ECZ 2020 · O-Level Paper 2 · Question 4 — Construction and Loci
Question from ECZ 2020 · O-Level Paper 2 · Question 4
(a) Construct a quadrilateral PQRS in which PQ = 8 cm, angle QPS = angle PQR = 120°, PS = 6 cm and QR = 5 cm.[1]
Verified working — step 1
Draw PQ = 8 cm.(b) Measure and write the length of RS.[1]
Verified working — step 1
Measure RS with a ruler on the finished construction: RS = …(c) Within the quadrilateral PQRS, draw the locus of points which are
(c(i)) 4.5 cm from Q,[1]
Verified working — step 1
The locus 4.5 cm from the point Q is a…(c(ii)) equidistant from P and Q,[1]
Verified working — step 1
Points equidistant from P and Q lie …(c(iii)) equidistant from QR and RS.[2]
Verified working — step 1
QR and RS meet at R, so points equidistant …(d) A point T, within the quadrilateral PQRS, is such that it is less than or equal to 4.5 cm from Q, nearer to Q than P and nearer to RS than QR. Indicate, by shading, the region in which T must lie.[2]
Verified working — step 1
At most 4.5 cm from Q: inside the arc 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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