BOULDER CREEK HIGH SCHOOL 40404 N. Gavilan Peak Parkway  (623) 445-8600  Fax: (623) 445-8680  dvusd.org Course AP Calculus BC Instructor Mrs. Julie Baldwin Name Contact Room: 432 Information Phone: 623-445-8823 E-mail: [email protected] Website: http://www.dvusd.org/Page/10981

This syllabus is subject to modification as determined by the instructor.

Office Hours I offer tutoring 2-3 afternoons per week. Since my schedule frequently changes, please refer to my website for the weekly tutoring days & times. Note: I strongly encourage all students to meet with an after school study group at least once per unit to refine and master the material presented in class.

Text & Calculus: Early Transcendentals (4 th edition), Stewart, Brooks/Cole Thomson Learning, Pacific Grove, CA, Materials 1999.

Students will also need: 1. Lined paper & loose graph paper for homework 2. 1 Composition Notebook (w/ graph paper) – These are available in our school store: The Spot 3. 2 Pencils, 2 Pens, Colored Pencils, a Highlighter, a Ruler, and an Eraser 4. TI-83, TI–83 Plus, or TI-84 graphing calculator is strongly recommended for success in this course. .

Course This course is approximately equivalent to the first and second semester of a standard college calculus Description program. Differentiation and integration involving polynomial, exponential, logarithmic, trigonometric, polar, parametric, and vector functions with practical applications as well as polynomial approximations and series are all key pieces of the curriculum.

Prerequisites: Students in this course should have taken AP Calculus AB with passing grades each semester of 70% or higher OR Precalculus Honors with passing grades each semester of 95% or higher.

AP Exam It is the expectation of the BCHS Advanced Academics Department that ALL students enrolled in an AP Testing class will take the AP exam for that course in May 2016. Funding is available for the exam on a financial need basis. Whether testing for Advanced Placement College Board credit or not, all students will sit for a full college board exam on Thursday, May 5, 2016. Students testing for college credit will test with the appropriate facilitator. Students testing as their final exam will test with Mrs. Baldwin. Exam check-in for all students is at 7:40 am and students will miss their 1st – 4th hour classes that day (as an excused internal school absence that will not count as an absence for school attendance policy purposes {code 8}). Participation in this exam date is not optional. In addition, it is a BCHS policy for all students to take a complete practice exam. This practice exam will be scheduled in advance and participation is also mandatory.

The results of the AP exam determine whether or not the course will be counted for university level credit. All of our in-state universities consider a score of 4 or 5 on the AP Calculus BC exam to be passing. To find the AP credit policies for other colleges or courses go to the following website to access the AP Credit Policy Information tool: www.collegeboard.com/ap/creditpolicy Course TOPICS Competencies Functions, Graphs, and Limits  Analysis of graphs  Limits of functions (including one-sided limits) 1. An intuitive understanding of the limiting process 2. Calculating limits using algebra 3. Estimating limits from graphs or tables of data  Asymptotic and unbounded behavior 1. Understanding asymptotes in terms of graphical behavior. 2. Describing asymptotic behavior in terms of limits involving infinity 3. Comparing relative magnitudes of functions and their rates of change  Continuity as a property of functions 1. An intuitive understanding of continuity 2. Understanding continuity in terms of limits 3. Geometric understanding of graphs of continuous functions  Parametric, polar, and vector functions Derivatives  Concept of the derivative 1. Derivative presented graphically, numerically, and analytically 2. Derivative interpreted as an instantaneous rate of change 3. Derivative defined as the limit of the difference quotient 4. Relationship between differentiability and continuity  Derivative at a point 1. Slope of a curve at a point. 2. Tangent line to a curve at a point and local linear approximation 3. Instantaneous rate of change as the limit of average rate of change 4. Approximate rate of change from graphs and tables of values  Derivative as a function 1. Corresponding characteristics of graphs f and f’1 2. Relationship between the increasing and decreasing behavior of f and the sign of f’ 3. The Mean Value Theorem and its geometric consequences 4. Equations involving derivatives.  Second derivative 1. Corresponding characteristics of the graphs f, f’, and f’’ 2. Relationship between the concavity of f and the sign of f’’ 3. Points of inflection as places where concavity changes  Applications of derivatives 1. Analysis of curves, including the notions of monotonicity and concavity 2. Analysis of planar curves given in parametric form, polar form, and vector form, including velocity and acceleration 3. Optimization, both absolute and relative extrema 4. Modeling rates of change, including related rate problems 5. Use of implicit differentiation to find the derivative of an inverse function 6. Interpretations of the derivative as a rate of change in varied applied contexts, including velocity, speed, and acceleration 7. Geometric interpretation of differential equations via slope fields and the relationship between slope fields and solution curves for differential equations 8. Numerical solution of differential equations using Euler’s method 9. L’Hospital’s Rule, including its use in determing limits and convergence of improper integrals and series  Computation of derivatives 1. Knowledge of derivatives of basic functions, including power, exponential, logarithmic, trigonometric, and inverse trigonometric functions 2. Basic rules for the derivative of sums, products, and quotients of functions 3. Chain rule and implicit differentiation 4. Derivatives of parametric, polar, and vector functions Integrals  Interpretations and properties of definite integrals 1. Definite integral as a limit of Riemann sums 2. Definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval 3. Basic properties of definite integrals  Applications of integrals (including polar and parametric)  Fundamental Theorem of Calculus 1. Use the Fundamental Theorem to evaluate definite integrals 2. Use of the Fundamental Theorem to represent a particular antiderivative, and the analytical and graphical analysis of functions so defined  Techniques of antidifferentiation 1. Antiderivatives following directly from derivatives of basic functions 2. Antiderivatives by substitution of variables, parts, and simple partial fractions 3. Improper integrals  Applications of antidifferentiation 1. Finding specific antiderivatives using intial conditions, including applications to motion along a line 2. Solving separable differential equations and using them in modeling 3. Solving logistic differential equations and using them in modeling  Numerical approximations to definite integrals 1. Use of Riemann sums and trapezoidal sums Polynomial Approximations and Series  Concept of series  Series of constants 1. Motivating examples, including decimal expansions 2. Geometric series with applications 3. The harmonic series 4. Alternating series with error bound 5. Terms of series as areas of rectangles and their relationship to improper integrals, including the integral test and its use in testing the convergence of p-series 6. The ratio test for convergence and divergence 7. Comparison test for convergence or divergence  Taylor series 1. Taylor polynomial approximation with graphical demonstration of convergence 2. Maclaurin series and the general Taylor series centered at x=a 1 3. Maclaurin series for functions e x , sin x,cos x, and 1 x 4. Formal manipulation of Taylor series and shortcuts to computing Taylor series, including substitution, differentiation, antidifferentiation, and the formation of new series form known series 5. Functions defined by power series 6. Radius and interval of convergence of power series 7. Lagrange error bound for Taylor polynomials

