GCSE · Constructions & loci

Loci & regionsExam-style questions

A locus as the set of points obeying a rule, the four standard loci, and how to combine several conditions — with scale drawings — to shade the region that satisfies all of them at once.

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11 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
$PQRS$ is a rectangular garden measuring $16$ m by $10$ m. The plan below is drawn to a scale of $1$ cm to $2$ m.A pond is to be built in the garden so that it is:

* more than $12$ m from corner $P$ , and * less than $6$ m from the side $QR$ , and * nearer to the side $PQ$ than to the side $SR$ .

On the plan, show by shading the region where the pond can be built. You must show all your construction lines.
Level 5 · 5 marksTry it
2
A goat is tied by a $10$ m rope to the corner $G$ of a shed which measures $8$ m by $6$ m. The shed stands in a large open field, and the goat cannot go inside the shed.Diagram NOT accurately drawn

Work out the total area of the field the goat can graze. Give your answer correct to 3 significant figures.
Level 5 · 4 marksTry it