​IB Math (Higher Level)
 

​Topic 1:  Mathematics as the science

• Number patterns: sequences, series and sigma notation
• Arithmetic sequences and series
• Geometric sequences and series
• Conjectures and proofs
• Mathematical induction
• Counting methods
• The binomial theorem

 



Topic 2:  Mathematics as a language

• Relations and functions
• Special functions and their graphs
• Operations with functions
• Transformations of graphs of functions

 



Topic 3: The long journey of mathematics

• Introduction to complex numbers
• Operations with complex numbers
• Polynomial functions: graphs and operations
• Polynomial functions: zeros, sum and product
• Polynomial equations and inequalities
• Solving systems of equations

 
 
 
 
Topic 4:  Modeling the real world

• Limits, continuity and convergence
• The derivative of a function
• Differentiation rules
• Exploring relationships between f, f ’ and f ’’
• Applications of differential calculus economics
• Optimization and modeling
• Differentiation of implicit functions
• Related rates

 




Topic 5: Aesthetics in mathematics

• Recursive functions
• Properties of exponents and logarithms
• Euler’s number and exponential functions
• Invariance and the exponential function- a different approach to Euler’s number
• Logarithms and bases
• Logarithmic functions and their behavior
• Derivatives of exponential and logarithmic functions
• Angles, arcs and areas

 
 

​

Topic 6: Exploring randomness

• Classification and representation of statistical data
• Measures of central tendency
• Measures of dispersion
• Theoretical probability
• Probability properties
• Experimental probability
• Conditional probability
• Independent events
• Probability tree diagrams
• Bayes’ theorem

 
Topic 7: The evolution of calculus

• Integration as anti-differentiation
• Definite integration
• Geometric significance of the definite integral

 
Topic 8:  Ancient mathematics and modern methods

• The right-angled triangle and trigonometric ratios
• The unit circle and trigonometric ratios
• Compound angle identities
• Double angle identities
• Graphs of trigonometric functions
• The inverse trigonometric functions
• Solving trigonometric equations
• The cosine rule
• The sine rule
• Area of a triangle

 
Topic 9:  The power of calculus

• Derivatives of trigonometric functions
• Related rates of change with trigonometric expressions
• Integration of trigonometric functions
• Integration by substitution
• Integration by parts
• Special substitution
• Applications and modeling

 


​
Topic 10:  Modeling randomness

• Discrete random variables and distributions
• Binomial distribution
• Poisson distribution
• Continuous random variables
• Normal distribution
• Modeling and problem solving

 



Topic 11:  Inspiration and formalism

• Geometric vectors and basic operations
• Introduction to vector algebra
• Vectors, points and equations of lines
• Scalar product
• Vector (cross) product and properties
• Vectors and equations of planes
• Angles, distances and intersections
• Modeling and problem solving

 
Topic 12:  Multiple perspectives in mathematics

• Complex numbers as vectors
• Complex plane and polar form
• Operations with complex numbers in modulus-argument form
• Powers and roots of complex numbers: De Moivre’s theorem and applications
• Mathematical connections

 
Topic 13:  Exploration

• About the exploration
• Internal assessment criteria
• How the exploration is marked
• Academic honesty
• Record keeping
• Choosing a topic
• Getting started