Source: https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/5-1-2-vectors-2

[Revision notes](https://senecalearning.com/en-gb/revision-notes.md) › [IGCSE](https://senecalearning.com/en-gb/revision-notes/igcse.md) › [Maths](https://senecalearning.com/en-gb/revision-notes/igcse/maths.md) › [Edexcel IGCSE](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse.md) › [Higher](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher.md) › Vectors 2

# Vectors 2

Maths: Edexcel IGCSE Higher, topic 5.1.2

## Scalars and Straight Lines

A scalar is any number such as 10, π, -4, 1⁄2, 4.52, √6.

### Scalars and vectors

![Scalars and vectors](https://image-v2.cdn.app.senecalearning.com/2018-03/c7f90a25-4eb9-4273-80b0-3ebb7ecc49cf/Screen%20Shot%202018-03-26%20at%2014.53.54.png)

- When a vector is multiplied by a scalar its direction does not change but its size does.
- A negative scalar switches the direction of the vector.
- To multiply a column vector by a scalar multiply both top and bottom numbers by the scalar.

### Straight lines

![Straight lines](https://image-v2.cdn.app.senecalearning.com/2018-03/31660317-a112-4f9c-a46b-fc43dc3c75f4/Screen%20Shot%202018-03-26%20at%2014.58.54.png)

- To show 3 points A, B and C lie in a straight line show that AB is a scalar multiple of BC.

### Ratios and lengths

![Ratios and lengths](https://image-v2.cdn.app.senecalearning.com/2018-03/1bc4d02e-ae75-4455-81ac-85c62fb3d425/Screen%20Shot%202018-03-26%20at%2015.00.05.png)

- If given side lengths in ratios you can translate this to vector form.
 - If AB : BC = 2 : 3 and A, B, C are in a straight line then 2 AB = 3 BC.

## Magnitude of Vectors

Vectors have a magnitude (size) and direction. The magnitude of a vector can be calculated from the column vector.

### Calculating the magnitude

![Calculating the magnitude](https://image-v2.cdn.app.senecalearning.com/2019-04/b55dfa6a-57c7-4cef-8fe4-49e910de75db/New%20Wave%201.1%20(13).png)

- You can use Pythagoras' theorem to calculate the magnitude of a vector ($$\large{x}\atop{y}$$).
- The magnitude of a vector $$({\large{x}\atop{y}})$$ is 
$$\sqrt{x^2+y^2}$$.

### Vector notation

![Vector notation](https://image-v2.cdn.app.senecalearning.com/2018-08/eee6bab5-d6a7-493a-8fb2-39322a189cd0/exam-sheet-answers.jpg)

- You will need to be careful when writing vectors in your exam.
- Vectors will be printed on the exam as $$\vec{AB}$$ or **a**.
- The magnitude of a vector will be shown using modulus signs.
 - I.e. magnitude of $$\vec{AB}$$ = 
|$$\vec{AB}$$|
 - I.e. magnitude of **a** = |**a**|

### Using vector notation

![Using vector notation](https://image-v2.cdn.app.senecalearning.com/2018-09/48aebd73-4676-49b6-97f4-595e3345bb94/writing-write-.jpg)

- In your exam, you will need to show the examiner that you know the difference between the vector a and the letter a.
- There are two ways to do this:
 - Using an arrow above the vector, e.g. $$\vec{AB}$$
 - Underlining the letter, e.g. $$\underline{a}$$

## Proof by Vector Method

Vectors can be used to prove geometric properties of shapes.

### Example

![Example](https://image-v2.cdn.app.senecalearning.com/2019-10/6874ce54-e20e-4214-87e8-88de26d72134/vectorproof1.png)

- By method of vectors, prove that STU is a straight line.

### Draw the diagram

![Draw the diagram](https://image-v2.cdn.app.senecalearning.com/2019-10/4a5632f3-d4a7-4e95-88bc-a1e2fea9d040/vectorproof2.png)

- Remember to label each points carefully.

### Work out the vectors

![Work out the vectors](https://image-v2.cdn.app.senecalearning.com/2019-10/073e012b-6c62-4118-a3d5-740d3cb1e231/vectorproof3.png)

- Work out the vectors for the points connecting the path from S to T to U, in terms of the vectors __p__ and __q__.

