1.
AP Calculus BC
Syllabus
Textbook:
Finney, Ross L., et al. Calculus: Graphical, Numerical, Algebraic. Boston,
Massachusetts: Pearson Prentice Hall, 2007, 3rd Edition.
Chapter 1: Prerequisites for Calculus (5 days)
Symbols in Calculus
Regression Analysis
Intervals, Boundaries, Domain and Range
Even/Odd functions
Absolute Value functions
Growth/Decay/Exponential functions
Inverses and Logarithmic functions
Parametric equations
Chapter 2: Limits and Continuity (7 days)
Average and Instantaneous Speed
Definition of limits
Properties of limits
One-sided and Two-sided limits
Sandwich/Squeeze Theorem
Asymptotes
End behavior models
Continuity/Discontinuity
Intermediate Value Theorem for Continuous functions
Tangent to a curve
Slope of a curve
Normal to a curve
Chapter 3: Derivatives (20 days)
Definition of derivative
Notation
Relationships between graphs of f and f’
Graphing derivatives
One-sided derivatives
Differentiability
Intermediate Value Theorem
Rules for differentiation
Horizontal tangents
Product and Quotient rules
Higher order derivatives
Distance/Velocity/Acceleration
Derivatives of Trigonometric functions
2.
Chain rule
Implicit Differentiation
Derivatives of Inverse Trigonometric functions
Derivatives of Exponential and Logarithmic functions
Chapter 4: Applications of Derivatives (14 days)
Extreme Values of functions
Absolute vs. Local
Extreme Value Theorem
Critical points
Mean Value Theorem
Increasing/Decreasing functions
First and Second derivative tests
Concavity/Points of inflection
Optimization
Linear Approximations
Newton’s Method
Differentials
Related rates
Chapter 5: The Definite Integral (15 days)
Estimating with Finite Sums
Rectangular Approximation
Riemann Sums
Definite Integrals
Integration
Area under a curve
Mean Value Theorem for Definite Integrals
Fundamental Theorem of Calculus
The Trapezoid Rule
Chapter 6: Differential Equations and Mathematical Modeling (19
days)
Slope fields
Euler’s Method
Antidifferentiation by Substitution
Leibniz Notation
Substitution in Definite and Indefinite Integrals
Integration by Parts
Tabular Integration
Exponential Growth and Decay
Newton’s Law of Cooling
Logistic Growth
3.
Chapter 7: Applications of Definite Integrals (14 days)
Net Change
Area
Volume
Cross Sections
Lengths of Curves
Sine waves
Vertical Tangents, Corners and Cusps
Fluid Force and Fluid Pressure
Normal Probabilities
Chapter 8: Sequences, L’Hôpital’s Rule, and Improper Integrals (11
days)
Arithmetic and Geometric sequences
Graphing sequences and limits
Sandwich Theorem for sequences
Absolute Value Theorem
L’Hôpital’s Rule
One-sided limits, Indeterminate forms
Rates of Growth
Improper Integrals
Partial Fractions
Integrands and Infinite limits
Integrands and Infinite discontinuities
Tests for convergence/divergence
Chapter 9: Infinite Series (19 days)
Power series
Infinite series
Differentiation and Integration
Taylor Series
Maclaurin and Taylor Series
Taylor’s Theorem
Remainder Estimation Theorem
Euler’s formula
Tests for Convergence/Divergence
Ratio Test
Radius and Intervals of Convergence
Chapter 10: Parametric, Vector, and Polar Functions (13 days)
Parametric functions
Slope and Concavity
Cycloids
Vectors
4.
Motion
Velocity/Acceleration/Speed
Polar Coordinates
Polar Graphing
Area Enclosed by Polar Curves
Teaching Strategies:
Many students will enter this class with a basic knowledge of the uses of
the graphing calculator. Throughout the course students will fine tune
their calculator skills using it as a tool to investigate, solve and support
their work.
Students will be assigned homework daily which will include
opportunities to practice with their graphing calculator, as well as pencil
and paper problems instigating verbal support of solutions, and
opportunities to make connections using both methods. Students will
practice regularly for the AP exam with sample tests taken from previous
AP exams. This practice may be in the form of in class group or
individual work as well as take home in addition to or in place of daily
homework.
Quizzes will be given once or twice a week and cover the most recent
material being taught as well as small pieces of review from previous
chapters. Tests are taken at the end of each chapter, and also include
questions pertaining to that chapter as well as review from previous
chapters and practice AP questions. At the end of each term (quarter)
students will take a term exam covering the material from the current
term as well as previous terms. Questions on quizzes and tests will be a
combination of multiple choice and free-response and will also be broken
into both calculator and noncalculator sections.
It is important for students to support their work verbally, so they will be
asked to present a topic once each semester. The class will be taught
using SMART Board technology which will allow the use of alternate
types of presentation and a variety of instructional tools both for the
instructor and the students. Students will also be able to refer back to
the daily lessons from their home computers.
Three weeks before the AP exam, students will do intense preparation for
the test including group collaboration and individual more structured
practice. The importance of complete solutions and clear verbal
explanations supporting the solutions will be stressed.
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