Source: https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/3-5-1-derivatives-of-functions

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# Derivatives of Functions

Maths: Edexcel IGCSE Higher, topic 3.5.1

## Derivatives

The derivative of a function, f(x), is the function that describes how the gradient changes as x changes. This is the same as saying that the derivative the rate of change of an equation.

### Derivatives

![Derivatives](https://image-v2.cdn.app.senecalearning.com/courseImages/chemistry/(s)%206.1.1%20-%20rate%20of%20reaction%20calculation%20from%20graph-min.png)

- The derivative of a function can be used to calculate the gradient of the function at any point.
- The derivative of f($$x$$) is called 
f'($$x$$).
 - f'($$x$$) can be called 
"*f dash of* $$x$$" or "*f prime*".

### Example

![Example](https://image-v2.cdn.app.senecalearning.com/2019-04/4b70f9e1-b8db-46e1-90ae-fd4e4671bfed/tangent-curve%20(1).png)

- A function, f($$x$$), 
has the derivative, f'($$x$$) = 
2$$x$$ + 5
- What is the gradient of f($$x$$) when 
$$x$$ = 3?
 - Gradient at $$x$$ = 3 is f'(3).
 - f'(3) = (2 × 3) + 5 = 11
- f($$x$$) has a gradient of 11 when 
$$x$$ = 3.

## Differentiation

The derivative of a function can be worked out through a process called differentiation.

### Differentiation

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

- There are different ways to display the derivative of a function. 
 - If your equation starts with y =, then the derivative of the equation is $$\large\frac{dy}{dx}$$.
 - If your function starts with f($$x$$) =, then the derivative of the equation is 
f'($$x$$).
 - The exam may also ask you to find the rate of change, the gradient of the tangent or to differentiate a function.

### General rule

![General rule](https://image-v2.cdn.app.senecalearning.com/2018-09/3bf436b2-5bb6-43b1-bf1c-a381fc5a26c0/rules-rule-board-.jpg)

- To differentiate a whole equation/function, each term should be differentiated individually.
- The general rule for differentiating a term is:
 - f($$x$$) = 
$$ax^n$$ → 
f'($$x$$) = 
$$nax$$
$$n$$−1

### Examples

![Examples](https://image-v2.cdn.app.senecalearning.com/2019-04/4b70f9e1-b8db-46e1-90ae-fd4e4671bfed/tangent-curve%20(1).png)

- f($$x$$) = 
$$ax^n$$ → 
f'($$x$$) = 
$$nax$$
$$n$$−1
 - f($$x$$) = 
$$x$$3 → 
f'($$x$$) = 
3$$x$$2
 - f($$x$$) = 
2$$x$$3 → 
f'($$x$$) = 
6$$x$$2
 - f($$x$$) = 
6$$x$$ → 
f'($$x$$) = 
6 
(remember f($$x$$) = 
6$$x$$ is the same as 
6$$x$$1)
 - f($$x$$) = 
3$$x$$4 → 
f'($$x$$) = 
12$$x$$3
 - f($$x$$) = 
9 → 
f'($$x$$) = 
0 (remember f($$x$$) = 9 is the same as 
9$$x$$0)

### Example 1 with multiple terms

![Example 1 with multiple terms](https://image-v2.cdn.app.senecalearning.com/2019-04/4b70f9e1-b8db-46e1-90ae-fd4e4671bfed/tangent-curve%20(1).png)

- For each term in an expression, use f($$x$$) = 
$$ax^n$$ → 
f'($$x$$) = 
$$nax$$
$$n$$−1
 - f($$x$$) = 
$$x$$3 + 
2$$x$$2 + 
7$$x$$
 - f'($$x$$) = 
3$$x$$2 + 
4$$x$$ + 
7

### Example 1 with multiple terms

![Example 1 with multiple terms](https://image-v2.cdn.app.senecalearning.com/2019-04/4b70f9e1-b8db-46e1-90ae-fd4e4671bfed/tangent-curve%20(1).png)

- For each term in an expression, use f($$x$$) = 
$$ax^n$$ → 
f'($$x$$) = 
$$nax$$
$$n$$−1
 - f($$x$$) = 
3$$x$$4 + 
5$$x$$3 + 
4$$x$$2
 - f'($$x$$) = 
12$$x$$3 + 
15$$x$$2 + 
8$$x$$

## Derivatives in Kinematics

Another use for the derivative is to analyse motion along a line.

### Velocity

![Velocity](https://image-v2.cdn.app.senecalearning.com/2019-10/7d7ace43-4b60-4f68-ba6b-58332dd2b955/velocity.png)

- The velocity of an object in motion is the rate of change of its displacement.
- So the derivative of an object's displacement as a function of time is equal to the velocity, or:
 - v(t) = s'(t)
- Where v(t) is the velocity and s(t) is the position, both as a function of time

### Acceleration

![Acceleration](https://image-v2.cdn.app.senecalearning.com/2019-10/b85bca2f-674b-442d-b638-5db128e3b11a/acceleration.png)

- Taking the derivative of the velocity gives the acceleration of the object, which is the rate of change of velocity.
 - a(t) = v'(t) = s''(t)
- So the acceleration can also be thought of as the second derivative of the object's displacement with respect to time.

## Test yourself on Derivatives of Functions

- What are the ways you can say f'(x) out loud?
- The derivative of a function, f(x), is f'(x) = 5x + 10. What is the gradient of f(x) when x = −1?
- The derivative of a function, f(x), is f'(x) = $$\large\frac{1}{2}$$x2 − 3x + 2. What is the gradient of f(x) when x = 4?
- The derivative of a function, f(x), is f'(x) = 2x − 1. What is the gradient of f(x) when x = 2?
- The derivative of a function, f(x), is f'(x) = 9x3 − 10x. What is the gradient of f(x) when x = −1?

[Practise this topic for free](https://app.senecalearning.com/classroom/course/641a6cb5-729a-404a-aeca-c7040cd18740/section/ca2e5446-68e5-46b4-952f-662f33ea2ae9/session)

- Previous topic: [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)
- Next topic: [3.5.2 Maxima & Minima](https://senecalearning.com/en-gb/revision-notes/igcse/maths/edexcel-igcse/higher/3-5-2-maxima-and-minima.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)