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Oxford IB Diploma Programme
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Table of Contents

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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Paul La Rondie, Jill Stevens, Natasha Awada, Jennifer Chang Wathall, Ellen Thompson, Laurie Buchanan, Ed Kemp

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