Limits of Functions (Including One-Sided Limits)

Course / AP Calculus AB
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, 8th edition, Larson, Hostetler, and Edwards, Houghton/Mifflin Publishing, Boston/New York, 2006.
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 semester of a standard college calculus program. Differentiation and integration involving polynomial, exponential, logarithmic, and trigonometric functions with practical applications will be a major part of the course content.
Prerequisites: Students in this course should have earned a passing score each semester of 70% or better in Precalculus Honors, an 80% or better in College Algebra & Trigonometry, OR a 95% or better in Algebra 3-4 Honors.
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 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 3 or higher on the AP Calculus AB 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

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
Optimization, both absolute and relative extrema
Modeling rates of change, including related rates 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

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

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

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

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

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

Attendance / Full attendance and active participation are necessary for success in this course. District and school attendance policies as stated in the student handbook will be strictly followed.
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.

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 AB 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 AB course syllabus. Return completed forms to Mrs. Baldwin by Wednesday, August 13th .

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