Oxford IB Diploma Programme: IB Mathematics: analysis and approaches, Standard Level, Print and Enhanced Online Course Book Pack

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

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