GCSE MATHS • HIGHER TIER
GCSE Loci Exam Questions
Build confidence with loci through clear rules, constructions and worked examples. Learn how to draw and interpret loci, solve exam-style questions and identify regions that satisfy given conditions.
Angle bisector
- Circles
- Parallel Lines
- Perpendicular Bisectors
- Angle Bisectors
- Regions
🎯 Exam Question Strategy
A simple step-by-step method to help you answer loci questions.
Practice Questions
Try the questions first, then check the answer panel.
✎ Try These Yourself
- 1. Draw the locus 5 cm from point A.
- 2. Draw the locus 2 cm from line L.
- 3. Construct the locus equidistant from points A and B.
- 4. Construct the locus equidistant from two intersecting lines.
- 5. Draw the region within 3 cm of point P.
- 6. Draw the region closer to A than B.
✓ Answers
- 1. Circle radius 5 cm.
- 2. Two parallel lines 2 cm away.
- 3. Perpendicular bisector.
- 4. Angle bisector.
- 5. Interior of a circle radius 3 cm.
- 6. Side of the perpendicular bisector containing A.
- Common GCSE Mistakes
- Inaccurate constructions.
- Forgetting to draw both parallel lines.
- Misunderstanding the wording (within, more than, closer to).
- Shading the wrong region.
- Not using a ruler and compass carefully.
- Exam Tips
- Circles for a fixed distance from a point.
- Parallel lines for a fixed distance from a line.
- Perpendicular bisectors for points equidistant from two points.
- Angle bisectors for points equidistant from two lines.
- Combine loci to find regions that satisfy multiple conditions.
Worked Examples
Six exam-style examples, from basic bearings to multi-step problems.
Example 1
4 cm from a point
The locus is a circle with centre A and radius 4 cm.
Answer: Circle centred at A with radius 4 cm.
Example 2
3 cm from a line
Draw two parallel lines 3 cm from the original line.
Answer: Two parallel lines each 3 cm away.
Example 3
Equidistant from two points
Draw the perpendicular bisector of AB.
Answer: Perpendicular bisector of AB.
Example 4
Equidistant from two lines
Draw the angle bisector.
Answer: Angle bisector.
Example 5
Dog on a 5 m rope
The locus is a circle centred on the post with radius 5 m.
Answer: Circle radius 5 m.
Example 6
More than 2 cm from a line
Draw the boundary line and shade the region beyond it.
Answer: The region outside the 2 cm boundary.
Example 7
Within 4 cm of a point
Draw a circle and shade the interior.
Answer: Region inside the circle of radius 4 cm.
Example 8
Closer to A than B
Draw the perpendicular bisector and shade the side containing A.
Answer: Side of the bisector containing A.
Exam-Style Question
A point must be more than 2 cm from line L.
1. Draw a line 2 cm from L on each side.
2 . Because it is “more than 2 cm”, shade the regions beyond the lines.
3 . Do not include the boundary lines.
Final Answer
Two parallel lines 2 cm from L with the regions outside shaded.
Valid region (more than 2 cm)
↕ 2 cm
L
↕ 2 cm
Valid region (more than 2 cm)
Build Your Confidence
How to Improve at This Topic
- Practise compass and ruler constructions regularly.
- Revise perpendicular bisectors, angle bisectors and circles.
- Pay close attention to the wording of each condition.
- Complete GCSE past-paper loci questions.
- Highlight and label diagrams clearly.
Topics to Revise Next
- Constructions
- Bisectors
- Circles
- Geometric Reasoning
- Transformations
- Bearings
Ready to Practise?
Printable Worksheet
Download and print practice questions with answers.
Interactive Quiz
Test your knowledge with instant feedback and hints.
Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Loci Exam Questions Tutorial
Step-by-step walk throughs of Loci Exam Questions with clear methods and exam tips.
Frequently Asked Questions
Three figures create a standard format, so 45° is written as 045°.
Bearings are always measured clockwise from North.
The bearing of East is 090°.
Add 180° if the bearing is below 180°, or subtract 180° if it is above 180°.
