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
Fundamentals of Arithmetic
Part I: - Calculations with fractions and decimals
- Rounding
- Writing numbers in exponential form
Polynomials and Rational Expressions
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
Percentages and Financial Mathematics
Part I: - Calculating percentages
- Standard percent problems with financial themes
Part II: - Calculating a percentage of another percentage
Part III: - Calculating interest
- More complex percent problems (price growth, inflation, interests)
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
Basics of Math