ECZ 2022 · O-Level Paper 2 · Question 1 — Sets

Question from ECZ 2022 · O-Level Paper 2 · Question 1

(a) Given that the determinant of matrix Q = 2b - 14-3b-5 is 15, find the

(a(i)) value of b,[2]

Verified working — step 1

det Q = (2b - 1)(-5) - (4)(-3b)

(a(ii)) inverse of matrix Q.[2]

Verified working — step 1

With b = 5: Q = 94-15-5 and det Q = 15.

(b) The Venn diagram shows the number of learners who took at least one of the three subjects Biology, Chemistry and Physics.

(b(i)) Given that the total number of learners was 170, calculate the value of x.[2]

Verified working — step 1

Add all seven regions of the Venn diagram and set equal to 170:

(b(ii)) How many learners took

(b(ii)(a)) Biology and Physics but not Chemistry,[1]

Verified working — step 1

"Biology and Physics but not Chemistry" is the …

(b(ii)(b)) two subjects only,[1]

Verified working — step 1

"Two subjects only" is th…

(b(ii)(c)) one subject only?[1]

Verified working — step 1

"One subject only" is the t…

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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