Course / AP Calculus BC
Instructor Name / Mrs. Julie Baldwin
Contact Information / Room: 432
Phone: 623-445-8823
E-mail:
Website:
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 & Materials / Calculus: Early Transcendentals (4th edition), Stewart, Brooks/Cole Thomson Learning, Pacific Grove, CA, 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 Description / This course is approximately equivalent to the first and second semester of a standard college calculus 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 piecesof 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 Testing / It is the expectation of the BCHS Advanced Academics Department that ALL students enrolled in an AP class will take the AP examfor that course in May 2015. 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 Tuesday, May 5, 2015. 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:
Course Competencies / TOPICS
Functions, Graphs, and Limits
  • Analysis of graphs

  • 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

  • Continuity as a property of functions
  • An intuitive understanding of continuity
  • Understanding continuity in terms of limits
  • Geometric understanding of graphs of continuous functions

  • Parametric, polar, and vector functions

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 curve at a point.
  • Tangent line to a curve 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

  • Derivative as a function
  • Corresponding characteristics of graphs f and f’1
  • Relationship between the increasing and decreasing behavior of f and the sign of f’
  • The Mean Value Theorem and its geometric consequences
  • Equations involving derivatives.

  • Second derivative
  • Corresponding characteristics of the graphs f, f’, and f’’
  • Relationship between the concavity of f and the sign of f’’
  • Points of inflection as places where concavity changes

  • Applications of derivatives
  • Analysis of curves, including the notions of monotonicity and concavity
  • Analysis of planar curves given in parametric form, polar form, and vector form, including velocity and acceleration
  • Optimization, both absolute and relative extrema
  • Modeling rates of change, including related rate problems
  • Use of implicit differentiation to find the derivative of an inverse function
  • Interpretations 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
  • Numerical solution of differential equations using Euler’s method
  • L’Hospital’s Rule, including its use in determing limits and convergence of improper integrals and series

  • Computation of derivatives
  • Knowledge of derivatives of basic functions, including power, exponential, logarithmic, trigonometric, and inverse trigonometric functions
  • Basic rules for the derivative of sums, products, and quotients of functions
  • Chain rule and implicit differentiation
  • Derivatives of parametric, polar, and vector functions

Integrals
  • Interpretations and properties of definite 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

  • Applications of integrals (including polar and parametric)

  • Fundamental Theorem of Calculus
  • Use 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 antidifferentiation
  • Antiderivatives following directly from derivatives of basic functions
  • Antiderivatives by substitution of variables, parts, and simple partial fractions
  • Improper integrals

  • Applications of antidifferentiation
  • Finding specific antiderivatives using intial conditions, including applications to motion along a line
  • Solving separable differential equations and using them in modeling
  • Solving logistic differential equations and using them in modeling

  • Numerical approximations to definite integrals
  • Use of Riemann sums and trapezoidal sums

Polynomial Approximations and Series
  • Concept of series

  • Series of constants
  • Motivating examples, including decimal expansions
  • Geometric series with applications
  • The harmonic series
  • Alternating series with error bound
  • 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
  • The ratio test for convergence and divergence
  • Comparison test for convergence or divergence

  • Taylor series
  • Taylor polynomial approximation with graphical demonstration of convergence
  • Maclaurin series and the general Taylor series centered at x=a
  • Maclaurin series for functions ,
  • Formal manipulation of Taylor series and shortcuts to computing Taylor series, including substitution, differentiation, antidifferentiation, and the formation of new series form known series
  • Functions defined by power series
  • Radius and interval of convergence of power series
  • Lagrange error bound for Taylor polynomials

Grading /
Semester grades will be determined based on a point system in each of the
following weighted categories:
72% Tests and Projects
8% Homework, Class Participation, Quizzes
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
Prepared /
  • Bring materials
  • Come prepared to learn

Respectful /
  • Respect others, their property, equipment, and the facility

Integrity /
  • Complete your own work
  • All electronic devices are off and out of sight

Discipline /
  • Arrive on time & be in your seat
  • Behave appropriately and use courteous language
  • Keep food and drink outside

Everyone United /
  • Encourage confidence
  • Cooperate and collaborate

Important resources for BCHS AP Calculus

Mrs. Baldwin’s website:

Mrs. Baldwin’s email address:

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

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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 2014-2015 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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