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**AS Mathematics Year 1: Pure: Vectors**

Throughout this unit, students learn how to represent vectors using column notation and use them to describe geometrical properties. Later, as learning progresses, they use vector notation to model real-life problems involving bearings and mechanics.

**Vectors Lessons**

**Prerequisite Knowledge**

- Describe translations as 2D vectors
- Apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors
- Use vectors to construct geometric arguments and proofs

**Success Criteria**

- Use vectors in two dimensions
- Calculate the magnitude and direction of a vector;
- Add vectors diagrammatically and perform the algebraic operations of vector addition and multiplication by scalars, and understand their geometrical interpretations;
- Understand and use position vectors; calculate the distance between two points represented by position vectors
- Use vectors to solve problems in pure mathematics and in context, including forces

**Teaching Points**

- Students should sketch diagrams whenever possible as part of their work, reinforcing the algebraic notation.
- By drawing and labelling diagrams, students can better identify a position vector from a direction vector.
- When simplifying or calculating vectors, students should be comfortable using column notation.
- Vector problems .often lead to setting up and solving a pair of simultaneous equations.
- Students need to know how a vector’s magnitude leads to working out a unit vector.
- Vector geometry often leads to problems in non-right-angled triangles, bearings and forces. Students need plenty of practise with these types of problems.
- The resultant vector is the sum of two or more vectors.
- Speed in the magnitude of a velocity vector
- Distance is the magnitude of a displacement vector.

**Misconceptions**

- Some students lose marks by writing the magnitude of a vector as a negative.
- When writing vectors in i and j notation, some students incorrectly think of it as a coordinate pair and write 3i – 2j as (3i, -2j).
- Some students get confused knowing when a vector gives a direction or a position.

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