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SECONDARY MATHEMATICS CURRICULUM GUIDE

AP Calculus BC

12023209

Textbook: Calculus Concepts and Calculators, 2nd

edition

Best, Carter, Crabtree, Venture Publishing

HILLSBOROUGH COUNTY SCHOOL DISTRICT

2010 - 2011

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AP CALCULUS BC OUTLINE

2010-2011

Use of the TI-83, TI-84, TI-89 series or equivalent is allowed on one portion only of the SDHC semester exam. . Page 2 of 8

GRAPHING CALCULATORS: Students are expected to use a graphing calculator throughout the course,

and to learn the paper-and-pencil techniques of calculus. County exams, as well as the AP exam, will have

both calculator and non-calculator parts. Students are expected to be able to do the following on their

graphing calculator:

Plot the graph of a function within an arbitrary viewing window;

Find the zeros of functions (solve equations numerically);

Numerically calculate the derivative of a function; and

Numerically calculate the value of a definite integral.

It is imperative that the teacher establish a level of rigor appropriate to the demands of this course.

Cumulative District exams are provided for Semester 1 and Semester 2. Use of the TI-83, TI-84, TI-89

series or equivalent is allowed on one portion only of the District semester exam.

This outline is based on material supplied by the textbook publisher. It is provided as a general guideline

to the teacher. The suggested problems are not meant to be exclusionary. The timeline is approximate.

The following points are offered:

The teacher may wish to significantly reduce the amount of time suggested for Chapter 1 Functions

and Graphs, and instead review these topics within the study of the Calculus.

Please make note of the cut-off point for material on the SDHC Semester One exam.

The AP Calculus AB syllabus also contains suggested problem assignments for each topic. This

information might be helpful to the AP Calculus BC teacher.

AP CALCULUS BC OUTLINE

2010-2011

Use of the TI-83, TI-84, TI-89 series or equivalent is allowed on one portion only of the SDHC semester exam. . Page 3 of 8

BEGINNING OF SEMESTER ONE/FIRST

QUARTER

Ch 1 Functions and Graphs (10 days)

Section Topic

1.1 What is a Function

1.2 Basic Functions and Transformations

1.3 Linear Functions and Models

1.4 Exponential Functions

1.5 Compound Interest and e

1.6 Inverse Functions

1.7 Logarithms

1.8 Polynomial and Rational Functions

1.9 Composition of Functions

1.10 Trigonometric Functions

Ch 2 Derivative Functions (15 days)

Section Topic

2.1 Average and Instantaneous Velocity

2.2 Derivative of a Function at a point

2.3 The Derivative Function

2.4 Calculating Derivative Numerically

2.5 Critical Numbers; Relative Max/Min

2.6 Inflection points and Second Derivative

2.7 The Limit of a Function

2.8 Continuity

AP CALCULUS BC OUTLINE

2010-2011

Use of the TI-83, TI-84, TI-89 series or equivalent is allowed on one portion only of the SDHC semester exam. . Page 4 of 8

Ch 3 The Definite Integral (9 days)

Section Topic

3.1 Calculating Distance Traveled

3.2 Calculation Areas; Riemann Sums

3.3 Definite Integrals

3.4 The Fundamental Theorem of Calculus

Review/Supplementary Exercises/Test

Ch 4 Differentiation Rules (15 days)

Section Topic

4.1 Derivative Rules for Basic Functions

4.2 Differentiating Exponential Functions

4.3 The Product and Quotient Rule

4.4 The Chain Rule

4.5 Functions Defined Implicitly

4.6 Related Rates of Change

4.7 Approximations

Derivative of Inverse Functions (use Resource Materials)

END OF FIRST QUARTER

AP CALCULUS BC OUTLINE

2010-2011

Use of the TI-83, TI-84, TI-89 series or equivalent is allowed on one portion only of the SDHC semester exam. . Page 5 of 8

Ch 5 More Applications of the Derivative (14 days)

