N/A Foerster textbook (Kendall Hunt) sections: 5-3, 5-4, 5-6, – textbook supplemental materials (explorations) TI-89 graphing calculator, desmos.com selected MC/FR items from released AP exams College AP Calculus AB course description Subject: AP Calculus AB 10/11/12 Suggested Timeline: 14 42 minute periods – Unit Title: Unit 8 Integral II – Unit Overview/Essential Understanding: In this unit, students learn some important applications of the definite integrals: physical area, physical volume, and accumulated change. Unit Objectives: Upon completion of this unit, students will demonstrate an understanding of the following topics and/or be able to do the following: determine whether a definite integral represents physical area calculate the physical area bound between 2 or more curves calculate volumes of revolution discs or washers calculate volume of a with known cross sections solve definite integral problems applied to other scenarios involving accumulated change Focus Standards Addressed in this Unit: EK 3.4A1 A function defined as an integral represents an accumulation of a rate of change – EK 3.4A2 The definite of the rate of change of a quantity over an interval the net change of the quantity over that interval – EK 3.4D1 Areas of certain regions in the plane can be calculated with definite integrals – EK 3.4D2 Volumes of solids with known cross sections, including discs and washers, can be calculated with definite integrals – EK 3.4E1 The definite integral can be used to express information about accumulation and net change in many applied contexts – Important Standards Addressed in this Unit: EK 3.3B2 If f is continuous on the interval and F is an antiderivative of f, then – Misconceptions: Students sometimes believe that there exists a different initial setup for finding volumes with integrals, when in fact the procedure is exactly the same as finding area with the definite integral. Students should be repeatedly asked to identify regions, draw
N/A Foerster textbook (Kendall Hunt) – sections: 5-3, 5-4, 5-6, textbook supplemental materials (explorations) TI-89 graphing calculator, desmos.com selected MC/FR items from released AP exams College AP Calculus AB course description Subject: AP Calculus AB 10/11/12 Suggested Timeline: 14 – 42 minute periods Unit Title: Unit 8 – Integral II Unit Overview/Essential Understanding: In this unit, students learn some important applications of the definite integrals: physical area, physical volume, and accumulated change. Unit Objectives: Upon completion of this unit, students will demonstrate an understanding of the following topics and/or be able to do the following: determine whether a definite integral represents physical area calculate the physical area bound between 2 or more curves calculate volumes of revolution discs or washers calculate volume of a with known cross sections solve definite integral problems applied to other scenarios involving accumulated change Focus Standards Addressed in this Unit: EK 3.4A1 – A function defined as an integral represents an accumulation of a rate of change EK 3.4A2 – The definite of the rate of change of a quantity over an interval the net change of the quantity over that interval EK 3.4D1 – Areas of certain regions in the plane can be calculated with definite integrals EK 3.4D2 – Volumes of solids with known cross sections, including discs and washers, can be calculated with definite integrals EK 3.4E1 – The definite integral can be used to express information about accumulation and net change in many applied contexts Important Standards Addressed in this Unit: EK 3.3B2 – If f is continuous on the interval and F is an antiderivative of f, then Misconceptions: Students sometimes believe that there exists a different initial setup for finding volumes with integrals, when in fact the procedure is exactly the same as finding area with the definite integral. Students should be repeatedly asked to identify regions, draw
2017-AP-Calculus-AB-BHASD-Math-Curriculum.docx