ECZ 2023 · O-Level Paper 2 · Question 4 — Construction and Loci
Question from ECZ 2023 · O-Level Paper 2 · Question 4
(a) Construct a trapezium ABCD in which AB = 10 cm, BC = 8 cm, AD = 7 cm, angle ABC = 60 degrees and angle BAD is 90 degrees.[1]
Verified working — step 1
Draw AB = 10 cm, construct 90 degrees at A and mark AD = 7 cm, construct 60 degrees at B and mark BC = …(b) Measure and write the length of CD.[1]
Verified working — step 1
Taking A(0, 0) and B(10, 0): D = (0, 7) and C = B + 8(cos 120, sin 120) = …(c(i)) Within the trapezium ABCD, draw the locus of points which are 2 cm from CD.[1]
Verified working — step 1
Erect perpendiculars to CD, mark 2 cm along …(c(ii)) Within the trapezium ABCD, draw the locus of points which are 9 cm from B.[1]
Verified working — step 1
Set compasses to 9 cm with centre B a…(c(iii)) Within the trapezium ABCD, draw the locus of points which are equidistant from AB and AD.[2]
Verified working — step 1
Points equidistant from two intersecting lines lie on the…(d) A point E, within the trapezium ABCD, is such that it is greater than or equal to 2 cm from CD, less than or equal to 9 cm from B and nearer to AD than AB. Indicate, by shading, the region in which E must lie.[2]
Verified working — step 1
At least 2 cm from CD: away from CD beyond the parallel 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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