AP Calculus

This course will uncover every topic outlined in the AP Calculus AB Course Description booklet. Additionally, we will discuss integration by parts and the logistic model before the AP exam. The purpose of this course is to present a strong understanding of calculus concepts and to be able to use these ideas in problem solving scenarios and be able to use the appropriate technology. At the end of this course, each student will be able to pass the AP exam and continue their success in any future calculus course taken at a university or college. 

Unit One: Prerequisites for Calculus (7 days: 1 quiz and 1 test)

                 Lines

                 Functions and Graphs

                 Exponential Functions

                 Functions and Logarithms

                 Trigonometric Functions

Unit Two: Limits and Continuity (7 days: 1 quiz and 1 test)

                 Rates of Change and Limits

                 Limits Involving Infinity

                 Continuity

                 Rate of Change

                 Tangent Lines           

Unit Three: Derivatives (12 days: 3 quizzes and 1 test)

                 Definition of a Derivative

                 Derivative of a Function

                 Differentiation Formulas

                 Derivatives of Trigonometric Functions

                 Chain Rule

                 Implicit Differentiation

                 Derivatives of Inverse Trigonometric Functions

Derivatives of Logarithmic and Exponential Functions

Unit Four: Applications of Derivatives (11 days: 2 quizzes and 1 test)

                 Rates of Change

                 Related Rates

                 Extreme Values of Functions

                 Mean Value Theorem

                 Connecting f’ and f” with the Graph of f

                 Limits at Infinity

                 Curve Sketching

                 Modeling and Optimization

                 Newton’s Method

Review and Derivative Exam (2 days)

Unit Five: The Definite Integral (6 days: 1 quiz and 1 test)

                 Areas and Distances

                 Definite Integrals

                 Definite Integrals and Antiderivatives

                 Fundamental Theorem of Calculus

                 Trapezoidal Rule

Unit Six: Indefinite Integrals and Mathematical Modeling (8 days: 1 quiz and 1 test)

                 Antiderivatives and Slope Fields

                 Integration by U-Substitution

                 Integration by Parts

Review and Final (Mock) Exam (2 days)

Unit Seven: Applications of Definite Integrals (11 days: 3 quizzes and 1 test)

                 Integral as Net Change

                 Areas in the Plane (between Curves)

                 Volumes

                 Work

                 Lengths of Curves or Average Value

Review and Preparation for the AP Exam (~10 days)

                 2 quizzes a week (5 multiple choice questions or an open ended question – taken

                 from previous AP exams)

                 Final Exam – A full AP exam 

The expectation of every student in this class is to understand calculus well enough to pass the AP exam in May, ideally with a score of 3, 4 or 5. As a class we must: be willing to make mistakes, but learn from them, work together, both in class and outside of class, ask questions in class and come in for help before or after school-we also meet occasionally during PPT time, learn to study at home, and learn how to take tests. But most importantly, striving to understand how the concepts work, not just   memorizing, and that takes practice.

                 Our school has 85 minute classes, five days a week during second semester. The class is a combination of lecture and group work. Typically each day will have lecture and collaborative work.  In class, students are given some time to work on assignments, but it is expected they work 30 minutes a night at home. Problems given come from our book, supplemental materials or texts mentioned earlier, various calculus prep books, and numerous past AP free response problems. In class we will present problems on the board, show multiple ways to get an answer and discuss any mistakes that arise. The students need to be able to explain why, not just how.

                 From the beginning, students are shown how to do a problem numerically, graphically, and analytically. In Calculus, it is important to use a calculator correctly and determine how the calculator can lie if not used correctly, i.e. using an inappropriate window and syntax.

Every student in class is expected to have a graphing calculator. We explore finding solutions graphically and numerically both with and without the calculator. The four required skills are explained (graphing within an arbitrary window, solving an equation, and calculating the derivative or definite integral), as are the restrictions of calculator use. I stress the use of the calculator as a tool, something to use to find a numerical value of a definite integral if it cannot be done analytically or using the table function to explore a solution numerically, not to use the calculator excessively.

                 I may use a TI Viewscreen so we can work together in class. It takes work and practice for the students to learn how to use the calculator. Assignments, quizzes, tests, and exams are divided into calculator and non-calculator sections. 

Quizzes, tests, and exams make up about 70% of the student’s grade. Points are accumulated over the semester for a final grade. Assignments and past AP open ended problems make up the remaining 30% of the grade.  Homework will be collected daily. All problems are graded on correctness, similar to the free response grading. This makes up 80% of the grade, while 20% is graded on completeness. Quizzes during the year will be multiple choice, short answer, or AP free response. Tests cover one chapter, while exams cover multiple chapters and will have the same set-up as quizzes.

                 During the second term, there will be assignments made of previous problems on AP exams. They are graded on the nine point AP system. The math labs make up about 20% of the semester grade. During the review period, we will quiz two or three times a week. The final exam is a previously released AP exam given over the course of two days. One day is the non-calculator and calculator multiple choice sections, while day two is the calculator and non-calculator open ended questions. This test will make up 10% of the course grade. After the exam, we discuss topics outside the AB curriculum and the students are responsible for presenting a project incorporating calculus.