AP Calculus BC
Ms. Nookala
Name____________
In the AP Calculus BC course students will learn the following important topics: limits, derivatives, indefinite
integrals, definite integrals, series and parametric equations. Students will know how to approach the problems
numerically, graphically, analytically and verbally.
Course Text Book
Larson, Hostetler, Edwards. Calculus of a single variable. The 8th edition. Houghton Mifflin Company, 2006
Graphing Calculator Use
Students are expected to have a graphing calculator for class work, homework, many tests and AP exam. I
strongly recommend students have his/her own calculator in the TI-83 or TI-84 with these built-in capabilities:
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Graph a function in an arbitrary viewing window
Find the zeros of function (solve equations numerically)
Numerically calculate the derivative of a function
Numerically calculate the value of a definite integral
Calculus BC Course Outline
AP Calculus BC classes will begin in early September, after Labor Day. It will include 174 teaching days and at
lease 13 days of formal assessment. The classes met five days a week. Students will have at least 3 weeks to
summarize, review and reflect what they have learned to be well preparing for their AP Calculus BC Exam in
May.
Chapter 1
Section
Topic
Number of
Days
1.1
A Preview of Calculus
1
1.2
Finding Limits Graphically and Numerically
1
1.3
Evaluating Limits Analytically
2
1.4
Continuity and One-Sided Limits
2
1.5
Infinite Limits
2
3.5
Limits at Infinity
2
Review and Assessment
3
Total
13
Chapter 2
Section
Topic
Number of Days
2.1
The Derivative and the Tangent Line Problem
3
2.2
Basic Differentiation Rules and Rates of Change
3
2.3
Product and Quotient Rules and Higher-Order Derivatives
2
2.4
The Chain Rule
2
2.5
Implicit Differentiation
2
2.6
Related Rates
3
Review and Assessment
3
Total
18
1
Section
3.1
3.2
3.3
3.4
3.6
3.7
3.9
Section
4.1
4.2
4.3
4.4
4.5
4.6
Section
5.1
5.2
5.3
5.4
5.5
5.6
5.7
Section
6.1
6.2
6.3
Chapter 3
Topic
Extrema on an Interval
Rolle’s Theorem and the Mean Value Theorem
Increasing & Decreasing Functions & the 1st Derivative Test
Concavity and the 2nd Derivative Test
A Summary of Curve Sketching
Review and Assessment
Optimization Problems
Differentials
Review and Assessment
Total
Number of Days
3
2
2
2
1
3
4
3
3
23
Chapter 4
Topic
Antiderivatives and Indefinite Integration
Area
Riemann Sums and Definite Integrals
The Fundamental Theorem of Calculus
Integration by Substitution
Numerical Integration
Review and Assessment
Total
Number of Days
2
2
3
2
2
1
3
15
Chapter 5
Topic
The Natural Logarithmic Function: Differentiation
The Natural Logarithmic Function: Integration
Inverse Functions
Exponential Functions: Differentiation and Integration
Bases Other Than e and Applications
Review and Assessment
Inverse Trigonometric Functions: Differentiation
Inverse Trigonometric Functions: Integration
Review and Assessment
Total
Number of Days
2
2
2
2
2
3
2
1
3
19
Chapter 6
Topic
Slope Fields and Euler’s Method
Differential Equations: Growth and Decay
Separation of Variables and the Logistic Equation
Review and Assessment
Total
Number of Days
3
3
3
3
12
2
Section
7.1
7.2
7.4
Section
8.1
8.2
8.3
8.5
8.7
8.8
Section
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
9.10
Section
10.2
10.3
10.4
10.5
11.1
12.2
12.3
Chapter 7
Topic
Area of a Region Between Two Curves
Volume: Disk Method, Washer Method, and Cross Section
Arc Length
Review and Assessment
Total
Number of Days
3
5
2
3
13
Chapter 8
Topic
Basic Integration Rules
Integration by Parts
Trigonometric Integrals
Partial Fractions (non-repeated linear factor only)
Indeterminate Forms and L’Hopital’s Rule
Improper Integrals
Review and Assessment
Total
Chapter 9
Topic
Sequences
Series and Convergence
The integral Test and p-Series
Comparison of Series
Alternating Series
The Ratio Test and Strategies for Testing Series
Review and Assessment
Taylor Polynomials & Approximations & the Lagrange form
Power Series
Representation of Functions by Power Series
Taylor and Maclaurin Series
Review and Assessment
Total
Number of Days
2
3
2
2
2
2
2
3
3
2
3
3
29
Chapter 10, 11, 12
Topic
Plane Curves and Parametric Equations
Parametric Equations and Calculus (including Arc Length)
Polar Equations and Polar Graphs
Area in Polar Coordinates
Vectors in the Plane
Differentiation and Integration of Vector-Valued functions
Velocity and Acceleration
Review and Assessment
Total
Number of Days
2
2
2
2
2
2
2
3
17
Number of Days
2
2
1
1
3
3
3
15
3
Student Resource Requirements
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Your class website: mnookala.wikispaces.com
Graphing Calculator for individual use inside and outside of the classroom.
Multiple-Choice & Free-Response Questions in Preparation for the AP Calculus Examinations
(BC), 8th Edition, 2003 by David Lederman.
Fast Track to a 5: preparing for the AP calculus AB and Calculus BC Examinations, by Sharon Cade,
Jeff Lucia, and Rhea Caldwell.
AP Calculus Preparing for the Advanced Placement Examination, 2000 by Jmes F. Bohan, AMSCO.
There are 5 complete model Exams, Review exercises and chapter assessments, use of graphing
calculators and complete answer key with solutions.
AP Central web site to find past free-response exams and AP Exam information: www.
apcentral.collegeboard.com.
Teacher Resources
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Anton, Howard, Ira Bivens, and Stephen Davis, Calculus: Early Transcendentals, 8th edition, Hoboken, NJ: John
Wiley & Sons, Inc., 2005
Finney, Ross, Franklin D. Demana, Bert Waites, and Daniel Kennedy, Calculus: Graphical,Numerical, Algebraic,
3rd edition, Boston: Pearson: Prentice Halll, 2007
Forrester, Paul, Calculus: Concepts and Applications, 2nd ed., Emeryville, CA, Key Curriculum Press, 2005
Hallett, Deborah, Andrew Gleason, and William McCallum, Calculus: Single Variable, 4th edition, Hoboken, NJ:
John Wiley & Sons, Inc., 2005
Larson, Ron Robert, P. Hostetler, and Bruce H. Edwards, Calculus with Analytic Geometry, 8th edition. Boston:
Houghton Mifflin, 2006
Stewart, James, Single Variable Calculus Concepts and Content with Vector Functions, Belmont, CA: Thompson
Brooks/Cole, 2007
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