A Level Maths

The old a level page can be found here.

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

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AS Pure Mathematics

• 1.1  Index Laws
• 1.2  Expanding Brackets
• 1.3  Factorising
• 1.4  Negative and Fractional Indices
• 1.5  Surds
• Question Set 1: Algebraic Expressions
  
• 2.1  Solving Quadratics
• 2.2  Completing the Square
• 2.3  Sketching Quadratic Graphs
• 2.4  The Discriminant
• 2.5  Modelling with Quadratics
• Question Set 2: Quadratics
  
• 3.1  Linear Simultaneous Equations
• 3.2  Quadratic Simultaneous Equations
• 3.3  Simultaneous Equations on Graphs
• 3.4  Linear Inequalities
• 3.5  Quadratic Inequalities
• 3.6  Inequalities on Graphs
• Question Set 3: Equations and Inequalities
  
• 4.1  Cubic Graphs
• 4.2  Quartic Graphs
• 4.3  Reciprocal Graphs
• 4.4  Points of Intersection
• 4.5  Translating Graphs
• 4.6  Stretching Graphs
• 4.7  Transforming Functions
• Question Set 4: Graphs and Transformations
  
• 5.1  y = mx + c
• 5.2  Equations of Straight Lines
• 5.3  Parallel and Perpendicular Lines
• 5.4  Length and Area
• 5.5  Modelling with Straight Lines
• Question Set 5: Straight Line Graphs
  
• 6.1  Midpoints and Perpendicular Bisectors
• 6.2  Equation of a Circle
• 6.3  Intersections of Straight Lines and Circles
• 6.4  Use Tangent and Chord Properties
• 6.5  Circles and Triangles
• Question Set 6: Circles
  
• 7.1  Algebraic Fractions
• 7.2  Dividing Polynomials
• 7.3  The Factor Theorem
• 7.4  Mathematical Proof
• 7.5  Methods of Proof
• Question Set 7: Algebraic Methods
  
• 8.1  Pascal's Triangle
• 8.2  Factorial Notation
• 8.3  The Binomial Expansion
• 8.4  Solving Binomial Problems
• 8.5  Binomial Estimation
• Question Set 8: The Binomial Expansion
  
• 9.1  The Cosine Rule
• 9.2  The Sine Rule
• 9.3  Areas of Triangles
• 9.4  Solving Triangle Problems
• 9.5  Graphs of Sine, Cosine and Tangent
• 9.6  Transforming Trigonometric Graphs
• Question Set 9: Trigonometric Ratios
  
• 10.1  Angles in all four Quadrants
• 10.2  Exact Values of Trigonometric Ratios
• 10.3  Trigonometric Identities
• 10.4  Solving Trigonometric Equations
• 10.5  Harder Trigonometric Equations
• 10.6  Equations and Identities
• Question Set 10: Trigonometric Identities and Equations
  
• 11.1  Vectors
• 11.2  Representing Vectors
• 11.3  Magnitude and Direction
• 11.4  Position Vectors
• 11.5  Solving Geometric Problems
• 11.6  Modelling with Vectors
• Question Set 11: Vectors
  
• 12.1  Gradients of Curves
• 12.2  Differentiation from first principles
• 12.3  Differentiating x^n
• 12.4  Differentiating Quadratics
• 12.5  Differentiating functions with two or more terms
• 12.6  Gradients, Tangents and Normals
• 12.7  Increasing and Decreasing Functions
• 12.8  Second Order Derivatives
• 12.9  Stationary Points
• 12.10  Sketching Gradient Functions
• 12.11  Modelling with Differentiation
• Question Set 12: Differentiation
  
• 13.1  Integrating x^n
• 13.2  Indefinite Integrals
• 13.3  Finding Functions
• 13.4  Definite Integrals
• 13.5  Areas under Curves
• 13.6  Areas under the x-axis
• 13.7  Areas between curves and lines
• Question Set 13: Integration
  
• 14.1  Exponential Functions
• 14.2  y = e^x
• 14.3  Exponential Modelling
• 14.4  Logarithms
• 14.5  Laws of Logarithms
• 14.6  Solving Equations using Logarithms
• 14.7  Working with Natural Logarithms
• 14.8  Logarithms and Non-Linear Data
• Question Set 14: Exponentials and Logarithms

