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  • Definitions, terminology and keys
  • Normalisation
  • What is a database
  • Fundamentals of Databases
  • Assembly Programming
  • Fetch Decode Execute Cycle
  • Input and Output Devices
  • Processor Architecture
  • Storage Devices
  • Introduction to Hashing Algorithms
  • Transaction and Master files and serial and sequential files
  • Data Representation
  • Data security and integrity
  • Data Transmission
  • Databases and Distributed Systems
  • Hardware and Communication
  • Organisation and Structure of Data
  • The need for different software
  • The Operating System
  • Quick Sort
  • Big-O
  • Data Compression
  • Fundamentals
  • Logical Operations
  • Modularity, Variables, Scope and Parameter Passing
  • Program Flow
  • Recursion
  • Searching Data
  • Sorting Data
  • Testing
  • Tree Traversal
  • Validation and Verification
  • Hash Tables
  • Linked Lists
  • Queues
  • Stacks
  • Static vs Dynamic Data Structures
  • Tree Traversal
  • Bitwise Manipulation
  • Boolean Algebra Laws
  • Lexical Analysis
  • Semantic Analysis
  • Syntax Analysis
  • Gantt Charts
  • IDEs
  • SSADM and CASE tools for project management
  • Backing Up Data
  • Methodologies
  • Stages of Software Analysis
  • Algorithms and Programs
  • Data Structures
  • Economic, moral, legal, ethical and cultural issues
  • Logical operations
  • Principles of programming
  • Program Construction
  • Software Engineering
  • Systems Analysis
  • Systems Design
  • testproblem1.png
  • TestProblem1
  • testproblem2.png
  • TestProblem2
  • testproblem3.png
  • TestProblem3
  • October 22 Test
  • Computer architecture, data, communications and applications
  • Programmed solution to a problem
  • Programming and Development
  • Visual Basic
  • Argand Diagrams
  • Loci in Argand Diagrams
  • Modulus and Argument
  • Modulus-Argument in the form of complex numbers
  • Regions in Argand Diagrams
  • Complex Conjugation
  • Imaginary and Complex Numbers
  • Multiplying Complex Numbers
  • Roots of Quadratic Equations
  • Solving Cubic and Quartic Equations
  • Enlargements and Stretches
  • Examples
  • Linear Transformations in three dimensions
  • Linear Transformations in two dimensions
  • Reflections and Rotations
  • Successive Transformations
  • The Inverse of a Linear Transformation
  • Determinants
  • Examples
  • Introduction to Matrices
  • Inverting a 2x2 Matrix
  • Inverting a 3x3 Matrix
  • Matrix Multiplication
  • Solving Systems of Equations using Matrices
  • Transposing Matrices
  • Proof by Mathematical Induction
  • Proving divisibility results
  • Proving Statements involving Matrices
  • Examples
  • Expressions relating to the Roots of Polynomials
  • Linear Transformations of Roots
  • Roots of a Cubic Equation
  • Roots of a Quadratic Equation
  • Roots of a Quartic Equation
  • Table of Polynomials
  • Examples
  • Sums of Natural Numbers
  • Sums of Squares and Cubes
  • Calculating Angles between Lines and Planes
  • Equation of a Line in Three Dimensions
  • Equation of a Plane in Three Dimensions
  • Finding Perpendiculars
  • Points of Intersection
  • Scalar Product
  • Adding and Subtracting Volumes
  • Modelling with Volumes of Revolution
  • Volumes of Revolution around the x-axis
  • Volumes of Revolution around the y-axis
  • Argand Diagrams
  • Complex Numbers
  • Linear Transformations
  • Matrices
  • Proof by Induction
  • Roots of Polynomials
  • Series
  • Vectors
  • Volumes of Revolution
  • Exponential Form of Complex Numbers
  • Multiplying and dividing complex numbers
  • Higher Derivatives
  • The Method of Differences
  • Complex Numbers
  • Series
  • Bin-packing Algorithms
  • Bubble Sort
  • Flow Charts
  • Order of an Algorithm
  • Quick Sort
  • Using and Understanding Algorithms
  • Applying Prim's Algorithm to a Distance Matrix
  • Floyd's Algorithm
  • Kruskal's Algorithm
  • Prim's Algorithm
