Basics of math

Logic and sets

A:

  • Basic set operations (intersection, union, set difference, complement)
  • Sets specified by a characteristic property

B:

  • Math logic statements, truth values of statements, quantifiers
  • Set operations – complex problems

C:

  • Word problems – solvable with aid of Venn diagrams

Elementary arithmetics

A:

  • Calculations with fractions and decimals
  • Rounding
  • Writing numbers in exponential form

B:

  • Numbers divisibility

C:

-

Polynomials and fractions

A:

  • Basic operations with polynomials (addition, subtraction, multiplication, use of formulas for (a+b)^2 and (a-b)^2)
  • Simplifying algebraic expressions
  • Evaluating algebraic expressions

B:

  • 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

C:

  • 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

A:

  • Powers with natural exponents
  • Second and third root
  • Simplifying fractions with roots in denominator

B:

  • Powers with integer or rational exponents
  • Higher roots
  • Comparing values of expressions

C:

  • Simplifying expressions with powers and roots – complex problems
  • Simplifying fractions with roots in denominator – complex problems
  • Comparing values of expressions - complex problems

Absolute value

A:

  • Evaluating absolute value of numerical expressions

B:

  • Geometric interpretation of the absolute value
  • Simplifying expressions with absolute value
  • Simple equations and inequalities with absolute value

C:

  • Properties of the absolute value 

Percent problems

A:

  • Calculation of percentages – standard problems

B:

  • Calculation of percentages and percentage points – complex problems

C:

  • Calculation of percentages – complex word problems (price growth, inflation, interests)
  • Problems leading to systems of equations

Matrices and determinants

A:

  • Classification of matrices 
  • Addition and multiplication of matrices
  • Matrix equations
  • Applications

B:

  • Matrix calculations - complex problems
  • Rank of a matrix
  • Inverse matrices 

C:

  • Determinant of a matrix 
  • Determinant properties