Presents a study of College Algebra and Analytic Geometry with an emphasis on mathematical modeling. The student will analyze functions in depth including transformations, inverses and compositions, while paying particular attention to quadratic, polynomial, rational, exponential and logarithmic functions and their graphs. Other topics include complex numbers, the binomial theorem, arithmetic and geometric sequences, series, systems of equations and inequalities, matrices and determinants, partial fractions, algebraic equations and inequalities, conic sections and probability. The student will solve applications and modeling problems related to the above topics. Upon completion, students should be able to solve practical problems and use appropriate models for analysis. This course is designed to prepare students for Calculus.

Prerequisite: Intermediate Algebra with a grade of C or better.

Equations and Inequalities

Lessons | Homework | HW Quiz | ||
---|---|---|---|---|

1.1 Linear Equations | 1.1 | 1.1 | ||

1.2 Linear Applications | 1.2 | 1.2 | ||

1.3 Complex Numbers | 1.3 | 1.3 | ||

1.4 Quadratic Equations | 1.4 | 1.4 | ||

1.5 Rational & other Nonlinear Equations | 1.5 | 1.5 | ||

1.6 Linear Inequalities | 1.6 | 1.6 | ||

1.7 Non-linear Inequalities | 1.7 | 1.7 | ||

Chapter 1 Test (25 questions) | ||||

Functions and Graphs

Lessons | Homework | HW Quiz | ||
---|---|---|---|---|

2.1 Linear Functions | 2.1 | 2.1 | ||

2.2 Distance and Midpoint Formulas | 2.2 | 2.2 | ||

2.3 Properties of Functions | 2.3 | 2.3 | ||

2.4 Combinations of Functions | 2.4 | 2.4 | ||

2.5 Graphs of Functions | 2.5 | 2.5 | ||

2.6 Transformation of Functions | 2.6 | 2.6 | ||

2.7 Inverse Functions | 2.7 | 2.7 | ||

Chapter 2 Test (22 questions) | ||||

Polynomial and Rational Functions

Lessons | Homework | HW Quiz | ||
---|---|---|---|---|

3.1 Quadratic Functions | 3.1 | 3.1 | ||

3.2 Polynomial Functions | 3.2 | 3.2 | ||

3.3 Division of Polynomials | 3.3 | 3.3 | ||

3.4 Zeros of Polynomial Functions | 3.4 | 3.4 | ||

3.5 More on Zeros of Polynomial Functions | 3.5 | 3.5 | ||

3.6 Graphs of Rational Functions | 3.6 | 3.6 | ||

Chapter 3 Test (19 questions) | ||||

Exponential and Logarithmic Functions

Lessons | Homework | HW Quiz | ||
---|---|---|---|---|

4.1 Exponential Functions | 4.1 | 4.1 | ||

4.2 Logarithmic Functions | 4.2 | 4.2 | ||

4.3 Properties of Logarithmic Functions | 4.3 | 4.3 | ||

4.4 Exponential and Logarithmic Equations | 4.4 | 4.4 | ||

4.5 Applications | 4.5 | 4.5 | ||

Chapter 4 Test (23 questions) | ||||

Systems of Equations and Inequalities

Lessons | Homework | HW Quiz | ||
---|---|---|---|---|

5.1 Systems of Equations and Inequalities | 5.1 | 5.1 | ||

5.2 Linear Systems in Three Variables | 5.2 | 5.2 | ||

5.3 Partial Fractions | 5.3 | 5.3 | ||

5.4 Nonlinear Systems in Two Variables | 5.4 | 5.4 | ||

Chapter 5 Test (13 questions) | ||||

Matrices and Determinants

Lessons | Homework | HW Quiz | ||
---|---|---|---|---|

6.1 Introduction to Matrices | 6.1 | 6.1 | ||

6.2 Matrix Multiplication | 6.2 | 6.2 | ||

6.3 Gauss-Jordan Elimination | 6.3 | 6.3 | ||

6.4 Systems without Unique Solutions | 6.4 | 6.4 | ||

6.5 Applications of Linear Systems using Matrices | 6.5 | 6.5 | ||

6.6 Determinants | 6.6 | 6.6 | ||

6.7 Inverse of a Matrix | 6.7 | 6.7 | ||

6.8 Cramer's Rule | 6.8 | 6.8 | ||

Chapter 6 Test (25 questions) | ||||

Sequence and Series

Lessons | Homework | HW Quiz | ||
---|---|---|---|---|

7.1 Sequences and Series | 7.1 | 7.1 | ||

7.2 Arithmetic Sequences | 7.2 | 7.2 | ||

7.3 Geometric Sequences | 7.3 | 7.3 | ||

7.4 Binomial Theorem | 7.4 | 7.4 | ||

Chapter 7 Test (22 questions) | ||||

Conic Sections

Lessons | Homework | HW Quiz | ||
---|---|---|---|---|

8.1 The Circle | 8.1 | 8.1 | ||

8.2 The Ellipse | 8.2 | 8.2 | ||

8.3 The Hyperbola | 8.3 | 8.3 | ||

8.4 The Parabola | 8.4 | 8.4 | ||

8.5 Systems of Inequalities | 8.5 | 8.5 | ||

Chapter 8 Test (21 questions) |

Probability

Lessons | Homework | HW Quiz | ||
---|---|---|---|---|

9.1 Counting | 9.1 | 9.1 | ||

9.2 Permutations and Combinations | 9.2 | 9.2 | ||

9.3 Finite Basic Probabilities | 9.3 | 9.3 | ||

9.4 Basic Laws of Probability | 9.4 | 9.4 | ||

9.5 Conditional Probability | 9.5 | 9.5 | ||

9.6 Independent Events | 9.6 | 9.6 | ||

Chapter 9 Test (22 questions) |

Final for College Algebra (56 questions) |

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