Grading Semester grades will be determined based on a point system in each of the Grading Scale A = 100% - 90% following weighted categories: B = 89% - 80% C = 79% - 70% 72% Tests and Projects D = 69% - 60% 8% Homework, Class Participation, & Quizzes F = below 60% 20% Final Exam

 Current grades and attendance can be viewed online at any time via the student’s DVUSD PowerSchool account. Please see information below regarding PowerSchool access.  Extra Credit is not available for this class. It is the belief of Boulder Creek High School that all work done for a class should receive regular credit and is more than sufficient to assess the understanding of material presented in the course.

Classroom Behavior Expectations and Consequences – PBIS

PRIDE Learning Environment  Bring materials Prepared  Come prepared to learn Respectful  Respect others, their property, equipment, and the facility  Complete your own work Integrity  All electronic devices are off and out of sight  Arrive on time & be in your seat Discipline  Behave appropriately and use courteous language  Keep food and drink outside  Encourage confidence Everyone United  Cooperate and collaborate

Adherence to the Boulder Creek Academic Integrity Code All students enrolled in AP Calculus BC will adhere to the framework and guidelines set forth in the Boulder Creek High School Academic Integrity Code. Cheating and Plagiarism will not be tolerated. The purpose of this code is to promote a positive learning environment for all involved. As humans, we will make mistakes as we grow. It is understood that we can learn from those mistakes and become better individuals in the future. Any student who violates this code will be referred to the Students Rights and Responsibilities handbook and assignment of appropriate consequences. Please refer to the Academic Integrity Code in your student handbook for more details.

Make-Up Work Policy Upon return to class after an absence, a student has one school day for each day missed to make up work/test assigned during his/her absence regardless of the number of days absent. For example, if a student is absent on Thursday and Friday, he/she will have Monday and Tuesday of the following week to make up work and must turn in the work that was assigned during the days absent on Wednesday.

Coursework and assessments assigned prior to the absence(s) may still be due on the date assigned. It is the student’s responsibility to check with teachers immediately upon return for work missed and possible adjustment of due dates. Teachers may choose to schedule an appointment with the student to arrange due dates as needed. Note: Homework assignments and lesson notes can be found on the class website.

Long Term Project Policy Long term projects are assignments given at least two weeks in advance. Teachers should note that the assignment is a long term project in the written instructions provided for the students. Long term projects are due on or before the date assigned, even if the student or teacher is absent on the due date. The project can be turned in at the front office. See the Student Handbook for additional details.

PowerSchool Access The PowerSchools site allows parents, guardians, and students to access a student’s grades, attendance, and other information. If you do not have your PowerSchool access information, please stop by the front desk during business hours with your photo ID to pick-up this information. The web address is: https://ps.dvusd.org/public/

The Deer Valley Unified School District does not discriminate on the basis of race, color, national The Deerorigin, Valley sex, Unified disability, School or age District in its does programs not discriminate and activities. on theFor basisany inquiries of race, regardingcolor, national nondiscriminationorigin, sex, policies disability, contact or age the in Superintendent'sits programs and Department, activities. For 20402 any inquiries N. 15th regardingAvenue, Phoenix, nondiscrimination policies contact the Superintendent'sAZ 85027. 623.445.5000. Department, 20402 N. 15th Avenue, Phoenix, AZ 85027. 623.445.5000. Important resources for BCHS AP Calculus

Mrs. Baldwin’s website: http://www.dvusd.org/Page/10981

Mrs. Baldwin’s email address: [email protected]

Note: I suggest that parents & students review PowerSchools weekly at https://ps.dvusd.org/menu/ to make sure they are aware of their student’s progress.

------Please read the course syllabus on my website before completing the form below! To view the syllabus, go to my website and click on “Class Calendars & Syllabi” in the sidebar on the left. Then click the link for the AP Calculus BC 2015-2016 Syllabus under the picture of the Jaguar. Read through the syllabus with your child and complete the information below. It would be a great idea to bookmark or add the site to your favorites so that you will be able to find it again easily in the future!

Complete the following, then sign below to indicate that you have read and understand the information in the AP Calculus BC course syllabus. Return completed forms to Mrs. Baldwin by Wednesday, August 13th .

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