A Level Maths

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• AS Pure
• AS Statistics
• AS Mechanics
• A-Level Pure
• A-Level Statistics
• A-Level Mechanics

AS Pure Mathematics

• Index Laws
• Expanding Brackets
• Factorising
• Negative and Fractional Indices
• Surds
• Question Set 1: Algebraic Expressions
  
• Solving Quadratics
• Completing the Square
• Sketching Quadratic Graphs
• The Discriminant
• Modelling with Quadratics
• Question Set 2: Quadratics
  
• Linear Simultaneous Equations
• Quadratic Simultaneous Equations
• Simultaneous Equations on Graphs
• Linear Inequalities
• Quadratic Inequalities
• Inequalities on Graphs
• Question Set 3: Equations and Inequalities
  
• Cubic Graphs
• Quartic Graphs
• Reciprocal Graphs
• Points of Intersection
• Translating Graphs
• Stretching Graphs
• Transforming Functions
• Question Set 4: Graphs and Transformations
  
• y = mx + c
• Equations of Straight Lines
• Parallel and Perpendicular Lines
• Length and Area
• Modelling with Straight Lines
• Question Set 5: Straight Line Graphs
  
• Midpoints and Perpendicular Bisectors
• Equation of a Circle
• Intersections of Straight Lines and Circles
• Use Tangent and Chord Properties
• Circles and Triangles
• Question Set 6: Circles
  
• Algebraic Fractions
• Dividing Polynomials
• The Factor Theorem
• Mathematical Proof
• Methods of Proof
• Question Set 7: Algebraic Methods
  
• Pascal's Triangle
• Factorial Notation
• The Binomial Expansion
• Solving Binomial Problems
• Binomial Estimation
• Question Set 8: The Binomial Expansion
  
• The Cosine Rule
• The Sine Rule
• Areas of Triangles
• Solving Triangle Problems
• Graphs of Sine, Cosine and Tangent
• Transforming Trigonometric Graphs
• Question Set 9: Trigonometric Ratios
  
• Angles in all four Quadrants
• Exact Values of Trigonometric Ratios
• Trigonometric Identities
• Solving Trigonometric Equations
• Harder Trigonometric Equations
• Equations and Identities
• Question Set 10: Trigonometric Identities and Equations
  
• Vectors
• Representing Vectors
• Magnitude and Direction
• Position Vectors
• Solving Geometric Problems
• Modelling with Vectors
• Question Set 11: Vectors
  
• Gradients of Curves
• Differentiation from first principles
• Differentiating x^n
• Differentiating Quadratics
• Differentiating functions with two or more terms
• Gradients, Tangents and Normals
• Increasing and Decreasing Functions
• Second Order Derivatives
• Stationary Points
• Sketching Gradient Functions
• Modelling with Differentiation
• Question Set 12: Differentiation
  
• Integrating x^n
• Indefinite Integrals
• Finding Functions
• Definite Integrals
• Areas under Curves
• Areas under the x-axis
• Areas between curves and lines
• Question Set 13: Integration
  
• Exponential Functions
• y = e^x
• Exponential Modelling
• Logarithms
• Laws of Logarithms
• Solving Equations using Logarithms
• Working with Natural Logarithms
• Logarithms and Non-Linear Data
• Question Set 14: Exponentials and Logarithms

AS Statistics

• Populations and Samples
• Sampling
• Non-Random Sampling
• Types of Data
• The Large Data Set
• Question Set 1: Data Collection
  
• Measures of Central Tendency
• Other Measures of Location
• Measures of Spread
• Variance and Standard Deviation
• Coding
• Question Set 2: Measures of Location and Spread
  
• Outliers
• Box Plots
• Cumulative Frequency
• Histograms
• Comparing Data
• Question Set 3: Representations of Data
  
• Correlation
• Linear Regression
• Question Set 4: Correlation
  
• Calculating Probabilities
• Venn Diagrams
• Mutually Exclusive and Independent Events
• Tree Diagrams
• Question Set 5: Probability
  
• Probability Distributions
• The Binomial Distribution
• Cumulative Probabilities
• Question Set 6: Statistical Distribution
  
• Hypothesis Testing
• Finding Critical Values
• One-Tailed Tests
• Two-Tailed Tests
• Question Set 7: Hypothesis Testing

AS Mechanics

• Constructing a Model
• Modelling Assumptions
• Quantities and Units
• Working with Vectors
• Question Set 1: Modelling in Mechanics
  
• Displacement-Time Graphs
• Velocity-Time Graphs
• Constant Acceleration Formulae 1
• Constant Acceleration Formulae 2
• Vertical Motion Under Gravity
• Question Set 2: Constant Acceleration
  
