ECZ 2022 · O-Level Paper 2 · Question 1 — Sets
Matrix Q = 2b - 14-3b-5 has determinant 15. The Venn diagram shows the number of learners who took at least one of the three subjects Biology, Chemistry and Physics.
(a(i)) Given that the determinant of matrix Q = 2b - 14-3b-5 is 15, find the value of b.[2]
Verified working — step 1
det Q = (2b - 1)(-5) - (4)(-3b)(a(ii)) Find the inverse of matrix Q.[2]
Verified working — step 1
With b = 5, Q = 94-15-5 and det Q = …(b(i)) Given that the total number of learners was 170, calculate the value of x.[2]
Verified working — step 1
Adding all seven regions of the Venn diagram:(b(ii)(a)) How many learners took Biology and Physics but not Chemistry?[1]
Verified working — step 1
That is the Biology-Physics region outside…(b(ii)(b)) How many learners took two subjects only?[1]
Verified working — step 1
The three "exactly two" regions are 5, 15 and x = …(b(ii)(c)) How many learners took one subject only?[1]
Verified working — step 1
The three "only" regions are x = 25, 10 and x - 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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