Topic 1: Number and Algebra(19 hours/39 hours) 

Standard Level 

• Arithmetic sequences and series

• Geometric sequences and series

• Exponent rules and laws

• Logarithms: base 10 and base e

• Logarithm laws and change of base

• Binomial theorem for positive integers

• Basic deductive proof

High Level (additional)

• Complex numbers in Cartesian form

• Polar form and Euler form

• De Moivre’s theorem

• Proof by mathematical induction

• Proof by contradiction

• Permutations and combinations

• Partial fractions

Topic 2: Functions(21 hours/32 hours)

Standard Level 

• Quadratic functions: graphs, vertex, roots

• Reciprocal and simple rational functions

• Graph transformations: translation, stretch, reflection

• Domain and range

• Vertical and horizontal asymptotes

• Composite and inverse functions

High Level (additional)

• Polynomial functions, factor and remainder theorems

• Oblique (slant) asymptotes

• Modulus graphs: |f(x)| and f(|x|)

• Odd and even functions

• Solutions of inequalities

Topic 3: Geometry and Trigonometry(25 hours/51 hours)

Standard Level 

• Unit circle definitions

• Trigonometric identities

• Sine rule and cosine rule

• Radians, arc length and sector area

• Sin, cos, tan graphs and properties

High Level (additional)

• 2D and 3D vectors

• Scalar product: magnitude, angle between vectors

• Vector product (cross product): area applications

• Vector equations of lines

• Vector equations of planes

• Intersections of lines and planes

Topic 4: Statistics and Probability(27 hours/33 hours)

Standard Level 

• Data presentation and analysis

• Binomial distribution

• Normal distribution

• Correlation and regression

• Basic probability rules

High Level (additional)

• Bayes’ theorem

• Continuous random variables

• Probability density functions

• Expectation and variance

Topic 5: Calculus(28 hours/55 hours)

Standard Level

• Basic differentiation rules

• Chain, product and quotient rules

• Tangents and normals

• Basic integration

• Area under curves

• Kinematics: displacement, velocity, acceleration

High Level (additional)

• Implicit differentiation

• Integration by parts

• Integration by substitution

• Volumes of revolution

• Differential equations

• Maclaurin series

IB Mathematics Exam Structure (AA)