MA28-10 Maths Coming soon
Vector arithmetic: addition, subtraction and scalar multiplication
MA28-10
This lesson is coming soon.
In this lesson
Add, subtract and multiply column vectors by a scalar, and calculate the magnitude of a vector using Pythagoras.
What it covers
- Distinguishing column-vector notation (two numbers stacked in brackets) from fraction notation before any arithmetic
- Adding and subtracting column vectors component by component
- Multiplying a column vector by a scalar (both components)
- Using the OA-arrow / bold-letter (a, b) naming convention for a vector
- Calculating the magnitude of a vector using Pythagoras: |a| = sqrt(x^2+y^2)
Key words
For: AQA GCSE 8300, Edexcel GCSE 1MA1, Eduqas GCSE C300, OCR GCSE J560, Edexcel IGCSE 4MA1, Cambridge IGCSE 0580
On the specification
| Board | Spec | Statement |
|---|---|---|
| AQA GCSE 8300 | G25 | Apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors |
| Edexcel GCSE 1MA1 | G25 | Apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors |
| Eduqas GCSE C300 | FG21 | Apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors |
| Eduqas GCSE C300 | HG25 | 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 |
| OCR GCSE J560 | 9.03a | Understand addition, subtraction and scalar multiplication of vectors. |
| OCR GCSE J560 | 9.03b | Represent a 2-dimensional vector as a column vector, and draw column vectors on a square or coordinate grid. |
| Edexcel IGCSE 4MA1 | H5.1C | Multiply vectors by scalar quantities |
| Edexcel IGCSE 4MA1 | H5.1D | Add and subtract vectors |
| Edexcel IGCSE 4MA1 | H5.1E | Calculate the modulus (magnitude) of a vector |
| Edexcel IGCSE 4MA1 | H5.1A | Understand that a vector has both magnitude and direction |
| Edexcel IGCSE 4MA1 | H5.1B | Understand and use vector notation including column vectors |
| Cambridge IGCSE 0580 | C7.2 | Extended content only. |
| Cambridge IGCSE 0580 | E7.2 | Describe a translation using a vector represented by (x y), AB or a. |
| Cambridge IGCSE 0580 | C7.3 | Extended content only. |
| Cambridge IGCSE 0580 | E7.3 | Calculate the magnitude of a vector (x y) as √(x² + y²). |
For teachers
This GCSE Maths lesson teaches vector arithmetic: addition, subtraction and scalar multiplication. By the end, students should be able to add, subtract and multiply column vectors by a scalar, and calculate the magnitude of a vector using Pythagoras. It works through three worked examples and the mistakes examiners report.