### Course content

Integers
- The notion of integer
- Ordering integers
- Sum, difference, product and factors
- Divisors
- Order of operations
- Factorization
- Prime numbers
- Factorization in prime numbers
- Division with remainder
Negative numbers
- Negative numbers
- Absolute value
Fractions
- Fractions
- Equivalent fractions
- Simplifying fractions
- Addition and subtraction of fractions
- Multiplication and division of fractions
- Integer powers of fractions
- Decimal numbers
Powers and roots
- Powers
- Integer powers of fractions
- Calculating with powers
- Negative exponents
- Roots
- Rules of calculation for roots
- Roots of fractions
- Standard form of powers
- Higher degree roots
- Rules of calculation for higher degree roots
- Standard form of higher degree roots
- Order of operations with powers and roots
- Irrational numbers
Decimal numbers
- Calculating with decimal numbers
- Rounding/approximating of decimal numbers
- Decimal numbers on the number line
Variables
- Variables
- Sum and product of variables
- Substitution
- Simplification
- Simplification with algebraic rules
Calculating with exponents and roots
- Integer powers
- Calculating with integer exponents
- Square roots
- Calculating with square roots
- Higher degree roots
- Calculating with fractional exponents
- Order of operations
Expanding brackets
- Expanding brackets
- Expanding double brackets
Factorization
- Factoring out
- Factorization
Notable products
- The square of a sum or a difference
- The difference of two squares
- Fractions
- Simplifying fractions
- Addition and subtraction of like fractions
- Making fractions similar
- Addition and subtraction of fractions
- Multiplication of fractions
- Division of fractions
- Fraction decomposition
Chapter 3: Linear functions and equations
Formulas
- Formula
- Dependent and independent variables
- Graphs
Linear functions
- Linear formula
- Slope and intercept
- Composing a linear formula
- Parallel and intersecting linear formulas
Linear equations and inequalities
- Linear equations
- The general solution of a linear equation
- Intersection points of linear formulas with the axes
- Intersection points of two linear formulas
- Linear inequalities
- General solution of a linear inequality
Chapter 4: Systems of linear equations
An equation of a line
- A linear equation with two unknowns
- Solution linear equation with two unknowns
- The equation of a line
- Composing the equation of a line
Two equations with two unknowns
- Systems of linear equations
- Solving systems of linear equations by substitution
- Solving systems of equations by elimination
- General solution system of linear equations
Parabola
- Parabola
- Solving quadratic equations by factorization
- Solving quadratic equations by completing the square
Drawing parabolas
- Intersection of parabolas with the axes
- Vertex of a parabola
- Drawing of parabolas
- Transformations of parabolas
Intersection points of parabolas
- Intersection points of a parabola with a line
- Intersection points of parabolas
Chapter 6: Functions
Domain and range
- Function and formula
- Function rule
- Intervals
- Domain
- Range
Power functions
- Power functions
- Transformations of power functions
- Equations with power functions
Higher degree polynomials
- Polynomials
- Equations with polynomials
- Solving higher degree polynomials with factorization
- Solving higher degree polynomials with the quadratic equation
- Higher degree inequalities
Power functions and root functions
- Root function
- Transformations of root functions
- Root equations
- Solving root equations with substitution
- Inverse functions
Fractional functions
- Asymptotes and hyperbolas
- Power functions with negative exponents
- Transformations of power functions with negative exponents
- Linear fractional functions
- Linear fractional equations
- Inverse of linear fractional functions
- Quotient functions
Chapter 7: Exponential functions and logarithms
Exponential functions
- The exponential function
- Exponential equations
- Transformations of the exponential function
Logarithmic functions
- The logarithmic function
- Logarithmic equations
- Exponential equations
- Isolating variables
- Rules for logarithms
- More logarithmic equations
- Change of base
- Solving equations using substitution
- Graph of logarithmic functions
- Transformations of the logarithmic function
Chapter 8: Trigonometry
Sinus, cosinus en tangens
- Angles
- Triangles
- Rules for right-angled triangles
- Symmetry in the unit circle
- Special values of trigonometric functions
- Addition formulas for trigonometric functions
- Sine and cosine rule
Trigonometric functions
- Trigonometric functions
- Transformations of trigonometric functions
- Inverse trigonometric functions
- Trigonometric equations 1
- Trigonometric equations 2
Chapter 9: Differentiation
The derivative
- The difference quotient
- The difference quotient at a point
- The tangent line
- The notion of derivative
The derivative of power functions
- The derivative of power functions
Sum and product rule
- The sum rule
- The product rule
Chain rule
- Composite functions
- The chain rule
The derivative of standard functions
- The derivative of trigonometric functions
- The base e and the natural logarithm
- The derivative of exponential functions and logarithms
Quotient rule
- The quotient rule
Applications of derivatives
- Increasing and decreasing
- Extreme values
- The second derivative
- Types of increasing and decreasing
- Inflection points
- Higher order derivatives
Chapter 10: Integration
Antiderivative function
- The antiderivative of a function
- The antiderivative of a power function
- Rules of calculation for antiderivatives
- Antiderivatives of some known functions
- Antiderivatives and the chain rule
Introduction integration
- Definite integral
- Area
- Area of a surface between curves
- Solid of revolution
Integration techniques
- Substitution method
- Trigonometric integrals
- Integration by parts
- Repeated integration by parts
- Known antiderivatives of some quotient functions
- Long division with polynomials
- Finding the antiderivatives of quotient functions 1
- Finding the antiderivatives of quotient functions 2