Chapter 1: Calculating with numbers

- Integers
- - The notion of integer
- - Calculating with integers
- Rational numbers
- - Equivalent fractions
- - Simplifying fractions
- - Addition and subtraction of fractions
- - Multiplication and division of fractions
- - Integer powers of fractions
- - Decimal numbers
- Roots
- - Roots of integers
- - Calculating with powers
- Order of operations
- - Order of operations

Chapter 2: Calculating with variables

- Variables
- - The notion of funtion
- Calculating with exponents
- - Positive integer exponents
- Expanding brackets
- - Expanding brackets
- Factorization
- - Factorization
- Notable products
- - Expanding brackets
- - The difference of two squares
- Adding and subtracting fractions
- - The notion of a rational number
- - Addition and subtraction of fractions
- - Multiplication and division of fractions
- - Finding a common denominator

Chapter 3: Equations

- Linear equations and inequalities
- - Linear equations
- - Linear inequalities
- Quadratic equations
- - Quadratic equations
- - The quadratic formula
- Two equations with two unknowns
- - A linear equation with two unknowns
- - The equation of a line
- - Systems of linear equations

Chapter 4: Functions

- Functions and graphs
- - Functions and graphs
- Linear functions
- - The notion of linear function
- - Equations and lines
- Quadratic equations and parabolas
- - Drawing of quadratic equations
- - Intersection points of parabolas
- Fractions of functions
- - The hyperbola
- - Linear fractional functions
- - Quotient functions
- Power functions and root functions
- - Root functions
- - Root equations

Chapter 5: Trigonometry

- Trigonometry in the right-angled triangle
- - Sine, cosine and tangent
- Degrees and radians
- - Measuring angles

Chapter 6: Exponential functions and logarithms

- - The natural exponential function and logarithm
- - Rules of calculation for exponential functions and logarithms

Chapter 7: Differentiation

- Tangents to a graph
- - Tangent line
- - The notion of difference quotient
- - The notion of derivative
- Derivatives of standard functions
- - Derivatives of polynomials and power functions
- - Derivatives of trigonometric functions
- - Derivatives of exponential functions and logarithms
- - Exponential functions and logarithm derivatives revisited
- Sum and product rule
- - The sum rule for differentiation
- - The product rule for differentiation
- Chain rule
- - Chain rule for differentiation
- Quatient rule
- - Quotient rule for differentiation
- Increasing, decreasing, extreme values
- - Monotonicity
- - Local minima and maxima
- - Analysis of functions

Chapter 8: Integration

- Antiderivative functions
- - Primitives o some known functions
- Definite integral and area
- - The fundamental Theorem of Calculus