### Work out the vectors

![Work out the vectors](https://image-v2.cdn.app.senecalearning.com/2019-10/073e012b-6c62-4118-a3d5-740d3cb1e231/vectorproof3.png)

### Compare

![Compare](https://image-v2.cdn.app.senecalearning.com/2019-10/daeec497-66e1-4674-9087-f7e75fbd8ac8/vectorproof4.png)

- Compare the vector ST with the vector TU.
- If STU is a straight line, then ST and TU will be multiples of one another with T as a common point.

### Compare

![Compare](https://image-v2.cdn.app.senecalearning.com/2019-10/daeec497-66e1-4674-9087-f7e75fbd8ac8/vectorproof4.png)

## Test yourself on Vectors 2

- What happens to a vector when it is multiplied by a scalar?
- What happens to a vector when it is multiplied by a negative scalar?
- What is the condition for A, B and C lying on a straight line?
- What is the condition for the points X, Y and Z lying on a straight line?
- How can you calculate the magnitude of a vector?

[Practise this topic for free](https://app.senecalearning.com/classroom/course/641a6cb5-729a-404a-aeca-c7040cd18740/section/af504e3f-8b8f-4f45-b158-069138ef85da/session)

- Previous topic: [5.1.1 Vectors](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/5-1-1-vectors.md)
- Next topic: [5.1.3 Exam-Style Questions - Vectors](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/5-1-3-exam-style-questions-vectors.md)

## Maths: Edexcel IGCSE Higher contents

### 1 Numbers
- 1.1 Integers
  - [1.1.1 Integers](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-1-1-integers.md)
  - [1.1.2 Ordering Numbers](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-1-2-ordering-numbers.md)
  - [1.1.3 The Four Rules of Operations](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-1-3-the-four-rules-of-operations.md)
  - [1.1.4 Hierarchy of Operations](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-1-4-hierarchy-of-operations.md)
  - [1.1.5 Definitions & Terms](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-1-5-definitions-and-terms.md)
  - [1.1.6 HCF & LCM](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-1-6-hcf-and-lcm.md)
  - [1.1.7 Standard Form](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-1-7-standard-form.md)
  - [1.1.8 Standard Form 2](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-1-8-standard-form-2.md)
  - [1.1.9 Prime Numbers](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-1-9-prime-numbers.md)
  - [1.1.10 End of Topic Test - Standard Form](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-1-10-end-of-topic-test-standard-form.md)
- 1.2 Fractions
  - [1.2.1 Fractions](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-2-1-fractions.md)
  - [1.2.2 Using Fractions](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-2-2-using-fractions.md)
  - [1.2.3 Conversion](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-2-3-conversion.md)
  - [1.2.4 Reciprocals](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-2-4-reciprocals.md)
- 1.3 Decimals
  - [1.3.1 Decimals](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-3-1-decimals.md)
  - [1.3.2 Decimals 2](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-3-2-decimals-2.md)
  - [1.3.3 Exam-Style Questions - Recurring Decimals](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-3-3-exam-style-questions-recurring-decimals.md)
  - [1.3.4 Comparing & Converting Decimals](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-3-4-comparing-and-converting-decimals.md)
  - [1.3.5 End of Topic Test - Fractions & Decimals](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-3-5-end-of-topic-test-fractions-and-decimals.md)
- 1.4 Powers & Roots
  - [1.4.1 Square Numbers](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-4-1-square-numbers.md)
  - [1.4.2 Index Notation](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-4-2-index-notation.md)
  - [1.4.3 Exam-Style Questions - Index Notation](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-4-3-exam-style-questions-index-notation.md)
  - [1.4.4 Advanced Indices](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-4-4-advanced-indices.md)
  - [1.4.5 Surds](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-4-5-surds.md)
  - [1.4.6 End of Topic Test - Powers & Roots](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-4-6-end-of-topic-test-powers-and-roots.md)
- 1.5 Set Language & Notation
  - [1.5.1 Sets](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-5-1-sets.md)
- 1.6 Percentages
  - [1.6.1 Percentages](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-6-1-percentages.md)
  - [1.6.2 Percentage Change](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-6-2-percentage-change.md)
  - [1.6.3 Percentages in Finance](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-6-3-percentages-in-finance.md)
  - [1.6.4 Compound Interest](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-6-4-compound-interest.md)
- 1.7 Ratio & Proportion
  - [1.7.1 Manipulating Ratios](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-7-1-manipulating-ratios.md)
  - [1.7.2 Proportion](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-7-2-proportion.md)
- 1.8 Degree of Accuracy
  - [1.8.1 Rounding & Significant Figures](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-8-1-rounding-and-significant-figures.md)
  - [1.8.2 Estimation](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-8-2-estimation.md)
  - [1.8.3 Upper & Lower Bounds](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-8-3-upper-and-lower-bounds.md)
  - [1.8.4 Limits of Accuracy](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-8-4-limits-of-accuracy.md)
  - [1.8.5 Limits of Accuracy 2](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-8-5-limits-of-accuracy-2.md)
  - [1.8.6 End of Topic Test - Rounding & Estimation](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/1-8-6-end-of-topic-test-rounding-and-estimation.md)

