COURSE IDENTIFICATION: TITLE: AP Calculus AB - Fall 2010

COURSE IDENTIFICATION: TITLE: AP Calculus AB - Fall 2010 ACADEMY: Engineering and Design ROOM: ED 120

INSTRUCTOR INFORMATION: NAME: Rob Keeney PHONE: 896-5600 EXT: 5773 EMAIL: [email protected] WEBSITE: www.orgsites.com/nm/keeneyj

PREREQUISITE: C or higher in Pre-AP Pre-Calculus, or permission of instructor. Note: Pre-calculus is recommended but not required. There are other paths to AP Calculus where students can be successful.

TEXTBOOK: Single Variable Calculus with Vector Functions, James Stewart, Thompson Brooks/Cole.

SUPPLIES: 1. Notebook or binder with a supply of writing paper. Writing implements (pens are fine but some assignments may require pencils) 2. TI-83, TI-84, or TI-89 graphics calculator or equivalent. Required. (Please talk with instructor if this poses a problem.) 3. Graph paper (not required but may be helpful in some graphing) - small grid preferable.

COURSE DESCRIPTION: Calculus AB is a college level calculus course designed to prepare students for success on the College Board’s Advanced Placement Exam. Its primary focus is to develop the student’s understanding of the concepts of calculus and provide experience with its methods and applications. The course emphasizes a multirepresentational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. Broad concepts and widely applicable methods are the focus, and include the topics of derivatives, integrals, limits, approximations, applications, and modeling. Technology is used regularly to reinforce the relationships among the multiple representations of functions, to confirm written work, implement experimentation, and assist in interpreting results.

COURSE EXIT STANDARDS: Upon successful completion of this course, students will meet the following proficiencies: 1. Be able to work with functions represented in a variety of ways: graphical, numerical, analytical, and verbal, and understand the connections among these representations. 2. Understand the meaning of the derivative in terms of a rate of change and local linear approximation, and be able to use derivatives to solve a variety of problems. 3. Understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change, and be able to use integrals to solve a variety of problems. 4. Understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus. 5. Be able to model a written description of a physical situation with a function, differential equation, or integral. 6. Be able to use technology to help solve problems, experiment, interpret results, and verify conclusions. 7. Be able to determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.

COURSE POLICY: This class will likely be different from any other you may have already had. It will no longer be sufficient to simply learn the techniques taught by the instructor, and then reproduce them on the exams. It is assumed that you have already mastered this. It is now simply a tool you will need to reach the next, and far more important aspect of your education. You will receive many problems that you have not previously seen, and you will be expected to solve them none-the-less. The real world does not usually present itself in pre-configured problems, to which the answers are already known. True challenges in life require creativity, cleverness and problem-solving abilities. These are not common skills, and are ones that will take time and dedication to develop. Homework and next-topic readings will be assigned daily. Expect 1-2 hours on average of work each school night. Assignments will be covered in class the next day and students will have the opportunity to ask questions concerning them. Only some of the assignments will be collected or included as part of a grade for the class. Unless otherwise stated, all assignments are due the following class meeting. They may be collected at the beginning of class, at the end, or even a number of days later, and without prior notice. In other words, keep all assignments! It is imperative and expected that students do ALL parts of ALL assignments and readings. However, this is the minimum expectation, and further work and study on the students’ parts may be necessary at times. The majority of the grade for the class will come from quiz and exam scores, and students will have little chance for success without the assigned preparatory work. The exams and quizzes are based on problems from the AP exam and are generally very difficult; however, please note the grading scale at the end of the syllabus. It is assumed that students will take on the responsibility to monitor their progress and seek out whatever extra help they may need (as with any college-level course). There is a lot of independent work and responsibility associated with the course. Progress reports will be sent out by email after each quiz or exam is updated in the grade book. Both students and parents are encouraged to send the instructor their email addresses. Daily assignments

1 are posted on the course website (www.orgsites.com/nm/keeneyj). It is critical that students keep up with the material. The class will move at a very quick pace. It is hoped that every student takes the AP exam. The cost is $86 and there is financial aid available if needed. Taking the exam is to the student’s benefit. A university will give college credit for the course only from AP exam scores, not from the class grade itself. A practice AP exam given in class will serve as the course’s final exam. If a student scores higher (by a letter grade or more) on the practice AP exam than they did for the two quarter grades’ average, then their course average will be raised a letter grade. An exception is if the final overall course average is below a 50%. Then the student must have scored at least a ‘C’ on the final to receive a letter-grade higher. Students may also elect to participate in the Student Research Expo for extra credit as established by the district Expo extra credit policy. Ask the instructor for more details.

COURSE OUTLINE: The following table is only a guideline. Variations will be made as class needs warrant. WEEK TOPICS EXIT STANDARDS 1-3 Functions, Graphs, and Limits 1, 5, 6, 7  Limits of functions – concepts, calculating, estimating, asymptotic and unbounded behavior, graphical interpretations, descriptions, comparisons  Continuity as a property of functions – intuition, relating to limits, Intermediate and Extreme Value Theorems  Concept – presentation forms, interpretation, difference quotient  Derivative at a point – slopes, tangent lines, local linear approximations, limits of average rates of change, approximations 3-10 Derivatives 1, 2, 5, 6, 7  Derivative as a function – graphs of f and f’, relating increase/decrease and sign of f’, Mean Value Theorem, verbal descriptions  Second derivatives - graphs of f, f’, and f”, concavity of f and sign of f”, points of inflection  Applications of derivatives – analysis of curves, optimization, related rates, implicit differentiation, velocity and acceleration, slope fields  Computation of derivatives – power, exponential, logarithmic, trigonometric, sums products quotients, chain rule, inverse functions 11-16 Integrals 1, 3, 4, 5, 6, 7  Interpretations and properties of definite integrals – Riemann sums, definition, basic properties  Applications – areas, volumes, average values of functions, linear distance on a curve  Fundamental Theorem of Calculus – definite integrals, antiderivatives, analytical and graphical analysis  Techniques of antidifferentiation – recognition, power rule, substitution, integration by parts, exponential, natural log, inverse trig, improper  Applications of antidifferentiation – initial conditions, separable differential equations, modeling  Numerical approximations to definite integrals – Riemann and trapezoidal sums, algebraic, graphical and tables 17-18 Review and reinforcement of course concepts 1, 2, 3, 4, 5, 6, 7  Practice AP exam questions and review  Construction of approximation of volumes of revolutions  Human Population: Part I – simple exponential growth model  Take-home and in-class practice AP exams

CRITERIA FOR EVALUATION: Each 9-week grade is comprised 90% of quiz and exam scores, and 10% class and homework. Homework will normally be graded as 50% completion, and 50% correct work on selected problems (not announced before-hand). The semester grade is calculated per school policy as follows: Each 9-weeks grade-40%, final exam-20%.

GRADING SCALE: A = 67%-100% B = 54%-66.9% C = 39%-53.9% D = 25%-38.9% F = Performance below 27% (This scale is based on the AP Calculus Exam scores 5-1.)

2 The class can be challenging, and students may not always receive the grades to which they are accustomed. However, the hard work, knowledge, and experience will open doors that can lead to many future successes. Most anything of true value does not come easily.