International · 111 topics

Mathematics Aa

G3N tutors you through the full International Mathematics Aa syllabus offline — from Laws of exponents, Logarithms, Laws of exponents with rational exponents and more — with adaptive lessons, instant quizzes, flashcards and exam-ready summaries.

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Syllabus

What you’ll cover in Mathematics Aa.

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

Exponents and logarithms

3 topics

Laws of exponents

Logarithms

Laws of exponents with rational exponents

Sequences

3 topics

Arithmetic sequences and series

Geometric sequences and series

Financial applications of geometric sequences and series

Functions

9 topics

Concept of a function

Sketching graphs

Composite functions

Inverse functions

Rational functions of the form f(x) = ax +b and f(x) = ax + bx + c (HL)

Solutions of g(x) f(x), both analytically and graphically (HL)

The graphs of the functions y = |f(x)| and y = f(|x |) (HL)

The graphs of the functions y = , y = f(ax + b) and y = [f(x)] (HL)

Properties of functions (HL)

Coordinate geometry

2 topics

Equations of straight lines in two dimensions

Three-dimensional coordinate geometry

Geometry and trigonometry

3 topics

Volumes and surface areas of three-dimensional solids

Rules of trigonometry

Applications of trigonometry

Statistics

4 topics

Sampling

Summarizing data

Presenting data

Correlation and regression

Probability

5 topics

Introduction to probability

Probability techniques

Bayes' theorem (HL)

Variance of a discrete random variable (HL)

Continuous random variables (HL)

Probability distributions

3 topics

Discrete random variables

Binomial distribution

The normal distribution

Differentiation

10 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

The chain rule for composite functions

The product and quotient rules

The second derivative

Local maximum and minimum points

Points of inflection with zero and non-zero gradients

Integration

5 topics

Anti-differentiation

Definite integration and the area under a curve

Further indefinite integration

Further links between area and integrals

Kinematics

Proof

1 topics

The structure of mathematical proof

Sequences and series

2 topics

The sum of infinite convergent geometric sequences

The binomial expansion

Quadratics

3 topics

Graphs of quadratic functions

Solving quadratic equations and inequalities

The discriminant

Graphs

3 topics

Transformations of graphs

Rational functions

Exponential and logarithmic functions

Equations

3 topics

Solving equations analytically

Solving equations graphically

Applications of equations

Trigonometry

7 topics

Radian measure of angles

Trigonometric functions

Trigonometric identities

Graphs of trigonometric functions

Trigonometric equations

Further trigonometric functions (HL)

Compound angle identities (HL)

Statistics and probability

3 topics

Linear regression

Conditional probability

Normal distribution

Counting principles (HL)

2 topics

Basic techniques

Problem solving

Algebra (HL)

3 topics

Extension of the binomial theorem to fractional and negative indices

Partial fractions

Solutions of systems of linear equations

Complex numbers (HL)

5 topics

Cartesian form

Modulus argument form and Euler form

Complex conjugate roots of quadratic and polynomial equations

Powers and roots of complex numbers

Trigonometric identities

Mathematical proof (HL)

3 topics

Proof by induction

Proof by contradiction

Disproof by counterexample

Polynomials (HL)

3 topics

Graphs and equations of polynomial functions

The factor and remainder theorems

Sum and product of roots of polynomial equations

Vectors (HL)

8 topics

Introduction to vectors

Vectors and geometry

Scalar product and angles

Equation of a line in three dimensions

Intersection of lines

Vector product and areas

Equation of a plane

Angles and intersections between lines and planes

Further calculus (HL)

9 topics

Fundamentals of calculus

L'Hôpital's rule

Implicit differentiation

Related rates of change

Optimization

Calculus applied to more functions

Integration by substitution

Integration by parts

Further geometric interpretation of integrals

Series and differential equations (HL)

5 topics

First order differential equations and Euler's method

Separating variables and homogeneous differential equations

Integrating factors

Maclaurin series

Using Maclaurin series to solve 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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