# Playlist for Core Maths / Pure Maths

## Other Playlists and Main Index

### Algebra and Functions

Indices

Surds

Functions

Factorising

Completing the Square

Polynomials

Graph Transformations

Graph Transformations

Simultaneous Equations

Inequalities

### Sequences and series

Recurrence relationships

Sigma notation

Arithmetic sequences and series

Geometric Series

Binomial Expansion (Positive integer powers)

### Coordinate geometry (1)

Lines

Intersection of graphs

Circles

### Trigonometry (1)

Right-Angled Triangles

Trigonometric Ratios

Graphs

Applications

Equations

Identities

### Differentiation(1)

Introduction

Tangents and Normals

Stationary Points

Increasing and Decreasing functions

### Algebra and Functions (2)

Algebraic Long Division

Factor Theorem

Remainder Theorem

Exponential functions

Logarithms

### Functions

Notation

Domain and Range

Combining Functions

Inverse Functions

Transformations of Graphs (Revision)

Modulus Functions

Exponential Function ex

Natural Log Functions

Modelling Curves of the form y=kxn and y=kax

### Trigonometry (2)

Secant, Cosecant and Cotangent

Inverse trig. functions

Identities

• Pythagorean type: sin²x + cos²x ≡1 ; 1 + tan²x ≡ sec²x ; 1 + cot²x ≡ cosec²x
• Examples : 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8

• Addition type: sin(A±B), cos(A±B) and tan(A±B)

• Double angle type for sin2A, cos2A and tan2A

• Factor Formulae

• A cos x ± B sin x and A sin x ± B cos x type

Equations using:

• the identities : sin²x + cos²x ≡1 ; 1 + tan²x ≡ sec²x ; 1 + cot²x ≡ cosec²x
• Examples: 1 | 2 | 3

• the identities for sin2A, cos2A and tan2A
• Examples: 1 | 2 | 3

• the identities for A cos x ± B sin x and A sin x ± B cos x

Miscellaneous Exam Practice

### Differentiation(2)

Using the Formula Book

The Chain Rule

The Product Rule

The Quotient Rule

A Special Result

Miscellaneous Exam Practice

Connected Rates of Change

### Algebra and Series (2)

Rational expressions

Partial Fractions

Binomial Expansion

### Coordinate Geometry (2)

Parametric Equations

Exam Questions

### Differentiation(3)

Exponential Functions

Parametric Functions

Implicit Functions

### Integration (2)

(ax+b)n types

The exponential functions : ex, eax and e(ax+b)

Reciprocal Functions : 1/x and 1/(ax+b)

Integrals of the form : f'(x)/f(x)

Integrals of the form : f'(x)ef(x)

Trigonometric types

Partial fraction types

Substitution

By Parts

Mixed examples

Applications

Differential equations

• Separating the variables
• Forming differential equations

## Other Playlists and Main Index

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