AP BC Calculus (6 hours per week) The Main Books Source:

Finney, Ross L., Franklin Demana, Bert Waits, and Daniel Kennedy. Calculus:

Graphical, Numerical, Algebraic. AP Edition. Fourth Edition. Pearson.2012

Supplemental Books Source:

S.P. Thompson Calculus Made Easy. Second Edition Enlarged. The Macmillan

Company, New York, 1943 (online version)

P. Dawkins. Calculus I. Complete Practice Problems (online version)

Course Revision:

Shirley O. Hockett, M.A. and David Bock, M.S. Barron’s AP Calculus 2008

Week Chapter Contents Critical Thinking

Questions

1

2

L.1-2 Review of AP

Calculus AB

L.3-4 Review of AP

Calculus AB

L.5-6 Review of AP

Calculus AB

L.7-8 Review of AP

Calculus AB

Fundamental Theorem of Calculus,

Part I. Graphing of function .)( dttff x

a

Integration by parts. Euler’s Method.

Logistic grows model. The logistic

differential equation.

Length of a curve. Rectangular

Approximation Method (RAM).

pp.306-309 #14-

20, 35-40, 45-48

pp.331-335 #21-

24, 29-34

pp.377-380 #30-

34, 38, 45-46, 50

pp.273-277 #4,

7, 9-12, 18

3

L9-10 Chapter 8.

Section 8.1.

Application of

Definite Integrals

pp.383-402

L11-12 Chapter 8.

Section 8.2.

Application of

Definite Integrals

pp.383-402

L13-14 Chapter 8.

Section 8.3.

Application of

Definite Integrals

pp.383-402

L15-16 Chapter 8

Section 8.4

Application of

Definite Integrals

pp.403-422

Integral as Net Change. Linear

motion revisited. Consumption over

time. Net change from data. Work.

Areas in the Plane. Area between

curves. Area enclosed by interesting

curves. Boundaries with changing

function. Integrating with respect to .

Saving time with geometry formulas.

Volumes. Volume as an integral.

Square cross section. Circular cross

section. Cylindrical shells. Other cross

section.

Lengths of Curves. A sine wave.

Length of smooth curve. Vertical

tangents, corners and cusps.

pp.389-393 #11;

17-20; 27

pp.399-402 #9;

10; 13; 14;

36-38; 43

pp.410-415 #2;

7-10; 26-28; 43;

48; 49

pp.419-422

#11-15; 22-24

L17-18 Chapter 8

Section 8.5

Application of

Definite Integrals

pp.423-433

Applications from Science and

Statistics. Work revisited. Fluid force

and fluid pressure. Normal

probabilities.

pp.429-433 #12;

17; 23; 24; 31;

32

4

5

L19-20 Chapter 9

Section 9.1

Sequences,

L’Hopital Rule and

Improper Integral

pp.439-456

L21-22 Chapter 9

Section 9.2

Sequences,

L’Hopital Rule and

Improper Integral

pp.439-456

L23-24 Chapter 9

Section 9.3

Sequences,

L’Hopital Rule and

Improper Integral

pp.457-462

L25-26 Chapter 9

Section 9.4

Sequences,

L’Hopital Rule and

Improper Integral

pp.463-472

Sequences. Defining a sequence.

Arithmetic and geometric sequences

Graphing a sequence. Limit a

sequence.

L’Hopital Rule. Indeterminate form

0

0. Indeterminate forms

, 0

and )( . Intermediate forms 1 ,

0 0 and 0 .

Related rates of grows. Comparing

rate of grows. Using L’Hopital rule to

compare grows rates. Sequential

versus binary search.

Improper Integrals. Infinite limits of

integration. Integrands with infinite

discontinuities.

pp.445-447 #19;

21; 31-40

pp.454-456 #27;

33-52 (even)

pp.461-462

#15-20; 35-38,

40, 45

pp.471-473

#35-42; 55

6

L27-28 Chapter 10 Section 10.1 Infinite Series pp.477-498 L29-30 Chapter 10 Section 10.2 Infinite Series pp.477-498 L31-32 Chapter 10 Section 10.3 Infinite Series pp.499-516 L33-34 Chapter 10 Section 10.4 Infinite Series

Power Series. Geometric series Representing functions by series. Differentiation and integration. Identifying a series. Taylor Series. Constructing a series.

Series for sinx and cosx. Beauty bare.

Maclain and Taylor series. Combining Taylor series. Table of Maclain series. Taylor’s Theorem. Taylor polynomials. The remainder. Bounding the remainder. Lagrange form of the reminder. Euler’s formula Radius of Convergence.

Convergence. n th term test.

Comparing nonnegative series. Ratio

pp.485-487 #2; 21-24; 48; 51 pp.496-498 #5-12 even; 18-21; 35 pp.504-506 #11-13; 27-29; 35; 39

pp.515-516 #18-22; 36-42;

7

8-9 10-12

pp.499-516 L35-36 Chapter 10 Section 10.5 Infinite Series pp.517-530

L37-38 Chapter 11 Section 11.1 Parametric functions pp.537-543 L39-40 Chapter 11 Section 11.2 Parametric functions pp.544-566 L41-42 Chapter 11 Section 11.3 Parametric functions pp.544-566 L43-55 Final Exam and Review L56-74 Review for AP BC Calculus Exam

test. Endpoint convergence. Testing Convergence at Endpoint. Integral test. Harmonic series and p-series. Comparison tests. Alternating series. Absolute and conditional convergence. Intervals of convergence. A world of caution. Parametric functions. Parametric curves in the plane. Slope and concavity. Arc length. Cycloids Vectors in the plane. Two-dimensional vectors. Vector operations. Modeling planar motion. Velocity, acceleration and speed. Displacement and distance traveled. Polar Functions. Polar coordinates. Polar curves. Slopes of polar curves. Areas enclosed by polar curves. A small polar gallery. In this course students take a comprehensive final exam in similar format to AP Exam. This exam consists of both free response and multiple-choice questions, including calculator and non-calculator active portions. During review, students work collaboratively in cooperative groups while working out AP style questions, including previously released AP questions. Students prepare for the AP Calculus BC exam during class time for approximately 3 weeks prior the exam date.

52-54 pp.528-530 #18-22; 46-50; 59; 62 pp.541-543 #13-16; 30-33; 36; 37; 43 pp.552-554 #25; 26; 33; 38; 51 pp.564-566 #26-30; 35-38; 42; 50; 52; 60 Use D. Bock, S. Hockett Barrons AP Calculus 11 Edition book