Number and algebra allow us to represent patterns, show equivalencies and make generalizations which enable us to model real-world situations. Algebra is an abstraction of numerical concepts and employs variables to solve mathematical problems. 

Models are depictions of real-life events using expressions, equations or graphs while a function is defined as a relation or expression involving one or more variable. Creating different representations of functions to model the relationships between variables, visually and symbolically as graphs, equations and/or tables represents different ways to communicate mathematical ideas. 

Geometry and trigonometry allow us to quantify the physical world, enhancing our spatial awareness in two and three dimensions. This branch provides us with the tools for analysis, measurement and transformation of quantities, movements and relationships. 

Statistics is concerned with the collection, analysis and interpretation of quantitative data and uses the theory of probability to estimate parameters, discover empirical laws, test hypotheses and predict the occurrence of events. Statistical representations and measures allow us to represent data in many different forms to aid interpretation.

Probability enables us to quantify the likelihood of events occurring and so evaluate risk. Both statistics and probability provide important representations which enable us to make predictions, valid comparisons and informed decisions. These fields have power and limitations and should be applied with care and critically questioned, in detail, to differentiate between the theoretical and the empirical/observed. Probability theory allows us to make informed choices, to evaluate risk and to make predictions about seemingly random events.

Calculus describes rates of change between two variables and the accumulation of limiting areas. Understanding these rates of change allows us to model, interpret and analyze real-world problems and situations. Calculus helps us understand the behaviour of functions and allows us to interpret the features of their graphs. 

Internal assessment is an integral part of the course and is compulsory for both SL and HL students. It enables students to demonstrate the application of their skills and knowledge and to pursue their personal interests without the time limitations and other constraints that are associated with written examinations. The internal assessment should, as far as possible, be woven into normal classroom teaching and not be a separate activity conducted after a course has been taught.

The internal assessment requirements at SL and at HL is an individual exploration. This is a piece of written work that involves investigating an area of mathematics. It is marked according to five assessment criteria.

Mathematics: Applications and Interpretation - Standard Level

• Paper 1 (90 minutes) - total of 80 marks, GDC required, compulsory short-response questions based on the syllabus, worth 40% of overall grade

• Paper 2 (90 minutes) - total of 80 marks, GDC required, compulsory extended-response questions based on the syllabus, worth 40% of overall grade

• Mathematical Exploration (Internal Assessment) - total of 20 marks, worth 20% of overall grade

 Mathematics: Applications and Interpretation - Higher Level

• Paper 1 (120 minutes) - total of 110 marks, GDC required, compulsory short-response questions based on the syllabus, worth 30% of overall grade

• Paper 2 (120 minutes) - total of 110 marks, GDC required, compulsory extended-response questions based on the syllabus, worth 30% of overall grade

• Paper 3 (60 minutes) - total of 55 marks, GDC required, two compulsory extended response problem-solving questions, worth 20% of overall grade

• Mathematical Exploration (Internal Assessment) - total of 20 marks, worth 20% of overall grade

Mathematics: Analysis and Approaches - Standard Level

• Paper 1 (90 minutes) - total of 80 marks, no technology allowed, Section A - compulsory short-response questions based on the syllabus, Section B - compulsory extended-response questions based on the syllabus, worth 40% of overall grade

• Paper 2 (90 minutes) - total of 80 marks, GDC required, Section A - compulsory short-response questions based on the syllabus, Section B - compulsory extended-response questions based on the syllabus, worth 40% of overall grade

• Mathematical Exploration (Internal Assessment) - total of 20 marks, worth 20% of overall grade

Mathematics: Analysis and Approaches - Higher Level

• Paper 1 (120 minutes) - total of 110 marks, no technology allowed, Section A - compulsory short-response questions based on the syllabus, Section B - compulsory extended-response questions based on the syllabus, worth 30% of overall grade

• Paper 2 (120 minutes) - total of 110 marks, GDC required, Section A - compulsory short-response questions based on the syllabus, Section B - compulsory extended-response questions based on the syllabus, worth 30% of overall grade

• Paper 3 (60 minutes) - total of 55 marks, GDC required, two compulsory extended response problem-solving questions, worth 20% of overall grade

• Mathematical Exploration (Internal Assessment) - total of 20 marks, worth 20% of overall grade