This course recognizes the need for analytical expertise in a world where innovation is increasingly dependent on a deep understanding of mathematics. This course includes topics that are both traditionally part of a pre-university mathematics course (for example, functions, trigonometry, calculus) as well as topics that are amenable to investigation, conjecture, and proof, for instance, the study of sequences and series at both SL and HL and proof by induction at HL.

The course allows the use of technology, as fluency in relevant mathematical software and hand-held technology is important regardless of the choice of course. However, Mathematics: analysis and approaches have a strong emphasis on the ability to construct, communicate and justify correct mathematical arguments.

##### Number and algebra

##### Functions

##### Geometry and trigonometry

##### Statistics and probability

- Collection of data and sampling
- Presentation of data
- Measures of central tendency and dispersion
- Linear correlation of bivariate data
- Concepts of trial, outcome
- Probability calculations
- Discrete random variables
- Binomial distribution
- The normal distribution
- Equation of the regression line
- Conditional probabilities
- Standardization of normal variables

##### Calculus