Legacy High School A Global Studies School Course Expectations
2016-2017
AP Calculus AB Instructor: Mr. Pauwelyn LHS Room 807 Phone: (702) 799-1777 Voice Mail (702) 799-1777 ext.3807 Email:
[email protected] Website Address: www.legacyhigh.net Course Scope: This one-year course is designed with an emphasis on meeting the requirements of the College Board Advanced Placement AP Calculus AB examination. This college-level curriculum is primarily concerned with developing the students’ understanding of the concepts of calculus and providing experience with its methods and applications. Before studying calculus, all students should complete four years of secondary mathematics designed for collegebound students: courses in which they study algebra, geometry, trigonometry, analytic geometry and elementary functions. Instructional practices incorporate integration of diversity awareness including appreciation of all cultures and their important contributions to society. The use of technology, including graphing calculators and computer software, is an integral part of this course. This course fulfills one of the mathematics credits required for high school graduation. Goals • Students should be able to work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal . They should understand the connections among these representations . • Students should understand the meaning of the derivative in terms of a rate of change and local linear approximation, and should be able to use derivatives to solve a variety of problems .
• Students should understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change, and should be able to use integrals to solve a variety of problems . • Students should understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus . • Students should be able to communicate mathematics and explain solutions to problems both verbally and in written sentences . • Students should be able to model a written description of a physical situation with a function, a differential equation, or an integral . • Students should be able to use technology to help solve problems, experiment, interpret results, and support conclusions . • Students should be able to determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement . • Students should develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment. Topic outline for Calculus AB I. Functions, Graphs, and Limits Analysis of graphs. With the aid of technology, graphs of functions are often easy to produce . The emphasis is on the interplay between the geometric and analytic information and on the use of calculus both to predict and to explain the observed local and global behavior of a function . Limits of functions (including one-sided limits) • An intuitive understanding of the limiting process . • Calculating limits using algebra . • Estimating limits from graphs or tables of data . Asymptotic and unbounded behavior • Understanding asymptotes in terms of graphical behavior . • Describing asymptotic behavior in terms of limits involving infinity . • Comparing relative magnitudes of functions and their rates of change (for example, contrasting exponential growth, polynomial growth, and logarithmic growth) . Continuity as a property of functions • An intuitive understanding of continuity . (The function values
can be made as close as desired by taking sufficiently close values of the domain .) • Understanding continuity in terms of limits . • Geometric understanding of graphs of continuous functions (Intermediate Value Theorem and Extreme Value Theorem) . II. Derivatives Concept of the derivative • • • •
Derivative presented graphically, numerically, and analytically . Derivative interpreted as an instantaneous rate of change . Derivative defined as the limit of the difference quotient . Relationship between differentiability and continuity .
Derivative at a point • Slope of a cur ve at a point . Examples are emphasized, including points at which there are vertical tangents and points at which there are no tangents . • Tangent line to a cur ve at a point and local linear approximation . • Instantaneous rate of change as the limit of average rate of change . • Approximate rate of change from graphs and tables of values . Deriv ativ e as a function • Corresponding characteristics of graphs of ƒ and ƒ∙ . • Relationship between the increasing and decreasing behavior of ƒ and the sign of ƒ∙ . • The Mean Value Theorem and its geometric interpretation . • Equations involving derivatives . Verbal descriptions are translated into equations involving derivatives and vice versa . Second derivatives • Corresponding characteristics of the graphs of ƒ, ƒ∙, and ƒ ∙ . • Relationship between the concavity of ƒ and the sign of ƒ ∙ . • Points of inflection as places where concavity changes . Applications of derivatives • Analysis of curves, including the notions of monotonicity and concavity . • Optimization, both absolute (global) and relative (local) extrema . • Modeling rates of change, including related rates problems . • Use of implicit differentiation to find the derivative of an inverse function . • Interpretation of the derivative as a rate of change in varied applied contexts, including velocity, speed, and acceleration .
