ECZ 2011 · O-Level Paper 2 · Question 3 — Circle Theorems
Question from ECZ 2011 · O-Level Paper 2 · Question 3
(a) In the diagram below, the diagonals of the cyclic quadrilateral ABCD meet at E, O is the centre of the circle. Given that angle DAB = 75° and angle DAC = 30°, calculate
(a(i)) angle BAC,[1]
Verified working — step 1
AC lies between AD and AB, so subtract the two given angles at A.(a(ii)) angle BCD,[1]
Verified working — step 1
ABCD is a cyclic quadrilateral.(a(iii)) angle OBD,[2]
Verified working — step 1
Angle DAB = 75 is at the circumference on arc BCD, so the central angle BOD = 150.(a(iv)) angle OBC.[1]
Verified working — step 1
Angle BAC = 45 is at the circumference on arc BC, so the central angle BOC = 90.(b) The cost of baking a birthday cake is K48 000.
(b(i)) Ireen has an order for 15 such cakes. How much did she spend on baking the cakes?[1]
Verified working — step 1
Multiply the cost of one cake by the number of cakes.(b(ii)) Given that each cake was sold at K57 600, find the percentage profit.[2]
Verified working — step 1
Profit per cake = selling price - cost = 57 600 - 48 000 = K9 600.(c) Solve the inequation 7 - 2t < 9.[2]
Verified working — step 1
7 - 2t < 9The 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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