College Algebra

Topic

Lesson

Subtopics

Objectives

1

Geometry and Measurement

1. Construction and Measurement of Geometric Solids

1. Identify the characteristics of different geometric shapes.
2. Apply formulas to measure geometric shapes.

2

Basic Algebraic Operations

1. Real Numbers and Polynomials
2. Rational Expressions
3. Rational Exponents and Radicals

1. Identify and use properties of real numbers.
2. Simplify algebraic expressions.
3. Write rational numbers in different formats.
4. Identify and classify polynomial and Radicals expressions.
5. Perform operations on polynomials.
6. Factor polynomials.
7. Write a rational expression in simplest form
8. Compute rational expressions.
9. Simplify radical expressions.
10. Multiply and divide radical expressions.

3

Linear Equations and Inequalities in One  Variable

1. Linear Equations and Applications
2. Linear Inequalities and Applications
3. Absolute Value in Equations and Inequalities

1. Solve linear equations by using all properties of equality and the rules.
2. Solve word problems using linear equations.
3. Solve and graph linear inequalities.
4. Solve an application using inequalities.
5. Solve absolute value equalities and inequalities.

4

Quadratic Equations

1. Factoring and solving Quadratic Equations using Factoring
2. Completing the Square
3. Quadratic Formula and Applications of the Quadratic Equations

1. Write a quadratic equation in the standard form.
2. Solve quadratic equations by factoring.
3. Solve quadratic equations by the square root property.
4. Solve quadratic equations by completing the square.
5. Solve quadratic equations by using the quadratic formula.
6. Solve word problems involving quadratic equations.
7. Use the discriminant to identify the number of solutions.

5

Polynomial and Other Equations

1. Polynomial Equations and Applications
2. Equations Involving Radicals and Rational Exponents
3. Complex Numbers

1. Solve polynomial equations using the zero factor property.
2. Solve rational equations.
3. Solve radical equations.
4. Identify and simplify complex numbers.
5. Add and subtract complex numbers.
6. Multiply and divide complex numbers.

6

Functions and Graphs

1. Rectangular Coordinates and the Graph of a Line

1. Use a table of values to graph linear equations.
2. Determine when lines are parallel or perpendicular.
3. Use linear graphs in an applied context.
4. Identify functions and state their domain and range.
5. Use function notation.
6. Write a linear equation in function form.
7. Use function form to identify the slope.
8. Use slope-intercept form to graph linear functions.
9. Write a linear equation in point-intercept form.
10. Use the function form, the slope-intercept form, and the point-intercept form to solve applications.

7

Operations and Functions

1. The Algebra and Composition Functions
2. One-to-One and Inverse Functions

1. Compute a sum or difference of functions and determine the domain of the result.
2. Compose two functions and find the domain.
3. Identify one-to-one functions.
4. Find inverse functions using an algebraic method.
5. Graph a function and its inverse.
6. Graph factorable quadratic equations.
7. Graph the square root, cubic, and cube root functions.
8. Compute a product or quotient of functions and determine the domain of the result.

8

Analyzing Graphs

1. Piecewise-Defined Functions
2. Graphs and Symmetry
3. Tranformations

1. State the domain of a piecewise-defined function.
2. Evaluate piecewise-defined functions.
3. Graph functions that are piece-wise defined.
4. Identify different symmetry types.
5. Use symmetry as an aid to graphing.
6. Perform vertical and horizontal shifts of a basic graph.
7. Perform vertical and horizontal reflections of a basic graph.
8. Perform stretches and compressions on a basic graph.
9. Transform the graph of a general function.

9

Graphing Polynomial Functions

1. Graphing General Quadratic Functions 
2. Graphing Polynomial Functions
3. Applications of Polynomial Functions

1. Graph quadratic functions by completing the square and using transformations.
2. Graph a general quadratic function using the vertex formula.
3. Solve applications involving quadratic functions.
4. Graph polynomial functions.
5. Describe the end behavior of a polynomial graph.

10

Graphing Rational Functions

1. Asymptotes and Rational Functions
2. Graphing Rational Functions
3. Applications of Rational Functions

1. Graph the reciprocal and reciprocal quadratic functions.
2. Identify horizontal and vertical asymptotes.
3. Use asymptotes to graph transformations.
4. Use asymptotes to determine the equation of a rational function from its graph.
5. Find the domain of a rational function.
6. Find the intercepts of a rational function.
7. Graph general rational functions.
8. Solve applications involving rational functions.

11

Exponential and Logarithmic Functions

1. Exponential Functions
2. Logarithms and Logarithmic Functions
3. The Exponential Function and Natural Logarithm

1. Evaluate an exponential function.
2. Graph exponential functions.
3. Solve certain exponential equations.
4. Solve applications of exponential equations.
5. Write exponential equations in logarithmic form.
6. Graph logarithmic functions and find their domains.
7. Solve applications of logarithmic functions.
8. Evaluate and graph base exponential functions.
9. Evaluate and graph the natural logarithm functions.
10. Apply the properties of logarithms.
11. Use the change-of-base formula.

12

Exponential and Logarithmic Equations

1. Exponential Equations
2. Logarithmic Equations
3. Applications of Exponential and Logarithmic Equations

1. Write logarithmic and exponential equations in simplified form.
2. Solve exponential equations.
3. Solve logarithmic equations.
4. Solve applications involving exponential and logarithmic equations.
5. Use exponential equations to find the interest compounded in times per year.
6. Use exponential equations to find the interest compounded continuously.
7. Solve exponential growth and decay problems.

13

Systems of Linear Equations in Two Variables

1. Solving Systems Graphically and by Substitution
2. Solving Systems using Elimination
3. Applications of Linear Systems

1. Verify ordered pair solutions. 
2. Solve linear systems by graphing.
3. Solve linear systems by substitution.
4. Solve linear systems by elimination.
5. Recognize inconsistent systems (no solutions) and dependent systems (infinitely many solutions).
6. Use a system of equations to mathematically model and solve applications.

14

Solving Linear Systems Using Augmented Matrices

1. Matrices
2. Solving Linear Systems using Matrix Equations
3. More Applications of Linear Systems

1. State the size of a matrix and identify entries in a specified row and column.
2. Form the augmented matrix of a system of equations.
3. Recognize inconsistent and dependent systems.
4. Model and solve applications using linear systems.
5. Solve a system of equations using row  operations.

15

Sequences and Series

1. Sequences and Series
2. Arithmetic Sequences
3. Geometric Sequences

1. Write out the terms of a sequence given the general term.
2. Determine the general term of a sequence.
3. Find the partial sum of a series.
4. Use summation notation to write and  evaluate the series.
5. Solve applications using mathematical sequences.
6. Find the sum of a geometric series.
7. Solve application problems involving geometric sequences and series.

16

Review and Graded Final Exam

1. Course Review

1. None