# Precalculus

**I. Course Prefix/Number: **
MAT 149

** Course Name: **
Precalculus

** Credits: **
5 (5 lecture; 0 lab)

**II. Prerequisite **

MAT 110 with minimum grade of C or appropriate score on the Mathematics Placement Test, and MAT 080 or geometry proficiency.

**III. Course (Catalog) Description **

This course focuses on the study of functions including polynomial, rational, exponential, logarithmic and trigonometric functions. Additional topics include the conic sections, series, parametric equations, and polar equations. Use of technology is integrated throughout.

**IV. Learning Objectives **

1. Classify functions and their graphs, and identify their domain and range.

2. Identify and apply transformations of graphs.

3. Solve linear and non-linear equations.

4. Solve polynomial and rational inequalities algebraically and graphically.

5. Sketch the graph of polynomials using zeros and end behavior.

6. Sketch the graph of rational functions using zeros, asymptotes, and end behavior.

7. Find, graph, and interpret the inverse of a function.

8. Graph exponential and logarithmic functions, and use their properties to simplify and solve equations involving them.

9. Classify and sketch the graphs of conic sections.

10. Analyze, evaluate and graph trigonmetric functions and their inverse functions.

11. Solve trigonmetric equations, and prove and apply trigonometric identities.

12. Solve trigonometric applications including polar equations, vectors, and parametric equations.

13. Expand, calculate and evaluate series and sequences.

14. Model and solve applications using the elementary functions studied in the course.

15. Use technology to graph, evaluate, and interpret functions, and to solve equations involving them.

2. Identify and apply transformations of graphs.

3. Solve linear and non-linear equations.

4. Solve polynomial and rational inequalities algebraically and graphically.

5. Sketch the graph of polynomials using zeros and end behavior.

6. Sketch the graph of rational functions using zeros, asymptotes, and end behavior.

7. Find, graph, and interpret the inverse of a function.

8. Graph exponential and logarithmic functions, and use their properties to simplify and solve equations involving them.

9. Classify and sketch the graphs of conic sections.

10. Analyze, evaluate and graph trigonmetric functions and their inverse functions.

11. Solve trigonmetric equations, and prove and apply trigonometric identities.

12. Solve trigonometric applications including polar equations, vectors, and parametric equations.

13. Expand, calculate and evaluate series and sequences.

14. Model and solve applications using the elementary functions studied in the course.

15. Use technology to graph, evaluate, and interpret functions, and to solve equations involving them.

**V. Academic Integrity **

Students and employees at Oakton Community College are required to demonstrate academic integrity
and follow Oakton's Code of Academic Conduct. This code prohibits:

• cheating,

• plagiarism (turning in work not written by you, or lacking proper citation),

• falsification and fabrication (lying or distorting the truth),

• helping others to cheat,

• unauthorized changes on official documents,

• pretending to be someone else or having someone else pretend to be you,

• making or accepting bribes, special favors, or threats, and

• any other behavior that violates academic integrity.

There are serious consequences to violations of the academic integrity policy. Oakton's policies and procedures provide students a fair hearing if a complaint is made against you. If you are found to have violated the policy, the minimum penalty is failure on the assignment and, a disciplinary record will be established and kept on file in the office of the Vice President for Student Affairs for a period of 3 years.

Details of the Code of Academic Conduct can be found in the Student Handbook.

• cheating,

• plagiarism (turning in work not written by you, or lacking proper citation),

• falsification and fabrication (lying or distorting the truth),

• helping others to cheat,

• unauthorized changes on official documents,

• pretending to be someone else or having someone else pretend to be you,

• making or accepting bribes, special favors, or threats, and

• any other behavior that violates academic integrity.

There are serious consequences to violations of the academic integrity policy. Oakton's policies and procedures provide students a fair hearing if a complaint is made against you. If you are found to have violated the policy, the minimum penalty is failure on the assignment and, a disciplinary record will be established and kept on file in the office of the Vice President for Student Affairs for a period of 3 years.

Details of the Code of Academic Conduct can be found in the Student Handbook.

