AP Calculus BC

Ms. Zhao Name______

AP Calculus BC course, students will learn the following important topics: limits, derivatives, indefinite integrals, definite integrals, series and parametric equations. The course will make sure students understand of the concepts of calculus, using methods and its applications for each equation. Students should know how to approach the problems by 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:

·  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

Chapter 3

Section / Topic / Number of Days
3.1 / Extrema on an Interval / 3
3.2 / Rolle’s Theorem and the Mean Value Theorem / 2
3.3 / Increasing & Decreasing Functions & the 1st Derivative Test / 2
3.4 / Concavity and the 2nd Derivative Test / 2
3.6 / A Summary of Curve Sketching / 1
Review and Assessment / 3
3.7 / Optimization Problems / 4
3.9 / Differentials / 3
Review and Assessment / 3
Total / 23

Chapter 4

Section / Topic / Number of Days
4.1 / Antiderivatives and Indefinite Integration / 2
4.2 / Area / 2
4.3 / Riemann Sums and Definite Integrals / 3
4.4 / The Fundamental Theorem of Calculus / 2
4.5 / Integration by Substitution / 2
4.6 / Numerical Integration / 1
Review and Assessment / 3
Total / 15

Chapter 5

Section / Topic / Number of Days
5.1 / The Natural Logarithmic Function: Differentiation / 2
5.2 / The Natural Logarithmic Function: Integration / 2
5.3 / Inverse Functions / 2
5.4 / Exponential Functions: Differentiation and Integration / 2
5.5 / Bases Other Than e and Applications / 2
Review and Assessment / 3
5.6 / Inverse Trigonometric Functions: Differentiation / 2
5.7 / Inverse Trigonometric Functions: Integration / 1
Review and Assessment / 3
Total / 19

Chapter 6

Section / Topic / Number of Days
6.1 / Slope Fields and Euler’s Method / 3
6.2 / Differential Equations: Growth and Decay / 3
6.3 / Separation of Variables and the Logistic Equation / 3
Review and Assessment / 3
Total / 12

Chapter 7

Section / Topic / Number of Days
7.1 / Area of a Region Between Two Curves / 3
7.2 / Volume: Disk Method, Washer Method, and Cross Section / 5
7.4 / Arc Length / 2
Review and Assessment / 3
Total / 13

Chapter 8

Section / Topic / Number of Days
8.1 / Basic Integration Rules / 2
8.2 / Integration by Parts / 2
8.3 / Trigonometric Integrals / 1
8.5 / Partial Fractions (non-repeated linear factor only) / 1
8.7 / Indeterminate Forms and L’Hopital’s Rule / 3
8.8 / Improper Integrals / 3
Review and Assessment / 3
Total / 15

Chapter 9

Section / Topic / Number of Days
9.1 / Sequences / 2
9.2 / Series and Convergence / 3
9.3 / The integral Test and p-Series / 2
9.4 / Comparison of Series / 2
9.5 / Alternating Series / 2
9.6 / The Ratio Test and Strategies for Testing Series / 2
Review and Assessment / 2
9.7 / Taylor Polynomials & Approximations & the Lagrange form / 3
9.8 / Power Series / 3
9.9 / Representation of Functions by Power Series / 2
9.10 / Taylor and Maclaurin Series / 3
Review and Assessment / 3
Total / 29

Chapter 10, 11, 12

Section / Topic / Number of Days
10.2 / Plane Curves and Parametric Equations / 2
10.3 / Parametric Equations and Calculus (including Arc Length) / 2
10.4 / Polar Equations and Polar Graphs / 2
10.5 / Area in Polar Coordinates / 2
11.1 / Vectors in the Plane / 2
12.2 / Differentiation and Integration of Vector-Valued functions / 2
12.3 / Velocity and Acceleration / 2
Review and Assessment / 3
Total / 17

Student Resource Requirements

·  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. See www. apcentral.collegeboard.com.

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