Oxford IB Diploma Programme IB Mathematics applications and interpretation Standard Level Print and Enhanced Online Course Book Pack 1st Edition by Jane Forrest, Paula Waldman, Jennifer Chang Wathall, Suzanne Doering, David Harris, Nadia Stoyanova Kennedy ISBN 9780198427056 0198427050

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