ECZ 2012 · O-Level Paper 2 · Question 6 — Vectors In Two Dimensions
Question from ECZ 2012 · O-Level Paper 2 · Question 6
(a) In the diagram below, OABC is a parallelogram in which OA = 2a and OC = 2b. P is a point on OA such that OP = (14)OA and Q is a point on CB such that CQ : QB = 3 : 1.
(a(i)) Express in terms of a and/or b
(a(i)(a)) OB,[1]
Verified working — step 1
OABC is a parallelogram, so AB = OC = 2b.(a(i)(b)) OP,[1]
Verified working — step 1
OP = (14)OA, and OA = 2a.(a(i)(c)) QC.[1]
Verified working — step 1
CB is parallel and equal to OA, so CB = 2a.(a(ii)) Given that OX = hOB, express OX in terms of a, b and h.[1]
Verified working — step 1
OX = h OB, and OB = 2a + 2b.(b) Factorise completely 2xy + x - 10y - 5.[2]
Verified working — step 1
Group the terms in pairs.(c) The width of a rectangle is 3 m. If its diagonal is 8.5 m long, calculate the length giving your answer correct to 2 decimal places.[2]
Verified working — step 1
The diagonal is the hypotenuse of a right-angled triangle.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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