Course Syllabus
Course Description:
Preparation for calculus: polynomial, absolute value, radical, rational, exponential, logarithmic, and trigonometric functions and their graphs; analytic geometry, polar coordinates.
Office
Hours
Before school, lunch, after
school
Text(s): Rice University Open Text Calculus 1
Materials to Bring to Class:
Paper, pencil, graphing calculator—there are some graphing calculators available to be checked
out from the school (they require AAA batteries).
Proper Heading for Papers:
Name, date, assignment, period in upper RIGHT hand corner of all papers turned in. The
majority of the homework will be done on-line and there will be posted due dates with potential
penalties for late work.
Course Syllabus:
Semester 1
Functions 1
1.1 Functions and Function Notation 2
1.2 Domain and Range 22
1.3 Rates of Change and Behavior of Graphs 38
Linear Functions
1.4 Composition of Functions
1.5 Transformation of Functions
1.6 Absolute Value Functions
1.7 Inverse Functions 100
Chapter 1 Review 113 Chapter 1 Review Exercises Chapter 1 Practice Test 123
2.1 Linear Functions 126
2.2 Graphs of Linear Functions 143
2.3 Modeling with Linear Functions 162
2.4 Fitting Linear Models to Data 175
Polynomial and Rational Functions 197
3.1 Complex Numbers 198
3.2 Quadratic Functions 208
3.3 Power Functions and Polynomial Functions 224
3.4 Graphs of Polynomial Functions 239
3.5 Dividing Polynomials 257
3.6 Zeros of Polynomial Functions 266
3.7 Rational Functions 278
3.8 Inverses and Radical Functions 299
3.9 Modeling Using Variation 310
Chapter 3 Review 317
Chapter 3 Review Exercises 322 Chapter 3 Practice Test 325
vii
4
Exponential and Logarithmic Functions 327
4.1 Exponential Functions 328
4.2 Graphs of Exponential Functions 343 4.3 Logarithmic Functions 355
4.4 Graphs of Logarithmic Functions 363
4.5 Logarithmic Properties 380
4.6 Exponential and Logarithmic Equations 390
4.7 Exponential and Logarithmic Models
4.8 Fitting Exponential Models to Data 416
Trigonometric Functions 439
5.1 Angles 440
5.2 Unit Circle: Sine and Cosine Functions 457
5.3 The Other Trigonometric Functions 473
5.4 Right Triangle Trigonometry 486
Chapter 5 Review 498
Chapter 5 Review Exercises 502 Chapter 5 Practice Test 504
Periodic Functions 505
6.1 Graphs of the Sine and Cosine Functions 506
6.2 Graphs of the Other Trigonometric Functions 523
6.3 Inverse Trigonometric Functions 541
Chapter 6 Review 552
Chapter 6 Review Exercises 554 Chapter 6 Practice Test 556
viii
Trigonometric Identities and Equations 559
7.1 Solving Trigonometric Equations with Identities 560
7.2 Sum and Difference Identities 570
7.3 Double-Angle, Half-Angle, and Reduction Formulas 584
7.4 Sum-to-Product and Product-to-Sum Formulas 596
7.5 Solving Trigonometric Equations 603
7.6 Modeling with Trigonometric Equations 617
8 Further Applications of Trigonometry 643
8.1 Non-right Triangles: Law of Sines 644
8.2 Non-right Triangles: Law of Cosines 658
8.3 Polar Coordinates 670
8.4 Polar Coordinates: Graphs 681
8.5 Polar Form of Complex Numbers
8.6 Parametric Equations 708
8.7 Parametric Equations: Graphs 719
8.8 Vectors 729
Chapter 8 Review 747
Chapter 8 Review Exercises 752 Chapter 8 Practice Test 755
9 Systems of Equations and Inequalities 75
9.1 Systems of Linear Equations: Two Variables 758
9.2 Systems of Linear Equations: Three Variables 774
9.3 Systems of Nonlinear Equations and Inequalities: Two Variables 785
9.4 Partial Fractions 795
9.5 Matrices and Matrix Operations 805
9.6 Solving Systems with Gaussian Elimination 816
9.7 Solving Systems with Inverses 829
9.8 Solving Systems with Cramer's Rule 843
Chapter 9 Review 854
Chapter 9 Review Exercises 858 Chapter 9 Practice Test 861
Analytic Geometry 863
10.1 The Ellipse 864
10.2 The Hyperbola 879
10.3 The Parabola 896
10.4 Rotation of Axis 909
10.5 Conic Sections in Polar Coordinates 922