Section Topic

5.1 Increasing and Decreasing Functions

5.2 Applications of the Second Derivative

5.3 Limits at Infinity

5.4 Optimization Problems

5.5 The Mean Value Theorem

5.6 Antiderivatives

Ch 6 Integrals (9 days)

Section Topic

6.1 The Definite Integral Again

6.2 Functions Defined by Integrals

6.3 The Fundamental Theorem Again

6.4 Areas of Plane Regions

Ch 7 Finding Antiderivatives (13 days)

Section Topic

7.1 Antiderivatives

7.2 The Chain Rule

7.3 Integration by Parts

7.4 Trig Functions and Inverses

7.5 Numerical Integration

Supp Review

END OF SEMESTER ONE/SECOND QUARTER

AP CALCULUS BC OUTLINE

2010-2011

Use of the TI-83, TI-84, TI-89 series or equivalent is allowed on one portion only of the SDHC semester exam. . Page 6 of 8

Ch 8 Using the Definite Integral (10 days)

Section Topic

8.1 Net and Total Distance Traveled

8.2 Volume by Slicing

8.3 Volume by Shell Method

8.4 Average Value of a Function

8.5 More Applications of the Definite Integral

Supp Review

Test Chapter 8

Ch 9 Differential Equations (9 days)

Section Topic

9.1 Introduction

9.2 Slope Fields

9.3 Euler's Method

9.4 Separation of Variables

Ch 10 L’Hopital’s Rule, Improper Integrals, Partial

Fractions (10 days)

Section Topic

10.1 L’Hopital’s Rule

10.2 Improper Integrals

10.3 Partial Fractions

10.4 The Logistic Equation

AP CALCULUS BC OUTLINE

2010-2011

Use of the TI-83, TI-84, TI-89 series or equivalent is allowed on one portion only of the SDHC semester exam. . Page 7 of 8

Ch 11 Taylor Polynomials and Series (16 days)

Section Topic

11.1 Polynomial Approximations of Functions

11.2 Sequences and Series

11.3 Power Series

11.4 Representing Functions with Series

11.5 Testing Convergence at Endpoints

11.6 Taylor’s Formula with Remainder (Lagrange)

Ch 12 Parametric Equations, Vectors and Polar

Coordinates (15 days)

Section Topic

12.1 Parametric Euqations

12.2 Length of Arc Described by Parametric Equations

12.3 Motions in a Plane; Vectors

12.4 Limits and Differentiability of Vector-Valued Functions

12.5 Polar Coordinates

12.6 Area and Arc Length in Polar Coordinates

Arc Length for Functions (use Resource Materials)

END OF THIRD QUARTER

AP CALCULUS BC OUTLINE

2010-2011

Use of the TI-83, TI-84, TI-89 series or equivalent is allowed on one portion only of the SDHC semester exam. . Page 8 of 8

Following the end of new material, approximately at the end of Quarter 3, the remaining time before the AP Exam

should be spent preparing for the exam through use of practice exams from various publishers, and through use of

released exams.

RESOURCES

Check the College Board’s Acorn Book, which is updated annually, for the AP Course Description.

The following books are good sources of activities and problems:

Barnes, Mary, Investigating Change. Curriculum Corporation, 1991. Reprinted 1993.

Best, George and Richard Lux, Preparing for the Calculus (AB) Exam 2004 Edition, Venture Publishing.

Finney, Calculus: Graphical, Numeric, Algebraic, Pearson/Prentice Hall DATE????

Hughes-Hallet, Deborah. Calculus. John Wiley & Sons, 1994.

Hyun, Thomas, Acing AP Calculus AB and BC, Greenhall Publishing, 2007

The Ithaca College Group, Calculus An Active Approach with Projects. John Wiley & Sons, 1994.

Note: The Instructor’s Guide for Calculus An Active Approach with Projects has several quizzes and

examinations in the back which contain some of the new types of questions.

Thomas-Finney, Calculus 9th Edition. Addison Wesley, 1996.