ECZ 2016 · O-Level Paper 2 · Question 3 — Vectors In Two Dimensions
OAB is a triangle in which OA = 3a and OB = 6b. OC : CA = 2 : 3 and AD : DB = 1 : 2. OD meets CB at E.
(a) The program below is given in the form of a pseudocode. Start Enter radius If radius < 0 Then display "error message" and re-enter positive radius Else enter height If height < 0 Then display "error message" and re-enter positive height Else Volume = (13) * pi * square radius * height End if Display volume Stop Draw the corresponding flowchart for the information given above.[5]
Verified working — step 1
Terminals (StartStop) are rounded; inputs and outputs are parallelograms; …(b(i)(a)) In the diagram, OAB is a triangle in which OA = 3a and OB = 6b, with OC : CA = 2 : 3 and AD : DB = 1 : 2, and OD meets CB at E. Express AB in terms of a andorb.[1]
Verified working — step 1
AB = OB - OA = …(b(i)(b)) Express OD in terms of a andorb.[1]
Verified working — step 1
Since AD : DB = 1 : 2, AD = …(b(i)(c)) Express BC in terms of a andorb.[2]
Verified working — step 1
Since OC : CA = 2 : 3, OC = (25)OA = …(b(ii)) Given that BE = hBC, express BE in terms of h, a and b.[1]
Verified working — step 1
BE = h BC = h((65)a - 6b) = …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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