  • Using Dijkstra's Algorithm to find the Shortest Path
  • Critical Activities
  • Dummy Activities
  • Early and Late Event Times
  • Gantt Charts
  • Modelling a Project
  • Resource Histograms
  • Scheduling Diagrams
  • The Float of an Activity
  • Graph Theory
  • Modelling with Graphs
  • Representing Graphs and Networks using Matrices
  • Special Types of Graph
  • The Planarity Algorithm
  • Examples
  • Graphical Methods
  • Linear Programming Methods
  • Locating the Optimal Point
  • Solutions with Integer Values
  • Review Exercise 1
  • Review Exercise 2
  • Eulerian Graphs
  • Networks with more than four odd nodes
  • Using the Route Inspection Algorithm
  • Formulating Linear Programming Problems
  • Problems Requiring Integer Solutions
  • The Big-M Method
  • The Simplex Method
  • Two-Stage Simplex Method
  • The Classical and Practical Travelling Salesman Problems
  • Using a Minimum Spanning Tree Method to find a Lower Bound
  • Using a Minimum Spanning Tree Method to find an Upper Bound
  • Using the Nearest Neighbour Algorithm to find an Upper Bound
  • Algorithms
  • Algorithms on Graphs
  • Critical Path Analysis
  • Graphs and Networks
  • Linear Programming
  • Review Exercises
  • Route Inspection
  • The Simplex Algorithm
  • The Travelling Salesman problem
  • Direct Collision with a Smooth Plane
  • Direct impact and Newton's law of restitution
  • Loss of Kinetic Energy
  • Conservation of Momentum
  • Momentum in one direction
  • Work done
  • Elastic collisions in one dimension
  • Momentum and Impulse
  • Work, Energy and Power
  • Core Pure 1
  • Core Pure 2
  • Further Decision 1
  • Further Mechanics 1
  • Constant Acceleration formulae 1
  • Constant Acceleration formulae 2
  • Displacement-Time Graphs
  • Velocity-Time Graphs
  • Vertical Motion due to Gravity
  • Force Diagrams
  • Forces as Vectors
  • Pulleys
  • Contructing a model
  • Modelling assumptions
  • Constant Acceleration
  • Forces and Motion
  • Modelling with Mechanics
  • Variable Acceleration
  • Expanding Brackets
  • Factorising
  • Index Laws
  • Negitive and fractional indices
  • Rationalising Denominators
  • Surds
  • Algebraic Fractions
  • Dividing Polynomials
  • Mathematical Proof
  • Methods of proof
  • The Factor Theorem
  • Circles and Triangles
  • Equation of a Circle
  • Intersections of Straight Lines and Circles
  • Midpoints and Perpendicular Bisectors
  • Using Tangent and Chord Properties
  • Differentiating functions with two or more terms
  • Differentiating Quadratics
  • Differentiating xn
  • Finding the Derivative
  • Gradients of Curves
  • Gradients, Tangents and Normal
  • Increasing and Decreasing Functions
  • Modelling with Differentiation
  • Second Order Derivatives
  • Sketching Gradient Functions
  • Stationary Points
  • Inequalities on Graphs
  • Linear Inequalities
  • Linear Simultaneous Equations
  • Quadratic Inequalities
  • Quadratic Simultaneous Equations
  • Regions
  • Simultaneous Equations on Graphs
  • Examples
  • Exponential Functions
  • Exponential Modelling
  • Laws of Logarithms
  • Logarithms
  • Logarithms and Non-Linear Data
  • Solving Equations using Logarithms
  • Working with Natural Logarithms
  • y = ex
  • Cubic Graphs
  • Examples
  • Points of Intersection
  • Quartic Graphs
  • Reciprocal Graphs
  • Stretching Graphs
  • Transforming Functions
  • Translating Graphs
  • Areas between curves and lines
  • Areas under Curves
  • Areas under the x-axis
  • Definite Integrals
  • Finding Functions
  • Indefinite Integrals
  • Integrating x to the n
  • Completing the Square
  • Functions
  • Modelling with Quadratics
  • Quadratic Graphs
  • Solving Quadratic Equations
  • The Discriminant
  • Equations of Straight Lines
  • Length and Area
  • Modelling with Straight Lines
  • Parallel and Perpendicular Lines
  • y=mx+c
  • Binomial Estimation
  • Examples
  • Factorial Notation
  • Pascal's Triangle
