Topics

Equations and inequalities

The topic is divided into the following subtopics:
  • Linear equations and inequalities
  • Quadratic equations and inequalities
  • Higher degree equations and inequalities
  • Systems of equations and inequalities
  • Rational equations and inequalities
  • Absolute value equations and inequalities
  • Radical equations and inequalities
  • Equations and inequalities with parameters

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

Systems of equations and inequalities

Part I:
  • Systems of two linear equations with two unknowns
  • Graphical solutions of systems of two linear equations with two unknowns
  • Single equation with two unknowns
Part II:
  • Systems of two linear inequalities with two unknowns
  • Graphical solutions of systems of two linear inequalities
  • One inequality with two unknowns
  • Word problems leading to systems of two linear equations or inequalities with two unknowns
Part III:
  • Systems of two linear equations with two unknowns and a parameter
  • Systems of three linear equations with three unknowns
  • Matrix calculus – matrix, the rank of a matrix
  • More complex systems of equations or inequalities (quadratic, with absolute value, with rational expressions, ….)
  • Word problems

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