ECZ 2017 · O-Level Paper 2 · Question 1 — Matrices
Matrix M = 3-25x. A survey carried out at Kamulima Farming Block showed that 44 farmers planted maize, 32 planted sweet potatoes, 37 planted cassava, 14 planted both maize and sweet potatoes, 24 planted both sweet potatoes and cassava, 20 planted both maize and cassava, 9 planted all the three crops and 6 did not plant any of these crops.
(a(i)) Given that matrix M = 3-25x, find the value of x for which the determinant of M is 22.[2]
Verified working — step 1
det M = (3)(x) - (-2)(5) = 3x + 10(a(ii)) Hence find the inverse of M.[2]
Verified working — step 1
With x = 4, M = 3-254 and det M = …(b(i)) Illustrate the farming-block information on a Venn diagram.[2]
Verified working — step 1
Centre first: n(all three) = 9.(b(ii)(a)) How many farmers were at this farming block?[1]
Verified working — step 1
19 + 3 + 2 + 5 + 15 + 11 + 9 = …(b(ii)(b)) How many farmers planted maize only?[1]
Verified working — step 1
Maize only = 44 - (5 + 9 + 11) = …(b(ii)(c)) How many farmers planted 2 different crops?[1]
Verified working — step 1
Exactly two crops = 5 + 15 + 11 = …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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