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Pre-Calculus (College Prep)
PRE-CALCULUS SYLLABUS (College Prep) Text Book: Pre-calculus by James Stewart, Lother Redlin and Saleem Watson. 4th Edition (Brooks/Cole) Course Description Precalculus is a program of mathematical studies focusing on the development of the student’s ability to understand and apply the study of functions and advanced mathematics concepts to solve problems. The course will include an in-depth study of polynomial, rational, exponential, logarithmic, and trigonometric functions. Other topics studied are sequences, series, vectors, conic sections, parametric equations, and polar curves. Emphasis is placed on active participation through modeling, technology lab activities, group activities, and communication in mathematics. Students are expected to use technology, including graphing calculators, computers, and data-gathering equipment throughout the course. Graphing calculators should be an integral part of all instruction. Recommended Prerequisites It is recommended that a student successfully complete Algebra 2 before taking Precalculus. Students who need a stronger background could follow Algebra 2 with Algebra 3 and then Precalculus. Algebra 3 is not part of the defined program and will need to be taught as an innovative approach course. Boldfaced items indicate additional material to be covered in Precalculus at the honors level. All topics should be taught in greater depth and difficulty at the honors level. Course Outline I. Functions. A. Characteristics and representations of functions. 1. Determine the domain and range from algebraic representations, graphs, and tables. Precalculus: I.A.2., II.A.1., II.B.3. 2. Describe symmetry of even and odd functions. Precalculus: I.A.5. B. Operations on functions. 1. Apply basic transformations. Precalculus: I.B.1. a. a • f(x), f(x) + d, f(x – c), f(b • x). b. . 2. Perform operations and describe the procedures and results verbally, numerically, algebraically, and graphically. Precalculus: I.B.2. a. Composition and decomposition. b. Inverses. II. Polynomial and rational functions. A. Polynomial functions. 1. Describe the general shape of the graph and the effect of transformations on the domain and range. Precalculus: I.A.1.,II.A.1. 2. Recognize the connections among the significant points of a function, the graph of the function, and the algebraic representation of the function. Precalculus: I.A.6. a. Roots. b. Maximum points and minimum points. 3. Investigate continuity and end behavior. Precalculus: I.A.7. 4. Solve equations and inequalities using graphs, tables, algebraic methods, and technology. Precalculus: II.A.3. B. Rational functions. 1. Describe the general shape of the graph and the effect of transformations on the domain and range. Precalculus: I.A.1., II.A.1. 2. Investigate continuity, asymptotes, and limits. Precalculus: I.A.7., II.A.1. 3. Solve equations and inequalities using graphs, tables, algebraic methods, and technology. Precalculus: II.A.3. 4. Decompose a rational expression into partial fractions. C. Problem situations. 1. Analyze a verbal, graphical, or tabular representation of a polynomial or rational function. Precalculus: II.A.2. 2. Analyze a problem situation by formulating an equation or an inequality. Precalculus: II.A.4. III. Exponential and logarithmic functions. A. Exponential functions. 1. Describe the general shape of a graph and the effect of transformations on the domain and range. Precalculus: I.A.1., II.B.2. 2. Investigate asymptotic behavior. Precalculus: II.B.2. 3. Investigate exponential properties graphically and algebraically. Precalculus: I.B.3. 4. Solve exponential equations and inequalities using graphs, tables, algebraic methods, and technology, including reasonableness of solutions. Precalculus: II.B.3.,4. B. Logarithmic functions. 1. Describe the general shape of a graph and the effect of transformations on the domain and range. Precalculus: I.A.1., II.B.2. 2. Develop the connection between exponential and logarithmic functions. Precalculus: II.B.1. 3. Investigate asymptotic behavior. Precalculus: II.B.2. 4. Investigate logarithmic properties graphically and algebraically. Precalculus: I.B.3. 5. Solve logarithmic equations and inequalities using graphs, tables, algebraic methods, and technology, including reasonableness of solutions. Precalculus: II.B.3., 4. C. Problem situation. 1. Analyze a verbal, graphical, or tabular representation of an exponential or logarithmic function. Precalculus: II.B.5. 2. Analyze a problem situation by formulating an equation or inequality. Precalculus: II.B.5. 3. Solve rate of change problems, such as inflation, spread of disease, population growth, tax brackets, pollution, or other such problems. Precalculus: II.B.6. 4. Analyze graphical data gathered by technical equipment. Precalculus: II.B.7. IV. Trigonometric functions. A. Circular functions. 1. Use the wrapping function to define and evaluate all six trigonometric functions. Precalculus: I.A.3. 