### 2 Equations, Formulae & Identities
- 2.1 Algebraic Manipulation
  - [2.1.1 Algebra Basics](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-1-1-algebra-basics.md)
  - [2.1.2 Power Rules & Collecting Terms](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-1-2-power-rules-and-collecting-terms.md)
  - [2.1.3 Expanding Brackets](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-1-3-expanding-brackets.md)
  - [2.1.4 Expanding Brackets 2](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-1-4-expanding-brackets-2.md)
  - [2.1.5 Factorising Quadratics](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-1-5-factorising-quadratics.md)
  - [2.1.6 Algebraic Fractions](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-1-6-algebraic-fractions.md)
  - [2.1.7 Proofs](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-1-7-proofs.md)
  - [2.1.8 End of Topic Test - Algebra & Proofs](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-1-8-end-of-topic-test-algebra-and-proofs.md)
  - [2.1.9 Exam-Style Questions - Algebraic Proof](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-1-9-exam-style-questions-algebraic-proof.md)
- 2.2 Expressions & Formulae
  - [2.2.1 Rearranging Formulae](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-2-1-rearranging-formulae.md)
  - [2.2.2 Simple Formulae](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-2-2-simple-formulae.md)
  - [2.2.3 End of Topic Test - Algebra Manipulation & Formula](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-2-3-end-of-topic-test-algebra-manipulation-and-formula.md)
- 2.3 Linear Equations
  - [2.3.1 Solving Linear Equations](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-3-1-solving-linear-equations.md)
  - [2.3.2 Simultaneous Linear Equations](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-3-2-simultaneous-linear-equations.md)
- 2.4 Quadratic Equations
  - [2.4.1 Solving Quadratics](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-4-1-solving-quadratics.md)
  - [2.4.2 Solving Quadratics 2](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-4-2-solving-quadratics-2.md)
  - [2.4.3 End of Topic Test - Solving Equations](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-4-3-end-of-topic-test-solving-equations.md)
  - [2.4.4 Simulateous Quadratic Equations](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-4-4-simulateous-quadratic-equations.md)
  - [2.4.5 Exam-Style Questions - Simultaneous Equations](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-4-5-exam-style-questions-simultaneous-equations.md)
  - [2.4.6 Graphs of Simultaneous Equations](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-4-6-graphs-of-simultaneous-equations.md)
  - [2.4.7 End of Topic Test - Simultaneous Equations](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-4-7-end-of-topic-test-simultaneous-equations.md)
- 2.5 Proportion
  - [2.5.1 Graphs & Proportion](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-5-1-graphs-and-proportion.md)
- 2.6 Inequalities
  - [2.6.1 Solving Inequalities](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-6-1-solving-inequalities.md)
  - [2.6.2 Graphs of Inequalities](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-6-2-graphs-of-inequalities.md)
  - [2.6.3 Exam-Style Questions - Inequalities](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-6-3-exam-style-questions-inequalities.md)
  - [2.6.4 End of Topic Test - Inequalities](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-6-4-end-of-topic-test-inequalities.md)

