IB Mathematics

High school mathematics.

Numbers and algebra

• Sequence and series
• Compound interest
• Logarithms and exponents
• Binomial theorem
• Combinatorics
• Complex number
• De Moivre’s theorem
  • Multiple angle identities
• Proofs
  • Direct proof
  • Proof by contradiction
  • Proof by induction

Functions

• Exponential function
• Logarithmic function

Geometry and trigonometry

• Area and volume
• Trigonometric function
• Trigonometric identity (sine, cosine laws, double angle, compound angle)
• Vector
  • Dot product
  • Cross product
  • Line
  • Plane
• Linear equation and row reduction

Statistics and probability

Probability

• Probability distribution
  • Binomial distribution
• Bayes’ theorem
• Continuous random variable Statistics
• Box-and-whisker diagram
  • Outlier
• Mean
• Variance
• Standard deviation
• Z-score
• Linear regression

Calculus

• Differentiation
  • Differentiation from first principles
  • Chain rule
  • Implicit differentiation
  • Related rates
  • Kinematics
• Integration
  • Integration by parts
• First-order ODE
  • Separation of variables
  • Integrating factor
  • Euler’s method
• Maclaurin polynomials