Chapter 10 Review 931
Chapter 10 Review Exercises 934 Chapter 10 Practice Test 936
Sequences, Probability and Counting Theory 937
11.1 Sequences and Their Notations 938
11.2 Arithmetic Sequences 951
11.3 Geometric Sequences 961
11.4 Series and Their Notations 969
11.5 Counting Principles 982
11.6 Binomial Theorem 992
11.7 Probability 999
Chapter 11 Review 1008
Chapter 11 Review Exercises 1012 Chapter 11 Practice Test 1015
12
Introduction to Calculus 1017
12.1 Finding Limits: Numerical and Graphical Approaches 1018
12.2 Finding Limits: Properties of Limits 1028
12.3 Continuity 1037
12.4 Derivatives 1051
Chapter 12 Review 1070
Chapter 12 Review Exercises 1073 Chapter 12 Practice Test 1075
Goals/Objectives:
Build content knowledge of algebraic and trigonometry in preparation for calculus work.
Develop strong organizational skills, thinking skills, and good habits of work.
Curriculum / Standards:
This course will be taught to district standards and district curriculum. Alaska State Standards
can be found on the Alaska Department of Education and Early Development website:
http://www.eed.state.ak.us/standards/.
Grading:
Grading will follow the policy adopted by Petersburg High School. As per board policy,
semester grades are calculated based on the cumulative average of the two quarters.
A = Outstanding. 4.0
A-= 3.7
B+ = 3.4
B= Above Avg 3.0
B- = 2.7
C+ = 2.4
C = Average 2.0
C- = 1.7
D+ = 1.4
D = Below Avg 1.0
D- = 0.7
F = Failing 0.0
“INC” = Incomplete
Listed below is the school adopted percentages for grades. What you see, for example, is
that for an “A” you must have 93 or above, for an A- you would need a 90 up to but not
including a 93, etc.
A 93
A- 90
B+ 87
B 83
B- 80
C+ 77
C 73
C- 70
D+ 67
D 63
D- 60
F 0
The following weights shall be used to earn a grade:
Tests/Quizzes: 75%
Homework/Assignments/Projects: 25%
Extra Credit: Assigned from time to time but not to replace missed work but to
supplement those working hard who are willing to do a bit more.
No late work without proper excuse. In a regular situation a student has 2 days to make up work
for each excused day from school. Communication is key with this.
Tests missed with no excuse cannot be made up. Other tests, not quizzes, can be retaken if the
student scores lower than 80%, AND they make corrections to their test and come in during
office hours to go over the concepts. I recommend this being done within the first few days to a
week so the material stays fresh. The score entered in the book will be the best of the two scores
on the tests, so make sure you prepare as well as possible. You will have two weeks after getting
the test back to take the re-take assessment. Quizzes may not be retaken but one quiz per unit can
be replaced with a test score if the student chooses and comes in and informs the instructor and
clearly states which one to change.
Resources/Extra Help:
I will make every effort to respond to e-mail or phone messages within one school day. I will do
my best to make students aware of my daily schedule and to provide extra assistance when
needed (see office hours above). Students and parents are encouraged to make appointments
ahead of time. There seems to be an excellent resource at http://www.khanacademy.org/ as well.
This a lecture format for a number of different topics and students can investigate the Algebra 2
or Trigonometry sections for early topics.
Behavioral Expectations:
One rule—respect your classmates and instructor. I believe students understand what proper
behavior in a classroom should be and I will require that and help them with their decisions.
Please note: Students are expected to adhere to PHS policies, as outlined in the Student
Handbook, at all times. Classroom policies may include more specific requirements, but they
cannot be relaxed beyond the minimums as set forth in the Student Handbook.
