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MATH 022.1 College Algebra II and Analytic Geometry Monday & Wednesday, 6:00-7:15 p.m., Olmstead E258 Derek L. Smith [email protected] Office Location: Library 301A Office Phone: 717-948-3527 Office Hours: Monday, Wednesday, Friday 2:20-3:15 p.m. This syllabus is subject to change. All course announcements shall be distributed via the course Canvas page.

Course Description: Relations, functions, graphs; polynomial, rational functions, graphs; word problems; nonlinear inequalities; inverse functions; exponential, logarithmic functions; conic sections; simultaneous equations. Prerequisite: MATH 021 or satisfactory performance on the mathematics placement examination. Text: Algebra and Trigonometry, 6th Edition, Robert Blitzer, 978-0134463216 Required Material: Textbook; homework will be completed using WebWork. Calculator policy: Calculators are not permitted on exams.

Grading: Grade weighted as follows: homework 60%, one midterm and a final exam each worth 20%. Your lowest homework score will be dropped. The following table gives the percentage needed to guarantee the corresponding final course grade: ≥ 93 90 87 83 80 76 70 60 < 60

A AB+ B BC+ C D F

Exams: The midterm exam will take place on October 13th, the final during the universityscheduled time. One letter-sized, double-sided page of notes allowed during exams; no calculators. Students are expected to take exams at the scheduled time. If you must miss an exam for a nonemergency situation, it is your responsibility to notify the instructor in writing prior to the exam. Make-up exams will only be given for valid reasons including a documented illness, universityapproved program and “final exam overload” as defined by university policy. An unexcused absence will result in a zero grade for that exam.

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Homework: Homework posted to WeBWork every Sunday; due the following Tuesday evening. Fourteen equally-weighted homework sets will be assigned (none during exam weeks). If you’d like more time on an assignment, simply email 24 hours prior to the due date. Once closed, an assignment will not be re-opened. Each assignment will have a corresponding discussion space on Canvas for homework questions, please avoid email for this purpose. Emailed homework questions may be (anonymously) re-posted to the public discussion space so that all students may benefit from the answer. I strongly suggest forming groups to complete homework.

Attendance policy: Attendence, though strongly encouraged, will not count towards your grade. There is no requirement to document your absence from lecture. However, I will stress certain concepts during lecture which will be crucical to perform well on the exams. Course Objectives: Upon successful completion of this course, a student should be able to: 1. 2. 3. 4. 5. 6.

Solve absolute value equations and inequalities. Identify and distinguish between relations and functions from graphs and formulas. Evaluate functions using function notation. Determine the domain of a function given a formula. Understand, identify and determine properties of a function’s graph. Know and sketch graphs of basic functions, such as: (a) (b) (c) (d) (e) (f)

y=k y = |x| y = x2 y =√ x3 y = √x y= 3x

7. Understand piecewise functions. 8. Transform basic graphs using horizontal/vertical translations, stretching and compression, reflections and combinations these transformations. 9. Add, subtract, multiply, divide and compose functions and find the domain of the resulting function. 10. Understand the definition of a one-to-one function and apply it to finding inverse functions. 11. Add, subtract, multiply and divide complex numbers. 12. Write equations of lines. 13. Analyze quadratic functions. 14. Translate applications of quadratic functions to models and solve. 15. Perform polynomial long division. 16. Understand the factored form of a polynomial. 17. Sketch graphs of polynomial functions. 18. Sketch graphs of rational functions. 19. Solve polynomial and rational inequalities. 20. Understand characteristics of and sketch exponential functions, y = bx . 21. Understand characteristics of and sketch logarithmic functions, y = logb x. 22. Know and apply laws of exponents and laws of logarithms. 23. Know and apply the change of base logarithm formula. 2

24. 25. 26. 27. 28. 29. 30.

Solve exponential equations. Solve logarithmic equations. Understand characteristics of parabolas. Understand characteristics of ellipses. Understand characteristics of hyperbolas. Solve a system of two linear equations in two variables by substitution or elimination. Solve a system of three linear equations in three variables by substitution or elimination.

Tentative Course Outline Week

Content

Week 1

Sets Definition of function, formula and graph The graph of a linear function

Week 2

Quadratic functions Completing the square The graph of a quadratic function

Week 3

Polynomial functions End behavior, roots and factoring The graph of a polynomial function

Week 4

Rational functions End behavior, roots, asymptotes The graph of a rational function

Week 5

Inverse and other elementary functions Translations, reflections and scaling of graphs

Week 6

Linear inequalities Polynomial and rational inequalities

Week 7

Exponential functions The graph of an exponential function

Week 8

Review Exam on Wednesday, October 13th

Week 9

Logarithmic functions The graph of a logarithmic function

Week 10

Solving exponential equations The complex number system

Week 11

Implicitly defined functions The parabola as a conic section

Week 12

Ellipses Hyperbolas

Week 13

Systems of two linear equations in two variables

Week 14

Thanksgiving break

Week 15

Systems of three linear equations in three variables

Week 16

Applications of linear equations

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Resources There are a number of resources available for help with this course: 1. 2. 3. 4.

Join or form a peer study group. Instructor office hours. The Russell E. Horn Sr. Learning Center. https://harrisburg.psu.edu/learning-center There is a great, Creative Commons licensed textbook, College Algebra, by Carl Stitz & Jeff Zeager http://www.stitz-zeager.com/ 5. Math Dr. Bob has many playlists relevant to this course. https://mathdoctorbob.org/ 6. Paul’s Online Notes http://tutorial.math.lamar.edu/

The Russell E. Horn Learning Center For the fall 2021 semester, all Russell E. Horn Sr. Learning Center tutoring will be conducted in-person or via Zoom, whichever the student prefers. The Learning Center may have a tutor who can assist with the content of this course. An appointment is recommended. You can make an appointment in one of the three ways listed below. 1. Online: starfish.psu.edu 2. Via phone: 717-948-6475 3. Via email: [email protected]

Additional Information:

Please check the following link for additional policy information, including academic integrity, important dates, etc.: http://math.hbg.psu.edu/additional-syllabus-info/

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