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 Strategy
Follow these 7 steps for bearing questions
Practice Questions
Try the questions first, then check the answer panel.
✎ Try These Yourself
- 1. Find the reverse bearing of 070°.
- 2. Find the reverse bearing of 240°.
- 3. A ship travels 5 km East and 12 km North. Find the straight-line distance.
- 4. A plane travels 9 km East and 12 km North. Find the straight-line distance.
- 5. A ship is 10 km East and 20 km North of a port. Find the bearing from the port.
- 6. A plane is 15 km East and 15 km North of an airport. Find the bearing from the airport.
✓ Answers
- 1. 250°
- 2. 060°
- 3. 13 km
- 4. 15 km
- 5. 027°
- 6. 045°
- Common GCSE Mistakes
- Measuring anti-clockwise.
- Forgetting North lines.
- Writing two-figure bearings.
- Incorrect reverse bearings.
- Choosing the wrong trigonometric method.
- Drawing inaccurate diagrams.
- Exam Tips
- Practise drawing bearings.
- Learn compass directions.
- Master reverse bearings.
- Revise Pythagoras and SOHCAHTOA.
- Complete GCSE past-paper questions.
- Always draw a diagram before solving.
Worked Examples
Six exam-style examples, from basic bearings to multi-step problems.
090°
Worked Example 1
A ship travels on a bearing of 090° for 20 km.
What direction is this?
090° corresponds to East
090° corresponds to East
135° → 315°
Worked Example 2
A plane travels on a bearing of 135°.
Find the reverse bearing.
135° + 180° = 315°.
135° + 180° = 315°.
060° → 240°
Worked Example 3
A ship travels 30 km on a bearing of 060°.
Find the reverse bearing.
060° + 180° = 240°.
060° + 180° = 240°.
Pythagoras
Worked Example 4
A boat travels 6 km East and then 8 km North.
Find the straight-line distance from the start.
6² + 8² = 100
Distance = 10 km.
6² + 8² = 100
Distance = 10 km.
SOHCAHTOA
Worked Example 5
A ship is 15 km East and 20 km North of a harbour.
Find the angle from North.
tan θ = 15/20
θ = 36.9°
Bearing ≈ 036.9°
tan θ = 15/20
θ = 36.9°
Bearing ≈ 036.9°
EXAM-STYLE MULTI-STEP
Worked Example 6
A plane flies 40 km on a bearing of 090° and then 30 km North.
Step 1
Draw a right-angled triangle.
Step 2
Use Pythagoras:
40² + 30² = 2500
Distance = 50 km
Step 3 Find the angle.
tan θ = 40/30
θ ≈ 53.1°
Bearing ≈ 053°.
Draw a right-angled triangle.
Step 2
Use Pythagoras:
40² + 30² = 2500
Distance = 50 km
Step 3 Find the angle.
tan θ = 40/30
θ ≈ 53.1°
Bearing ≈ 053°.
50 km
40 km East
30 km North
Final Answer
Distance = 50 km, Bearing = 053°.
Key Methods
Reverse Bearings
- Many GCSE questions require reverse bearings.
- Rule:
- • Add 180° if the bearing is less than 180°.
- • Subtract 180° if the bearing is greater than 180°.
Combining Bearings with Trigonometry
- Higher Tier questions often combine bearings with:
- • Basic Pythagoras
- • 3D Pythagoras
- • SOHCAHTOA
- • Sine Rule
- • Cosine Rule
- Students should be comfortable switching between these methods.
Real-Life Applications
Bearings are used by pilots, sailors, surveyors, engineers, emergency services and GPS navigation systems. Accurate directional calculations are essential in many careers.
Build Your Confidence
How to Improve at This Topic
- Practise drawing bearings.
- Learn compass directions.
- Master reverse bearings.
- Revise Pythagoras and SOHCAHTOA.
- Complete GCSE past-paper bearing questions.
- Always draw a diagram before solving.
Topics to Revise Next
- Three-Figure Bearings
- Basic Pythagoras
- 3D Pythagoras
- SOHCAHTOA
- Sine Rule
- Cosine Rule
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 Bearings Exam Questions Tutorial
Step-by-step walk throughs of Bearings 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°.
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GCSE MATHS
Loci Exam Questions
(Extended Revision Guide)
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.
Circles
Parallel Lines
Perpendicular Bisectors
Angle Bisectors
Regions
Angle bisector
Points equidistant from two intersecting lines
lie on the angle bisector.
Introduction
Loci Exam Questions are a common GCSE Geometry topic that combines constructions, bisectors and geometric reasoning. A locus is the path traced out by a point that follows a specific rule. GCSE questions often ask students to draw loci, interpret diagrams and solve exam-style problems involving distances from points, lines or shapes.
What Is a Locus?
A locus is a set of points that satisfy a given condition. For example, a point may be exactly 5 cm from another point, or the same distance from two lines. Every point on the locus must follow the rule given in the question.
Common Types of Loci
🔵 Points a fixed distance from a point (circles).
🔵 Points a fixed distance from a line (parallel lines).
🔵 Points equidistant from two points (perpendicular bisectors).
🔵 Points equidistant from two intersecting lines (angle bisectors).
Exam Question Strategy
A simple step-by-step method to help you answer loci questions.
1
Read the condition carefully.
2
Identify the type of locus.
3
Draw the locus accurately.
4
Shade or mark the valid region.
5
Check that every point satisfies the condition.
Worked Examples
Eight step-by-step examples, from basic loci to exam-style 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)
Key Methods
🔵 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.
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.
Practice Questions
Try these GCSE-style questions, then check the answers.
Questions
- Draw the locus 5 cm from point A.
- Draw the locus 2 cm from line L.
- Construct the locus equidistant from points A and B.
- Construct the locus equidistant from two intersecting lines.
- Draw the region within 3 cm of point P.
- 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.
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
Extended Conclusion
Loci examine construction skills, geometric reasoning and accurate diagram drawing. By understanding the common types of loci and practising regularly, you can solve GCSE questions with confidence. Loci are used in many real-life applications and form an important part of the GCSE Geometry curriculum.
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