Consequences of Misbehavior:
1. Talk to student about behavior
2. Talk to parent about behavior
3. Refer student to administration (I have very rarely ever had to do this)
Please note: Any action that endangers others, seriously interferes with the learning process, or is
significantly disrespectful to staff or students may result in immediate removal from the
classroom and/or direct referral to an administrator, thus by-passing above consequences.
ACADEMIC DISHONESTY—
Cheating does not allow for any type of true analysis and is not tolerated. Cheating is defined as,
but not limited to:
1. Procuring, possessing, using, or distributing test, quizzes, answer keys, teacher manuals or
teacher textbooks and the like;
2. Any attempt to tamper with or alter a teacher's record or grades;
3. Representing the work of others as one’s own work; including materials from the Internet.
4. Making use of notes, homework assignments, information slips (“crib sheets”) except for
those notes a teacher specifically authorizes for student use during a particular test or quiz, and;
6. Plagiarism
The academic penalty for all parties involved in cheating is a zero or failing grade for any copied
or plagiarized assignment, exam, or quiz. Students will not be allowed to make-up the work.
Also, the disciplinary penalty for cheating may include an office referral for disciplinary action.
Possession and/or unauthorized distribution of materials or altering a teacher's records call for
severe disciplinary consequences. Repeat offenses could result in loss of credit for an entire
course.
Electronic Devices:
Cell phones and other electronic devices are to be turned off and out of sight during class unless
the teacher has given specific permission for their use. If an item is confiscated for violation of
class rules, it may be retrieved from the teacher on the first offense. For subsequent offenses, the
item will be turned over to your administrator for retrieval.
Student Learning Outcomes:
Upon successful completion of the course, students will be able to:
- Graph functions and relations in rectangular coordinates and polar coordinates;
- Synthesize results from the graphs and/or equations of functions and relations;
- Apply transformations to the graphs of functions and relations;
- Recognize the relationship between functions and their inverses graphically and algebraically;
- Solve and apply equations including rational, linear, polynomial, exponential, absolute value, radical, and logarithmic, and solve linear, nonlinear, and absolute value inequalities;
- Solve systems of equations and inequalities;
- Apply functions to model real world applications;
- Identify special triangles and their related angle and side measures;
- Evaluate the trigonometric function of an angle given in degree and radian measure;
- Manipulate and simplify a trigonometric expression;
- Solve trigonometric equations, triangles, and applications;
- Graph the basic trigonometric functions and apply changes in period, phase and amplitude to generate new graphs; and
- Prove trigonometric identities
Course Content:
- Functions including linear, polynomial, rational, radical, exponential, absolute value, logarithmic, trigonometric; definitions, evaluation, domain and range;
- Inverses of functions;
- Algebra of functions;
- Graphs of functions including asymptotic behavior, intercepts, and vertices;
- Transformations of quadratic, absolute value, radical, rational, logarithmic, exponential functions;
- Equations including rational, linear, radical, polynomial, exponential, trigonometric, logarithmic, and absolute value;
- Linear, nonlinear, and absolute value inequalities;
- Systems of equations and inequalities;
- Characterization of real and complex zeros of polynomials;
- Unit circle and right triangle trigonometry;
- Trigonometric and inverse trigonometric identities and formulas;
- Graphing trigonometric functions: period, amplitude, phase shift, inverse trigonometric functions; and
- Polar coordinates
Textbook:
Great news: your textbook for this class is available online!
Precalculus from OpenStax, ISBN 1-947172-06-9
You have several options to obtain this book:
- View online (Links to an external site.) (Links to an external site.)
- Download a PDF (Links to an external site.) (Links to an external site.)
- Order a print copy (Links to an external site.) (Links to an external site.)
You can use whichever formats you want. Web view is recommended -- the responsive design works seamlessly on any device.
Important Notes:
- Any student needing accommodations should inform the instructor.
- Academic dishonesty and plagiarism will result in a failing grade on the assignment. Using someone else's ideas or phrasing and representing those ideas or phrasing as our own, either on purpose or through carelessness, is a serious offense known as plagiarism. "Ideas or phrasing" includes written or spoken material, from whole papers and paragraphs to sentences, and, indeed, phrases but it also includes statistics, lab results, art work, etc. Please see the PHS Handbook for policies regarding plagiarism, harassment, etc.
Course Summary:
| Date | Details | Due |
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