Calculus AB
2010-2011
Brief Description of Course
Calculus AB is primarily concerned with developing the student’s understanding of the concepts of calculus and providing experience with its methods and applications. The course emphasizes a multi-representational approach to calculus, with concepts, results, numerically, analytically, and verbally. This course is a rigorous and intense study of calculus requiring a minimum of five hours per week outside the class. A graphing calculator is provided.
Unit Information
Unit Name or Timeframe: Prerequisites for Calculus (1 - 2 weeks)
Content and/or Skills Taught: Linear equations. Functions and Graphs. Exponential Functions. Functions and Logarithms. Trigonometric Functions. {Review graphing functions using the TI83. Calculating intersections and zeros}
Major Assignments and/or Assessments: Chapter Test
Unit Name or Timeframe: Limits and Continuity (2 - 3 weeks)
Content and/or Skills Taught: Rates of Change and Limits. Limits involving Infinity. Continuity. {Explain the relationships between continuity and limits} Rates of Change and Tangent Lines.
Major Assignments and/or Assessments: Chapter Test. {Most tests include a combination of questions. Some multiple choice, short answer, and free response. Students are required to communicate their work mathematically as well as in the written form to gain practice for the AP exam, college, and real life.}
Unit Name or Timeframe: Derivatives (3 - 4 weeks)
Content and/or Skills Taught: Derivative of a Function. Differentiability. Rules for Differentiation.
1 {Calcululating Numerical Derivatives on the Calculuator} Velocity and Other Rates of Change. {Analyzing Numerical Tables of Velocity and Acceleration} Derivatives of Trigonometric Functions. Chain Rule. {Derivatives of tables of numerical values} Implicit Differentiation. Derivatives of Inverse Trigonomteric Functions. Derivatives of Exponential and Logarithmic Functions.
Major Assignments and/or Assessments: Two Chapter Tests.
Unit Name or Timeframe: Applications of Derivatives (3 weeks)
Content and/or Skills Taught: Extreme Values of Functions. Mean Value Theorem. Connecting the first and second derivatives graphically and analytically. {Connecting the first and second derivatives numerically using tables} Modeling and Optimization. Linearizations and Newton’s Method. Related Rates. {Solving and analyzing related rate word problems}
Major Assignments and/or Assessments: Two Chapter Tests. Optimization/Related Rate Project. {Students are required to create their own Related Rate problem with all appropriate descriptions and conclusions}
Unit Name or Timeframe: The Definite Integral (3 - 4 weeks)
Content and/or Skills Taught: Estimating with Finite Sums. {Interpreting tables and charts to calculate Riemann Sums} {RAM program on the TI 83 for calculating Riemann sums} Definite Integrals. {Calculate Integrals using the TI83 Calculutor} Definite Integrals and Antiderivatives. Fundamental Theorem of Calculus. Trapezoidal Rule. {Trapezoidal rule gievn a table of values. Numerical representations}
Major Assignments and/or Assessments: Chapter Test. Trapezoidal Rule Project. {Project requires detailed descrition of the application and purpose of the Trapezoidal Rule. Students must be able to analyze a table of numerical values and calculate the trapezoidal area and explain the results and the relationship to Calculus}
2 Unit Name or Timeframe: Differential Equations and Mathematical Modeling.
Content and/or Skills Taught: Antiderivatives and Slope Fields. {Slope Fields on the TI 83} Integration by Substitution. Integration by Parts. (Cover after the AP exam in May) Exponential Growth and Decay. Population Growth.
Major Assignments and/or Assessments: Chapter Test.
Unit Name or Timeframe: Applications of Definite Integrals. (2 - 3 weeks)
Content and/or Skills Taught: Integral as Net Change. Areas in the Plane. Volumes. (Washer method only. Cover the Shell Method after the AP exam in May) {Using the TI 83 to calculate areas and volumes of regions}
Major Assignments and/or Assessments: Chapter Test. {Two day test. One day calculator, one without}.
Unit Name or Timeframe: L’Hopital’s Rule. (2 days)
Content and/or Skills Taught: L’Hopital’s Rule for Limits.
Major Assignments and/or Assessments: Quiz on L’Hopital’s Rule
Textbooks
Title:Calculus: Graphical, Numerical, and Algebraic
Publisher: Pearson Prentice Hall
Published Date: January, 2010
Author: Franklin Demana
Second Author: Bert K. Waits
Description:
3 Other Course Materials
Material Type:Graphing Calculator
Description: TI-83 plus Graphing Calculator.
Material Type:Software
Description: Derive Mathematical Software.
Material Type:Other
Description: Workbook. Published by D&S Marketing Systems, INC. Multiple Choice & Free Response Questions in Preparation for the AP Calculus (AB) Examination. 8th Edition.
Websites
URL:Collegeboard.com
Description: Previous AP exam questions.
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