A Level Maths Revision Notes

On this page you will find a complete set of lesson notes for the A Level Maths syllabus as taught from September 2017. These notes are lessons delivered by myself to my own students so if you have missed any lessons or just feel the need to brush up, please take a look.

1PureProofImplication and Proof By Deduction
1PureProofSets and Interval Notation
1PureIndices and SurdsIntro to Indices
1PureIndices and SurdsWriting One Number as a Power of Another
1PureIndices and SurdsBasic Surd Operations
1PureIndices and SurdsRationalising the Denominator
1PureQuadraticsFactorising and Solving Quadratic Equations
1PureQuadraticsCompleting the Square
1PureQuadraticsSimultaneous Equations
1PureQuadraticsLinear Inequalities
1PureQuadraticsQuadratic Inequalities
1PureQuadraticsStealth Quadratics
1PurePolynomialsPolynomial Division and Factor Theorem
1PureGraphs and FunctionsStandard Graphs
1PureGraphs and FunctionsSketching Cubic Graphs
1PureGraphs and FunctionsSketching Quartic Graphs
1PureGraphs and FunctionsTransformations of Graphs and Functions
1PureStraight LinesIntroduction to Straight Lines
1PureStraight LinesParallel and Perpendicular Lines
1PureCirclesEquations of Circles
1PureCirclesTangents and Normals To Circles
1PureExponentials and LogarithmsIntro to Logarithms
1PureExponentials and LogarithmsLaws of Logarithms
1PureExponentials and LogarithmsSolving Exponential Equations
1PureExponentials and LogarithmsSolving Logarithmic Equations
1PureExponentials and LogarithmsLogarithmic Graphs
1PureExponentials and LogarithmsModelling with Exponentials
1PureExponentials and Logarithmse and Natural Logarithms
1PureExponentials and LogarithmsExponential Growth
1PureExponentials and LogarithmsDifferential of exp(kx)
1PureBinomial ExpansionIntro to Binomial Expansion
1PureBinomial ExpansionFurther Binomial Expansion
1PureTrigonometryEquations and Trig Identities
1PureTrigonometryFinding a Trigonometric Quantity Given Another
1PureTrigonometryFurther Solving Trig Equations
1PureTrigonometrySolving Trig Equations
1PureVectorsCollinear Vectors
1PureVectorsGeometric Problems Using Vectors
1PureVectorsMagnitude and Direction of a Vector
1PureDifferentiationBasic Differentiation of Powers of x
1PureDifferentiationDifferentiation (Tangents and Normals)
1PureDifferentiationDifferentiation from First Principles
1PureDifferentiationFinding and Classifying Stationary Points
1PureDifferentiationFurther Differentiation from First Principles
1PureDifferentiationSuccessive Approximatons in Differentiation
1PureDifferentiationModelling with Differentiation
1PureDifferentiationPractical Differentiation Problems
1PureIntegrationArea Between a Curve and the x-Axis
1PureIntegrationDefinite Integrals
1PureIntegrationIntroduction to Integration
1PureIntegrationSolving Differential Equations
1MechKinematicsVariable Acceleration
1MechKinematicsS-T and V-T Graphs
1MechKinematicsDeriving SUVAT Equations
1MechKinematicsIntro to SUVAT
1MechKinematicsMotion Under Gravity
1MechForces and MotionNewton’s Second Law (F=ma) in One and Two Dimensions
1MechForces and MotionResolving Perpendicular Forces
1MechConnected ParticlesParticles Over a Pulley
1MechConnected ParticlesHorizontally Connected Particles
1StatsSamplingSampling Techniques
1StatsStatistical DiagramsCumulative Frequency Diagrams
1StatsStatistical DiagramsHistograms
1StatsMeasures of Location and SpreadOutliers and Cleaning Data
1StatsMeasures of Location and SpreadAverages and Spread
1StatsCorrelation and RegressionCorrelation and Regression
1StatsDiscrete Random VariablesDiscrete Random Variables
1StatsDiscrete Random VariablesCalculating Binomial Probabilities
1StatsDiscrete Random VariablesCumulative Binomial Probabilities
