# Edexcel FP2 Further Pure Maths

### Inequalities

Fractional Inequalities

- Example 1
- Example 2

Modulus Inequalities (including fractional types)

- Example 1
- Example 2
- Exam Questions

### Series

Method of Differences

### Further complex numbers

- Modulus-argument form
- Exponential Form (Euler's relation)
- Multiplication rule for the mod and argument of two complex numbers
- Division rule for the mod and argument of two complex numbers

de Moivre's Theorem

- de Moivre's theorem
**Expressing sin nθ and cos nθ in terms of sinθ and cosθ**- Expressing sin
^{n}θ and cos^{n}θ in terms of sin*k*θ and cos*k*θ

- nth roots of a complex number

Loci in the complex plane

- The locus of a point moving in a circle : | z- z
_{1}| = r - The locus of a point moving along a perpendicular bisector : | z-z
_{1 }| = | z-z_{2 }| - The locus of a point moving along a half-line : arg(z-z
_{1}) = θ - The locus of a point moving on the arc of a circle : arg[ (z-z
_{1}) / (z-z_{2}) ] = θ - Using complex numbers to represent regions on an Argand diagram
- Exam Questions

Transformations of the complex plane

### First order differential equations

Separating the variables (Revision)

- Finding a general solution and a particular solution
- Working with constants in log types
- Exponential and trig type (a little more challenging)

Family of curves

Exact equations (integrating factors)

- Exact equations where one side is the exact derivative of a product
- Solving equations of the form dy/dx + Py = Q using an integrating factor
- Exam Questions

Substitution types

### Second order differential equations

Equations of the form *a* d²y/dx² + *b* dy/dx + *c*y =
0

- Introduction
- Solving equations where
*b*² - 4*ac > 0* - Solving equations where
*b*² - 4*ac = 0* - Solving equations where
*b*² - 4*ac < 0*

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

- General solutions
- Exam Questions

- Particular solutions
- Exam Questions

Using a Substitution

### Maclaurin and Taylor series

### Polar coordinates and curves

Coordinates

- Defining the position of a point
- Converting cartesian coordinates to polar coordinates
- Converting polar coordinates to cartesian coordinates

Equations of Curves

- Converting the equation of a polar curve to cartesian form
- Converting the equation of a cartesian curve to polar form

- Sketching the polar equation of:

Area Bounded by a Polar Curve

Tangents