• Force Diagrams
• Forces as Vectors
• Forces and Acceleration
• Motion in 2 Dimensions
• Connected Particles
• Pulleys
• Question Set 3: Forces and Motion
  
• Functions of Time
• Using Differentiation
• Maxima and Minima Problems
• Using Integration
• Constant Acceleration Formulae
• Question Set 4: Variable Acceleration

A Level Pure Mathematics

• Proof by Contradiction
• Algebraic Fractions
• Partial Fractions
• Repeated Factors
• Algebraic Division
• Question Set 1: Algebraic Methods
  
• The Modulus Function
• Functions and Mappings
• Composite Functions
• Inverse Functions
• y=|f(x)| and y=f(|x|)
• Combining Transformations
• Solving Modulus Problems
• Question Set 2: Functions and Graphs
  
• Arithmetic Sequences
• Arithmetic Series
• Geometric Sequences
• Geometric Series
• Sum to Infinity
• Sigma Notation
• Recurrence Relations
• Modelling with Series
• Question Set 3: Sequences and Series
  
• Expanding (1 + x)^n
• Expanding (a + bx)^n
• Using Partial Fractions
• Question Set 4: Binomial Expansion
  
• Radian Measure
• Arc Length
• Areas of Sectors and Segments
• Solving Trigonometric Equations
• Small Angle Approximations
• Question Set 5: Radians
  
• Secant, Cosecant and Cotangent
• Graphs of Sec x, Cosec x and Cot x
• Using Sec x, Cosec x and Cot x
• Trigonometric Identities
• Inverse Trigonometric Functions
• Question Set 6: Trigonometric Functions
  
• Addition Formulae
• Using the Angle Addition Formulae
• Double Angle Formulae
• Solving Trigonometric Equations
• Simplifying a cos x +- b sin x
• Proving Trigonometric Identities
• Modelling with Trigonometric Functions
• Question Set 7: Trigonometry and Modelling
  
• Parametric Equations
• Using Trigonometric Identities
• Curve Sketching
• Points of Intersection
• Modelling with Parametric Equations
• Question Set 8: Parametric Equations
  
• Differentiating sin x and cos x
• Differentiating exponentials and logarithms
• The Chain Rule
• The Product Rule
• The Quotient Rule
• Differentiating Trigonometric Functions
• Parametric Differentiation
• Implicit Differentiation
• Using Second Derivatives
• Rates of Change
• Question Set 9: Differentiation
  
• Locating Roots
• Iteration
• The Newton-Raphson Method
• Applications to Modelling
• Question Set 10: Numerical Methods
  
• Integrating Standard Functions
• Integrating f(ax + b)
• Using Trigonometric Identities
• Reverse Chain Rule
• Integration by Substitution
• Integration by Parts
• Partial Fractions
• Finding Areas
• The Trapezium Rule
• Solving Differential Equations
• Modelling with Differential Equations
• Question Set 11: Integration
  
• 3D Coordinates
• Vectors in 3D
• Solving Geometric Problems
• Application to Mechanics
• Question Set 12: Vectors

A Level Statistics

• Exponential Models
• Measuring Correlation
• Hypothesis Testing for Zero Correlation
• Question Set 1: Regression, Correlation and Hypothesis Testing
  
• Set Notation
• Conditional Probability
• Conditional Probabilities in Venn Diagrams
• Probability Formulae
• Tree Diagrams
• Question Set 2: Conditional Probability
  
• The Normal Distribution
• Finding Probabilities for Normal Distributions
• The Inverse Normal Distribution Function
• The Standard Normal Distribution
• Finding the mean and standard deviation
• Approximating a Binomial Distribution
• Hypothesis Testing with the Normal Distribution
• Question Set 3: The Normal Distribution

A level Mechanics

• Moments
• Resultant Moments
• Equilibrium
• Centres of Mass
• Tilting
• Question Set 1: Moments
  
• Resolving Forces
• Inclined Planes
• Friction
• Question Set 2: Forces and Friction
  
• Horizontal Projection
• Horizontal and Vertical Components
• Projection at Any Angle
• Projctile Motion Formulae
• Question Set 3: Projectiles
  
• Static Particles
• Modelling with Statics
• Friction and Static Particles
• Static Rigid Bodies
• Dynamics and Inclined Planes
• Connected Particles
• Question Set 4: Applications of Forces
  
• Vectors in Kinematics
• Vector Methods with Projectiles
• Variable Acceleration in One Dimension
• Differentiating Vectors
• Integrating Vectors
• Question Set 5: Further Kinematics