89x1x, find the value of x for which the determinant of K is 2.[2]
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det K = (8)(x) - (9x)(1) = 8x - 9x = -x(a(ii)) Find the inverse of K.[2]
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With x = -2, K = 8-181-2 and det K = -16 + 18 = …(b(i)) Illustrate the survey information in a Venn diagram.[2]
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Centre first: n(all three) = 21.(b(ii)(a)) How many teachers taught none of the subjects carried out in the survey?[1]
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215 teachers altogether and 211 taught at least one subject, so 215 - 211 = …(b(ii)(b)) How many teachers taught Additional Mathematics or Computer Studies but not Mathematics?[1]
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Take the regions of A a…(b(ii)(c)) How many teachers taught two subjects only?[1]
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Exactly two subjects = 44 + 9 + 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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