ECZ 2023 · O-Level Paper 2 · Question 2 — Sets
Question from ECZ 2023 · O-Level Paper 2 · Question 2
(a) Given that matrix K = 89x1x, find the
(a(i)) value of x for which the determinant of K is 2,[2]
Verified working — step 1
det K = (8)(x) - (9x)(1) = 8x - 9x = -x(a(ii)) inverse of K.[2]
Verified working — step 1
With x = -2: K = 8-181-2 and det K = (8)(-2) - (-18)(1) = -16 + 18 = 2.(b) 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.
(b(i)) Illustrate this information in a Venn diagram.[2]
Verified working — step 1
Fill from the CENTRE outwards: all three = 21.(b(ii)) How many teachers taught
(b(ii)(a)) none of the subjects carried out in the survey,[1]
Verified working — step 1
211 teachers taught at least one s…(b(ii)(b)) Additional Mathematics or Computer Studies but not Mathematics,[1]
Verified working — step 1
"A or C but not M" keeps every r…(b(ii)(c)) two subjects only?[1]
Verified working — step 1
"Two subjects only" is th…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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