Linear equations and inequalities
A:
- Simple linear equations
- Equivalent equations
- Graphical solutions of linear equations
- Linear equations specified by word description
B:
- Simple linear inequalities
- Graphical solutions of linear inequalities
- Linear inequalities specified by word description
C:
- Word problems leading to linear equations and inequalities
Quadratic equations and inequalities
B:
- Quadratic inequalities
- Vieta’s formulas
- Word problems leading to quadratic equations and inequalities
C:
- Quadratic equations and inequalities with absolute value
- Word problems – more complex
Higher degree equations and inequalities
A:
- Equations solvable by factoring polynomials to products of linear and quadratic factors
B:
- 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
C:
- 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
A:
- Rational equations
- Domains of rational equations
B:
- Rational inequalities
- Domains of rational inequalities
C:
- Rational equations and inequalities with absolute values
Absolute value equations and inequalities
A:
- Linear equations and inequalities with single absolute value - solutions based on geometric interpretation of the absolute value
B:
- Linear equations with one or more absolute values
C:
- Linear inequalities with one or more absolute values
- Linear equations and inequalities with absolute values inserted in absolute values
Radical equations and inequalities
A:
- Equations with an unknown under a single radical
- Domain of an equation
- Domain of an expression with an unknown under a radical
B:
- Equations with unknown under several radicals
- Inequalities with unknowns under radicals
C:
- Word problems
- More complex equations – combinations of radicals and absolute values
Equations and inequalities with parameters
A:
- Linear equations with a parameter
- Equations and inequalities with a parameter solved for a given value of the parameter
B:
- Linear inequalities with a parameter
- Quadratic equations and inequalities with a parameter
C:
- Rational equations and inequalities with a parameter
Systems of linear equations and inequalities
A:
- Systems of two equations with two unknowns
- One equation with two unknowns
B:
- 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
C:
- Systems of inequalities
- One inequality with two unknowns
- Two inequalities with one unknown
Systems of nonlinear equations and inequalities
A:
- Systems with linear and quadratic equations
- One nonlinear equation with two unknowns
- Systems with an unknown in the denominator
B:
- Systems of polynomial equations
- Graphical solutions of systems of polynomial equations
C:
- Systems with the unknown in absolute value
- Systems with the unknown under the square root
- Systems with parameter
- Systems of inequalities
