The International Baccalaureate (IB) Mathematicscurriculum is designed to provide students with a comprehensive and rigorous mathematical education. It is divided into different courses to cater to varying levels of ability and interest, typically offered at both the Standard Level (SL) and Higher Level (HL). The IB Math curriculum was recently revised, and now it is categorized into two main courses: Mathematics: Analysis and Approaches (AA) and Mathematics: Applications and Interpretation (AI). Both courses are offered at SL and HL.
### Mathematics: Analysis and Approaches (AA)
This course is designed for students who enjoy developing their mathematics to become fluent in the construction of mathematical arguments and develop strong skills in mathematical thinking. It is ideal for students who want to study mathematics or related subjects at university.
#### Core Topics (SL and HL)
1. **Number and Algebra**:
– Arithmetic and geometric sequences and series
– Exponents and logarithms
– Binomial theorem
– Complex numbers (HL only)
2. **Functions**:
– Types of functions and their graphs
– Transformations of functions
– Composite and inverse functions
– Polynomials and rational functions (HL only)
3. **Geometry and Trigonometry**:
– Trigonometric functions and their graphs
– Trigonometric identities and equations
– Vectors in 2D and 3D (HL only)
– Conic sections (HL only)
4. **Calculus**:
– Limits and continuity
– Differentiation and its applications
– Integration and its applications
– Differential equations (HL only)
5. **Statistics and Probability**:
– Descriptive statistics
– Probability concepts and distributions
– Statistical inference (HL only)
#### Additional HL Topics
– Complex numbers
– Proof by induction
– Further calculus
– Differential equations
### Mathematics: Applications and Interpretation (AI)
This course is designed for students who are interested in developing their mathematics for describing our world and solving practical problems. It is ideal for students who enjoy mathematics applied to real-life contexts and wish to pursue subjects such as social sciences, natural sciences, statistics, business, engineering, and technology.
#### Core Topics (SL and HL)
1. **Number and Algebra**:
– Arithmetic and geometric sequences and series
– Financial mathematics (interest rates, annuities)
– Exponents and logarithms
2. **Functions**:
– Types of functions and their graphs
– Transformations of functions
– Modeling with functions
3. **Geometry and Trigonometry**:
– Trigonometric functions and their graphs
– Vectors in 2D
– Coordinate geometry
4. **Statistics and Probability**:
– Descriptive statistics
– Probability concepts and distributions
– Correlation and regression
– Statistical inference
5. **Calculus**:
– Introduction to differentiation and its applications
– Introduction to integration and its applications
#### Additional HL Topics
– Further calculus
– Further statistical methods
– Further functions and equations
### Internal Assessment
Both courses require an Internal Assessment (IA), which is a mathematical exploration. This is an individual project where students investigate an area of mathematics that interests them, applying their knowledge and skills to explore and solve problems.
### Differences Between SL and HL
– **Content Depth**: HL covers additional topics and goes into greater depth than SL.
– **Difficulty Level**: HL problems are generally more complex and challenging.
– **Assessment**: Both SL and HL students take exams, but HL exams are longer and more demanding.
The IB Mathematics curriculum emphasizes both conceptual understanding and practical application, preparing students for higher education and careers that require strong mathematical skills. Students are encouraged to think critically, develop problem-solving skills, and appreciate the beauty and power of mathematics.