AP CALCULUS B/C SYLLABUS for 2007-2008
PEDAGOGICAL APPROACH: The Calculus will be extended as a consistent body of ideas to include the B/C content standards that complement
the single variable Calculus of A/B. Lessons from the A/B syllabus will be used in accelerated fashion to review and reinforce the A/B component
and contextualize new B/C content, but the sequence and extent will be determined in dialogue with the B/C students as their needs become
apparent. Initial emphasis will be given to new B/C content most of which is outlined in the matrix below, while other new B/C content will need
to be contextualized in the A/B content review. Although the formal definition of limit will not be introduced, rigorous proofs for all subsequent
rules and theorems will be demonstrated and discussed. Then, these ideas will be exercised in challenging problem sets that expose students to a
broad range of applications, interpretation of data and explorations with graphing calculator, with lighter representative problem sets for A/B
review and heavier exhaustive problem sets for new B/C content. Writing assignments will assess depth of understanding, study problem solutions
that integrate content ideas and strengthen class dialogue on important anchor problems. AP multiple-choice question format will be emphasized
on benchmark assessments typically given at the end of each chapter. AP rubric for free-response questions will be emphasized by publicly grading
group efforts. TI calculator use will be demonstrated often on the TI Overhead Projection Screen, will be used to explore key concepts and
interpret data. Finally, practice AP exams will raise student awareness of time constraints and individual preparedness, and students will have
multiple opportunities to improve in these areas through class dialogue, concept review and practice.
TEXTBOOK EXAMPLES & HOMEWORK PROBLEM SETS [taken from:] Larson, Ron. CALCULUS (8th Ed.). Houghton Mifflin (2006):
Boston. ISBN 0-618-50300-5. Each student will be provided this textbook in the classroom and one to take home.
SUPPLEMENTAL ACTIVITIES [taken from:] “Mr. V’s Curriculum for the Jaime Escalante Accelerated Math & Science Program/ELAC”
PROBLEM SET FOR PORTFOLIO ESSAYS [taken from:] Third International Study of Mathematics & Science (TIMSS) & Mathematics
Framework for California Public Schools Appendix E (Sample Mathematics Problems for Calculus). California Department of Education (2000):
Sacramento. ISBN 0-8011-1508-6.
PRACTICE TESTS & BENCHMARK ASSESSMENTS [taken/adapted from:] Lederman, David. Multiple-Choice & Free-Response Questions in
Preparation for the AP Calculus (BC) Examination (8th Ed.). D&S Marketing Systems Inc. (2004): Brooklyn. Cade, Sharon, Rhea Caldwell, Jeff
Lucia. Fast Track to a 5: Preparing for the AP Calculus AB and Calculus BC Examinations. Houghton Mifflin (2006): Boston. ISBN 0-61814944-9.
HOMEWORK POLICY: Homework may be submitted for full credit at the beginning of the next class meeting only—for partial credit thereafter.
PORTFOLIO ESSAY POLICY: Although understanding may be achieved by collaboration and solution strategies sometimes borrowed, all writing
must be synthesized individually and must represent the author’s grasp of the material. Then, portfolio essays will be graded by the rubric.
CLASS PARTICIPATION: Active respectful listening and cooperation on class topic always is the expectation.
TOOLS: TI-84 Graphing Calculator (or equivalent). NOTE: Use of this calculator will be demonstrated on the TI Overhead Projection Screen.
