This course recognizes the increasing role that mathematics and technology play in a diverse range of fields in a data-rich world. As such, it emphasizes the meaning of mathematics in context by focusing on topics that are often used as applications or in mathematical modeling. To give this understanding a firm base, this course also includes topics that are traditionally part of a pre-university mathematics course such as calculus and statistics.

The course makes extensive use of technology to allow students to explore and construct mathematical models. Mathematics: applications and interpretation will develop mathematical thinking, often in the context of a practical problem, and using technology to justify conjectures.

##### 1. Number and algebra

- 1.1 Scientific notation
- 1.2 Arithmetic sequences and series
- 1.3 Geometric sequences and series
- 1.4 Financial applications
- 1.5 Exponents and logarithms
- 1.6 Approximation
- 1.7 Amortization and annuity
- 1.8 Equations and equation systems
- 1.9 Laws of logarithms
- 1.10 Rational exponents
- 1.11 Sum of infinite geometric sequences
- 1.12 Introduction to complex numbers
- 1.13 Further complex numbers
- 1.14 Matrices
- 1.15 Eigenvalues and eigenvectors

##### 2. Functions

##### 3. Geometry and trigonometry

- 3.1 Three-dimensional space
- 3.2 Triangle trigonometry
- 3.3 Applications of trigonometry
- 3.4 The circle
- 3.5 Perpendicular bisectors
- 3.6 Voronoi diagrams
- 3.7 The circle revisited
- 3.8 Trigonometric ratios beyond acute angles
- 3.9 Planar transformations
- 3.10 Vectors
- 3.11 Vector equation of a line
- 3.12 Vector kinematics
- 3.13 Products of vectors
- 3.14 Introduction to graph theory
- 3.15 Further matrices
- 3.16 Graph algorithms

##### 4. Probability and statistics

- 4.1 Collection of data and sampling
- 4.2 Presentation of data
- 4.3 Measures of central tendency and dispersion
- 4.4 Linear correlation of bivariate data
- 4.5 Probability and expected outcomes
- 4.6 Probability calculations
- 4.7 Discrete random variables
- 4.8 The binomial distribution
- 4.9 The normal distribution and curve
- 4.10 Further linear regression
- 4.11 Hypothesis testing
- 4.12 Collecting and analysing data
- 4.13 Non-linear regression
- 4.14 Variance
- 4.15 The central limit theorem
- 4.16 Confidence intervals
- 4.17 The Poisson distribution
- 4.18 Population tests
- 4.19 Markov chains

##### 5. Calculus

- 5.1 Introduction to differentiation
- 5.2 Increasing and decreasing functions
- 5.3 Derivatives of power functions
- 5.4 Tangents and normals
- 5.5 Introduction to integration
- 5.6 Stationary points
- 5.7 Optimisation
- 5.8 Area of a region
- 5.9 Further differentiation
- 5.10 Second derivative
- 5.11 Further integration
- 5.12 Area and volume
- 5.13 Kinematics
- 5.14 Differential equations
- 5.15 Graphical approximations to differential equations
- 5.16 Numerical solutions to differential equations
- 5.17 Qualitative and analytical techniques for coupled systems
- 5.18 Second order differential equations

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