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
A goat is tied to a post $P$ in the middle of a large field by a rope of length $9$ m.

A plan of the field is drawn using a scale of $1$ cm to $2$ m.

(a) Work out the radius, in centimetres, of the circle that should be drawn on the plan to show how far the goat can reach.

(b) Describe the region of the plan that represents the grass the goat can eat.
Level 2 · 3 marksTry it
2
A plan is drawn to a scale of $1$ cm to $5$ m.

(a) A water sprinkler reaches every point within $20$ m of the tap $T$ . Work out the radius of the circle that shows this region on the plan.

(b) Describe fully the locus of points that are exactly $20$ m from $T$ (in the real garden).
Level 2 · 4 marksTry it