Year 11 - Maths
Solving loci problems in context
Loci and construction
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit, pupils construct triangles and construct diagrams following specific restrictions using their knowledge of loci and their work on constructions.
Lesson Summary
You will learn to solve problems involving a combination of loci.
Key Notes
- Loci problems involve performing various constructions
- The problem asks for these constructions within the context of the question
- All construction lines should be left on the diagram to show your working
Vocabulary To Learn
- Locus/loci: A locus is a set of points that satisfy a given set of conditions. Multiple sets of points are referred to as loci.
- Perpendicular: Two lines are perpendicular if they meet at right angles.
- Bisect: To bisect means to cut or divide an object into two equal parts.
Common Mistakes To Avoid
- Pupils may erase their construction marks.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Loci problems involve performing various constructions. The problem asks for these constructions within the context of the question.
2. Use this key word in a maths sentence and explain it clearly. 'Locus/loci'
A locus is a set of points that satisfy a given set of conditions. Multiple sets of points are referred to as loci. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils may erase their construction marks. Correction: Remind pupils that they should always leave their construction marks on their diagrams but encourage them not to press to hard with their pencils.
More Lessons In This Unit
- Advanced problem solving with loci and constructions Study Guide
- Applying constructions to loci problems Study Guide
- Checking and securing understanding of bisecting an angle Study Guide
- Checking and securing understanding of constructing a perpendicular to a given line through a point Study Guide
- Checking and securing understanding of constructing the perpendicular bisector of a line segment Study Guide
- Constructing a right-angled triangle given the length of the hypotenuse and one other side length Study Guide
- Constructing a triangle given three side lengths using compasses Study Guide
- Constructing a triangle given two angles and the side length between them Study Guide
- Constructing a triangle given two side lengths and an angle not between them Study Guide
- Constructing a triangle given two side lengths and the angle between them using a compass Study Guide
- Constructing angles of 90° and 45° Study Guide
- Constructing loci Study Guide
- Problem solving with loci and constructions Study Guide
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