AP Calculus BC

AP Calculus BC:This Advanced Placement course completes the study of the BC level of Advanced Placement Calculus. The students are required to pay the fee and take the Calculus BC Advanced Placement Exam in order to receive the weighted final grade. The final exam is a departmental exam.

Unit 1

Transcendental Functions- Trig Functions

September

Section

Concepts

Anton Resources

2.5

Find the limit of trig functions

2.5

Find derivatives of all six trig functions

2.5

Find anti-derivatives of all six trig functions

2.5

Find derivatives and evaluate integrals of trig based functions.

2.5

Find the derivatives of inverse sine/tangent functions.

Unit 2

Tools of Integration

Sep-Oct

Section

Concepts

Anton Resources

4.1

An Overview of the Area Problem

4.2

The Indefinite Integral

4.3

Integration by Substitution

4.4

The Definition of Area as a Limit

Pages 281-286

4.5

The Definite Integral

Pages 287-299

4.6

The Fundamental Theorem of Calculus – Parts I & II

4.7

Rectilinear Motion and Integration

Pages 309-321

4.8

Average Value of Function and its Applications

Pages 322-331

4.9

Evaluating Definite Integrals by Substitution

Pages 332-336

Pages

Unit 3

Applications of Integrals

October

Section

Concepts

Anton Resources

5.1

Area between two curves

Pages 347-354

5.2

Volume by Slicing – disks and washers

5.3

Volume by Cylindrical Shell

5.4

Length of a Plane Curve

5.5

Work

Optional: Find surface area of a solid of revolution.

Optional: Use integration methods to investigate fluid pressure.

Unit 4

Motion

October

Section

Concepts

Anton Resources

4.7

Motion

4.7

Find the velocity given position in terms of time

4.7

Find the acceleration from velocity

4.7

Find linear approximations by means of differentials

 End of Quarter 1

Unit 5

 Exponential, Logarithmic, and Inverse Trigonometric Functions

Nov-Dec

Section

Concepts

Anton Resources

6.1

Exponential and Logarithmic Functions

6.2

Derivatives and Integrals Involving Logarithmic Functions

6.3

 Derivatives of Inverse Functions; Derivatives and Integrals Involving Exponential Functions

6.4

 Graphs and Applications Involving Logarithmic and Exponential Functions

6.5

 L’Hopital’s Rule; Indeterminate Form

6.6

Logarithms and other functions defined by integrals

6.7

Derivatives and Integrals involving Inverse Trig Functions

Unit 6

Integration Techniques

Dec-Jan

Section

Concepts

Anton Resources

7.1

Overview of Integration Methods

7.2

Integration by Parts

7.3

Integrating Trig Functions (powers of sine and cosine)

7.4

Trig Substitution

7.5

Integrating Rational Functions by Partial Fractions

7.7

Numerical Integration; Simpson’s Rule

7.8

Improper Integrals

 End of Quarter 2

Unit 7

Series and Sequences

March

Section

Concepts

Anton Resources

10.1

Parametric Equations: Tangent Lines and Arc Length for Parametric Curves

10.2

Polar Coordinates

10.3

Tangent Lines, Arc length, and Area for Polar Curves

Unit 8

Modeling with Differential Equations

February

Section

Concepts

Anton Resources

8.1

Modeling with Differential Equations

8.2

Separation of Variables

8.3

Slope Fields, Euler’s Method

8.4

First-Order Differential Equations and Applications

 End of Quarter 3

Unit 9

Series and Sequences

Feb-Mar

Section

Concepts

Anton Resources

9.1

Sequences

9.2

Monotone Sequences

9.3

Infinite Series

9.4

Convergence Tests

9.5

The Comparison, Ratio, and Root Tests

9.6

Alternating Series; Absolute and Conditional Convergence

9.7

Maclaurin and Taylor Polynomials

9.8

Maclaurin and Taylor Series; Power Series

9.9

Convergence of Taylor Series

9.10

Differentiating and Integrating Power Series; Modeling with Taylor Series

Unit 10

Parametric, Polar and Vector Calculus

April

Section

Concepts

Anton Resources

10.1

Parametric Equations

10.2

Polar Review

10.3

Area of Polar Curves

12.1

Vectors

12.6

Vector Valued Functions

Review for AP Exam

 Final Exam