### Course content

Integers
- The notion of integer
- Calculating with integers
- Divisors of integers
- Division with remainder
- Prime numbers
- Greatest common divisor and least common divisor
Rational numbers
- The notion of rational number
- Addition and subtraction of fractions
- Multiplication and division of fractions
- Ordering of rational numbers
- Integer powers of fractions
- Decimal numbers
Roots
- Roots of integers
- Roots of fractions
- Higher roots
- Fractional powers
- Absolute value
Real numbers
- Ordering of real numbers
- The notion of real number
- Ordering and decimal development
- Approximations of real numbers
- Calculating with real numbers
- Applications of real numbers
Arithmetic with variables
- Order of operations
- Calculating with powers
- Expanding brackets
- Moving terms outside brackets
Notable products
- Expanding brackets
- The square of a sum or a difference
- The difference of two squares
Rational expressions
- Simplifying fractions
- Finding a common denominator
Binomial Coefficient
- Third and fourth powers of binomials
- Pascal's triangle
- Binomial coefficients and factorials
- Binomial theorem and sigma notation
- Applications of combinatorics
Applications
- Applications of algebra
Chapter 3: Linear equations with a single unknown
Notion
- The notion of linear equation
- Solving by reduction
- The general solution
Variations
- Fractional linear equations
- Equations with absolute values
- Substitution
- Solving by factorization
Applications
- Applications of linear equations with a single unknown
Chapter 4: Systems of linear equations
Simple systems of linear equations
- The notion of parameter
- The notion of system of equations
- The linear equation of a line
Two linear equations
- Solving systems of equations by substitution
- Solving systems of equations by elimination
- Equations and lines
Applications
- Applications of systems of linear equations
Chapter 5: Quadratic equations
Quadratic equations with one unknown
- The notion of quadratic equation
- The general solution to a quadratic equation
Variations
- Substitution
- Fractional equations
- Root equations
- Case distinction
Applications
- Applications of quadratic equations