Ap calculus bc


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Ap calculus bc

  1. 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. 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. 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. 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.