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A Level Further Mathematics CCEA
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A Level Further Mathematics CCEA
free revision notes.
A Level Further Mathematics CCEA
– Topics
Algorithms on Graphs (Applied Mathematics)
Dijkstra's Algorithm
Use of Binary Trees
Prim's Algorithm
Solve Problems involving Critical Path Analysis
Algorithms on graphs (Applied Mathematics)
Solve variable linear programming problems
PERT
Hamiltonian Cycle
Bivariate Distributions (Applied Mathematics)
Dangers of Extrapolation
Independent and Dependent Variables
Regression lines
Product moment correlation coefficient
Boolean Algebra (Applied Mathematics)
Use of Truth Tables
Centre of Mass (Applied Mathematics)
Find the centre of mass of composite laminae
Find the centre of mass of rectangular, triangular and circular laminae
Find the centre of mass of systems
Circular Motion (Applied Mathematics)
Acceleration of a Particle moving in a Circle
Angular Speed
Complex numbers (Pure Mathematics)
Use and Conversion of the Cartesian form
Use the modulus-argument form of a complex number
Radian and Measure for angles
Use and Interpret Agrand diagrams
Fucntions with complex numbers in the form x + iy with x and y real;
nth theory
Solving cubic or quartic equations with real coefficients
Solving Quadratic Equations
De Moivre's Theorem
Counting (Applied Mathematics)
Enumeration of restricted positions, including the use of Rook polynominals
Principle of Inclusion and Exclusion
Damped Oscilliations (Applied Mathematics)
odel damped oscilliations using second order differential equations
Differential equations (Pure Mathematics)
Use differential equations in modelling
General and Particular solutions to differential equations
Dimensions (Applied Mathematics)
Dimensional Consistency
Force systems in two dimensions (Applied Mathematics)
Find the general resultant of a system of coplanar forces
Frameworks (Applied Mathematics)
Solve problems using Frameworks
Further Calculus (Pure Mathematics)
Reduction Formulas
Integration with Partial Fractions
Calculus with Inverse Trig Functions
Further Centre of Mass (Applied Mathematics)
Solve sliding/toppling problems
Solve problems involving suspended bodies
Find the centre of mass of composite bodies
Find the centre of mass of laminae and solids
Further Circular Motion (Applied Mathematics)
Solve problems involving motion in a vertical cirlce
Solve more complex problems onvolving motion
Further Kinematics (Applied Mathematics)
Solve problems involving variable acceleration
Solve problems using i, j and k unit vectors
Further Particle Equilibrum (Applied Mathematics)
Solve more complex problems involving particle equilibrium
Further algebra and functions (Pure Mathematics)
Mclaurin series of a function
Use of formulae for the sums of integers, squares and cubes
Relationship between roots and coefficents of quadratic equations
Decompose rational functions into partial fractions
Generating functions (Applied Mathematics)
Proof of simple formulae
Solve simple summation problems
Graph Theory (Applied Mathematics)
Understanding of trees
Hall's marriage theorem
Understanding of basic graphs and language
Bipartite Graphs
Gravitation (Applied Mathematics)
Solve problems involving satellite motion
Use of the universal law of gravitation
Group Theory (Applied Mathematics)
Isomorphism
Lagrange's Theorem
Binary Operations
Group theory (Applied Mathematics)
Use Polya's Enumeration Theorem
Use a table of cycle indices
Understand the concept of a cycle index
Working with Symmetry groups
Hooke's Law (Applied Mathematics)
Applicatoin of Hooke's Law
Modulus of Elasticity
Hyperbolic functions (Pure Mathematics)
Inverse hyperbolic functions
Differentiate and integrate hyprbolic functions
Understanding of definitions of hyperbolic functions
Linear combinations of independent variables (Applied Mathematics)
Linear combinations of independent variables
Matrices (Pure Mathematics)
Diagonalisation
Eigenvectors and Eigenvalues
Factorising Determinants
Matrices and Simultaneous Equations
Inverting Matrices
Determinants
Matrix Transformations
Matrices
Polar co-ordinates (Pure Mathematics)
Area
Sketching curves
Conversion between Polar and Cartesian coordinates
Use of Polar Coordinates
Polar co-ordinates
Power (Applied Mathematics)
Solve Problems using Power
Definition of Power
Probability (Applied Mathematics)
Evaluate Probability
Use of Probability formulas
Proof (Pure Mathematics)
Construct Proof using mathematical induction
Recurrence Relationships (Applied Mathematics)
Solve homogenous, constant coefficient and linear recurrence relations
Recurrence Relationships
Restitution (Applied Mathematics)
Use of Newton's Law of Restitution
Resultant and Relative Velocity (Applied Mathematics)
Solve problems involving relative velocity
Solve problems involving resultant velocity
Sampling (Applied Mathematics)
Understanding of sampling methods
Sampling and estimation (Applied Mathematics)
Calculate confidence intervals
Standard error of the mean
Central Limit Theorem
Simple Harmonic Motion (Applied Mathematics)
Solve problems involving osciliation of a particle attached to the end of an elastic spring or string
Solve problems involving the simple pendulum
Solve equations using Simple Harmonic motions
Statistical Distributions (Applied Mathematics)
Poisson Distributions
Calculating Probabilities with a continuous random variable
Discree Probability Model
Geometric Distribution
The t-distribution (Applied Mathematics)
Formulatoin of a hypothesis
Hypothesis tests
Vectors (Pure Mathematics)
Vector Product
Intersections and Distances
Plane Geometry
Scalar Products
Use of Vectors in i, j and k unit
Work and Energy (Applied Mathematics)
Principle of Conservation of Mechanical Energy
Gravitatinal Potential Energy
Kinetic Enrgy
Elastic Energy
𝝌𝟐 tests (Applied Mathematics)
Use of an 𝝌𝟐 test
Fitting a theoretical distribution to given data