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A Level Further Mathematics OCR
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A Level Further Mathematics OCR
free revision notes.
A Level Further Mathematics OCR
– Topics
Additional Pure
Partial differentiation: Tangent planes
Further Calculus: Reduction formulae
Further Calculus: Arc lengths and surface areas
Partial differentiation: Stationary points
Partial differentiation
Surfaces: Sections and contours
Surfaces: 3-D surfaces
Further Vectors: Vector product
Groups: Abstract groups
Groups: Isomorphism
Groups: Lagrange's theorem
Groups: Properties of groups
Groups: Generators
Groups: Cyclic groups
Groups: Subgroups
Groups: Orders of elements and groups
Groups: Defintion of a group
Groups: Binary operations
Number Theory: Binomial theorem
Number Theory: The order of a modulo p
Number Theory: Fermat's little theorem
Number Theory: Euclid's lemma
Number Theory: Prime numbers
Number Theory: Finite (modular) arithmetics
Number Theory: The division algorithm
Number Theory: Divisibility tests
Number Theory: Number bases
Sequences and Series: Modelling
Sequences and Series: Solving recurrence systems
Sequences and Series: Fibonacci and related numbers
Sequences and Series: Properties of sequences
Sequences and Series: Recurrence relations
Algorithm
Strategies for packing
Strategies for sorting
Efficiency and complexity
The order of algorithms
Working with algorithms
Awareness of the uses and practical limitations of algorithms
Definition of an algorithm
Centre of Mass
Motion in a vertical circle
Uniform motion in a circle
Rigid Bodies
Centre of Mass
Chi Squared Tests
Goodness of fit test
Fitting a theoretical distribution
Contingency tables
Complex numbers
Roots of unity
nth roots
De Moivre's theorem
Loci
Euler's formula
Agrand Diagrams
Solution of Equations
Basic operations
The language of complex numbers
Continuous random variables
Cumulative distribution functions
Probability density functions
Continuous random variables
Correlation
Use of the regression line
Calculation of the equation of the regression line
Dependent and independent variables
Hypothesis tests using Spearman's coefficient
Comparison of coefficients
Spearman's rank correlation coefficient
Hypothesis tests using Pearson's product-moment correlation coefficient
Pearson's product-moment correlation coeffecient
Decision Making in Project Management
Critical path analysis
Differential Equations
Linear systems
Damped oscillations
Simple harmonicmotion
Second order non-homogeneous differential equations
Second order homogeneous differential equations
Integrating factor method for first order differential equations
Modelling
General and particular solutions
Dimensional Analysis
Dimensional Analysis
Discrete
Game theory: Mixed strategies
Game theory: Pure strategies
Game theory: Pay-off matrix
The Simplex Algorithm: Graphical and algebraic interpretations of iterations
The Simplex Algorithm: Terminology
The Simplex Algorithm: Use a simplex tableau
Graphical Linear Programming: Graphical solutions
Graphical Linear Programming: Working with constraints
Graphical Linear Programming: Formulating LP problems
Critical path analysis
Network Algorithms: Network Problems
Network Algorithms: Least weight route through all vertices thatt raverses every arc at least once
Network Algorithms: Least weight cycle through all vertices
Network Algorithms: Least weight set of arcs connecting all vertices
Network Algorithms: Least weight path between two vertices
Algorithm: Strategies for packing
Algorithm: Strategies for sorting
Algorithm: Efficiency and complexity
Algorithm: The order of algorithms
Algorithm: Working with algorithms
Algorithm: Awareness of their uses and practical limitations
Algorithm: Definition
Graphs and Networks: Using graphs and networks
Graphs and Networks: Planar graphs
Graphs and Networks: Digraphs
Graphs and Networks: Isomorphism
Graphs and Networks: Hamiltonian Graphs
Graphs and Networks: Eulerian graphs
Graphs and Networks: Bipartite Graphs
Graphs and Networks: Complete Graphs
Graphs and Networks: Terminology and notation
Mathematical Preliminaries: The inclusion- exclusion principle
Mathematical Preliminaries: Arrangement and selection problems
Mathematical Preliminaries: The pigeon hole principle
Mathematical Preliminaries: Set Notation
Mathematical Preliminaries: Types of Problem
Discrete Random Variables
The Poisson distribution
The geometric distribution
The discrete uniform distribution
The binomial distribution
Probability distributions for general discrete random variables
Further Algebra
Partial fractions
Transformation of equations
