Year 11 - Maths
Dividing vectors into ratios
Vectors
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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, pupil understanding of vectors is deepened with pupils exploring column vector notation and arithmetic procedures.
Lesson Summary
You will learn to solve geometric problems in 2D where vectors are divided in a given ratio.
Key Notes
- A vector can be divided into parts using a ratio.
- By converting the ratio to a fraction, you can express each part in terms of the original vector.
- This allows you to perform further manipulations.
Vocabulary To Learn
- Vector: A vector can be used to describe a translation.
- Displacement: Displacement is the distance from the starting point when measured in a straight line.
- Resultant vector: A resultant vector is the single vector that produces the same effect as a combination of other vectors.
Common Mistakes To Avoid
- When calculating the resultant vector, pupils can incorrectly sum vectors due to opposite directions or proportions of vectors.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A vector can be divided into parts using a ratio. By converting the ratio to a fraction, you can express each part in terms of the original vector.
2. Use this key word in a maths sentence and explain it clearly. 'Vector'
A vector can be used to describe a translation. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: When calculating the resultant vector, pupils can incorrectly sum vectors due to opposite directions or proportions of vectors. Correction: Encourage pupils to write a clear vector pathway, sometimes using highlighters can help visualise this pathway.
More Lessons In This Unit
- Addition with vectors Study Guide
- Advanced problem solving with vectors Study Guide
- Algebraic vector notation Study Guide
- Calculating the magnitude of a vector Study Guide
- Checking and securing understanding of translations Study Guide
- Column vectors Study Guide
- Fluency in arithmetic procedures with algebraic vector notation Study Guide
- Fluency in arithmetic procedures with vectors Study Guide
- Geometric proofs with vectors Study Guide
- Multiplication with vectors Study Guide
- Parallel vectors Study Guide
- Parallel vectors in algebraic vector notation Study Guide
- Problem solving with vectors Study Guide
- Subtraction with vectors Study Guide
- The sum and difference with algebraic vector notation Study Guide
Browse all guides in the Year 11 Maths guide library.