  • Solving Binomial Problems
  • The Binomial Expansion
  • Angles in all four Quadrants
  • Equations and Identities
  • Exact Values of Trigonometric Ratios
  • Harder Trigonometric Equations
  • Simple Trigonometric Equations
  • Trigonometric Identities
  • Trigonometric Identities and equations practice problems
  • Areas of Triangles
  • Graphs of Sine, Cosine, and Tangent
  • Solving Triangle Problems
  • The Cosine Rule
  • The Sine Rule
  • Transforming Trigonometric Graphs
  • Magnitude and Direction
  • Modelling with Vectors
  • Position Vectors
  • Representing Vectors
  • Solving Geometric Problems
  • Vectors
  • Algebraic Expressions
  • Algebraic Methods
  • Circles
  • Differentiation
  • Equations and Inequalities
  • Exponentials and Logarithms
  • Graphs and Transformations
  • Integration
  • Quadratics
  • Straight Line Graphs
  • The Binomial Expansion
  • Trigonometric Identities and equations
  • Trigonometric Ratios
  • Vectors
  • Algebraic Fractions
  • Partial Fractions
  • Proof by Contradiction
  • Expanding (1-x) to the n
  • Expanding (a+bx) to the n
  • Differentiating Exponentials and Logarithms
  • Differentiating sin(x) and cos(x)
  • Differentiating Trigonometric Functions
  • Implicit Differentiation
  • Parametric Differentiation
  • Product and Quotient Rules
  • Rates of Change
  • The Chain Rule
  • Using Second Derivatives
  • Combining Functions
  • Composite Functions
  • Functions and Mappings
  • Inverse Functions
  • The Modulus Function
  • y=mod(f(x)) and y = f(mod(x))
  • Finding Areas
  • Integrating f(ax+b)
  • Integrating Standard Functions
  • Integration by parts
  • Integration by Substitution
  • Partial Fractions
  • Reverse Chain Rule
  • Solving Differential Equations
  • The Trapezium Rule
  • Using Trigonometric Identities
  • Parametric Equations
  • Points of Intersection
  • Using Trigonometric Identities
  • Arc Length
  • Areas of Sectors and Segments
  • Radian Measure
  • Small Angle Approximations
  • Solving Trigonometric Equations
  • Arithmetic Sequences
  • Arithmetic Series
  • Geometric Sequences
  • Geometric Series
  • Graphs of sec(x), cosec(x) and cot(x)
  • Inverse Trigonometric Functions
  • Secant, Cosecant and Cotangent
  • Trigonometric Identities
  • Using sec(x), cosec(x), and cot(x)
  • Addition Formulae
  • Double-angle formulae
  • Simplifying a cos(x) +- b sin(x)
  • Arithmetic Progressions
  • Reciprocal of Polynomials
  • 3D Coordinates
  • Application to Mechanics
  • Solving Geometric Problems
  • Algebraic Methods
  • Binomial Expansion
  • Differentiation
  • Functions and Graphs
  • Integration
  • Parametric Equations
  • Radians
  • Sequences and Series
  • Trigonometric Functions
  • Trigonometry and Modelling
  • Underground Maths
  • Vectors
  • Big Data HW
  • Non-random sampling
  • Populations and Samples
  • Sampling
  • The Large Data Set
  • Types of Data
  • Coding
  • Examples
  • Measures of Central Tendency
  • Measures of location
  • Measures of spread
  • Variance and Standard Deviation
  • Calculating Probabilities
  • Mutually Exclusive and Independent Events
  • Tree Diagrams
  • Venn Diagrams
  • Correlation
  • Data Collection
  • Hypothetical Testing
  • Measures of Location and Spread
  • Probability
  • Representations of Data
  • Statistical Distributions
  • Probability Formulae
  • Hypothesis testing for zero correlation
  • Probability
  • Regression, correlation and hypothesis testing
  • The Normal Distribution
  • Mechanics 1
  • Pure 1
  • Pure 2
  • Statistics 1
  • Statistics 2
  • Circuit Diagrams
  • Conservation of Energy and Charge in Circuits
  • Current and Potential Difference
  • Determining the Resistivity of a Wire
  • E.M.F and Internal Resistance
  • I-V Characteristics
  • Power and Electrical Energy
  • Resistance
  • Resistivity
  • The Potential Divider
  • Discrete Energy Levels in Atoms
  • Electron Transitions
  • Electrons moving energy levels
