Topics

Basics of Math

Equations and Inequalities

Functions

Exponentials and Logarithms

Trigonometry

Plane Geometry

Space Geometry

Analytical Geometry

Complex Numbers

Combinatorics, Probability, and Statistics

Sequences and Series

Differential and Integral Calculus

Equations and Inequalities

The topic is divided into the following subtopics:
  • Linear Equations and Inequalities
  • Quadratic Equations and Inequalities
  • Higher Degree Equations and Inequalities 
  • Rational Equations and Inequalities
  • Absolute Value Equations and Inequalities
  • Radical Equations and Inequalities
  • Equations and Inequalities with Parameters
  • Systems of Linear Equations and Inequalities
  • Systems of Nonlinear Equations and Inequalities

Linear Equations and Inequalities

Part I:
  • Simple linear equations
  • Equivalent equations
  • Graphical solutions of linear equations
  • Linear equations specified by word description
Part II:
  • Simple linear inequalities
  • Graphical solutions of linear inequalities
  • Linear inequalities specified by word description
Part III:
  • Word problems leading to linear equations and inequalities

Quadratic Equations and Inequalities

Part I:
  • Quadratic equations
Part II:
  • Quadratic inequalities
  • Vieta’s formulas
  • Word problems leading to quadratic equations and inequalities
Part III:
  • Quadratic equations and inequalities with absolute value
  • Word problems – more complex

Higher Degree Equations and Inequalities

Part I:
  • Equations solvable by factoring polynomials to products of linear and quadratic factors
Part II:
  • Equations solvable by substitution method
  • Cubic equations with one of the roots known
  • Inequalities solvable by factoring polynomials to products of linear and quadratic factors
Part III:
  • Equations of 4th degree with two of the roots known
  • Equations of higher degrees, guessing of some of the roots is necessary

Rational Equations and Inequalities

Part I:
  • Rational equations
  • Domains of rational equations
Part II:
  • Rational inequalities
  • Domains of rational inequalities
Part III:
  • Rational equations and inequalities with absolute values 

Absolute Value Equations and Inequalities

Part I:
  • Linear equations and inequalities with single absolute value - solutions based on geometric interpretation of the absolute value
Part II:
  • Linear equations with one or more absolute values
Part III:
  • Linear inequalities with one or more absolute values
  • Linear equations and inequalities with absolute values inserted in absolute values

Radical Equations and Inequalities

Part I:
  • Equations with an unknown under a single radical
  • Domain of an equation
  • Domain of an expression with an unknown under a radical 
Part II:
  • Equations with unknown under several radicals
  • Inequalities with unknowns under radicals
Part III:
  • Word problems
  • More complex equations – combinations of radicals and absolute values

Equations and Inequalities with Parameters

Part I:
  • Linear equations with a parameter
  • Equations and inequalities with a parameter solved for a given value of the parameter
Part II:
  • Linear inequalities with a parameter
  • Quadratic equations and inequalities with a parameter
Part III:
  • Rational equations and inequalities with a parameter

Systems of Linear Equations and Inequalities

Part I:
  • Systems of two equations with two unknowns
  • One equation with two unknowns
Part II:
  • Systems of three equations with three unknowns
  • Using matrices to solve systems of equations 
  • Solvability of systems of equations 
  • Cramer's rule 
  • Word problems 
  • Systems of equations with parameters
Part III:
  • Systems of inequalities
  • One inequality with two unknowns
  • Two inequalities with one unknown

Systems of Nonlinear Equations and Inequalities

Part I:
  • Systems with linear and quadratic equations
  • One nonlinear equation with two unknowns
  • Systems with an unknown in the denominator
Part II:
  • Systems of polynomial equations
  • Graphical solutions of systems of polynomial equations
Part III:
  • Systems with the unknown in absolute value
  • Systems with the unknown under the square root
  • Systems with parameter
  • Systems of inequalities