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
  • Matrices and determinants

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:

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

Matrices and determinants

Part I:
  • Classification of matrices 
  • Addition and multiplication of matrices
  • Matrix equations
  • Applications
Part II:
  • Matrix calculations - complex problems
  • Rank of a matrix
  • Inverse matrices 
Part III:
  • Determinant of a matrix 
  • Determinant properties