Topics

Basics of math

Equations and inequalities

Functions

Exponents and logarithms

Trigonometry

Triangle trigonometry

Geometry

Analytic geometry

Complex numbers

Combinatorics, probability and statistics

Sequences and series

Differential and integral calculus

Basics of math

The topic is divided into the following subtopics:
  • Logic and sets
  • Elementary arithmetics
  • Polynomials and fractions
  • Expressions with exponents and radicals
  • 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:
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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 exponents and radicals

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 exponents and radicals – 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