MAT 097 - Intermediate Algebra

1. Solve Linear Equations
2. Solve Quadratic Equations
3. Solve Root Equations
4. Solve Rational Equations
5. Solve Systems of Equations
6. Solve Absolute Equations
7. Solve Linear and Absolute Value Inequalities
8. Graph Linear Equations

1. Solve Linear Equations
   1. Solve Linear Equations that include grouping symbols, and decimal/fraction coefficients.
   2. Solve Linear Equations in the context of linear applications that include simple formula problems.  Include problems where values are first plugged into a formula and the remaining unknown variable is solved for.
2. Solve Quadratic Equations
   1. Introduction to multiplication of polynomials
   2. Introduction to factoring polynomials 
   3. Solve Quadratic Equations by factoring using the techniques of (1) factoring out the greatest common factor, (2) factoring by grouping, (3) factoring trinomials, and the difference of squares, and (4) the square root method.
   4. Solve Quadratic Equations using the Quadratic Formula and Completing the Square.  Include solutions that require techniques to simplify numerical irrational solutions.
   5. Solve Quadratic Equations in the context of quadratic applications, including the Pythagorean Theorem and area problems.
3. Solve Root Equations
   1. Introduction to simplification of radical variable expressions
   2. Identify values that are not in the domain of root equations
   3. Solve Root Equations that include square roots and higher order roots
   4. Solve Root Equations that result in linear and quadratic equations. 
   5. Solve root equations that require the squaring of a binomial.  
4. Solve Rational Equations
   1. Identify values that result in division by zero
   2. Introduction to simplification of rational expressions
   3. Solve Rational Equations that include two and three terms
   4. Solve Rational Equations using the technique of eliminating the denominators
   5. Solve Rational Equations that result in linear and quadratic equations
   6. Solve Rational Equations that result in extraneous solutions.
5. Solve Systems of Equations
   1. Solve 2 x 2 systems of equations by graphing, elimination and substitution
   2. Solve 2 x 2 systems of equations in the context of application problems, including investment, mixture problems, and motion problems.
   3. Include systems that result in independent, dependent, and inconsistent solutions
6. Solve Absolute Equations
   1. Solve Absolute Value Equations that result in linear and quadratic equations
   2. Solve Absolute Value Equations that result in a finite number of solutions, an infinite number of solutions, and no solution.
7. Solve Linear and Absolute Value Inequalities
   1. Solve Linear Inequalities that include grouping symbols, and decimal/fraction coefficients
   2. Solve Absolute Value Inequalities that result in linear inequalities
   3. Provide answers in interval notation, set notation, and inequality notation.
8. Graph Linear Equations
   1. Introduce graphing a line using the slope and y-intercept of a line
   2. Graph a line using the slope and intercept of a line that is in slope-intercept form or in standard form.
   3. Find the equation of a line in slope-intercept form given two points or a single point and slope using the point-slope formula or the slope intercept formula.
   4. Find the equation of a line that is parallel or perpendicular to another line
   5. Solve Application problems involving the interpretation of slope as a rate of change.
9. Optional Topics
   1. Introduction to functions as a concept
   2. Introduction to function notation

1. Linear Equations
   1. Solve linear equations
   2. Applications of linear equations
2. Polynomial Expressions
   1. Multiply polynomial expressions
   2. Factor polynomial expressions
      1. GCF
      2. Grouping
      3. Quadratic Trinomials
      4. Difference of squares
3. Quadratic Equations
   1. Solve quadratic equations
      1. Factoring
      2. Square root method
      3. Completing the square
      4. Quadratic formula
   2. Applications of quadratic equations
4. Root Expressions and Equations
   1. Simplify numeric and variable radical expressions
   2. Multiply radical expressions
   3. Add and subtract radical expressions
   4. Divide radical expressions
   5. Solve radical equations
   6. Applications of radical equations
5. Rational Expressions and Equations
   1. Simplify rational expressions
   2. Multiply and divide rational expressions
   3. Solve rational equations
6. Functions (optional)
   1. Definition
   2. Function notation
7. Graph Linear Equations
   1. Graph linear equation from
      1. x and y-intercepts
      2. Slope-intercept form
      3. Parallel and perpendicular to a given line
   2. Applications of slope
   3. Write equations of lines
      1. Given slope and a point
      2. Given two points
      3. Parallel and perpendicular to a given line
8. Linear Inequalities
   1. Solve linear inequalities
9. Linear 2x2 Systems of Equations
   1. Solve linear 2x2 system
      1. Elimination method
      2. Substitution method
   2. Types of solutions
   3. Applications of linear 2x2 systems
10. Absolute Value Equations and Inequalities
    1. Solve absolute value equations
    2. Solve absolute value inequalities