Oxford IB Diploma Programme

Measuring space: accuracy and geometry 1.1: Representing numbers exactly and approximately 1.2: Angles and triangles 1.3: three-dimensional geometry Representing and describing data: descriptive statistics 2.1: Collecting and organizing data 2.2: Statistical measures 2.3: Ways in which we can present data 2.4: Bivariate data Dividing up space: coordinate geometry, lines, Voronoi diagrams, vectors 3.1: Coordinate geometry in 2 and 3 dimensions 3.2: The equation of a straight line in 2 dimensions 3.3: Voronoi diagrams 3.4: Displacement vectors 3.5: The scalar and vector product 3.6: Vector equations of lines Modelling constant rates of change: linear functions and regressions 4.1: Functions 4.2: Linear models 4.3: Inverse functions 4.4: Arithmetic sequences and series 4.5: Linear regression Quantifying uncertainty: probability 5.1: Theoretical and experimental probability 5.2: Representing combined probabilities with diagrams 5.3: Representing combined probabilities with diagrams and formulae 5.4: Complete, concise and consistent representations Modelling relationships with functions: power and polynomial functions 6.1: Quadratic models 6.2: Quadratic modelling 6.3: Cubic functions and models 6.4: Power functions, inverse variation and models Modelling rates of change: exponential and logarithmic functions 7.1: Geometric sequences and series 7.2: Financial applications of geometric sequences and series 7.3: Exponential functions and models 7.4: Laws of exponents - laws of logarithms 7.5: Logistic models Modelling periodic phenomena: trigonometric functions and complex numbers 8.1: Measuring angles 8.2: Sinusoidal models: f(x) = asin(b(x-c))+d 8.3: Completing our number system 8.4: A geometrical interpretation of complex numbers 8.5: Using complex numbers to understand periodic models Modelling with matrices: storing and analyzing data 9.1: Introduction to matrices and matrix operations 9.2: Matrix multiplication and properties 9.3: Solving systems of equations using matrices 9.4: Transformations of the plane 9.5: Representing systems 9.6: Representing steady state systems 9.7: Eigenvalues and eigenvectors Analyzing rates of change: differential calculus 10.1: Limits and derivatives 10.2: Differentiation: further rules and techniques 10.3: Applications and higher derivatives Approximating irregular spaces: integration and differential equations 11.1: Finding approximate areas for irregular regions 11.2: Indefinite integrals and techniques of integration 11.3: Applications of integration 11.4: Differential equations 11.5: Slope fields and differential equations Modelling motion and change in 2D and 3D: vectors and differential equations 12.1: Vector quantities 12.2: Motion with variable velocity 12.3: Exact solutions of coupled differential equations 12.4: Approximate solutions to coupled linear equations Representing multiple outcomes: random variables and probability distributions 13.1: Modelling random behaviour 13.2: Modelling the number of successes in a fixed number of trials 13.3: Modelling the number of successes in a fixed interval 13.4: Modelling measurements that are distributed randomly 13.5: Mean and variance of transformed or combined random variables 13.6: Distributions of combined random variables Testing for validity: Spearman's hypothesis testing and x2 test for independence 14.1: Spearman's rank correlation coefficient 14.2: Hypothesis testing for the binomial probability, the Poisson mean and the product moment correlation coefficient 14.3: Testing for the mean of a normal distribution 14.4: Chi-squared test for independence 14.5: Chi-squared goodness-of-fit test 14.6: Choice, validity and interpretation of tests Optimizing complex networks: graph theory 15.1: Constructing graphs 15.2: Graph theory for unweighted graphs 15.3: Graph theory for weighted graphs: the minimum spanning tree 15.4: Graph theory for weighted graphs - the Chinese postman problem 15.5: Graph theory for weighted graphs - the travelling salesman problem Exploration