Vectors - AQA GCSE Mathematics Revision

Topic overview

What you need to know

Vectors is a key part of GCSE Mathematics. Build fluency with the method, then apply it to unfamiliar and multi-step problems. A quantity that has both magnitude (size) and direction. Represented by a column vector or an arrow. A quantity that has magnitude only, with no direction. E.g. speed, mass, temperature. A vector written as (x, y) where x is the horizontal component and y is the vertical component.

Exam tip

Write every stage of your method. Method marks can still be earned when the final answer is wrong.

Revision notes

Core ideas

Secure these ideas first. Say each definition in your own words, then connect it to the topic overview.

Vector: A quantity that has both magnitude (size) and direction. Represented by a column vector or an arrow.
Scalar: A quantity that has magnitude only, with no direction. E.g. speed, mass, temperature.
Column Vector: A vector written as (x, y) where x is the horizontal component and y is the vertical component.
Adding Vectors: Add the corresponding components: (a, b) + (c, d) = (a+c, b+d).

Revision notes

Apply it in the exam

The exam will rarely ask for an isolated definition. Practise selecting the right idea and using it as part of a complete explanation or method.

Subtracting Vectors: Subtract components: a⃗ − b⃗ means go along a⃗ then backwards along b⃗.
Scalar Multiplication: Multiply each component by the scalar: k(a, b) = (ka, kb). This scales the vector.
Magnitude of a Vector: |v⃗| = √(x² + y²) for vector (x, y). This gives the length of the vector.
Resultant Vector: The single vector that has the same effect as two or more vectors combined. Found by adding vectors.

Core knowledge

Key facts for Vectors

8 essentials

Vector

A quantity that has both magnitude (size) and direction. Represented by a column vector or an arrow.

Scalar

A quantity that has magnitude only, with no direction. E.g. speed, mass, temperature.

Column Vector

A vector written as (x, y) where x is the horizontal component and y is the vertical component.

Adding Vectors

Add the corresponding components: (a, b) + (c, d) = (a+c, b+d).

Subtracting Vectors

Subtract components: a⃗ − b⃗ means go along a⃗ then backwards along b⃗.

Scalar Multiplication

Multiply each component by the scalar: k(a, b) = (ka, kb). This scales the vector.

Magnitude of a Vector

|v⃗| = √(x² + y²) for vector (x, y). This gives the length of the vector.

Resultant Vector

The single vector that has the same effect as two or more vectors combined. Found by adding vectors.

Active recall

Close the notes and answer these

1.Without looking, explain vector and give one example or consequence.
2.Without looking, explain scalar and give one example or consequence.
3.Without looking, explain column vector and give one example or consequence.
4.Without looking, explain adding vectors and give one example or consequence.

Content reviewed 23 July 2026 against the current linked specification.

Finished learning?

Mark the notes complete, then test what you can recall.

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