ECZ 2019 · GCE Paper 2 · Question 2 — Matrices
The determinant of matrix Q = 812x-4x is 8. Venn diagram of optional subjects at Kusambilila Secondary: History only = 59, History∩Music only = x - 3, Music only = x + 2, Music∩Geography only = x - 2, Geography only = 43 (three circles in a row; no History∩Geography region, no triple region).
(a(i)) Find the value of x.[2]
Verified working — step 1
det(Q) = 8x - 12(x-4) = 8(a(ii)) Find the inverse of Q.[2]
Verified working — step 1
With x = 10, Q = 812610, det(Q) = …(b(i)) Given that 12 learners took Music, find the value of x.[2]
Verified working — step 1
Music = Music only + (H∩M only) + (M∩G only)(b(ii)) How many learners were in Grade 10 this particular year?[1]
Verified working — step 1
Using x = 5: History only = 59, H∩M only = x-3 = 2, Music only = x+2 = 7, M∩G only = x-2 = 3, Geography only = …(b(iii)(a)) Find the number of learners who took one optional subject only.[1]
Verified working — step 1
One subject only = …(b(iii)(b)) Find the number of learners who took two optional subjects only.[1]
Verified working — step 1
Two subjects only = …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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