International · 103 topics

Mathematics Ai

G3N tutors you through the full International Mathematics Ai syllabus offline — from Laws of exponents, Operations with numbers in standard form (a×10ᵏ), Logarithms and more — with adaptive lessons, instant quizzes, flashcards and exam-ready summaries.

Study Mathematics Ai now All International subjects

Syllabus

What you’ll cover in Mathematics Ai.

The complete topic outline G3N teaches, mapped to the International curriculum.

Exponents and logarithms

6 topics

Laws of exponents

Operations with numbers in standard form (a×10ᵏ)

Logarithms

Laws of exponents with rational exponents (HL)

Sum of infinite convergent geometric sequences (HL)

Using logarithmic scales on graphs (HL)

Sequences

3 topics

Arithmetic sequences and series

Geometric sequences and series

Financial applications of geometric sequences and series

Functions

2 topics

Concept of a function

Sketching graphs

Coordinate geometry

2 topics

Equations of straight lines in two dimensions

Three-dimensional coordinate geometry

Geometry and trigonometry

6 topics

Volumes and surface areas of three-dimensional solids

Rules of trigonometry

Applications of trigonometry

Radian measure (HL)

Further trigonometry (HL)

Matrices as transformations (HL)

Statistics

11 topics

Sampling

Summarizing data

Presenting data

Correlation and regression

Statistical design and unbiased estimators (HL)

Further tests (HL)

Non-linear regression (HL)

Confidence intervals for the mean (HL)

Hypothesis tests for the mean (HL)

Hypothesis tests using the binomial and Poisson distributions (HL)

Type I and Type II errors (HL)

Probability

6 topics

Introduction to probability

Probability techniques

Transforming variables (HL)

Distribution of X (HL)

Poisson distribution (HL)

Markov chains (HL)

Probability distributions

3 topics

Discrete random variables

Binomial distribution

The normal distribution

Differentiation

9 topics

Limits and derivatives

Graphical interpretation of derivatives

Finding an expression for the derivative

Tangents and normals at a given point and their equations

Extending differentiation (HL)

The chain rule (HL)

The product and quotient rules (HL)

Related rates of change (HL)

The second derivative (HL)

Integration

6 topics

Anti-differentiation

Definite integration and the area under a curve

Further indefinite integration (HL)

Definite integrals and the area between a curve and the x-axis (HL)

Further geometric interpretations of integrals (HL)

Integration by substitution (HL)

Number and finance

2 topics

Approximation

Further financial mathematics

Solving equations with technology

2 topics

Systems of linear equations

Polynomial equations

Mathematical models

6 topics

Linear models

Quadratic models

Exponential models

Direct and inverse variation and cubic models

Sinusoidal models

Modelling skills

Geometry

2 topics

Arcs and sectors

Voronoi diagrams

Hypothesis testing

3 topics

Chi-squared tests

t-tests

Spearman's rank correlation

Calculus

3 topics

Maximum and minimum points

Optimization

Trapezoidal rule

Vectors (HL)

4 topics

Introduction to vectors

Vector equation of a line

Vector applications to kinematics

Scalar and vector product

Matrices (HL)

4 topics

Definition and arithmetic of matrices

Determinants and inverses

Solutions of systems of equations using the inverse matrix

Eigenvalues and eigenvectors

Functions and modelling (HL)

4 topics

Composite functions

Inverse functions

Transformations of graphs

Further modelling

Complex numbers (HL)

3 topics

Cartesian form

Modulus argument form and exponential form

Geometric representation

Graphs and algorithms (HL)

6 topics

Introduction to graph theory

Moving around a graph

Weighted graphs

Minimum spanning tree algorithms

The Chinese postman problem

The travelling salesman problem

Kinematics (HL)

2 topics

Derivatives and integrals in kinematics

Motion with variable velocity in two dimensions

Differential equations (HL)

4 topics

Separation of variables

Slope fields and Euler's method

Coupled systems and phase portraits

Second order differential equations

Independent mathematical exploration (coursework)

4 topics

Modelling and problem-solving with the mathematical toolkit

Use of technology (GDC and mathematical software)

Mathematical proof, reasoning and communication

The internal assessment: the mathematical exploration

How G3N helps

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Concept-led learning

Lessons that match inquiry-based, conceptual international curricula rather than rote answers.

Practice on demand

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Summarise anything

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