Vectors – Year 1

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

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

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

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.

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.