GRADE: 40%Homework + 30%Portfolio Essays + 20%Multiple-Choice/Free-Response Benchmarks + 10%Class Participation
AP CALCULUS B/C LESSON MODULES ORGANIZED IN SEQUENCE FROM LEFT COLUMN TO RIGHT COLUMN
INTEGRATION TECHNIQUES,
INFINITE SERIES
PARAMETRIC EQUATIONS & POLAR
L’HOPITAL RULE & IMPROPER
COORDINATES
INTEGRALS
Lesson: 8.1
Lesson: 9.1
Lesson: 10.2
Set: odds
Set: odds
Set: odds
Concept: Basic Integration Rules
Concept: Sequences
Concept: Plane Curves & Parametric
Equations
Lesson: 9.2
Lesson: 8.2
Lesson: 10.3
Set: odds
Set: odds
Set: odds
Concept: Integration By Parts
Concept: Series & Convergences
Concept: Parametric Equations & Calculus
Portfolio Essay: CA Calculus Standard 19.0
Portfolio Essay: CA Calculus Standard 6.0
Lesson: 8.5
Lesson: 9.3
Lesson: 10.4
Set: odds
Set: odds
Set: odds
Concept: Partial Fractions
Concept: The Integral Test & p-Series
Concept: Polar Coordinates & Polar Graphs
Lesson: 9.4
Lesson: 8.7
Lesson: 10.5
Set: odds
Set: odds
Set: odds
Concept: Indeterminate Forms and L’Hopital’s Concept: Comparisons of Series
Concept: Area in Polar Coordinates
Rule
Portfolio Essay: CA Calculus Standard 8.0
Lesson: 8.8
Multiple-Choice Assessment on Parametric
Lesson: 9.5
Set: odds
Set: odds
Equations & Polar Coordinates
Concept: Improper Integrals
Concept: Alternating Series
Portfolio Essay: CA Calculus Standard 22.0
Multiple-Choice Assessment on Integration
Lesson: 9.6
Free-Response Group Project on
Techniques, L’Hopital’s Rule & Improper
Set: odds
Parametric Equations & Polar Coordinates
Integrals
Concept: Ratio & Root Tests
Public Evaluation
Lesson: 9.7
Free-Responses Group Project on
Integration Techniques, L’Hopital’s Rule &
Set: odds
Improper Integrals
Concept: Taylor Polynomials &
Approximations
Public Evaluation
Lesson: 9.8
Set: odds
Concept: Power Series
Portfolio Essay: CA Calculus Standard 24.0
Lesson: 9.9
Set: odds
Concept: Representation of Functions by
Power Series
Lesson: 9.10
Set: odds
Concept: Taylor & Maclaurin Series
Portfolio Essays: CA Calculus Standard 25.0,
26.0
Multiple-Choice Assessment on Infinite
Series
Free-Response Group Project on Infinite
Series
Public Evaluation
VECTORS & VECTOR-VALUED
FUNCTIONS
Lesson: 11.1
Set: odds
Concept: Vectors in the Plane
Lesson: 11.2
Set: odds
Concept: Space Coordinates & Vectors in
Space
Lesson: 11.3
Set: odds
Concept: The Dot Product of Two Vectors
Lesson: 11.4
Set: odds
Concept: The Cross Product of Two Vectors in
Space
Lesson: 12.1
Set: odds
Concept: Vector-Valued Functions
Lesson: 12.2
Set: odds
Concept: Differentiation & Integration of
Vector-Valued Functions
Lesson: 12.3
Set: odds
Concept: Velocity & Acceleration
Lesson: 12.4
Set: odds
Concept: Tangent Vectors & Normal Curves
Multiple-Choice Assessment on Vectors &
Vector-Valued Functions
Free-Response Group Project on Vectors &
Vector-Valued Functions
Public Evaluation
A/B COMPONENT LESSON MODULES (WITH NEW B/C LESSONS EMBEDDED)
LIMITS, CONTINUITY,
DERIVATIVES
APPLICATIONS OF
IVT
DERIVATIVES
Lesson: 2.1
Lesson: 3.3
Lesson: 1.2
Ex: p54:1-24
Set: p103:1-41, 71-95odd
Set: p186:1-45odd