• Geometric interpretation of differential equations via slope fields and the relationship between slope fields and solution curves for differential equations . Computation of derivatives • Knowledge of derivatives of basic functions, including power, exponential, logarithmic, trigonometric, and inverse trigonometric functions . • Derivative rules for sums, products, and quotients of functions . • Chain rule and implicit differentiation . III. Integrals Interpretations and properties of defin ite integrals • Definite integral as a limit of Riemann sums . • Definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval Basic properties of definite integrals (examples include additivity and linearity) . Application s of integrals. Appropriate integrals are used in a variety of applications to model physical, biological, or economic situations . Although only a sampling of applications can be included in any specific course, students should be able to adapt their knowledge and techniques to solve other similar application problems . Whatever applications are chosen, the emphasis is on using the method of setting up an approximating Riemann sum and representing its limit as a definite integral . To provide a common foundation, specific applications should include finding the area of a region, the volume of a solid with known cross sections, the average value of a function, the distance traveled by a particle along a line, and accumulated change from a rate of change . Fundamental Theorem of Calculus • Use of the Fundamental Theorem to evaluate definite integrals . • Use of the Fundamental Theorem to represent a particular antiderivative, and the analytical and graphical analysis of functions so defined . Techniques of anti-differentiation • Antiderivatives following directly from derivatives of basic functions . • Antiderivatives by substitution of variables (including change of limits for definite integrals) . Applications of anti-differentiation • Finding specific antiderivatives using initial conditions, including applications to motion along a line .
• Solving separable differential equations and using them in modeling (including the study of the equation y∙ = ky and exponential growth) . Numerical approximations to definite integrals. Use of Riemann sums (using left, right, and midpoint evaluation points) and trapezoidal sums to approximate definite integrals of functions represented algebraically, graphically, and by tables of values . Textbooks The following text(s) will be utilized in this course: Calculus, AP Edition, Finney/Demana/Waits/Kennedy $84.00 Student Supplies Students are expected to have and maintain the following supplies all year: Spiral Notebook for homework and in-class assignments – 1 large 180 – 200 sheet notebook is preferred which should be enough to last the year or 3 smaller single subject 70 sheet notebooks can be used. All unit test questions will be similar to homework questions, classwork examples or classwork practice. There will be no separate practice test before the unit test so students will need a well maintained and organized notebook with all their homework problems in it from which to study. Pencils, pencil sharpener, eraser Binder, folder or notebook for note taking Ruler (6 or 12 inch preferably in standard (inches) and metric units) A graphing calculator is not required but an investment in a TI-Nspire CX calculator would be very beneficial. This is the calculator that we use in the class but we don’t have enough of these to check out to the students for home use. Having the same calculator at home to do homework with would greatly magnify the students learning. TI-Nspire CAS would also be a good option – the CAS stands for a computer algebra system which the CX does not have. Both calculators are allowed on the AP Calculus AB test. We also have TI-84 graphing calculators that can be check out to the students to take home for the year which will definitely serve your student’s needs if buying a calculator is not the desired option.
Tardy Policy Tardiness is a serious disruption to the educational program. Every student is required to be in his/her seat when the tardy bell rings. With that in mind, the Legacy High School Tardy Policy will be strictly enforced. On the first and second tardy, the student will be warned; on the third tardy, the parent will be contacted; on the fourth tardy, a detention will be assigned; on the fifth and all subsequent tardies, the student will be sent to the deans’ office and placed on a Required Parent Conference. Grading Policy
Grading Scale: 90% - 100% A 80% - 89% B 70% - 79% C 60% - 69% D Below 60% F Rounding policy: I will round all percentages to the nearest whole number in order to determine borderline grades. For Example, a student who receives a 89.5% would be rounded up to 90% and receive an A. However a 89.4% would be rounded down to 89% and the grade would be a B. Grading Procedures- The grade for each nine week grading period will be based on the following percentages. o Test/Quizzes 60% o Classwork/Participation 15% o Homework 25 %
Semester Grades: 40% Quarter 1/3 Grade 40% Quarter 2/4 Grade 20% Semester Examination
Tests will follow the end of every major unit of study. If a student is absent on the day of the test, it is their responsibility to schedule a time to take the test with me within 3 days of their return to school. Students will be allowed to retake 1 unit test per semester. The retake score will replace the original score even if it is lower.
Quizzes will be given mid unit to determine comprehension of the material. Some quizzes may be given without notice. Similarly, students absent on the day of the quiz, need to schedule a time to take the test with me within 3 days of their return to school. Students may schedule to retake quizzes after school.
Homework: Students are expected to maintain a notebook with all of their homework problems in it for the year. At times, the students will want to work out the problems first on scrape paper and then write them neatly in their notebook. This “homework notebook” will then serve as a source of example problems that the students should study before every test.
Homework Grading –The students “homework notebooks” will be checked 2 or 3 times per quarter. A detailed rubric of how this grade will be determined will be given in class and will contain the following items: completion, organization, neatness.
