Specification points
OCR AS Level Further Mathematics A H235
199 points in 6 topics, with OCR's codes and titles.
Codes and titles are read by a script from OCR's published specification and have not been checked by a person. What each point covers is in the specification itself: OCR’s specification.
4 Pure Core
- 4.01 Proof
- 4.01a Mathematical induction
- 4.02 Complex Numbers
- 4.02a The language of complex numbers
- 4.02b Cartesian and modulus-argument forms
- 4.02c Complex number notation
- 4.02e Basic operations
- 4.02f Converting forms of complex numbers
- 4.02g Solution of equations
- 4.02h Square roots of a complex number
- 4.02i Quadratics with complex roots
- 4.02j Cubic and quartic equations with complex roots
- 4.02k Argand diagrams
- 4.02l Geometry of conjugates, sums and differences
- 4.02o Loci
- 4.02p Set notation for loci
- 4.03 Matrices
- 4.03a The language of matrices
- 4.03b Matrix addition and multiplication
- 4.03c Matrix multiplication: associative, not commutative
- 4.03d Linear transformations
- 4.03e Matrices for successive transformations
- 4.03f Matrices for 3-D transformations
- 4.03g Invariance
- 4.03h Determinants
- 4.03i Determinant as area scale factor
- 4.03j Determinant of a 3 × 3 matrix
- 4.03k Determinant as volume scale factor
- 4.03l Singular and non-singular matrices
- 4.03m Determinant of a product
- 4.03n Inverses
- 4.03o Inverse of a 3 × 3 matrix
- 4.03p Properties of inverse matrices
- 4.03q Inverse matrices and inverse transformations
- 4.03r Solution of simultaneous equations
- 4.04 Further Vectors
- 4.04a Equation of a straight line
- 4.04c Scalar product
- 4.04e Intersections
- 4.04g Vector product
- 4.05 Further Algebra
- 4.05a Roots of equations
- 4.05b Transformation of equations
5 Statistics
- 5.01 Probability
- 5.01a Probability
- 5.01b Probabilities from selections and arrangements
- 5.02 Discrete Random Variables
- 5.02a Probability distributions for general discrete random variables
- 5.02b Expectation and variance of a discrete variable
- 5.02c Linear coding of mean and variance
- 5.02d The binomial distribution
- 5.02e The discrete uniform distribution
- 5.02f The geometric distribution
- 5.02g Geometric distribution probabilities
- 5.02h Mean and variance of a geometric distribution
- 5.02i The Poisson distribution
- 5.02j Poisson probability formula
- 5.02k Poisson probabilities with a calculator
- 5.02l Conditions for a Poisson distribution
- 5.02m Mean and variance of a Poisson distribution
- 5.02n Sum of independent Poisson variables
- 5.06 Chi-squared Tests
- 5.06a Contingency tables
- 5.06b Fitting a theoretical distribution
- 5.06d Goodness of fit test
- 5.08 Correlation
- 5.08a Pearson’s product-moment correlation coefficient
- 5.08b Correlation coefficient unaffected by linear coding
- 5.08c Pearson's correlation as closeness to a line
- 5.08d Hypothesis tests using Pearson’s product-moment correlation coefficient
- 5.08e Spearman’s rank correlation coefficient
- 5.08f Hypothesis tests using Spearman’s coefficient
- 5.08g Comparison of coefficients
- 5.09 Linear Regression
- 5.09a Dependent and independent variables
- 5.09b Calculation of the equation of the regression line
- 5.09c Regression line of y on x
- 5.09d Linear coding and regression lines
- 5.09e Use of the regression line
6 Mechanics
- 6.01 Dimensional Analysis
- 6.01a Dimensional analysis
- 6.01b Units and dimensions
- 6.01c Dimensional analysis as an error check
- 6.01d Finding unknown indices by dimensional analysis
