Course content

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
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

College Calculus

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