Roots of equations
Further Calculus
Further integrations
Inverse trigonometric and hyperbolic functions
Partial fractions
Mean values
Volumes of solidsof revolution
Improper integrals
Arc lengths and surface areas
Reduction formulae
Maclaurin series
Further Dynamics and Kinematics
Linear Motion under a variable force
Further Vectors
Shortest distances
Vector product
Intersections
Scalar product
Equation of a plane
Equation of a straight line
Game theory
Mixed strategies
Pure strategies
Pay-off matrix
Graphical Linear Programming
Graphical solutions
Working with constraints
Formulating LP problems
Graphs and Networks
Using graphs and networks
Planar graphs
Isomorphism
Digraphs
Hamiltonian Graphs
Eulerian graphs
Bipartite Graphs
Complete Graphs
Terminology and notation
Groups
Abstract groups
Isomorphism
Lagrange's theorem
Properties of groups
Generators
Cyclic groups
Subgroups
Orders of elements and groups
Defintion of a group
Binary operations
Hyperbolic Functions
Inverse hyperbolic functions
Differentiation and integration
Defintion
Hypothesis Tests and Confidence Intervals
Confidence intervals
Using the normaldistribution in hypothesis tests
Unbiased estimates of population mean and variance
The distribution of X and the central limit theorem
Linear combinations of any random variables
Linear combinations of any normal random variables
Linear combinations of any random variables
Mathematical Preliminaries
The inclusion- exclusion principle
Arrangement and selection problems
The pigeon hole principle
Set Notation
Types of Problem
Matrices
Intersection of planes
Solution of simultaneous equations
Inverses
Determinants
Invariance
Linear transformations
Matrix addition and multiplication
The language of matrices
Mechanics
Linear Motion under a variable force
Centre of Mass: Motion in a vertical circle
Centre of Mass: Uniform motion in a circle
Centre of Mass: Rigid Bodies
Centre of Mass
Restitution
Impulse
Linear Momentum
Power
Conservation of Energy
Hooke's law
Energy
Work
Dimensional Analysis
Network Algorithms
Network Problems
Least weight route through all vertices thatt raverses every arc at least once
Least weight cycle through all vertices
Least weight set of arcs connecting all vertices
Least weight path between two vertices
Non-parametric tests
Normal approximations
Paired-sample and two-sample hypothesis tests
Single-sample hypothesis tests
The basis of non-parametric tests
Non-parametric tests
Number Theory
Binomial theorem
The order of a modulo p
Fermat's little theorem
Euclid's lemma
Prime numbers
Finite (modular) arithmetics
The division algorithm
Divisibility tests
Number bases
Polar Coordinates
Area
Sketching curves
Polar Coordinates
Probability
Probability
Proof
Proof
Sequences and Series
Modelling
Solving recurrence systems
Fibonacci and related numbers
Properties of sequences
Recurrence relations
Series
Method of differences
Summation of series
Statistics
Use of the regression line
Calculation of the equation of the regression line
Correlation: Dependent and independent variables
Correlation: Comparison of coefficients
Hypothesis tests using Spearman's coefficient
Spearman's rank correlation coefficient
Hypothesis tests using Pearson's product-moment correlation coefficient
Pearson's product-moment correlation coeffecient
Non-parametric tests: Normal approximations
Paired-sample and two-sample hypothesis tests
Single-sample hypothesis tests
The basis of non-parametric tests
Non-parametric tests
Chi Squared Tests: Goodness of fit test
Chi Squared Tests: Fitting a theoretical distribution
Chi Squared Tests: Contingency tables
Confidence intervals
Using the norma ldistribution in hypothesis tests
Unbiased estimates of population mean and variance
The distribution of X and the central limit theorem
Linear combinations of any normal random variables
Linear combinations of any random variables
Continuous random variables: Cumulative distribution functions
Continuous random variables: Probability density functions
Continuous random variables
Discrete Random Variables: The Poisson distribution
Discrete Random Variables: The geometric distribution
Discrete Random Variables: The discrete uniform distribution
Discrete Random Variables: The binomial distribution
Discrete Random Variables: Probability distributions
Probability
Surfaces and Partial Differentiation
Tangent planes
Stationary points
Partial differentiation
Sections andcontours
3-D surfaces
The Simplex Algorithm
Graphical and algebraic interpretations of iterations
Terminology
Use a simplex tableau
Work, Energy and Power
Restitution
Impulse
Linear Momentum
Power
Conservation of Energy
Hooke's law
Energy
Work