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    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.

     
     
     
     

     Please note that the timelines listed below are a guide. Teachers modify their pacing based on student needs in order to ensure concept mastery.
     

    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