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: analysis and approaches SL 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: analysis and approaches SL syllabus, for first teaching in September 2019.
Paul La Rondie, Jill Stevens, Natasha Awada, Jennifer Chang Wathall, Ellen Thompson, Laurie Buchanan, Ed Kemp
Inhaltsangabe
* From patterns to generalizations: sequences and series * 1.1: Number patterns and sigma notation * 1.2: Arithmetic and geometric sequences * 1.3: Arithmetic and geometric series * 1.4: Modelling using arithmetic and geometric series * 1.5: The binomial theorem * 1.6: Proofs * Representing relationships: introducing functions * 2.1: What is a function? * 2.2: Functional notation * 2.3: Drawing graphs of functions * 2.4: The domain and range of a function * 2.5: Composition of functions * 2.6: Inverse functions * Modelling relationships: linear and quadratic functions * 3.1: Parameters of a linear function * 3.2: Linear functions * 3.3: Transformations of functions * 3.4: Graphing quadratic functions * 3.5: Solving quadratic equations by factorization and completing the square * 3.6: The quadratic formula and the discriminant * 3.7: Applications of quadratics * Equivalent representations: rational functions * 4.1: The reciprocal function * 4.2: Transforming the reciprocal function * 4.3: Rational functions of the form ax+b/cx+d * Measuring change: differentiation * 5.1: Limits and convergence * 5.2: The derivative function * 5.3: Differentiation rules * 5.4: Graphical interpretation of first and second derivatives * 5.5: Application of differential calculus: optimization and kinematics * Representing data: statistics for univariate data * 6.1: Sampling * 6.2: Presentation of data * 6.3: Measures of central tendency * 6.4: Measures of dispersion * Modelling relationships between two data sets: statistics for bivariate data * 7.1: Scatter diagrams * 7.2: Measuring correlation * 7.3: The line of best fit * 7.4: Least squares regression * Quantifying randomness: probability * 8.1: Theoretical and experimental probability * 8.2: Representing probabilities: Venn diagrams and sample spaces * 8.3: Independent and dependent events and conditional probability * 8.4: Probability tree diagrams * Representing equivalent quantities: exponentials and logarithms * 9.1: Exponents * 9.2: Logarithms * 9.3: Derivatives of exponential functions and the natural logarithmic function * From approximation to generalization: integration * 10.1: Antiderivatives and the indefinite integral * 10.2: More on indefinite integrals * 10.3: Area and definite integrals * 10.4: Fundamental theorem of calculus * 10.5: Area between two curves * Relationships in space: geometry and trigonometry in 2D and 3D * 11.1: The geometry of 3D shapes * 11.1: Right-angles triangle trigonometry * 11.3: The sine rule * 11.4: The cosine rule * 11.5: Applications of right and non-right angled trigonometry * Periodic relationships: trigonometric functions * 12.1: Radian measure, arcs, sectors and segments * 12.2: Trigonometric ratios in the unit circle * 12.3: Trigonometric identities and equations * 12.4: Trigonometric functions * Modelling change: more calculus * 13.1: Derivatives with sine and cosine * 13.2: Applications of derivatives * 13,3: Integration with sine, cosine and substitution * 13.4: Kinematics and accumulating change * Valid comparisons and informed decisions: probability distributions * 14.1: Random variables * 14.2: The binomial distribution * 14.3: The normal distribution * Exploration
* From patterns to generalizations: sequences and series * 1.1: Number patterns and sigma notation * 1.2: Arithmetic and geometric sequences * 1.3: Arithmetic and geometric series * 1.4: Modelling using arithmetic and geometric series * 1.5: The binomial theorem * 1.6: Proofs * Representing relationships: introducing functions * 2.1: What is a function? * 2.2: Functional notation * 2.3: Drawing graphs of functions * 2.4: The domain and range of a function * 2.5: Composition of functions * 2.6: Inverse functions * Modelling relationships: linear and quadratic functions * 3.1: Parameters of a linear function * 3.2: Linear functions * 3.3: Transformations of functions * 3.4: Graphing quadratic functions * 3.5: Solving quadratic equations by factorization and completing the square * 3.6: The quadratic formula and the discriminant * 3.7: Applications of quadratics * Equivalent representations: rational functions * 4.1: The reciprocal function * 4.2: Transforming the reciprocal function * 4.3: Rational functions of the form ax+b/cx+d * Measuring change: differentiation * 5.1: Limits and convergence * 5.2: The derivative function * 5.3: Differentiation rules * 5.4: Graphical interpretation of first and second derivatives * 5.5: Application of differential calculus: optimization and kinematics * Representing data: statistics for univariate data * 6.1: Sampling * 6.2: Presentation of data * 6.3: Measures of central tendency * 6.4: Measures of dispersion * Modelling relationships between two data sets: statistics for bivariate data * 7.1: Scatter diagrams * 7.2: Measuring correlation * 7.3: The line of best fit * 7.4: Least squares regression * Quantifying randomness: probability * 8.1: Theoretical and experimental probability * 8.2: Representing probabilities: Venn diagrams and sample spaces * 8.3: Independent and dependent events and conditional probability * 8.4: Probability tree diagrams * Representing equivalent quantities: exponentials and logarithms * 9.1: Exponents * 9.2: Logarithms * 9.3: Derivatives of exponential functions and the natural logarithmic function * From approximation to generalization: integration * 10.1: Antiderivatives and the indefinite integral * 10.2: More on indefinite integrals * 10.3: Area and definite integrals * 10.4: Fundamental theorem of calculus * 10.5: Area between two curves * Relationships in space: geometry and trigonometry in 2D and 3D * 11.1: The geometry of 3D shapes * 11.1: Right-angles triangle trigonometry * 11.3: The sine rule * 11.4: The cosine rule * 11.5: Applications of right and non-right angled trigonometry * Periodic relationships: trigonometric functions * 12.1: Radian measure, arcs, sectors and segments * 12.2: Trigonometric ratios in the unit circle * 12.3: Trigonometric identities and equations * 12.4: Trigonometric functions * Modelling change: more calculus * 13.1: Derivatives with sine and cosine * 13.2: Applications of derivatives * 13,3: Integration with sine, cosine and substitution * 13.4: Kinematics and accumulating change * Valid comparisons and informed decisions: probability distributions * 14.1: Random variables * 14.2: The binomial distribution * 14.3: The normal distribution * Exploration
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