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Mrs. Regina Ramey


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Calculus Graphical, Numerical, Algebraic, 3rd edition;  Finney, Demana, Waits, Kennedy





3-ring binder, Pencil, Notebook, and Graphing Calculator (TI-83+, TI-84, TI-84 Silver, TI-89, or TI-Nspire )




Before studying calculus, all students should complete four courses of secondary mathematics designed for college-bound students: courses in which they study algebra, geometry, trigonometry, analytic geometry, and elementary functions. These functions include those that are linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise defined. In particular, before studying calculus, students must be familiar with the properties of functions, the algebra of functions, and the graphs of functions. Students must also understand the language of functions (domain and range, odd and even, periodic, symmetry, zeros, intercepts, and so on) and know the values of the trigonometric functions of the numbers 0, pi/6, pi/4, pi/3, pi/2, and their multiples.



Advanced Placement (AP) Calculus BC is a college-level mathematics course for students that have previously demonstrated mastery of' algebra, geometry, coordinate geometry, trigonometry, and AP Calculus AB. This course will develop the students' understanding of the concepts of calculus and provide experience with its methods and applications. The course will emphasize a multi-representational approach to calculus, with concepts, results, and problems being expressed geometrically, numerically, analytically, and verbally. The connections among these representations also are important. Technology is used regularly to reinforce the relationships among the multiple representations of functions, to confirm written work, to implement experimentation, and to assist in interpreting results.


Students should be able to:



The topic outline for Calculus BC includes all Calculus AB topics. Additional topics are found in paragraphs that are marked with a plus sign (+) or an asterisk (*). The additional topics can be taught anywhere in the course. Some topics will naturally fit immediately after their Calculus AB counterparts. Other topics may fit best after the completion of the Calculus AB topic outline. Although the examination is based on the topics listed here, the course may be enriched with additional topics.

I. Functions, Graphs, and Limits

A. 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.

B. Limits of Functions (incl. one-sided limits)

C. Asymptotic and Unbounded Behavior

D. Continuity as a Property of Functions

E. *Parametric, Polar, and Vector Functions

The analysis of planar curves includes those given in parametric form, polar form, and vector form.

II. Derivatives

A. Concept of the Derivative

B. Derivative at a Point

C. Derivative as a Function

D. Second Derivatives

E. Applications of Derivatives

F. Computation of Derivatives

III. Integrals

A. Interpretations and Properties of Definite Integrals


B. *Applications of Integrals

Appropriate integrals are used in a variety of applications to model physical, social, 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 (including a region bounded by polar curves), 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 for BC only the length of a curve (including a curve given in parametric form).

C. Fundamental Theorem of Calculus

D. Techniques of Antidifferentiation

E. Applications of Antidifferentiation

F. 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.

IV. *Polynomial Approximations and Series

A. *Concept of Series

A series is defined as a sequence of partial sums, and convergence is defined in terms of the limit of the sequence of partial sums. Technology can be used to explore convergence or divergence.

B. *Series of constants

C. *Taylor Series



Chapter 1 Prerequisites for Calculus

4 days

Chapter 2 Limits and Continuity

6 days

Chapter 3 Derivatives

22 days

Chapter 4 Applications of Derivatives

14 days

Chapter 5 The Definite Integral

16 days

Chapter 6 Differential Equations and Mathematical Modeling

22 days

Chapter 7 Applications of Definite Integrals

15 days

Chapter 8 L'Hôpital's Rule, Improper Integrals, and Partial Fractions

7 days

Chapter 9 Infinite Series

23 days

Chapter 10 Parametric, Vector, and Polar Functions

16 days

This timeline gives approximately 15 days to “review” the course before the exam.  These times are approximate and subject to change.


Put your knowledge to the test: The AP Calculus BC Exam assesses your mastery of Calculus BC concepts and techniques. It also gives you the chance to earn college credit while in high school. 

About the Exam

The AP Calculus BC Exam is 3 hours and 15 minutes. The 105-minute, 45-question multiple-choice section tests your proficiency on a wide variety of topics. The 90-minute, six-problem free-response section gives you the chance to demonstrate your ability to solve problems using an extended chain of reasoning.

Section I: Multiple-Choice

The multiple-choice section of the exam has two parts. For Part A, you'll have 55 minutes to complete 28 questions without a calculator. For Part B, you'll have 50 minutes to answer 17 questions using a graphing calculator. For more information, see the calculator policy for the AP Calculus Exams.

Unlike other multiple-choice tests, random guessing can hurt your final score. While you don't lose anything for leaving a question blank, one quarter of a point is subtracted for each incorrect answer on the test. But if you have some knowledge of the question and can eliminate one or more answers, it's usually to your advantage to choose what you believe is the best answer from the remaining choices.

Section II: Free-Response

The free-response section tests your ability to solve problems using an extended chain of reasoning. You'll have 45 minutes for each of the two parts of the free-response section. In Part A, you'll answer three questions using a graphing calculator. In Part B, you'll answer three questions without a calculator. During the second timed portion of the free-response section (Part B), you are permitted to continue work on problems in Part A, but you are not permitted to use a calculator during this time. For more information, see the calculator policy for the AP Calculus Exams.

Scoring the Exam

The multiple-choice and free-response sections each account for one-half of your final exam grade. Since the exams are designed for full coverage of the subject matter, it is not expected that all students will be able to answer all the questions.

Exam Grades

AP Grade Reports are sent in July to the college you designated on your answer sheet, to you, and to your high school. Each report is cumulative and includes grades for all the AP Exams you have ever taken, unless you have requested that one or more grades be withheld from a college or canceled.




AP:Calculus BC  


Ask Dr. Math  


Calculus textbook website  




InterAct Math  


Karl's Calculus Tutor  


Mr. Calculus  


PowerPoint Lectures


Slopefields on TI-89


TI Graphing Calculators  


Tutorials for the Calculus Phobe  


Using the TI-89 Calculator


Visual Calculus  




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65 - 74


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