# Playlist for Further Maths / Further Pure Maths

## Other Playlists and Main Index

### Numerical solutions to equations

Solving equations of the form f(x)=0

### Binary operations

Binary Operations

### Coordinate systems

Parabola

• Cartesian Form
• Parametric form
• Tangents and Normals
• Cartesian Form :
• Parametric Form :
• Exam Questions

Hyperbola (rectangular)

• Cartesian and Parametric Forms
• Tangents and Normals
• Cartesian Form :
• Parametric Form :
• Exam Questions

### Matrix algebra

Applications

• Simultaneous Equations
• Linear Transformations
• Rotations about the origin of:
• Reflections in the:
• Enlargement, scale factor k, centre (0,0) where:
• Transformations Test:
• Combinations of Transformations:
• Inverse Matrices:
• Area Scale Factor:

Exam Questions

### Series

Exam Questions

Method of Differences

### Proof by mathematical induction

Series

Divisibility and Multiple Tests

Recurrence Relations

Matrices

### Inequalities

Fractional Inequalities

• Example 1
• Example 2

Modulus Inequalities (including fractional types)

### Further complex numbers

de Moivre's Theorem

• de Moivre's theorem
• Expressing sin nθ and cos nθ in terms of sinθ and cosθ
• Expressing sinnθ and cosnθ in terms of sinkθ and coskθ
• nth roots of a complex number

Loci in the complex plane

Transformations of the complex plane

### First order differential equations

Separating the variables (Revision)

Family of curves

Exact equations (integrating factors)

Substitution types

### Second order differential equations

Equations of the form a d²y/dx² + b dy/dx + cy = 0

Equations of the form a d²y/dx² + b dy/dx + cy = f(x)

Substitution types

### Maclaurin and Taylor series

Maclaurins series

Taylor's series

### Polar coordinates and curves

Coordinates

Equations of Curves

• Sketching the polar equation of:

Area Bounded by a Polar Curve

Tangents

### Further matrix algebra

Transposed and symmetric matrices

• Still to be completed (see note at end)

## Other Playlists and Main Index

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