📐 Foundations
🔢 Number & Algebra
01
Sequences & Series SL
Arithmetic/geometric sequences, sigma notation, financial applications (compound interest, amortization)
02
Exponents & Logarithms SL
Laws of exponents and logarithms, exponential/logarithmic equations, natural log
03
Proof, Binomial Theorem & Counting SL
Simple proof (LHS→RHS), binomial expansion, Pascal's triangle, permutations and combinations
04
Systems of Linear Equations SL
3×3 systems, row operations, unique/infinite/no-solution cases
05
Complex Numbers HL
Cartesian and polar form, De Moivre's theorem, the Argand diagram, geometric applications
06
Advanced Proof Methods HL
Proof by induction, proof by contradiction, use of counterexamples
📊 Functions
07
Function Concepts & Graphing SL
Domain/range, function notation, graphing, basic transformations
08
Function Families & Composition SL
Linear, quadratic, exponential, logarithmic, rational functions, composite and inverse functions
09
Polynomial & Rational Functions HL
Factor/remainder theorem, rational functions, asymptotes, modulus equations and inequalities
📏 Geometry & Trigonometry
10
3D Geometry & Trigonometry Basics SL
Volume/surface area, angles, sine/cosine rule, area of a triangle
11
Trigonometric Functions & Identities SL
Unit circle, core trig identities, graphs of trig functions
12
Introduction to Vectors SL
Vector algebra, dot product, geometric applications with vectors
13
Vector Cross Product, Lines & Planes HL
Cross product, equations of lines and planes, intersections
14
Advanced Trigonometric Identities HL
Inverse trig functions (arcsin, arccos, arctan), compound-angle formulae, double angle
📉 Statistics & Probability
15
Descriptive Statistics SL
Data presentation, measures of central tendency and spread, correlation, linear regression
16
Probability SL
Probability fundamentals, conditional probability, independence, Venn/tree diagrams
17
Probability Distributions SL
Binomial distribution, normal distribution, expected value
18
Poisson & Continuous Distributions HL
Poisson distribution, continuous random variables, probability density functions
∫ Calculus
19
Limits & Derivatives SL
The concept of a limit, definition of the derivative, differentiation rules (product, quotient, chain rule)
20
Applications of Derivatives SL
Increasing/decreasing functions, maxima/minima, optimization problems
21
Integrals & Area SL
Indefinite/definite integrals, area calculations, core integration techniques
22
Advanced Integration Techniques HL
Integration by substitution, integration by parts, partial fractions
23
Differential Equations HL
Separable differential equations, slope fields, Euler's method
24
Maclaurin Series HL
Series expansions, approximation, polynomial approximation
25
Kinematics & Vector-Valued Functions HL
Vector-valued functions, velocity and acceleration, motion problems
✍️ Practice & Exams
26
SL Practice Problems
Solved questions in Paper 1 & Paper 2 format, covering all SL topics
27
HL Practice Problems
Includes HL-only topics, solved Paper 1 & Paper 2 questions
28
Paper 3: Extended Investigations HL
Investigative problems, reasoning and generalization questions
29
Full-Length Mock Exams
Timed, IB-format full exams for SL and HL with answer keys
30
Internal Assessment (IA) Guide
Mathematical exploration topic selection, structure, assessment criteria