Muncy Junior-Senior High School Mathematics Department Course Number: 454 Course Name: Pre-Calculus Instructor: Mr. Smith Meeting Times: Periods 1 and 8 Meeting Location: Room 256 Prerequisite Course: Accelerated Algebra II or Algebra III Phone Number: 546-3127 ext. 3000 Email: gsmith@muncysd.org Course Description Pre-Calculus is a rigorous elective course designed to provide students with essential background for the study of calculus, with emphasis on preparing students for taking Advanced Placement Calculus AB in the following school year. Prerequisite topics for AP Calculus AB, as listed in The College Board s Advanced Placement Calculus AB course syllabus, will be covered. This course will extend algebraic and trigonometric concepts covered in earlier courses and give students a solid foundation in the study of functions. Families of functions that will be discussed are polynomial, rational, exponential, logarithmic, trigonometric and algebraic, along with transformations of these functions. Additional topics will be added as time permits. This course also examines the representations of functions in four ways graphically, numerically, analytically and verbally and emphasis is placed on problem-solving applications. Students will use the Texas Instruments TI-84 Plus graphing calculator as a problem-solving tool throughout the course. Goals A balance among analytical, graphical, numerical and verbal methods of representing functions will be used in the course. Students must understand the value of each approach and learn to choose the most appropriate representation for solving a particular problem. With that understanding, the goals of the course are listed below. Students should be able to work with functions and function concepts represented in a variety of ways analytical, graphical, numerical and verbal. Students should be able to model a written description of a physical situation with a function and apply analytic methods and/or a graphing calculator to analyze function behavior and characteristics. Students should be able to communicate mathematics both orally and in well-written, grammatically correct sentences and should be able to explain their reasoning for using a specific method of solution. Students should be able to determine the reasonableness of solutions, including sign, size, relative accuracy and units of measurement.
Course Topical Outline The topics covered in this course are listed below and address all prerequisites listed by The College Board in its Advanced Placement Calculus AB syllabus. Algebra Review and Extensions 1. Algebra with Polynomial, Rational and Radical Expressions a. Factoring Expressions b. Operations with Rational Expressions c. Operations with Radical Expressions d. Solving Equations 2. Parent Functions 3. Transformations of Functions Polynomial and Rational Functions 1. Polynomial Functions 2. Rational Functions 3. Solving Polynomial and Rational Inequalities Exponential and Logarithmic Functions 1. Exponential Functions 2. Logarithmic Functions 3. Properties of Logarithms 4. Exponential and Logarithmic Equations 5. Exponential and Logarithmic Models 6. Non-Linear Models Trigonometry 1. Right Triangle Trigonometry 2. Radian and Degree Measure 3. The Unit Circle 4. Circular Definitions of Trigonometric Ratios 5. Graphs of Sine and Cosine Functions 6. Graphs of Other Trigonometric Functions 7. Inverse Trigonometric Functions 8. Applications and Models Analytic Trigonometry 1. Fundamental Identities 2. Verifying Trigonometric Identities 3. Solving Trigonometric Equations 4. Sum and Difference Formulas 5. Multiple-angle formulas Additional Topics in Trigonometry 1. Law of Sines 2. Law of Cosines
Systems of Equations 1. Solving Systems of Equations 2. Multivariable Linear Systems 3. Linear Programming 4. Partial Fraction Decomposition Analytic Geometry 1. Circle and Parabolas 2. Ellipses 3. Hyperbolas 4. Parametric Equations 5. Polar Coordinates 6. Graphs of Polar Equations Sequences and Series 1. Sequences and Series 2. Arithmetic Sequences and Partial Sums 3. Geometric Sequences and Series Vectors 1. Vectors in the Plane 2. Dot Products 3. Trigonometric Form of a Complex Number Limits and an Introduction to Calculus 1. Introduction to Limits 2. Techniques for Evaluating Limits 3. The Tangent Line Problem 4. Limits at Infinity and Infinite Limits 5. The Area Problem Classroom Expectations This is a Pre-Advanced Placement course and it is expected that student effort and behavior reflect this. At no time should a student interrupt instructional time and thus the learning environment for other students. Specific expectations for each class period include: 1. Be present and be on time. The fast pace of a Pre-AP course will have you soon discover how much you miss when not in class for only one class period. 2. Enter the classroom quietly and get prepared to begin class as soon as the bell rings. For Period 8 class, there should be no talking during the PM announcements and you should be ready to start once the announcements are over. 3. Be prepared have all materials with you each class period and be ready to start class when the bell rings. 4. Work to the best of your ability. 5. Be respectful of others. 6. Use a pencil. 7. Use the restroom on your way to class, but be in your seat when the bell rings or you will be marked tardy. Asking to use the restroom during the class period should only be done in an emergency.