There will also be class work that the student will complete in class that the student will receive a grade for. If the student is present the day of class, the class work must be completed in class and will not be accepted late.
Participation: Every 3 weeks each student will received a grade for class participation that will be part of her/his classwork grade. This will be a 10 point grade. Students will be automatically given 10 points and then start losing points for non-participation. My definition of participating in class includes: coming to class prepared to work and prepared to ask questions on the previous night’s homework, asking questions during class when you need help or clarifications, working on class assignments (including the warm-ups), working with partners and teams when asked to do so, and staying awake and alert at all times during class.
W hen a student is absent they need to check the homework/classwork files in the room to find their missing assignments or they can go on-line to our webpage. Students have 3 days from the date of their return to class to make up these missed assignments.
Notebook - Keeping an organized notebook is an important part of the class. Students who miss a class should ask to copy the class notes from a set that I maintain in the class or from a friend who has the notes.
Standards of Preparation. Part of the purpose of leaning mathematics is also to learn to communicate effectively. Work that is neat, organized and properly communicates the mathematical ideas involved shows a clear understanding of this principle and will receive top grades. W ork that is hard to read and/or disorganized will receive a reduced grade. All work is expected to be completed in pencil – test and
assignments that are done in pen will receive a 10% reduction in grade.
Academic Dishonesty – There will be a zero tolerance policy for any form of cheating on test. Any student found to have been cheating on a test will receive a grade of zero for that test and not be allowed to make it up. Student’s blatantly copying assignments that are to be turned in and graded will also receive a zero on that assignment and not be allowed to make the assignment up.
M ake-up W ork, Late W ork, and Attendance Make-up procedures- after an absence o Assignments - students will be expected to check the make-up files in the class after they return from an absence. The student will be expected to return the completed make -up work within two class periods (3 days), or receive a no grade on the assignments. o Test - Students are responsible for making arrangements with the teacher to take missed quizzes or test before or after school. Students will not be allowed to use class time to take missed test. o It is the student’s responsibility to make sure that they complete all missed assignments and test after an absence.
Hours of Availability- I will make myself available for student questions and assistance after school every day until at least 2:00PM unless I have a meeting and I will post a note on the door indicating when I will return.
Attendance After the seventh unexcused absence, students will be denied credit and will receive an “F” for the course.
Classroom Behavior Expectations My classroom management philosophy is guided by this statement. I HAVE A RIGHT TO TEACH, AND ALL STUDENTS HAVE A RIGHT TO LEARN. THEREFORE, ANYTHING DONE TO INTERFERE WITH THIS PROCESS WILL BE DEALT WITH AS A DISCIPLINE ISSUE.
Classroom Do’s: 1: Respect others. Respect others right to learn and to make mistakes in the process. Laughing at other people’s mistakes in class will be treated as a bullying matter. Use polite language Wait your turn - raise your hand when you wish to say something and don’t interrupt others. Hands off policy 2: Respect the classroom. Water in water bottles only (no other food or beverages) Treat the classroom as a place of learning. It is not a playground or a gym. No horseplay will be tolerated 3: Respect yourself. Always do your best Arrive on time (The 3rd tardy of each quarter will result in a Dean’s referral and a “U” in citizenship. Arrive with all necessary materials ready to work While in this class, you are must be working on class assignments and tasks. 1. 2. 3. 4.
Classroom Don’ts Don’t come to class unprepared to work (pencils, paper, notebook textbook) Don’t talk when someone else is talking (the teacher or another student) No food, candy or drinks allowed in the class. (except water in clear water bottles) No cell phones or listening to music. Nuisance items will be confiscated and turned in to the Dean’s office. There will be no warnings.
Consequence plan for rule breaking 1) Teacher –Student Conference (Verbal Warning) 2) Student home contact 3) Teacher Detention. 4) Counselor Referral 5) Dean’s Referral
Please complete this page, remove from packet and return to school by September 25, 2016.
Acknowledgement of Course Expectations AP Calculus AB We have read and discussed the course description and expectations. ________________________________ ________________________________ Student’s name [last, first] Student’s Signature ________________________________ Parent Name
________________________________ Parent Signature
________________________________ Home phone
________________________________ Work/Cell phone
Email Address: __________________________________________________________
Electronic Textbook If my child’s course has an electronic version of the textbook, that can be accessed at home through the internet, I am giving permission to not check out a text book for this course. I have internet access at home to use the electronic version. Note: Not all classes offer an electronic version and a textbook will be checked out to the student.
Parent Signature:
___________________________
Leg acy High School
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