ECZ 2024 · O-Level Paper 2 · Question 5 — Construction and Loci

Question from ECZ 2024 · O-Level Paper 2 · Question 5

(a) Construct a quadrilateral PQRS in which PQ = 8 cm, angle QPS = 110°, angle PQR = 88°, PS = 7 cm and QR = 10 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, construct the locus of points which are

(c(i)) 6 cm from QR,[1]

Verified working — step 1

The locus 6 cm from the line QR …

(c(ii)) equidistant from PS and RS.[2]

Verified working — step 1

PS and RS meet at S, so points equidistant …

(d) A point M, within the quadrilateral PQRS, is such that it is 6 cm from QR and equidistant from PS and RS. Label the point M.[1]

Verified working — step 1

M must lie on BO…

(e) Another point N, within the quadrilateral PQRS, is such that it is less than or equal to 6 cm from QR and nearer to PS than RS. Indicate, by shading, the region in which N must lie.[2]

Verified working — step 1

At most 6 cm from QR: the strip between QR and the parallel line.

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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