Vectors

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

4 Part Lesson
Modelling with Vectors
4 Part Lesson
Introduction to Vectors
4 Part Lesson
Representing Vectors
4 Part Lesson
Vectors – Magnitude and Direction
4 Part Lesson
Position Vectors

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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