ECZ 2022 · O-Level Paper 2 · Question 5 — Construction and Loci
Question from ECZ 2022 · O-Level Paper 2 · Question 5
(a) Construct a parallelogram ABCD in which AB = 10 cm, AD = BC = 6.5 cm, angle BAD = 110 degrees and angle ABC = 70 degrees.[1]
Verified working — step 1
Draw AB = 10 cm, construct 110 degrees at A and 70 degrees at B, mark AD = BC = …(b) Measure and write the length AC.[1]
Verified working — step 1
In triangle ABC, AB = 10, BC = 6.5 and angle ABC = 70 degrees.(c(i)) Within parallelogram ABCD, construct the locus of points which are 3 cm from AB.[1]
Verified working — step 1
Erect perpendiculars to AB, mark 3 cm along …(c(ii)) Within parallelogram ABCD, construct the locus of points which are 6 cm from C.[1]
Verified working — step 1
Set compasses to 6 cm with centre C and…(c(iii)) Within parallelogram ABCD, construct the locus of points which are equidistant from BC and CD.[2]
Verified working — step 1
Points equidistant from two intersecting lines lie on the…(d) A point Z, within parallelogram ABCD, is such that it is less than or equal to 3 cm from AB, less than or equal to 6 cm from C and nearer to CD than BC. Indicate clearly, by shading, the region in which Z must lie.[2]
Verified working — step 1
At most 3 cm from AB: between AB and the line from (c)(i).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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