**VI. Sequence of Topics **

A. Functions and their graphs

1. Operations on functions: combinations

2. Graphing techniques

3. Translations and Rotations

4. Inverse functions

B. Polynomial functions: graphs and zeros

1. Quadratic functions

2. Polynomial functions of higher degree

3. Remainder and Factor Theorems

4. Complex zeros of polynomial functions

5. Fundamental Theorem of Algebra

6. Applications

C. Rational functions and conic sections

1. Rational functions and their graphs

2. Conic sections

a) Center at origin

b) Translations

D. Exponential and logarithmic functions

1. Exponential functions and their graphs

2. Logarithmic functions and their graphs

3. Properties of logarithms

4. Solving exponential and logarithmic equations

5. Applications

E. Find the intersection of two polynomial functions (substitution method)

F. Sequences and series

1. Fundamentals of sequences and series

2. Arithmetic sequences

3. Geometric sequences

4. Applications

G. Trigonometric Functions

1. Measurement of angles

2. Circular functions

3. Graphs of sines and cosines

4. Graphs of the other trigonometric functions

5. Inverse trigonometric functions and their graphs

6. Trigonometric identities

a. Pythagorean identities

b. Sum and difference formulas

c. Multiple and half angle formulas

d. Sum-to-product; product-to-sum

7. Solving trigonometric equations

8. Applications

a. Complex numbers and their trigonometric form

b. Solving right triangles

c. Law of Sines, Law of Cosines

d. Roots and powers of complex numbers

e. Polar coordinates

f. Parametric equations

H. Vectors

1. Geometric and algebraic representation of vectors

2. Basic operations with vectors

I. Technology

1. Generate the complete graph of each trigonometric and inverse trigonometric function including setting a proper window, tracing and zooming.

2. Graphically locate the x-intercepts, the relative extrema and determine asymptotic behaviors.

3. Solve equations graphically, numerically and/or symbolically.

1. Operations on functions: combinations

2. Graphing techniques

3. Translations and Rotations

4. Inverse functions

B. Polynomial functions: graphs and zeros

1. Quadratic functions

2. Polynomial functions of higher degree

3. Remainder and Factor Theorems

4. Complex zeros of polynomial functions

5. Fundamental Theorem of Algebra

6. Applications

C. Rational functions and conic sections

1. Rational functions and their graphs

2. Conic sections

a) Center at origin

b) Translations

D. Exponential and logarithmic functions

1. Exponential functions and their graphs

2. Logarithmic functions and their graphs

3. Properties of logarithms

4. Solving exponential and logarithmic equations

5. Applications

E. Find the intersection of two polynomial functions (substitution method)

F. Sequences and series

1. Fundamentals of sequences and series

2. Arithmetic sequences

3. Geometric sequences

4. Applications

G. Trigonometric Functions

1. Measurement of angles

2. Circular functions

3. Graphs of sines and cosines

4. Graphs of the other trigonometric functions

5. Inverse trigonometric functions and their graphs

6. Trigonometric identities

a. Pythagorean identities

b. Sum and difference formulas

c. Multiple and half angle formulas

d. Sum-to-product; product-to-sum

7. Solving trigonometric equations

8. Applications

a. Complex numbers and their trigonometric form

b. Solving right triangles

c. Law of Sines, Law of Cosines

d. Roots and powers of complex numbers

e. Polar coordinates

f. Parametric equations

H. Vectors

1. Geometric and algebraic representation of vectors

2. Basic operations with vectors

I. Technology

1. Generate the complete graph of each trigonometric and inverse trigonometric function including setting a proper window, tracing and zooming.

2. Graphically locate the x-intercepts, the relative extrema and determine asymptotic behaviors.

3. Solve equations graphically, numerically and/or symbolically.

**VII. Methods of Instruction **

(To be completed by instructor.)

Methods of presentation can include lectures, discussions, demonstrations, experimentation, audio-visual aids and regularly assigned homework. Calculators/computers will be used when appropriate.

Course may be taught as face-to-face, media-based, hybrid or online course.

Methods of presentation can include lectures, discussions, demonstrations, experimentation, audio-visual aids and regularly assigned homework. Calculators/computers will be used when appropriate.

Course may be taught as face-to-face, media-based, hybrid or online course.

**VIII. Course Practices Required **

(To be completed by instructor.)

Course practices may include attending class, completing homework assignments, participating in discussions and taking quizzes and exams.

Course practices may include attending class, completing homework assignments, participating in discussions and taking quizzes and exams.

**IX. Instructional Materials **

**Note:**Current textbook information for each course and section is available on Oakton's Schedule of Classes.

Within the Schedule of Classes, textbooks can be found by clicking on an individual course section and looking for the words "View Book Information".

Textbooks can also be found at our Mathematics Textbooks page.

A graphics calculator is required. A TI-83/84 will be used for instructional purposes.

**X. Methods of Evaluating Student Progress **

(To be completed by instructor.)

Evaluation methods can include grading homework, chapter or major tests, quizzes, individual or small group projects and a final exam.

Evaluation methods can include grading homework, chapter or major tests, quizzes, individual or small group projects and a final exam.

**XI. Other Course Information **

Individual instructors will establish and announce specific policies regarding attendance, due dates and make-up work, incomplete grades, etc.

If you have a documented learning, psychological, or physical disability you may be entitled to reasonable academic accommodations or services. To request accommodations or services, contact the Access and Disability Resource Center at the Des Plaines or Skokie campus. All students are expected to fulfill essential course requirements. The College will not waive any essential skill or requirement of a course or degree program.

If you have a documented learning, psychological, or physical disability you may be entitled to reasonable academic accommodations or services. To request accommodations or services, contact the Access and Disability Resource Center at the Des Plaines or Skokie campus. All students are expected to fulfill essential course requirements. The College will not waive any essential skill or requirement of a course or degree program.