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° and angle BAD is 90°.[1]
Verified working — step 1
Draw AB = 10 cm.(b) Measure and write the length of CD.[1]
Verified working — step 1
Measure CD with a ruler on the finished construction: CD = …(c) Within the trapezium ABCD, draw the locus of points which are
(c(i)) 2 cm from CD,[1]
Verified working — step 1
The locus 2 cm from the line CD is a para…(c(ii)) 9 cm from B,[1]
Verified working — step 1
The locus 9 cm from the point B is a…(c(iii)) equidistant from AB and AD.[2]
Verified working — step 1
AB and AD meet at A, so points equidistant …(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: beyond the parallel line from (c)(i), away from CD.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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