Vectors – Year 1

Scheme of work: Year 12 A-Level: Pure 1: 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 

Key Concepts

  • 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.

Common 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.

Vectors Resources

Mr Mathematics Blog

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