ECZ 2017 · GCE Paper 2 · Question 6 — Vectors In Two Dimensions

OABC is a parallelogram in which OA = a and AB = 2b. OB and AC intersect at D. E is the midpoint of CD.

(a(i)) Express OB in terms of a andorb.[1]

Verified working — step 1

In parallelogram OABC, OB is a diagonal from O to B.

(a(ii)) Express OE in terms of a andorb.[2]

Verified working — step 1

Since OABC is a parallelogram, OC = AB = 2b.

(a(iii)) Express CD in terms of a andorb.[2]

Verified working — step 1

D is the midpoint of OB (diagonals of a parallelogram bisect each other):

(b) Write a pseudo code corresponding to the flow chart (input a, r; if |r| < 1 compute S∞ = a1 - rand display, else stop).[5]

Verified working — step 1

Pseudocode:

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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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