ECZ 2012 · O-Level Paper 2 · Question 11 — Linear Programming
Question from ECZ 2012 · O-Level Paper 2 · Question 11
(a) The graph below shows three inequalities that satisfy Kashita's intentions to purchase Science and Mathematics text books.
(a(i)) Given that x represents the number of Science text books and y represents Mathematics text books, write the three inequalities that represent the unshaded region R.[4]
Verified working — step 1
The vertical line is x = 5, shaded to its left: x ≥ 5.(a(ii)) Given that a Science textbook costs K25 000 and a Mathematics textbook K10 000, find the largest number of Science and Mathematics textbooks that can be bought. Hence calculate the total cost of the textbooks.[3]
Verified working — step 1
The question asks for the largest NUMBER of books, so maximise x + y.(b) A box has 7 identical sweets. 3 of these are green and the rest are red. Kamwanga picks one sweet at random and eats it. After sometime, he picks another one and eats it.
(b(i)) Construct a tree diagram to illustrate the outcomes of the two sweets taken.[3]
Verified working — step 1
7 sweets at the first pick, and only 6 at the second since none is replaced.(b(ii)) Calculate the probability that the first sweet was red and the second was green.[2]
Verified working — step 1
This asks for one specific ORDER: red first, then green.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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