Syllabus For IB Maths
The syllabus for IB Mathematics is divided into two main courses:
Mathematics:Analysis and Approaches (AA) and
Mathematics: Applications and Interpretation (Al).
Each course is offered at both Standard Level (SL) and Higher Level (HL),with HL covering additional content and going into greater depth.
1. Mathematics:Analysis and Approaches (AA)
This course is more focused on theoreticalmathematics, idealfor students who enjoy mathematical reasoning and abstract problem-solving.
Core Topics (Both SL and HL)
1.Number and Algebra:
• Arithmetic sequences and series
• Exponents and logarithms
• Functions,including inverse and composite functions
• Polynomial and rational functions
• Complex numbers (HL covers these in greater depth)
2.Functions:
• Understanding the concept of a function
• Graphs and transformations
• Types of functions (exponential,logarithmic, trigonometric,etc.)
• Solving equations graphically and algebraically
3.Geometry and Trigonometry:
• Basic geometry,including triangles and circles
• Trigonometric functions and identities
• Vectors (more depth in HL)
• Geometry of 3D shapes and their properties
4.Calculus:
• Limits and continuity
• Differentiation and its applications (e.g., optimization,related rates)
• Integration and its applications (e.g.,area under curves)
5. Statistics and Probability:
• Descriptive statistics (mean,median,mode, standard deviation)
• Probability concepts and rules
• Distributions (normaldistribution,binomial distribution)
• Hypothesis testing (more in HL) AdditionalTopics (HL Only)
• Advanced calculus,including more complex integration techniques
• Differentialequations and their applications
• Complex numbers in more depth
• Proof by induction
• Additionaltopics in series and sequences
2. Mathematics:Applications and Interpretation (Al)
This course is geared toward students interested in applying mathematics in real-world contexts,such as social sciences,naturalsciences,and business.
Core Topics (Both SL and HL)
1.Number and Algebra:
• Sequences and series,including arithmetic and geometric
• Financialmathematics {loans,interest rates)
• Functions,including polynomialand exponential functions
2.Functions:
• Understanding and interpreting various types of functions
• Use of technology to solve functionalequations
• Transformations of graphs
3.Geometry and Trigonometry:
• Geometry of shapes,both 2D and 3D
• Trigonometric functions and applications (e.g., navigation,waveforms)
• Vectors in two and three dimensions
4. Statistics and Probability:
• Descriptive statistics.
• Probability concepts.
• Distributions and inferentialstatistics
• Use of statisticaltools and software
5.Calculus:
• Basic differentiation and integration
• Applications of calculus in real-life contexts (e.g.,growth models,optimization}
Additional Topics (HL Only}
• More complex statisticaltechniques
• Advanced applications of calculus in real-world scenarios
• Non-linear modeling
• Use of more sophisticated mathematicalsoftware
Assessment Components:
• Internal Assessment (IA}: A mathematical exploration or
• investigation of a topic chosen by the student. This is a major part of the assessment and allows students to demonstrate their understanding of mathematical concepts in a practical context.
External Examinations:
• Paper 1:Non-calculator paper,focused on algebra, functions,and calculus.
• Paper 2:Calculator-allowed paper,covering the entire syllabus.
• Paper 3 (HL only):Focuses on a particular area of the syllabus in more depth,often involving more complex problem-solving or applied mathematics.