8. The bell does not dismiss the class. Students will be dismissed by the instructor when the period s activities are finished. There will no congregating at the door waiting for the bell to ring. Please refer to the Pathfinder for the district policy on student attire, cell phones/electronic devices, food/beverage in the classroom and locker and rest room use throughout the school day. Absences and Make-Up Work If you are absent for any reason, it is your responsibility to see me in the morning before the start of Period 1 to discuss what was missed and to receive any materials that were distributed during the class period(s) you missed. Time will not be taken during the class period to take care of this. Make-up work will be allowed as outlined in the Pathfinder. Failure to make up the work in the allotted time will result in a score of zero for that work. In the event that an assessment was missed during an absence, students will be given a different version of the assessment. This may take on an entirely different format than the missed assessment. Students present in school but not in attendance during the class period on the day of an assessment are expected to take the assessment that day. This includes, but is not limited to, participation in a school-sponsored field trip, HOPES, luncheons associated with school clubs, early dismissals for scheduled athletic events, etc., and may require you to take the assessment in the morning before the start of homeroom. You should notify me immediately when you are aware that these absences will occur. Failure to take the assessment on the same day will result in a score of zero for that assessment. Students who are going to miss several consecutive class periods should see me immediately upon return to school to receive any materials and to find out what was missed during the absence. In rare instances, an extension may be granted for making up an assessment that is missed because of an absence at a school-related activity. Extra Help Daily hours for extra help are 7:30-7:39 a.m. and 2:30-2:45 p.m. If you need additional time, see me so that we can make the necessary arrangements. Grading Marking period grades will be calculated on the basis of a point system the percent of points earned out of the number of possible points. Graded material will consist of any combination of the following each marking period: Quizzes Exams Graded homework assignments In-class activities and explorations Notebooks
A cumulative final exam will be given at the end of the year and course grades will be computed according to district policy. Retests may be given, at my discretion. Unless you are required to be given extra time for completing quizzes and exams, please do not ask for additional time. Assessments are designed to be completed in one class period. Progress Reports Periodically, Progress Reports will be sent home with students to be signed by a parent/guardian and returned, counting as a homework grade. Notification of student grade deficiency will be made through mid-marking period progress reports for students of parents/guardians that request this type of notification. If a parent/guardian has indicated that they will keep up-to-date by using Power School, then paper progress reports will not be sent through the Guidance Office. Possibility of failure notifications will be sent (if needed) at the end of the first semester and at the end of the third marking period. Academic Dishonesty Academic dishonesty includes plagiarizing, cheating on in-class and out-of-class assessments, engaging in collaboration on out of class work when not allowed, copying another student s homework and sharing information relating to in-class assessments to individuals/groups that have yet to take the assessment. Any indication of academic dishonesty will be dealt with as a serious offense and will result in a grade of zero for that assessment item for all students involved and a referral to the Principal s Office will be made. Academic dishonesty devalues the achievements of students who are earning their grades honestly. If a student is aware of any form of academic dishonesty, it is expected that they will see their instructor privately and in strict confidence to report it. Homework Homework is assigned to reinforce and practice the concepts covered in class and is an essential component of the course. You need to complete the assignments to have a chance to be successful in Pre-Calculus. Complete it in a manner that will aid you for review and study purposes. You have access to the Instructor s Solutions Manual in the classroom and access to an online solutions manual for this textbook. Details will be provided in a separate handout. Homework may be checked at any time, both for completion and accuracy. According to the policy of the Mathematics Department, late assignments are not accepted for credit. Expect to spend between 30-40 minutes per night completing assignments throughout this course. In Advanced Placement Calculus, bald answers receive no credit and the same will hold true in Pre-Calculus. When homework is completed, it is required that your work is shown and is neat and orderly. With the exception of vocabulary check or true/false questions, all work should be shown for all exercises. Problems (other than vocabulary checks and word problems) should be copied down. Answers should be clearly identified and labeled. Notebook It is recommended that you keep a three-ring binder for this class. You will be given numerous handouts as classroom note-taking guides and keeping things in order will help you review for assessments.
Textbook and Graphing Calculators You are financially responsible for the textbook and graphing calculator you are issued. Lost or damaged materials whether cosmetically or functionally will be your financial responsibility and replacement/repair costs will be done in accordance with district policy. The only graphing calculators that are acceptable for use in Pre-Calculus are those in the Texas Instruments TI-83 and TI-84 families of calculators. Students will be issued a TI-84 Plus for use in the course, but will have to supply the batteries for the calculator. The use of programs in Pre- Calculus is strictly prohibited unless approved by the instructor. If you have a program that you would like to use and are unsure whether it is acceptable, then you should ask before using it. If a student wishes to use their own calculator throughout the year, the calculator may be periodically inspected by the instructor so that inappropriate programs or applications are not being used. Any non-approved programs/applications for use in Pre-Calculus can be removed from student-owned calculators at any time. Record the textbook and graphing calculator identification numbers in your Pathfinder for future reference. Students often mistakenly pick up a calculator that was not issued to them when they are working collaboratively. School-issued graphing calculators are for use in Pre- Calculus, but you may use them for other courses that require the use of a calculator. Textbook Larson, Ron. Precalculus With Limits: A Graphing Approach, 7th Edition. Brooks/Cole Cengage Learning, Boston, MA. 2016. Replacement Cost: $123.09 Graphing Calculator Texas Instruments TI-84 Plus Replacement Cost: $100.00 Changes to Course Syllabus Information in this syllabus is subject to change. If any changes are made, you will be notified through an addendum to the syllabus and a posting on my district web page.