1StatsHypothesis TestingOne Tail Binomial Hypothesis Testing
1StatsHypothesis TestingTwo Tail Binomial Hypothesis Testing
1StatsHypothesis TestingCritical Regions in Hypothesis Testing
1StatsHypothesis TestingExam Questions Involving Trial and Improvement
2PureSequences and SeriesArithmetic Sequences
2PureSequences and SeriesGeometric Sequences
2PureSequences and SeriesSum To Infinity of Geometric Sequences
2PureSequences and SeriesInductive Sequences
2PureRational Functions and Partial FractionsFurther Polynomial Division
2PureRational Functions and Partial FractionsRational Functions
2PureRational Functions and Partial FractionsPartial Fractions
2PureGeneral Binomial ExpansionGeneral Binomial Expansion
2PureFunctionsComposite Functions
2PureFunctionsDomain and Range
2PureFunctionsInverse of a Function
2PureFunctionsMultiple Transformations of Functions
2PureFunctionsSketching Modulus Functions
2PureFunctionsModulus Inequalities
2PureTrigonometryRadians, Circle Sectors and Triangles
2PureTrigonometryInverse Trig Functions
2PureTrigonometryCompound Angle Formulae
2PureTrigonometryDouble Angle Formulae
2PureTrigonometryRcos(x+a) and Rsin(x+a)
2PureTrigonometrySmall Angle Approximations
2PureTrigonometrySolving Equations With Reciprocal Trig Functions
2PureTrigonometryFurther Reciprocal Trig Functions and Proofs
2PureDifferentiationChain Rule
2PureDifferentiationProduct Rule
2PureDifferentiationQuotient Rule
2PureDifferentiationDifferentiating Trig Functions
2PureDifferentiationChain Rule
2PureDifferentiationImplicit Differentiation
2PureIntegrationStandard Integrals
2PureIntegrationMethods for Trig Integration
2PureIntegrationIntegration by Substitution
2PureIntegrationIntegration by Parts
2PureIntegrationIntegration Using Partial Fractions
2PureIntegrationFurther Integration With Partial Fractions
2PureIntegrationStandard Integrals
2PureIntegrationIntegration – Choosing the Correct Method
2PureIntegrationArea Between a Curve and the y-Axis
2PureIntegrationArea Between Two Curves
2PureProofProof By Contradiction
2PureDifferentiationConvexity, Concavity and Points of Inflection
2PureParametric EquationsIntro to Parametric Equations
2PureParametric EquationsParametric Differentiation
2PureParametric EquationsParametric Integration
2PureDifferentiationConnected Rates of Change
2PureIntegrationFurther Integration and Area
2PureIntegrationDifferential Equations – Separating the Variables
2PureNumerical MethodsFixed Point Iteration
2PureNumerical MethodsLocating Roots with a Change of Sign
2PureNumerical MethodsNewton Raphson Method
2PureNumerical MethodsTrapezium Rule and Numerical Integration
2PureVectorsVectors in 3d
2MechKinematicsConstant Acceleration in 2d
2MechKinematicsVariable Acceleration in 2d
2MechKinematicsParticles Projected Horizontally
2MechKinematicsTrajectory of a Projectile
2MechForces and MotionVectors in 3d
2MechForces and MotionResolving Non-Perpendicular Forces
2MechForces and MotionStatic Bodies in 2d
2MechForces and MotionForces on a Slope with Friction
2MechMomentsIntro to Moments
2MechMomentsNon-Uniform Rods
2MechMomentsMoments in 2d
2StatsConditional ProbabilityProbabilities and Venn Diagrams
2StatsConditional ProbabilityConditional Probabilities on Venn Diagrams
2StatsConditional ProbabilityConditional Probability on Tree Diagrams
2StatsConditional ProbabilityFurther Conditional Probability
2StatsNormal DistributionNormal Distribution – Calculating Probabilities
2StatsNormal DistributionNormal Distribution – Calculating Unknown Mean and Variance
2StatsNormal DistributionInverse Normal Distribution
2StatsNormal DistributionHypothesis Test for Sample Mean
2StatsNormal DistributionNormal Approximation to Binomial Distribution
2StatsCorrelation and RegressionHypothesis Tests for Correlation