2. Describe the general shape of a graph and the effect of transformations on the domain and range. Precalculus: I.A.1., 3. Investigate transformations of graphs including periodicity, amplitude, phase shift, and vertical shift. 4. Investigate identities graphically, and verify algebraically. Precalculus: I.B.3. 5. Solve trigonometric equations. B. Triangle trigonometry. 1. Evaluate all six trigonometric functions using a right triangle. Precalculus: I.A.3. 2. Solve problems using the law of sines and law of cosines. Precalculus: II.C.3. 3. Find the area of a triangle. C. Vectors. 1. Model situations defined by magnitude and direction. Precalculus: III.C.1, .2. 2. Find distance graphically. Precalculus: III.C.3. D. Problem situations. 1. Analyze a verbal, graphical, or tabular representation of a trigonometric function. Precalculus: II.C.1., 2., 3. 2. Analyze a problem situation by formulating an equation or inequality. Precalculus: II.C.1., 2., 3. 3. Analyze graphical data gathered by technical equipment. Precalculus: II.C.1., 2., 3. E. Inverse trigonometric functions. 1. Describe the general shape of a graph and the effect of transformations on the domain and range. 2. Evaluate inverse trigonometric functions. V. Conic sections, parametric representations, and polar representations. A. Conic sections. 1. Use conic sections to model motion and planetary motion. Precalculus: III.B.1. 2. Use conic sections to model the reflective properties of light and sound. Precalculus: III.B.2. 3. Solve systems of second-degree equations and inequalities. B. Parametric equations. 1. Convert between rectangular and parametric form. Precalculus: III.B.3. 2. Graph parametric equations. Precalculus: III.B.3. 3. Use parametric equations to simulate problems involving motion. Precalculus: III.B.4. C. Polar equations. 1. Convert between rectangular and polar form. Precalculus: III.B.5. 2. Graph polar equations. Precalculus: III.B.5. 3. Write complex numbers in polar form. 4. Find products, quotients, powers, and roots of complex numbers in polar form. VI. Sequences and series. A. Sequences. 1. Represent patterns using arithmetic and geometric sequences. Precalculus: III.A.1. 2. Solve real-life problems using arithmetic, geometric, and other sequences. Precalculus: III.A.2. 3. Describe limits of sequences. Precalculus: III.A.4. B. Series. 1. Represent patterns using arithmetic and geometric series, including sigma notation. 2. Solve real-life problems using arithmetic, geometric, and other series. 3. Investigate convergent and divergent series. Precalculus: III.A.4. C. Problem solving. 1. Solve problems including sums, binomial expansion, the binomial theorem, combinations, and Pascal’s triangle. Precalculus: III.A.5. 2. Use the principle of mathematical induction. Precalculus: III.A.6. 3. Apply informal concepts of successive approximations, upper and lower bounds, and limits in measurement situations, such as estimated lengths of curves, areas of curved regions, and volume of curved solids. Precalculus: III.A.3. VII. Iteration and fractals. A. Iteration functions using real numbers. B. Investigate fractals. III GENERAL GUIDELINES 1. Follow the directions the first time they are given. 2. Follow the policies and rules set forth in the student agenda/handbook. 3. Be in the classroom and seated in your assigned seat when the bell rings. 4. Bring all required materials as is listed in the daily requirement to every class. Failure to bring the proper materials to class will result in detention, a call to parents, and/or referral. 5. If you are absent, see me about the work you missed. Any work not made up within five school days will result in a grade of zero. Tests will be made up before or after school, not during class. 6. Major assignments and projects should be turned in on the due date, so plan and organize your time well. There will be a 10-point grade deduction for each day that an assignment is late. 7. Bring homework to class each day. You will not be allowed to leave class to get it. 8. Field trips are NOT counted as absences; therefore, you will not have any extra time to do or turn in assignments or take tests. Assignments due on the day of the field trip should be turned in before leaving; you will also be responsible the next class period for work or tests assigned on the day of the field trip. 9. Make Up Work (Daily Assignments) After an excused absence, students are responsible for asking for the “missing” assignment from the teacher 10. Extra-help: Students are encouraged to come for extra help before/after school or during my planning periods (3rd and 6th). 11. No student walks in the class without permission when the teacher is teaching. Students are expected to be on task, working on only assigned work or as directed by the teacher. Work from other classes will not be accepted. Playing games on calculators may be allowed only after the class work is completed. 12. Cooperative Learning: Only your group members should hear what you are saying during group discussion. Noise level should be low. 13. Expect unannounced quizzes. 