Mathematics

All the mathematics revision material is based on the Edexcel syllabus.

The main topics that can be found in my revision notes are the following:

Core 2: 

• Polynomials
• Algebra of Polynomials
• Remainder Theorem
• Factor Theorem
• Functions
• The Modulus Function
• Circles
• Sequences and Series
• Arithmetic Progression
• Geometric Progression
• Infinite sum of a geometric progression
• Radians

Core 3: 

• Trigonometry
• Reciprocal Functions
• Proving Identities
• Compound Angle Formulae
• Harmonic Form
• Logarithms
• 3 Laws of Logs
• Stationary Points
• Increasing and decreasing functions
• Differentiation
• Product Rule
• Chain Rule
• Quotient Rule
• Exponentials and Logs

Statistics 1: 

• Probability
• p(A or B)
• p(A and B)
• Bayes' Theorem
• Tree Diagrams
• Discrete Random Variables
• Cumulative Distribution Function
• Expected Value
• Discrete Uniform Distribution
• Basic Statistics
• Diagrams
• Histograms
• Stem and Leaf
• Box and Whisker plot
• Finding Medians and Quartiles
• Determining Skewness
• Outliers
• Statistics
• Average
• Spread
• Correlation
• Scatter Diagrams
• Product-Moment Correlation Coefficient (PMCC)
• Regression
• Normal Distribution
• Standard Normal Distribution

Statistics 2: 

• Definitions
• Binomial Distribution
• Poisson Distribution
• Continuous Random Variables
• Probability Density Functions
• Cumulative Distribution Function
• Population, Census and Sampling
• Random Sampling
• Methods of Collection
• Sampling Distribution of a Statistic
• Continuous Distributions
• Continuous Uniform Distribution
• Normal approximation to Binomial
• Normal approximation to Poisson
• Hypothesis Testing

Statistics 3: 

• Combination of Random Variables
• Sampling
• Taking a Census
• Sampling
• Random Sampling
• Simple Random Sampling
• Random Number Sampling
• Lottery or Ticket Sampling
• Systematic Sampling
• Stratified Sampling
• Non-Random Sampling
• Quota Sampling
• Primary and Secondary Sources of Data
• Estimation, Confidence, Intervals and Tests
• Estimating Population Parameters using a Sample
• Standard error of the mean
• Central Limit Theorem
• Confidence Intervals for a population parameter
• Interpreting Confidence Intervals
• Hypothesis Testing about the mean of a Normal Distribution
• Testing Hypotheses about the difference between means of two independent normal distributions
• Testing Hypotheses and finding Confidence Intervals for large samples
• Goodness of fit and Contingency Tables
• Degrees of Freedom
• Testing a Binomial as a model
• Testing a Poisson as a model
• Testing a Normal as a model
• Testing a Continuous Uniform as a model
• Contingency Tables
• Regression and Correlation
• Spearman's Rank Correlation Coefficient

Mechanics 1: 

• Kinematics
• Friction
• Momentum and Impulse
• Moments

Mechanics 2: 

• Centres of Mass
• For Particles
• For Rigid Bodies
• Work
• Kinetic Energy
• Power
• Gravitational Potential Energy
• Coefficient of Restituion

Mechanics 3: 

• Further Kinematics
• Elastic String and Springs
• Energy stored in an Elastic String or Spring
• Further Dynamics
• Impulse and Momentum
• Work and Energy
• Newton's Law of Gravitation
• Simple Harmonic Motion
• Motions in a Circle
• Horizontal Circle
• Vertical Circle
• Statics of Rigid Bodies
• Centre of Mass of a Lamina
• Centre of Mass of a Uniform Solid of Revolution
• Suspension of a Body from a Fixed Point
• Equilibrium of Bodies resting on a Plane Surface
• Determining whether a Body will remain in Equilibrium

Further Pure 2: 

• Inequalities
• Series - Method of Differences
• Further Complex Numbers
• Euler's Formula
• De Moivre's Theorem
• Solving Equations using Exponential Forms
• Multiple Angles to Powers
• Powers to Multiple Angles
• Loci in the Complex Plane
• Transformations of the Complex Plane
• First-Order Differential Equations
• Separation of Variables
• Integrating Factor
• Substitution
• Second-Order Differential Equations
• Maclaurin and Taylor Series
• Polar Coordinates
• Polar and Cartesian forms
• Tangents to Polar Curves
• Area of a Sector of a Polar Curve

Further Pure 3: 

• Hyperbolic Functions
• Identities
• Osborn's Rule
• Further Coordinate Systems
• Differentiation
• Integration
• Length of an Arc
• Area of Surface of Revolution
• Vectors
• Areas using Vector Products
• Triple Scalar Product
• Volumes using Triple Scalar Products
• Equations of Lines
• Equations of Planes
• Angles between plane-line and plane-plane
• Shortest Distances
• From a point to a line
• From a point to a plane
• Between two skew lines
• From origin to a plane
• Further Matrix Algebra
• Determinant of 3x3 matrix
• Inverse
• Eigenvectors
• Orthogonal Matrices
• Diagonal Matrices