ECZ 2019 · GCE Paper 2 · Question 2 — Matrices

Question from ECZ 2019 · GCE Paper 2 · Question 2

(a) The determinant of matrix Q = 812x - 4x is 8. Find

(a(i)) the value of x,[2]

Verified working — step 1

Q = 812x - 4x with det Q = 8.

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

Verified working — step 1

With x = 10, Q = 812610 and det Q = 8.

(b) The Venn diagram below shows the optional subjects that all the Grade 10 learners at Kusambilila Secondary School took, in a particular year.

(b(i)) Given that 12 learners took Music, find the value of x.[2]

Verified working — step 1

Add the regions lying inside the Music circle.

(b(ii)) How many learners were in Grade 10 this particular year?[1]

Verified working — step 1

Substitute x = 5 into every region: History only 59, History-and-Music only 2, Music only 7, Music-and-Geography only 3, Geography only 43.

(b(iii)) Find the number of learners who took

(b(iii)(a)) one optional subject only,[1]

Verified working — step 1

One subject only = History only + Music only + Geography only.

(b(iii)(b)) two optional subjects only.[1]

Verified working — step 1

Two subjects only = (History and Music only) + (Music and Geography only).

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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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