- 6.01e Models from dimensional arguments
- 6.02 Work, Energy and Power
- 6.02a Work
- 6.02b Work done by a constant force
- 6.02d Energy
- 6.02e Gravitational potential and kinetic energy
- 6.02i Conservation of energy
- 6.02k Power
- 6.02l Power, tractive force and velocity
- 6.03 Impulse and Momentum
- 6.03a Linear momentum
- 6.03b Conservation of momentum in one dimension
- 6.03e Impulse
- 6.03f Impulse and change in momentum
- 6.03i Restitution
- 6.03j Perfectly elastic and inelastic collisions
- 6.03k Newton's experimental law in one dimension
- 6.05 Motion in a circle
- 6.05a Uniform motion in a circle
- 6.05b Circular motion with constant speed
- 6.05c Motion in a horizontal circle
- 6.05d Motion in a vertical circle
7 Discrete Mathematics
- 7.01 Mathematical Preliminaries
- 7.01a Types of problem
- 7.01b Set notation
- 7.01c The pigeonhole principle
- 7.01d Arrangement and selection problems
- 7.01e Permutations
- 7.01f Combinations
- 7.01g Arrangements in a line
- 7.01i Selections with constraints
- 7.01k The inclusion-exclusion principle
- 7.02 Graphs and Networks
- 7.02a Terminology and notation
- 7.02b Trees, simple and connected graphs
- 7.02c Walks, trails, paths, cycles and routes
- 7.02d Complete graphs
- 7.02e Bipartite graphs
- 7.02g Eulerian graphs
- 7.02j Isomorphism
- 7.02k Digraphs
- 7.02p Using graphs and networks
- 7.02q Adjacency and weighted matrices
- 7.02r Modelling with graphs and networks
- 7.03 Algorithms
- 7.03a Definition of an algorithm
- 7.03b Awareness of the uses and practical limitations of algorithms
- 7.03c Working with algorithms
- 7.03d The order of an algorithm
- 7.03e Efficiency and complexity
- 7.03f Worst case time complexity
- 7.03g Orders of complexity O(nᵏ)
- 7.03j Strategies for sorting
- 7.03l Strategies for packing
- 7.04 Network Algorithms
- 7.04a Least weight path between two vertices
- 7.04b Least weight set of arcs connecting all vertices
- 7.04f Network problems
- 7.05 Decision Making in Project Management
- 7.05a Critical path analysis
- 7.05b Forward pass and earliest start times
- 7.05c Total float
- 7.06 Graphical Linear Programming
- 7.06a Formulating LP problems
- 7.06c Working with constraints
- 7.06d Graphical solutions
- 7.08 Game Theory
- 7.08a Pay-off matrix
- 7.08b Reducing a matrix by dominance
- 7.08c Pure strategies
- 7.08e Mixed strategies
8 Additional Pure Mathematics
- 8.01 Sequences and Series
- 8.01a Recurrence relations
- 8.01b Induction for sequences and series
- 8.01c Properties of sequences
- 8.01d Limits of sequences and steady states
- 8.01e Fibonacci and related numbers
- 8.01f Solving recurrence systems
- 8.01h Modelling
- 8.02 Number Theory
- 8.02a Number bases
- 8.02b Divisibility tests
- 8.02c Divisibility tests for primes under 50
- 8.02d The division algorithm
- 8.02e Finite (modular) arithmetics
- 8.02f Single linear congruences
- 8.02i Prime numbers
- 8.02j Divisibility of linear combinations
- 8.02k Euclid’s lemma
- 8.03 Groups
- 8.03a Binary operations
- 8.03b Cayley tables
- 8.03c Definition of a group
- 8.03d Latin square property
- 8.03e Orders of elements and groups
- 8.03f Subgroups
- 8.03g Cyclic groups
- 8.03h Generators
- 8.03i Properties of groups
- 8.04 Further Vectors
- 8.04a Vector product
- 8.04b Properties of the vector product
- 8.04c Areas using the vector product
- 8.04d Significance of a zero vector product
- 8.05 Surfaces and Partial Differentiation
- 8.05a 3-D surfaces
- 8.05c Sections and contours
- 8.05d Partial differentiation
- 8.05e Stationary points