### 3 Sequences, Functions & Graphs
- 3.1 Sequences
  - [3.1.1 Sequence Rules](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/3-1-1-sequence-rules.md)
  - [3.1.2 Finding Terms](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/3-1-2-finding-terms.md)
  - [3.1.3 Exam-Style Questions - Sequences](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/3-1-3-exam-style-questions-sequences.md)
  - [3.1.4 End of Topic Test - Sequences](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/3-1-4-end-of-topic-test-sequences.md)
- 3.2 Functions
  - [3.2.1 Functions](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/3-2-1-functions.md)
  - [3.2.2 Composite & Inverse](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/3-2-2-composite-and-inverse.md)
  - [3.2.3 End of Topic Test - Functions](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/3-2-3-end-of-topic-test-functions.md)
- 3.3 Graphs
  - [3.3.1 Plotting Graphs](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/3-3-1-plotting-graphs.md)
  - [3.3.2 Straight Line Graphs](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/3-3-2-straight-line-graphs.md)
  - [3.3.3 Properties of Graphs](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/3-3-3-properties-of-graphs.md)
  - [3.3.4 Quadratic Graphs](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/3-3-4-quadratic-graphs.md)
  - [3.3.5 Practical Graphs](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/3-3-5-practical-graphs.md)
  - [3.3.6 Graphs of Polynomials](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/3-3-6-graphs-of-polynomials.md)
  - [3.3.7 End of Topic Test Graphs](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/3-3-7-end-of-topic-test-graphs.md)
- 3.4 Common Graphs
  - [3.4.1 Graphs of Common Functions](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/3-4-1-graphs-of-common-functions.md)
  - [3.4.2 Transformations of Graphs](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/3-4-2-transformations-of-graphs.md)
  - [3.4.3 End of Topic Test - Transformations and Graph](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/3-4-3-end-of-topic-test-transformations-and-graph.md)
- 3.5 Calculus
  - [3.5.1 Derivatives of Functions](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/3-5-1-derivatives-of-functions.md)
  - [3.5.2 Maxima & Minima](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/3-5-2-maxima-and-minima.md)

### 4 Geometry
- 4.1 Angles, Lines & Triangles
  - [4.1.1 Angles & Lines](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-1-1-angles-and-lines.md)
  - [4.1.2 Angle Rules](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-1-2-angle-rules.md)
  - [4.1.3 Angles in Triangles](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-1-3-angles-in-triangles.md)
  - [4.1.4 Exam-Style Questions - Angles](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-1-4-exam-style-questions-angles.md)
- 4.2 Polygons
  - [4.2.1 Polygons](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-2-1-polygons.md)
  - [4.2.2 Quadrilaterals](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-2-2-quadrilaterals.md)
  - [4.2.3 Congruence](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-2-3-congruence.md)
  - [4.2.4 Scale Factor](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-2-4-scale-factor.md)
  - [4.2.5 Exam-Style Questions - Enlargements](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-2-5-exam-style-questions-enlargements.md)
  - [4.2.6 End of Topic Test - Geometry](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-2-6-end-of-topic-test-geometry.md)
- 4.3 Symmetry
  - [4.3.1 Symmetry](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-3-1-symmetry.md)
  - [4.3.2 Exam-Style Questions - Reflection](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-3-2-exam-style-questions-reflection.md)
- 4.4 Measures
  - [4.4.1 Measurements](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-4-1-measurements.md)
  - [4.4.2 Time](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-4-2-time.md)
  - [4.4.3 Bearings](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-4-3-bearings.md)
  - [4.4.4 Speed](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-4-4-speed.md)
- 4.5 Circle Properties
  - [4.5.1 Properties of a Circle](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-5-1-properties-of-a-circle.md)
  - [4.5.2 Circle Theorems](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-5-2-circle-theorems.md)
  - [4.5.3 Circle Theorems 2](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-5-3-circle-theorems-2.md)
  - [4.5.4 Circle Theorems 3](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-5-4-circle-theorems-3.md)
  - [4.5.5 Exam-Style Questions - Circle Theorems](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-5-5-exam-style-questions-circle-theorems.md)
- 4.6 Trigonometry & Pythagoras’ theorem
  - [4.6.1 Pythagoras' Theorem](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-6-1-pythagoras-theorem.md)
  - [4.6.2 Trigonometry](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-6-2-trigonometry.md)
  - [4.6.3 Sine & Cosine for Obtuse Angles](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-6-3-sine-and-cosine-for-obtuse-angles.md)
  - [4.6.4 Triangle Formulae](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-6-4-triangle-formulae.md)
  - [4.6.5 Exam-Style Questions - Trigonometry & Area](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-6-5-exam-style-questions-trigonometry-and-area.md)
- 4.7 Mensuration of 2D Shapes
  - [4.7.1 Standard Units](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-7-1-standard-units.md)
  - [4.7.2 Perimeter of 2D Shapes](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-7-2-perimeter-of-2d-shapes.md)
  - [4.7.3 Area of 2D Shapes](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-7-3-area-of-2d-shapes.md)
  - [4.7.4 Area & Circumference of Circle](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-7-4-area-and-circumference-of-circle.md)
  - [4.7.5 End of Topic Test - Trigonometry & Shapes](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-7-5-end-of-topic-test-trigonometry-and-shapes.md)
- 4.8 3D Shapes & Volume
  - [4.8.1 3D Shapes](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-8-1-3d-shapes.md)
  - [4.8.2 Surface Area](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-8-2-surface-area.md)
  - [4.8.3 Volume](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-8-3-volume.md)
  - [4.8.4 Exam-Style Questions - Volume](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/4-8-4-exam-style-questions-volume.md)

