College Algebra or Precalculus, 1st edition

Module 1:  Solving Linear Equations and Inequalities; Formulas

1.1 Linear Equations in One Variable

1. 1.Distinguish between expressions and equations.
2. 2.Solve linear equations in one variable using the addition property of equality.
3. 3.Solve linear equations in one variable using the multiplication property of equality.
4. 4.Solve linear equations in one variable using both properties of equality.  
5. 5.Translate sentences into equations.
6. 6.Solve applications involving linear equations in one variable.

1.2 Linear Inequalities in One Variable

1. 1.Write inequality statements using real numbers and inequality symbols.
2. 2.Graph linear inequalities in one variable on a number line.
3. 3.Write solutions to inequalities in set-builder notation.
4. 4.Write solutions to inequalities in interval notation.
5. 5.Solve linear inequalities in one variable.
6. 6.Translate sentences into linear inequalities in one variable.
7. 7.Solve applications involving linear inequalities in one variable. 

1.3 Compound Inequalities

1. 1.Find the union of two sets.  
2. 2.Find the intersection of two sets.  
3. 3.Graph compound inequalities on a number line.
4. 4.Solve compound inequalities and write the solution sets in set-builder and interval notation.

1.4 Formulas

1. 1.Solve a formula for a specific variable.  
2. 2.Find the perimeter of a figure.
3. 3.Find the circumference of a circle.
4. 4.Find the area of a figure.
5. 5.Find the volume of a figure.
6. 6.Solve applications involving distance, rate, and time.

Module 2: Graphing Linear Equations and Inequalities in Two Variables

2.1 The Rectangular Coordinate System

1. 1.Write ordered pairs.
2. 2.Plot points in the rectangular coordinate system.
3. 3.Complete a table of values of ordered pair solutions for a linear equation in two variables.
4. 4.Graph linear equations in two variables using a table of values. 

2.2 Intercepts

1. 1.Find the intercepts of a line.
2. 2.Graph a linear equation in two variables given its intercepts.

2.3 Slope

1. 1.Find the slope of a line given two points on the line.
2. 2.Find the slope of a line given its graph.
3. 3.Graph a line given its equation in slope-intercept form.
4. 4.Graph a line given one point on the line and the slope.
5. 5.Graph vertical lines.

6. Graph horizontal lines.

7. Use slope with parallel and perpendicular lines.

8. Interpret slope as a rate of change.

2.4 Equations of Lines

1. 1.Find the slope of a line given its equation.
2. 2.Write the slope-intercept form of a line.  
3. 3.Write the equation of a line given the slope and a point on the line.  
4. 4.Write the equation of a line through two given points.

2.5 Graphs of Linear Inequalities in Two Variables

1. 1.Graph linear inequalities in two variables.  

Module 3:  Exponents and Polynomials

3.1 Exponential Expressions and Rules for Exponents

1. 1.Evaluate exponential expressions with positive exponents. 
2. 2.Use the product rule for exponents.
3. 3.Use the power rules for exponents.
4. 4.Use the quotient rule for exponents.
5. 5.Evaluate exponential expressions with integer exponents.
6. 6.Simplify exponential expressions using the rules for exponents.  

3.2 Polynomial Expressions

1. 1.Identify parts of a polynomial (coefficient, term, degree, factor, constant).
2. 2.Classify polynomials.
3. 3.Evaluate polynomial expressions.  
4. 4.Add polynomials.  
5. 5.Subtract polynomials.
6. 6.Multiply monomials.
7. 7.Multiply a monomial and a polynomial.
8. 8.Multiply polynomials.
9. 9.Multiply the sum and difference of two terms.
10. 10.Square binomials.

3.3 Factoring

1. 1.Factor out the GCF of a polynomial.  
2. 2.Factor trinomials with a leading coefficient of 1.

       3. Factor trinomials with a leading coefficient other than 1.

       4. Factor polynomials by grouping.

       5. Factor a difference of squares.

       6. Factor the sum or difference of two cubes.

       7. Factor polynomials completely.

3.4 Division of Polynomials 

1. 1.Divide a polynomial by a nominal
2. 2.Divide polynomials using long division 

Module 4:  Systems of Equations

4.1 Systems of Linear Equations in Two Variables

1. 1.Determine if an ordered pair is a solution to a system of linear equations in two variables.
2. 2.Solve a system of linear equations in two variables by graphing.
3. 3.Solve a system of linear equations in two variables by substitution.
4. 4.Solve a system of linear equations in two variables by addition.
5. 5.Solve applications involving systems of linear equations in two variables.

4.2 Systems of Linear Equations in Three Variables

1. 1.Determine whether an ordered triple is a solution to a system of linear equations in three variables.
2. 2.Solve a system of linear equations in three variables.

Module 5:  Rational Expressions and Equations

5.1 Rational Expressions   

1. 1.Evaluate rational expressions.
2. 2.Identify values that make a rational expression undefined.
3. 3.Simplify rational expressions.
4. 4.Multiply or divide rational expressions.
5. 5.Add or subtract rational expressions.

5.2 Complex Fractions

1. 1.Simplify complex fractions without variables.
2. 2.Simplify complex fractions with variables.

5.3 Rational Equations

1. 1.Solve rational equations.
2. 2.Solve applications that involve rational equations (motion, mixture, proportion, geometric)
3. 3.Solve problems that involve variation.

Module 6:  Radical Expressions and Equations

6.1 Roots 

1. 1.Find square roots.  
2. 2.Approximate square roots.  
3. 3.Find cube roots.
4. 4.Find nth roots.

6.2 Radical Expressions

1. 1.Simplify radical expressions.
2. 2.Multiply or divide radicals.
3. 3.Add or subtract radicals.
4. 4.Multiply radical expressions.
5. 5.Rationalize denominators with one term.
6. 6.Rationalize denominators with two terms.

6.3 Rational Exponents

1. 1.Write expressions containing rational exponents in radical form.
2. 2.Simplify expressions containing rational exponents.
3. 3.Use rational exponents to simplify radical expressions.

6.4 Radical Equations

1. 1.Solve radical equations.
2. 2.Solve radical equations that contain rational exponents.
3. 3.Use the distance formula to find the distance between two points in a coordinate plane.
4. 4.Solve applications that involve radical equations.

Module 7:  Quadratic Equations 

7.1 Quadratic Equations

1. 1.Solve quadratic equations by factoring.  
2. 2.Solve quadratic equations by the square root property.  

1. 3.Solve quadratic equations by completing the square.  
2. 4.Solve quadratic equations by using the quadratic formula
3. 5.Use the discriminant to describe the solutions of a quadratic equation.  
4. 6.Solve applications that involve quadratic equations and models (including the Pythagorean theorem).  

7.2 Graphs of Quadratic Equations 

1. 1.Graph quadratic equations.
2. 2.Find the vertex of a parabola.
3. 3.Graph horizontal parabolas.

Module 8:  Absolute Value Equations and Inequalities

8.1 Absolute Value Equations

1. 1.Solve absolute value equations.

8.2 Absolute Value Inequalities

1. 1.Solve absolute value inequalities.
2. 2.Identify absolute value inequalities that are contradictions or identities.

Module 9:  Introduction to Functions

9.1 Relations and Functions

1. 1.Identify relations and functions.  
2. 2.Evaluate functions using function notation.  
3. 3.Find the domain and range of a function.
4. 4.Use the vertical line test to determine if a graph is a function.

9.2 Linear Functions

1. 1.Identify linear functions.  
2. 2.Evaluate linear functions.  
3. 3.Interpret the graph of a linear function (domain, range, slope, intercepts).
4. 4.Solve applications that involve linear functions as models.