14. Restroom: All students are entitled to only three restroom passes per quarter. Students should endeavor to use their lockers, restroom, phone and water fountain before the tardy bell. 15. Trash: All trash should be thrown away at the end of the period unless or otherwise instructed. 16. Pencil Sharpening: Pencils should be sharpened before the tardy bell rings. IV DAILY REQUIREMENTS: 1) A note book (three ring binder and loose leafs) Your note book should be organized into 5 sections, section A--(Newsletter, syllabus and standard). Section B--(Essential questions, answers to essential questions, and objectives. Section C--Notes, class examples and class work. Section D--Home work and Section E--I LEARNED and I DID NOT UNDERSTAND. 2) A mathematical set containing the following: (a) A ruler (b) a protractor (c) a compass (d) at least one pencil (e) An eraser (f) a pair of scissors (g) a tape measure 3) A T1 83 calculator is highly recommended 4) Graph note book 5) Text book V CLASS EXPECTATIONS: 1. Respect yourself, the teacher and fellow students. 2. Bring all required materials every time you come to class. 3. Be in assigned seat when the tardy bell rings. 4. Food, drinks, use of cell phones and chewing gum will not be allowed in the classroom. 5. No students are allowed to stand at the door before the bell. 6. Follow the rules listed on the students’ handbook. VI CONSEQUENCES 1st Offense: Verbal Warning 2nd Offense: Lunch detention. 3rd offence: a call to parents followed by a referral. Severe disruption will result to a call to an administrator for immediate removal to ISS. VII REWARDS Good Grades and mastery of content Praise (daily) Student of the month Candy (occasionally) VIII Assessments Major assessments will occur at the end of each unit as test, quizzes, and or projects. All assessments will be graded and recorded in the teacher’s grade book under the appropriate heading. At the end of each 9 weeks, the final grade will be calculated as follows: (A project might be assigned a test grade) Quizzes and Tests--------------- ----60% Class Work ------------------------ 20% Homework---------------------------10% Notebook/Problem of the day--------- 10% IX GRADING SCALE The following state mandated grading scale will be enforced: A = 100-93 B = 92-85 C = 84-77 D = 70-76 F = 63-69 Partial GPR Credit F = 62 or below (No GPR Credit) Homework will be assigned daily. It will be checked to make sure you are making an honest attempt at the work. To make an honest attempt is to copy the problem (except word problems) and to show all work. Class work will be any work assigned and completed during class, such as problems of the day, group work, and various other assignments. Major tests will be given at the end of each unit. Alternative assessments, such as presentations, reports, and projects may be counted as major test grades. Warm-ups will be posted on the overhead or board at the beginning of most classes as a review of a previous lesson. Warm-ups should be kept together in a section of your binder. Your notebook will be checked periodically for completed warm-ups and organization of notes and returned work. A cumulative semester exam will be given at the end of first semester and will count 20% of the first semester grade. A cumulative final exam will be given at the end of the year and will count 20% of the second semester grade. X Student Records The following procedures will be used to record student progress: 1. Grade book – All grades will be recorded in the teacher’s grade book on a regular basis. The teacher will also record these grades in a computer grade book. 2. Other means of recording and reporting student grades include progress reports and report cards. Parents may also request reports at any time XI Attendance 1. It is extremely important that you attend class everyday! Missed explanations are almost impossible to make up. Attendance will be taken during each class. The school attendance and tardy policy will be followed. 2. Assignments may be made up if absence is excused and admission slip is shown within two days of absence. An unexcused absence will result in a zero on each missed assignment. 3. State law mandates that any student exceeding 5 unexcused absences may be denied course credit. XII. Communication with Parents Parents of my students will be contacted several times during the school year. Parents will receive the syllabus, mid-nine weeks progress reports, nine weeks report cards, telephone calls, e-mails when necessary, and parent/teacher conferences as needed. Parents can stay up-to-date on school events by visiting www.greenville.k12.sc.us/southside. The effort you put forth will result in the grade you receive. Please feel free to ask for help when you need it; I am available during the 3rd and 6th periods and before or after school. An exciting, busy year awaits us! _______________________ Mrs. Roxanna E. Ezenekwe Student, please file the signed copy of this document on the first page of your three ring binder for reference purposes. I have read the syllabus, guidelines and class rules and will see that my son/daughter will follows them. Parent Signature__________________Date_________ Student Signature _________________________Date________ |