### 5 Vectors & Transformation Geometry
- 5.1 Vectors
  - [5.1.1 Vectors](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/5-1-1-vectors.md)
  - [5.1.2 Vectors 2](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/5-1-2-vectors-2.md)
  - [5.1.3 Exam-Style Questions - Vectors](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/5-1-3-exam-style-questions-vectors.md)
- 5.2 Transformation Geometry
  - [5.2.1 Transformations](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/5-2-1-transformations.md)
  - [5.2.2 Rotations](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/5-2-2-rotations.md)
  - [5.2.3 Translations & Reflections](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/5-2-3-translations-and-reflections.md)
  - [5.2.4 Enlargements](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/5-2-4-enlargements.md)
  - [5.2.5 Effects of Transformations](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/5-2-5-effects-of-transformations.md)

### 6 Statistics & Probability
- 6.1 Statistical Measures
  - [6.1.1 Basic Statistics](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/6-1-1-basic-statistics.md)
  - [6.1.2 Frequency Table](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/6-1-2-frequency-table.md)
- 6.2 Graphical Representation of Data
  - [6.2.1 Pictograms, Bar Charts & Pie  Charts](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/6-2-1-pictograms-bar-charts-and-pie-charts.md)
  - [6.2.2 Histograms](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/6-2-2-histograms.md)
  - [6.2.3 Cumulative Frequency](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/6-2-3-cumulative-frequency.md)
  - [6.2.4 Cumulative Frequency 2](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/6-2-4-cumulative-frequency-2.md)
  - [6.2.5 Exam-Style Questions - Cumulative Frequency](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/6-2-5-exam-style-questions-cumulative-frequency.md)
  - [6.2.6 End of Topic - Datasets](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/6-2-6-end-of-topic-datasets.md)
- 6.3 Probability
  - [6.3.1 Probability](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/6-3-1-probability.md)
  - [6.3.2 Theoretical Probability](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/6-3-2-theoretical-probability.md)
  - [6.3.3 Experimental Probability](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/6-3-3-experimental-probability.md)
  - [6.3.4 Venn Diagrams](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/6-3-4-venn-diagrams.md)
  - [6.3.5 Sample Space Diagrams](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/6-3-5-sample-space-diagrams.md)
  - [6.3.6 Tree Diagrams](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/6-3-6-tree-diagrams.md)
  - [6.3.7 Independent Events](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/6-3-7-independent-events.md)
  - [6.3.8 Conditional Probability](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/6-3-8-conditional-probability.md)
  - [6.3.9 End of Topic Test - Probability](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/6-3-9-end-of-topic-test-probability.md)
  - [6.3.10 Exam-Style Questions - Probability](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/6-3-10-exam-style-questions-probability.md)