This course is designed to emphasize topics which are fundamental to the study of calculus. 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 right triangle trigonometry, trigonometric identities and equations, vectors, complex numbers, laws of sines and cosines, the binomial theorem, arithmetic, geometric sequences and series, systems, partial fractions, matrices and determinants, conic sections and probability. The student will solve applications and modeling problems related to the above topics. Upon completion, students will be able to solve practical problems and use appropriate models for analysis.

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

Functions and their Graphs

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

1.1 Relations & Functions | 1.1 | 1.1 | ||

1.2 Domain and Range of a Function | 1.2 | 1.2 | ||

1.3 Linear Equations and Functions | 1.3 | 1.3 | ||

1.4 Combinations of Functions | 1.4 | 1.4 | ||

1.5 Graphs of Functions | 1.5 | 1.5 | ||

1.6 Transformation of Functions | 1.6 | 1.6 | ||

1.7 Inverse Functions | 1.7 | 1.7 | ||

1.8 Complex Numbers | 1.8 | 1.8 | ||

Chapter 1 Test (37 questions) |

Polynomial and Rational Functions

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

2.1 Quadratic Functions | 2.1 | 2.1 | ||

2.2 Polynomial Functions | 2.2 | 2.2 | ||

2.3 Division of Polynomials | 2.3 | 2.3 | ||

2.4 Zeros of Polynomial Functions | 2.4 | 2.4 | ||

2.5 More on Zeros of Polynomial Functions | 2.5 | 2.5 | ||

2.6 Graphs of Rational Functions | 2.6 | 2.6 | ||

Chapter 2 Test (29 questions) | ||||

Exponential and Logarithmic Functions

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

3.1 Exponential Functions | 3.1 | 3.1 | ||

3.2 Logarithmic Functions | 3.2 | 3.2 | ||

3.3 Properties of Logarithmic Functions | 3.3 | 3.3 | ||

3.4 Exponential and Logarithmic Equations | 3.4 | 3.4 | ||

3.5 Applications | 3.5 | 3.5 | ||

Chapter 3 Test (28 questions) | ||||

Trigonometric Functions

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

4.1 Geometry Review | 4.1 | 4.1 | ||

4.2 Angles, Degrees and Special Triangles | 4.2 | 4.2 | ||

4.3 Trigonometric Functions | 4.3 | 4.3 | ||

4.4 Introduction to the Unit Circle | 4.4 | 4.4 | ||

4.5 Right Triangle Trigonometry | 4.5 | 4.5 | ||

4.6 Other Angles and Trigonometric Functions | 4.6 | 4.6 | ||

4.7 Solving Right Triangles | 4.7 | 4.7 | ||

4.8 Applications | 4.8 | 4.8 | ||

Chapter 4 Test (29 questions) | ||||

Radian Measure & Trigonometric Identities

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

5.1 Reference Angle | 5.1 | 5.1 | ||

5.2 Radians and Degrees | 5.2 | 5.2 | ||

5.3 Circular Functions | 5.3 | 5.3 | ||

5.4 Proving Identities | 5.4 | 5.4 | ||

5.5 Sum and Difference Formula | 5.5 | 5.5 | ||

5.6 Double-Angle Formula | 5.6 | 5.6 | ||

5.7 Half-Angle Formula | 5.7 | 5.7 | ||

Chapter 5 Test (27 questions) | ||||

Additional Trigonometry Topics

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

6.1 Graphs of Basic Trigonometric Functions | 6.1 | 6.1 | ||

6.2 Inverse Trigonometric Functions | 6.2 | 6.2 | ||

6.3 Trigonometric Equations | 6.3 | 6.3 | ||

6.4 Law of Cosines | 6.4 | 6.4 | ||

6.5 Law of Sines | 6.5 | 6.5 | ||

6.6 Vectors | 6.6 | 6.6 | ||

6.7 Trigonometric Form of a Complex Number | 6.7 | 6.7 | ||

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

Systems of Equations

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

7.1 Linear Systems in Two Variables | 7.1 | 7.1 | ||

7.2 Linear Systems in Three Variables | 7.2 | 7.2 | ||

7.3 Partial Fractions | 7.3 | 7.3 | ||

7.4 Nonlinear Systems in Two Variables | 7.4 | 7.4 | ||

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

Matrices

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

8.1 Introduction to Matrices | 8.1 | 8.1 | ||

8.2 Matrix Multiplication | 8.2 | 8.2 | ||

8.3 Gauss-Jordan Elimination | 8.3 | 8.3 | ||

8.4 Systems without Unique Solutions | 8.4 | 8.4 | ||

8.5 Applications of Linear Systems using Matrices | 8.5 | 8.5 | ||

8.6 Determinants | 8.6 | 8.6 | ||

8.7 Inverse of a Matrix | 8.7 | 8.7 | ||

Chapter 8 Test (27 questions) | ||||

Sequence, Series, Counting and Probability

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

9.1 Sequences and Series | 9.1 | 9.1 | ||

9.2 Arithmetic Sequences | 9.2 | 9.2 | ||

9.3 Geometric Sequences | 9.3 | 9.3 | ||

9.4 Binomial Theorem | 9.4 | 9.4 | ||

9.5 Counting | 9.5 | 9.5 | ||

9.6 Permutations and Combinations | 9.6 | 9.6 | ||

9.7 Finite Basic Probabilities | 9.7 | 9.7 | ||

9.8 Basic Laws of Probability | 9.8 | 9.8 | ||

Chapter 9 Test (28 questions) | ||||

Conic Sections

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

10.1 The Circle | 10.1 | 10.1 | ||

10.2 The Parabola | 10.2 | 10.2 | ||

10.3 The Ellipse | 10.3 | 10.3 | ||

10.4 The Hyperbola | 10.4 | 10.4 | ||

10.5 Systems of Inequalities | 10.5 | 10.5 | ||

Chapter 10 Test (28 questions) |

Final for Precalculus (44 questions) |

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