  • Line Absorption Spectra
  • Line Emmission Spectra
  • Questions
  • Explaining the Photoelectric Effect
  • The Photoelectric Effect and Wave Theory
  • What is the Photoelectric Effect
  • Electron Diffraction
  • Electron Microscopes
  • Is Light a particle or a wave
  • Questions
  • Wave Particle Duality Theory
  • Energy Levels in Atoms
  • Exam Style Questions
  • Summary
  • The Photoelectric Effect
  • Wave-Particle Duality
  • Brittle Materials
  • Density
  • Hooke's Law
  • Stress and Strain
  • Stress-Strain and Force-Extension Graphs
  • The Young Modulus
  • Acceleration due to Gravity
  • Acceleration-Time Graphs
  • Centre of Mass and Moments
  • Conservation of Energy
  • Conservation of Momentum
  • Displacement-Time Graphs
  • Drag, Lift and Terminal Speed
  • Force, Momentum and Impulse
  • Forces in Equilibrium
  • Moments
  • Newton's Laws of Motion
  • Projectile Motion
  • Scalars and Vectors
  • Uniform Acceleration
  • Velocity-Time Graphs
  • Work and Power
  • Annihilation
  • Antiparticles
  • Electromagnetic Radiation
  • Pair Production
  • Photons
  • Inside the Atom
  • Isotopes
  • Nucleon Number
  • Proton Number
  • Specific Charge
  • Uses of Isotopic Data
  • Baryons
  • Conservation Laws
  • Hadrons
  • Leptons
  • Mesons
  • Particle Exchange
  • Particle interaction diagrams
  • Antiquarks
  • Quark composition of Baryons
  • Quark composition of Mesons
  • Quark Confinement
  • Quarks
  • Searching for particles
  • Weak Interaction
  • Forces in the Nucleus
  • Nuclear Decay
  • The Strong Nuclear Force
  • Conservation of Properties
  • Strange Particles
  • Antiparticles and Photons
  • Atomic Structure
  • Hadrons and Leptons
  • Particle Interactions
  • Quarks and Antiquarks
  • Stable and Unstable Nuclei
  • Strange Particles and the Conservation of Properties
  • All the Equations
  • Critical Angle and TIR
  • Optical Fibres
  • About Diffraction Gratings
  • Diffraction Gratings Practical
  • Frequency and Period
  • Wave Basics
  • Questions
  • Refractive Index Info
  • Longitudinal Waves
  • Polarisation in the real world
  • Polarised waves
  • Transverse Waves
  • Calculating Wave Speed
  • Electromagnetic Wave Speed in a Vacuum
  • Measuring the Speed of Sound
  • Measuring Wave Speed in Water
  • Double-Slit Interference of Light
  • Evidence of the Wave Nature of Light
  • The Double Slit Formula
  • Critical Angle and TIR
  • Diffraction
  • Diffraction Gratings
  • Investigating Resonance
  • Progressive Waves
  • Refractive Index
  • Stationary Waves
  • Superposition and Interference
  • Transverse and Longitudinal Waves
  • Two-Source Interference
  • Wave Speed
  • Young's Double Slit Experiment
  • Electricity
  • Electromagnetic Radiation and Quantum Phenomena
  • Materials
  • Mechanics
  • Particles and Radiation
  • Waves
  • Capacitors
  • Charging and Discharging
  • Dielectrics
  • Energy Stored by Capacitors
  • Calculations with SHM
  • Centripetal Force and Acceleration
  • Circular Motion
  • Simple Harmonic Motion
  • The Mass-Spring System as a Simple Harmonic Oscillator
  • The Simple Pendulum and Other Types of SHO
  • Electric Fields
  • Electric Potential
  • Exam Style Questions
  • Fields
  • Gravitational Fields
  • Gravitational Potential
  • Orbits
  • question 5.2.excalidraw
  • Electromagnetic Induction
  • Faraday's Law and Lenz's Law
  • Forces on Charged Particles
  • Magnetic Flux Density
  • Transformers
  • Exponential Law of Decay
  • Mass Defect and Binding Energy
  • Measuring Nuclear Radius
  • Nuclear Fission Reactors
  • Nuclear Radius and Density
  • Properties of Nuclear Radiation
  • Rutherford Scattering
  • Capacitors
  • Further Mechanics
  • Gravitational and Electric Fields
  • Magnetic Fields
  • Nuclear Physics
  • Year 1
  • Year 2
  • A-Level
  • Computer Science
  • dataset.xlsx
  • Further Maths
  • Maths
  • Physics
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