Source: https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/2-3-1-solving-linear-equations

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# Solving Linear Equations

Maths: Edexcel IGCSE Higher, topic 2.3.1

## Solving a Linear Equation

When we rearrange an equation, if we do something to one side, we must do the same to the other side of the equation. To solve the linear equation 6x - 3 = 5 + 2x to find x:

### Write equation

![Write equation](https://image-v2.cdn.app.senecalearning.com/2018-04/a2ab9306-1f79-42fa-be09-18464d958f51/Screen%20Shot%202018-04-13%20at%2011.26.03.png)

### Add 3 to both sides

![Add 3 to both sides](https://image-v2.cdn.app.senecalearning.com/2018-04/2a1cfe9e-9047-4d85-8355-c2bbef01ff02/Screen%20Shot%202018-04-13%20at%2011.26.08.png)

### Subtract 2x from both sides

![Subtract 2x from both sides](https://image-v2.cdn.app.senecalearning.com/2018-04/af2b8b7c-08aa-4147-a904-aaefd021ba5a/Screen%20Shot%202018-04-13%20at%2011.26.18.png)

### Divide both sides by 4

![Divide both sides by 4](https://image-v2.cdn.app.senecalearning.com/2018-04/7819e536-b866-4426-8ae0-d637a4678284/Screen%20Shot%202018-04-13%20at%2011.26.24.png)

### x = 2 is the solution

![x = 2 is the solution](https://image-v2.cdn.app.senecalearning.com/2018-04/303cd321-6fee-4941-a654-4ea2f875b262/Screen%20Shot%202018-04-13%20at%2011.26.30.png)

### Check your answer

![Check your answer](https://image-v2.cdn.app.senecalearning.com/2018-04/ab4411b0-29dd-4b6e-ac77-8342ed8bd537/Screen%20Shot%202018-04-13%20at%2011.26.36.png)

- So x = 2 does solve the equation.

## Solving Linear Equations

Get rid of fractions and brackets first.

### Example 1 - Fractions

![Example 1 - Fractions](https://image-v2.cdn.app.senecalearning.com/2018-03/5ab4419c-9926-4bd1-8bf8-f4340195d7eb/Screen%20Shot%202018-03-22%20at%2015.23.56.png)

- If the equation has fractions in it, multiply by the denominators (bottom part).
- Here we should multiply both sides by (1 - x).

### Remove the fraction by multiplying by the bottom part

![Remove the fraction by multiplying by the bottom part](https://image-v2.cdn.app.senecalearning.com/2018-04/7f637d42-c533-4e76-9590-8ac89ccc6945/Screen%20Shot%202018-04-13%20at%2012.15.25.png)

### Example 2 - Brackets

![Example 2 - Brackets](https://image-v2.cdn.app.senecalearning.com/2018-03/f04684fd-d4b1-40c0-ac09-472449bc6732/Screen%20Shot%202018-03-22%20at%2015.24.25.png)

- After removing fractions, if the equation has brackets in it, multiply those out before rearranging.
- Here we should expand 7(4 - x) → 28 - 7x.

### Expand the brackets

![Expand the brackets](https://image-v2.cdn.app.senecalearning.com/2018-04/452a7225-06f0-4070-ba44-b3050dfb8632/Screen%20Shot%202018-04-13%20at%2012.20.35.png)

## Solving Linear Equations Graphically

### One line

![One line](https://image-v2.cdn.app.senecalearning.com/2018-04/db02a03a-5ea1-4be9-847b-fc4e984db8a3/Screen%20Shot%202018-04-13%20at%2012.30.42.png)

- To solve a linear equation, plot the line and see where it crosses the x axis.
- The line y = 2x - 6 crosses the x axis at (2, 0) so the solution is x = 2.

### Two lines

![Two lines](https://image-v2.cdn.app.senecalearning.com/2018-03/90b51a2f-64bb-4b42-9327-a1912ca2e20f/desmos-graph%20(37).png)

- For an equation where x is on both sides, plot both lines and find the x-coordinate of the point where they intersect.

### Two lines - example

![Two lines - example](https://image-v2.cdn.app.senecalearning.com/2018-04/104ca3bf-e985-49b7-b69e-1f2f104b9467/Screen%20Shot%202018-04-13%20at%2012.41.04.png)

- The example shows 2x + 2 = x + 3. Both lines are plotted.

### Two lines - example

![Two lines - example](https://image-v2.cdn.app.senecalearning.com/2018-04/104ca3bf-e985-49b7-b69e-1f2f104b9467/Screen%20Shot%202018-04-13%20at%2012.41.04.png)

- They intersect at (1, 4) so the solution is x = 1.

## Test yourself on Solving Linear Equations

- What is 7(4 - x) equal to?
- What is 12(x + 2) equal to?
- What is 2(x + 8) equal to?
- The equation $$\frac{x - 2}{x + 6} = 10 - x$$ contains an algebraic fraction.  What do we get when we multiply both sides by (x + 6)?
- The equation $$\frac{x + 2}{x + 3} = 10 - x$$ contains an algebraic fraction.  What do we get when we multiply both sides by (x + 3)?

[Practise this topic for free](https://app.senecalearning.com/classroom/course/641a6cb5-729a-404a-aeca-c7040cd18740/section/084cb73b-8260-4f73-93f0-d54e154f9732/session)

- Previous topic: [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)
- Next topic: [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)

## 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)