Edexcel FP2

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Each app in this series covers the essential topics for the module, presenting them in short video tutorials and explained in a clear mathematical style so as you can progress quickly and smoothly through the topics. There are further supplementary exercises and worked solutions from the Edexcel exam boards past papers for you to try, essential to improving your grade.

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Module Content

Inequalities:
- Fractional Inequalities
- Solution by graphical methods
- Solution by analytical methods
- Modulus Inequalities (including fractional types)

Series:
- Method of Differences

Further complex numbers:
- Modulus-argument form
- Exponential Form (Eulers 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
- Expressing sin(nθ) and cos(nθ) in terms of sinθ and cosθ
- Expressing sin^n(θ) and cos^n(θ) in terms of sin(kθ) and cos(kθ)
- Introduction - new identities you will need
- nth roots of a complex number
- Loci in the complex plane
- The locus of a point moving in a circle, |z-z1|=r
- The locus of a point moving along a perpendicular bisector, |z-z1|=|z-z2|
- The locus of a point moving along a half-line, arg(z-z1) = θ
- The locus of a point moving on the arc of a circle, arg[(z-z1)/(z-z2)]=θ
- Using complex numbers to represent regions on an Argand diagram
- 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
- Separating the variables and sketching a 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
- Substitution types
- Using substitution to reduce a differential equation to a known form

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)
- General solutions
- Introduction where f(x) = k (constant types)
- where f(x) = linear types or quadratic types or exponential types
- where f(x) = m cosωx + n sinωx (trig types)
- Particular solutions
- Using boundary conditions to solve differential equations
- Using a Substitution
- Using substitution to reduce a differential equation to a known form

Maclaurin and Taylor series:
- Maclaurin’s series
- Taylor’s 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
- Area Bounded by a Polar Curve
- Tangents

Past Exam Papers (selection)