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### Course Syllabus

AP Calculus AB Syllabus

Instructor: Mr. Minnier

Shikellamy School District

School Year: 2015 – 2016

Course Overview

This course is designed to cover all of the topics listed in “Topic Outline for Calculus AB” listed in the AP Course Description. This is accomplished through direct instruction, student assignments, projects, and AP Test practice. A major goal of this course is that students will develop a comprehensive understanding of limits, derivatives, integrals, approximation, and their applications. To accomplish this, students will be asked to approach the calculus concepts graphically, numerically, analytically, and verbally.

This course begins with a quick review of some important pre-calculus topics. This will include but will not be limited to the following: basic functions, analysis of graphs, equations of functions, domain and range, odd and even functions, finding trig values, and, working with basic exponential and logarithm rules. We will use this prerequisite knowledge of multiple representations of functions to develop a deeper understanding of the differential and integral calculus concepts. The course then progresses through all the topics that are listed in the “Topic Outline for Calculus AB”.

All students will take the AP Calculus AB exam at the end of the course. Therefore, we will be completing practice AP test problems throughout the year. This will include multiple choice and free response problems. Therefore, students are expected to communicate both in written form and verbally about the connections they see graphically, numerically, and analytically throughout this course.

Graphing Calculators

Graphing calculators are used throughout this course. The TI83+ is the calculator that is used. Students who do not have their own calculator are provided with one. Calculators are used to look at functions, find zeros of functions, numerically calculate the derivative of a function, and numerically calculate the value of a definite integral. This is accomplished by using the calculator to investigate functions and develop familiarity with the capabilities of the calculators. While calculators are valuable, students are expected to find solutions with and without the calculator.

Calculator Activities

Students using calculators to both interpret their results and support their conclusions. An example of this is through the use of calculator activities.  Students will complete various investigations and activities throughout the course. One example of this is an investigation on limits. Students are asked to look at various functions on their calculators to estimate limits. Students look at tables and graphs to approximate limits. Students then find limits analytically and compare their findings to their approximations.

Other activities include an activity on “Zooming to See Differentiability”. Students are given two functions and asked if either function is differentiable at x=0. By using the zoom feature, students soon discover the concept of local linearity. Group and class discussion quickly leads to the topic of when the derivative might fail. The graphing calculator allows students to support their work graphically and to make conjectures regarding the behavior of functions, limits, and other topics.

Instruction

Topics are covered in a variety of ways including lecture, student investigation, and discussion. Students are encouraged to ask questions as they arise. Connections are made between current topics and previous material. The goal of this is to help students see calculus as a “cohesive whole” and not merely a “collection of recipes or algorithms”.

Proper techniques for showing work and justifying solutions are modeled throughout the course. Students are required to present their work to the class at various times. This provides the students with necessary practice in both written and verbal explanation of the topics that are covered.

Assessment

Grades will be issued on a point value basis. Each quarter grade can be calculated by dividing the number of points earned by the total points possible.

Students are assessed in a variety of ways. Problems and exercises are assigned from the textbook and other sources. Released AP questions are used throughout the course on assessments, homework, and other assignments. Students are required to show understanding in their written work. This is especially true of free response questions.

Throughout the course, students will keep a journal. Within their journal, students will be asked to explain and justify solutions in written sentences. Justifying work helps students gain a deeper understanding of the material and gives them practice in verbalizing their work.

A variety of in-class and out-of-class investigations and projects are also used both develop and enhance student understanding throughout the course.

Students take quizzes and tests throughout the year on all topics. Quizzes and tests will include multiple choice and free response questions. Students will be asked to explain and justify their work in written sentences.

Students will also complete a released AP exam in order to gain experience prior to taking the actual test.

Primary Textbook

Larson, Ron; Edwards, Bruce. Calculus of a Single Variable, Ninth and AP Edition, California: Brooks/Cole, 2010.

Topic and Pacing Outline

This is a general guide. Extra days will be added as needed. The goal is to have at least 2 weeks before the test in May to focus on AP test.

 Section Topic Days Review Precalculus 6 Chapter 1: Limits and Their Properties 1.2 Finding Limits Graphically and Numerically 1 1.3 Evaluating Limits Analytically 1 1.4 Continuity and One-Sided Limits 2 1.5 Infinite Limits 2 3.5 Limits at Infinity 2 Review and Assessment 3 Chapter 2: Differentiation 2.1 The Derivative and Tangent Line Problem 2 2.2 Basic Differentiation Rules and Rates of Change 4 2.3 Product and Quotient Rules and Higher-Order 3 2.4 The Chain Rule 3 2.5 Implicit Differentiation 3 2.6 Related Rates 3 Review and Assessment 3 Chapter 3: Applications of Differntiation 3.1 Extrema on an Interval 3 3.2 Rolle's Theorem and the Mean Value Theorem 3 3.3 Increasing and Decreasing Functions and the First Derivative Test 2 3.4 Concavity and the Second Derivative Test 2 3.6 A Summary of Curve Sketching 2 3.7 Optimization Problems 5 3.9 Differentials 3 Review and Assessment 3 Chapter 4: Integration 4.1 Antiderivatives and Indefinite Integrals 3 4.2 Area 3 4.3 Riemann Sums and Definite Integrals 3 4.4 The Fundamental Theorem of Calculus 3 4.5 Integration by Substitution 3 4.6 Numerical Integration 1 Review and Assessment 3 Chapter 5: Logarithmic, Exponential, and OtherTranscendental Functions 5.1 The Natural Logarithmic Function: Differentiation 2 5.2 The Natural Logarithmic Function: Integration 2 5.3 Inverse Functions 3 5.4 Exponential Functions: Differntiation and Integration 3 5.5 Bases Other Than e and Applications 2 5.6 Inverse Trigonometric Functions: Differentiation 2 5.7 Inverse Trigonometric Functions: Integration 1 Review and Assessment 4 Chapter 6: Differential Equations 6.1 Slope Fields 3 6.2 Differential Equations: Growth and Decay 5 6.3 Separation of Variables and the Logistic Equation 3 Review and Assessment 3 Chapter 7: Applications of Integration 7.1 Area of a Region Between Two Curves 3 7.2 Volume: The Disk Method 5 Volume: Washers and volumes of solids with known cross sections 4 Review and Assessment 3 Chapter 8: Integration Techniques, L'Hopital's Rule, and Improper Integrals 8.1 Basic Integration Rules 2 Review and Assessment 3 Practice Test – Saturday, April 9th – 8:30am Review for AP Calculus Exam – 15 to 20 days     AP Calculus Exam – Thursday, May 5th – 8am   Students who do not take the AP Exam will take a written Final Exam. Students who take the AP Exam will complete a project for their final.