Concept: Informal Definition
Concept: Derivative & the
Concept: Applications of
of Limit; Finding Limits of
Tangent Line Problem;
Derivatives: 1st Derivative
Polynomial, Rational,
Definition of Derivative
Test
Absolute Value,
Trigonometric & Piece-Wise
Discuss Calculator Usage:
Functions Graphically &
Zeroes
Numerically
INTEGRALS
Lesson: 4.1
Set: p255:1-41odd
Concept: Antiderivatives &
Indefinite Integration
APPLICATIONS OF
INTEGRALS
Lesson: 6.1
Set: 1-67,79odd
Concept: Slope Fields; Euler’s
Method
EXTENTION TO
INVERSES
Lesson: 5.1
Set: 1-87odd
Concept: Natural Logs:
Differentiation
Lesson: 6.2
Set: 1-71odd
Concept: Slope Fields; Euler’s
Method; Differential
Equations (Growth/Decay)
Lesson: 5.2
Set: 1-95odd
Concept: Natural Logs:
Integration
Discuss Results & Calculator
Usage: Trace Estimates,
Holes, Zoom
Explore Limits & Interpret
Data w/ TI
Lesson: 1.3
Set: p67:1-85odd
Concept: Evaluating Limits
Analytically
Lesson: 1.4
Set: p78:1-85odd
Concept: Continuity & OneSided Limits; IVT
Explore Limits & Interpret
Data w/ TI
Lesson: 1.5
Set: p88:1-51odd
Concept: Infinite Limits
Lesson: 2.2
Set: p115:1-65odd
Concept: Computation of
Derivatives: Scalar
Multiplication; Additivity
Lesson: 3.4
Set: p195:1-39odd
Concept: Applications of
Derivatives: 2nd Derivative
Test
Lesson: 4.2
Set: p267:1-29, 47-61odd,
Concept: Area Under a Curve
Lesson: 2.3
Set: p126:1-61odd
Concept: Computation of
Derivatives: Product, Quotient
& Higher-Order Rules, Trig &
Special Trig Rules
Lesson: 3.6
Set: p215:1-45odd
Concept: Applications of
Derivatives: Curve Sketching
Lesson: 4.3
Set: p278:1-31odd
Concept: Riemann Sums &
Definite Integrals
Lesson: 2.4
Set: p137:1-65odd
Concept: Computation of
Derivatives: Chain Rule
Lesson: 3.7
Set: p223:1-20
Concept: Applications of
Derivatives: Optimization
Lesson: 4.4
Set: p291:1-49odd
Concept: Fund’l Thm of
Calculus: MVT for Integrals
(Average Value of a Function)
Explore Limits & Interpret
Data w/ TI
Lesson: 3.5
Set: p205;1-33odd
Concept: Limits-at-Infinity
Lesson: 2.5
Set: p146:1-41odd
Concept: Implicit
Differentiation
Lesson: 4.5
Set: p304:1-81odd
Concept: Integration by
Substitution
Lesson: 2.6
Set: p154:1-27odd
Concept: Related Rates
Lesson: 4.6
Set: p314:1-20, 39-40
Concept: Numerical
Integration
Explore Slope Fields w/ TI
Lesson: 6.3
Set: odds
Concept: Separable
Differential Equations;
Logistic Differential
Equations
Lesson: 5.3
Set: 1-89odd
Concept: Derivatives of
Inverses
Lesson: 7.1
Set: 1-89odd
Concept: Area of a Region
between Two Curves
Lesson: 5.4
Set: 1-81odd
Concept: Exponentials:
Differentiation
Discuss Calculator Usage:
Calculating Points of
Intersection, Calculating the
Area Between Two Curves
Lesson: 7.2
Set: 1-77odd
Concept: Volume by Disk
Method
Lesson: 5.5
Set: 1-93odd
Concept: Exponentials:
Integration
Explore Limits & Interpret
Data w/ TI
Lesson: 7.4
Set: 1-65odd
Concept: Arc Length
Lesson: 5.6
Set:1-65,89,91,99odd
Concept: Inverse Trig:
Differentiation
Lesson: 7.5
Set: 1-41odd
Concept: Work
Lesson: 5.7
Set: 1-83odd
Concept: Inverse Trig:
Integration
Discuss Trapezoidal Rule
Discuss Accumulation
Function