# Basics of math

The topic is divided into the following subtopics:
• Logic and sets
• Elementary arithmetics
• Polynomials and fractions
• Expressions with powers and roots
• Absolute value
• Percent problems

### Logic and sets

Part I:
• Basic set operations (intersection, union, set difference, complement)
• Sets specified by a characteristic property
Part II:
• Math logic statements, truth values of statements, quantifiers
• Set operations – complex problems
Part III:
• Word problems – solvable with aid of Venn diagrams

### Elementary arithmetics

Part I:
• Calculations with fractions and decimals
• Rounding
• Writing numbers in exponential form
Part II:
• Numbers divisibility
Part III:
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### Polynomials and fractions

Part I:
• Basic operations with polynomials (addition, subtraction, multiplication, use of formulas for (a+b)^2 and (a-b)^2)
• Simplifying algebraic expressions
• Evaluating algebraic expressions
Part II:
• Factoring polynomials into products
• Simplifying algebraic expressions – complex problems
• Problems solvable with use of formulas for (a+b)^3 and (a-b)^3
• Finding of all values such that an expression is not defined
• Finding of all values such that an expression equals zero
• Word problems – isolating the variable out of a formula
Part III:
• Division of two polynomials
• Problems solved using Binomial theorem
• Problems solved using formulas for a^3+b^3 and a^3-b^3, …

### Expressions with powers and roots

Part I:
• Powers with natural exponents
• Second and third root
• Simplifying fractions with roots in denominator
Part II:
• Powers with integer or rational exponents
• Higher roots
• Comparing values of expressions
Part III:
• Simplifying expressions with powers and roots – complex problems
• Simplifying fractions with roots in denominator – complex problems
• Comparing values of expressions - complex problems

### Absolute value

Part I:
• Evaluating absolute value of numerical expressions
Part II:
• Geometric interpretation of the absolute value
• Simplifying expressions with absolute value
• Simple equations and inequalities with absolute value
Part III:
• Properties of the absolute value

### Percent problems

Part I:
• Calculation of percentages – standard problems
Part II:
• Calculation of percentages and percentage points – complex problems
Part III:
• Calculation of percentages – complex word problems (price growth, inflation, interests)
• Problems leading to systems of equations