Featuring a wealth of digital content, this concept-based Print and Enhanced Online Course Book Pack has been developed in cooperation with the IB to provide the most comprehensive support for the new DP Mathematics: applications and interpretation HL syllabus, for first teaching in September 2019.
Featuring a wealth of digital content, this concept-based Print and Enhanced Online Course Book Pack has been developed in cooperation with the IB to provide the most comprehensive support for the new DP Mathematics: applications and interpretation HL syllabus, for first teaching in September 2019.
Panayiotis Economopoulos, Tony Halsey, Suzanne Doering, Michael Ortman, Nuriye Sirinoglu Singh, Peter Gray, David Harris, Jennifer Chang Wathall
Inhaltsangabe
* 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 x^2 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
* 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 x^2 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
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