(PDF) AP Calculus AB Syllabus - SAU 14 Calculus Syllabus final.pdf · AP Calculus AB Syllabus Primary Textbook ... 2 3.7 Implicit Differentiation ... around the room and visually check - DOKUMEN.TIPS (2024)

AP Calculus AB Syllabus

Primary Textbook Text: Ross L. Finney, Franklin D, Demana, Bert K. Waits, and Daniel Kennedy, Calculus: Graphical, Numerical, Algebraic, 3rd edition. Boston, Massachusetts: Pearson Education Inc., 2007 Two other books are used for supplementary material, including: Ron Larson, Robert Hostetler, Bruce Edwards, Calculus with Analytic Geometry, 6th edition. Boston, Massachusetts: Houghton Mifflin Co, 1998

Course Overview:

This course covers all topics included in the Calculus AB topic outline as it appears in the AP® Calculus Course Description. The AB Calculus course is approximately the equivalent of one

semester of freshman Calculus for students majoring in mathematics, the natural sciences offered or engineering at the local four-year university (MATH 425, University of New Hampshire at Durham). As will be noted, the course covers all of the AB topics as well as others on the university syllabus. The objectives of the course are to have students acquire the skills and knowledge that will enable them to have an appreciation for the power and elegance of calculus, prepare them for college and university course work in mathematics and science, and to enable them to test out of one semester of calculus by scoring well on the AP Calculus exam.

Course Planner A summer review packet is assigned for the students to complete before the start of the school year. This packet covers much of the pre-calculus material in chapter 1 of the text with an emphasis on trigonometry and logarithms. Parts of the assignment are collected electronically over the summer so that students will be making progress throughout the summer and keeping their skills sharp. During the school year students are encouraged to come in outside of class if they have any questions on the material, and to form study groups. The timeline that follows indicates the approximate number of days for each topic covered. The syllabus is meant to be a guideline and adjustments are made throughout the year to reflect the pacing of the students.

Chapter 2

Day Section Topic

2 2.1 Quick Review Summer/Quiz

2 2.1 Rates of Change and Limits

1 2.2 Limits involving Infinity

2 2.3 Continuity

2 2.4 Rates of Change; Tangent lines

2 Review/Test Chapter 2

Chapter 3

Day Section Topic

1 3.1 Derivative of a Function

1 3.2 Differentiability

2 3.3 Rules for Differentiation

1 Quiz; 3.4 Intro Velocity

1 3.4 Velocity and other rates

1 3.5 Derivatives of Trig Functions

2 3.6 Chain Rule

2 3.1-3.6 Review

1 Quiz 3.1-3.6

2 3.7 Implicit Differentiation

2 3.8 Derivatives of Inverse Trig Functions

2 3.9 Derivatives of exponential and logarithmic functions

2 Review/Test Chapter 3

Chapter 4

Day Section Topic

1 4.1 Extreme Values

1 4.2 Increasing/Decreasing

1 4.2 Extreme Values of Functions Mean Value Theorem

1 Quiz 4.1-4.2

1 4.3 Connecting f’ and f” with f

2 4.4 Modeling and Optimization

1 Quiz 4.3-4.4

1 4.5 Linearization and Newton’s Method

2 4.6 Related Rates

1 Review Chapter Review

1 Test Chapter

Chapter 5

Day Section Topic

1 5.1 Estimating with Finite Sums

2 5.2 Definite Integrals

1 Quiz 5.1-5.2

2 5.3 Definite Integral and Antiderivatives

2 5.4 Fundamental Theorem of Calculus

2 5.5 Trapezoidal and Simpson’s Rules

2 Review/Test Chapter 5

Chapter 6

Day Section Topic 1 6.1 Antiderivatives and Indefinite Integrals 2 6.2 Integration by Substitution 1 Quiz 6.1-6.2 1 6.1 IVP 1 6.1 Slope Fields 2 6.3 Integration by Parts 2 6.4 Exponential Growth and Decay 1 Quiz 6.1-6.4 2 6.6 Euler's Method and Slope Fields 2 Review/Test Chapter Review

Chapter 7

Day Section Topic

1 7.1 Integral as Net Change

2 7.2 Area

1 Quiz 7.1-7.2

2 7.3 Volumes

1 Quiz 7.3

1 8.1 L’Hôpital’s Rule

10 Review AP Review

Review and Preparation for the AP Exam – Approximately 4 weeks Practice exams are given, scored and analyzed. Some are done in groups while others are completed individually. Some review time over the April vacation will be scheduled.

Teaching Style My classes are a combination of lecture and group work. I encourage students to work together as much as possible during class and when doing their assignments outside of class. A typical class period will have a short warm-up problem that may deal with the current material, or a review problem of material covered earlier in the year. While the students are working on the warm-up, I will walk around the room and visually check the homework. Students let me know at this time what problems are the ones that need to be discussed. After going over the warm-up problem, we will discuss the homework. Often I will have students present their solutions on the board, or have them orally describe their solution while I write on the board. I encourage as many different approaches to a problem as I can foster. I expect that the students will use numerical methods or technology to ensure that their answers are reasonable. Students are shown, and are expected to know, how to do problems numerically, graphically and symbolically. I use many old AP free response questions in class and on tests, with an emphasis on the questions that ask for explanations and justifications of answers.

Weekly AP Free Response Problem(s) On a weekly basis, students are given up to six free response questions to solve. Students are encouraged to work with each other on these, but individual written work is required on the part of all students. These are graded in class using scoring guidelines similar to those developed by the College Board. Students grade each other’s papers.

Technology It is essential that students multiple methods of attacking any given problem. Students are encouraged through modeling to use graphical, numeric and algebraic methods to both solve problems and express their ideas. All students in the class have their own TI-83 or 84. Steps are taken to ensure the appropriate use of calculators without fostering dependence. Many topics in calculus lend themselves to using technology as a learning tool. Students are shown how to zoom in on differentiable functions to see that they are locally linear, while non-differentiable functions are not. During the second semester students are shown how to calculate the numerical integral on their calculator and are expected to verify results when they have access to a calculator. There are PowerPoint lectures that accompany the text. While I do not use them in class when I am presenting the material, I do make them available as a resource for students who are either absent or who feel they need a bit more instruction on a particular topic.

Student Evaluation Quarter grades are determined by quizzes, chapter tests and homework checks. Depending on the material, quizzes may be either with or without calculator. Chapter tests are divided into a calculator part and a non-calculator part. There is a semester exam that closely models a shortened AP exam (1.5 hours in length divided into a calculator part and a non-calculator part as well as multiple choice and open response questions). The final exam is a 1.5 hour exam given about four weeks after the AP exam. It is modeled closely on the sample Calculus I (MATH 425) final exam provided by the University of New Hampshire.