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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 Distributions
  
• Hypothesis Testing
• Finding Critical Values
• One-Tailed Tests
• Two-Tailed Tests
• Question Set 7: Hypothesis Testing

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AS Mechanics

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

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A Level Pure Mathematics

• 1.1  Proof by Contradiction
• 1.2  Algebraic Fractions
• 1.3  Partial Fractions
• 1.4  Repeated Factors
• 1.5  Algebraic Division
• Question Set 1: Algebraic Methods
  
• 2.1  The Modulus Function
• 2.2  Functions and Mappings
• 2.3  Composite Functions
• 2.4  Inverse Functions
• 2.5  y=|f(x)| and y=f(|x|)
• 2.6  Combining Transformations
• 2.7  Solving Modulus Problems
• Question Set 2: Functions and Graphs
  
• 3.1  Arithmetic Sequences
• 3.2  Arithmetic Series
• 3.3  Geometric Sequences
• 3.4  Geometric Series
• 3.5  Sum to Infinity
• 3.6  Sigma Notation
• 3.7  Recurrence Relations
• 3.8  Modelling with Series
• Question Set 3: Sequences and Series
  
• 4.1  Expanding (1 + x)^n
• 4.2  Expanding (a + bx)^n
• 4.3  Using Partial Fractions
• Question Set 4: Binomial Expansion
  
• 5.1  Radian Measure
• 5.2  Arc Length
• 5.3  Areas of Sectors and Segments
• 5.4  Solving Trigonometric Equations
• 5.5  Small Angle Approximations
• Question Set 5: Radians
  
• 6.1  Secant, Cosecant and Cotangent
• 6.2  Graphs of Sec x, Cosec x and Cot x
• 6.3  Using Sec x, Cosec x and Cot x
• 6.4  Trigonometric Identities
• 6.5  Inverse Trigonometric Functions
• Question Set 6: Trigonometric Functions
  
• 7.1  Addition Formulae
• 7.2  Double Angle Formulae
• 7.3  Solving Trigonometric Equations
• 7.4  Simplifying a cos x +- b sin x
• 7.5  Proving Trigonometric Identities
• 7.6  Modelling with Trigonometric Functions
• Question Set 7: Trigonometry and Modelling
  
• 8.1  Parametric Equations
• 8.2  Using Trigonometric Identities
• 8.3  Curve Sketching
• 8.4  Points of Intersection
• 8.5  Modelling with Parametric Equations
• Question Set 8: Parametric Equations
  
• 9.1  Differentiating sin x and cos x
• 9.2  Differentiating exponentials and logarithms
• 9.3  The Chain Rule
• 9.4  The Product Rule
• 9.5  The Quotient Rule
• 9.6  Differentiating Trigonometric Functions
• 9.7  Parametric Differentiation
• 9.8  Implicit Differentiation
• 9.9  Using Second Derivatives
• 9.10  Rates of Change
• Question Set 9: Differentiation
  
• 10.1  Locating Roots
• 10.2  Iteration
• 10.3  The Newton-Raphson Method
• 10.4  Applications to Modelling
• Question Set 10: Numerical Methods
  
• 11.1  Integrating Standard Functions
• 11.2  Integrating f(ax + b)
• 11.3  Using Trigonometric Identities
• 11.4  Reverse Chain Rule
• 11.5  Integration by Substitution
• 11.6  Integration by Parts
• 11.7  Partial Fractions
• 11.8  Finding Areas
• 11.9  The Trapezium Rule
• 11.10  Solving Differential Equations
• 11.11  Modelling with Differential Equations
• Question Set 11: Integration
  
• 12.1  3D Coordinates
• 12.2  Vectors in 3D
• 12.3  Solving Geometric Problems
• 12.4  Application to Mechanics
• Question Set 12: Vectors

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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

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A level Mechanics

This section is currently under development

• 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
• Projectile Motion Formulae
• Question Set 3: Projectiles
  
• Static Particles
• Modelling with Statics
• Friction and Static Particles
• Static Rigid Bodies
• Dynamics and Inclined Planes
• Connected Particles 2
• 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