AP Calculus AB Syllabus Beth Denzin Lake Mills High School Curricular Requirements...ii Course Overview...1 Technology Requirement...1 Textbook...1 Course Expectations...1 Additional Resources...1 Course Outline...2 Limits and Continuity...2 Derivatives...2 Integrals and the Fundamental Theorem of Calculus... 3 AP Review... 5 Updated Jan, 2017 i
Curricular Requirements CR1a The course is structured around the enduring understandings within Big Idea 1: Limits. See pages 2 and 5 CR1b The course is structured around the enduring understandings within Big Idea 2: Derivatives. CR1c The course is structured around the enduring understandings within Big Idea 3: Integrals and the Fundamental See pages 3, 4, and 5 CR2a The course provides opportunities for students to reason with definitions and theorems. See pages 4, and 5 CR2b The course provides opportunities for students to connect concepts and processes. CR2c The course provides opportunities for students to implement algebraic/computational processes. CR2d The course provides opportunities for students to engage with graphical, numerical, analytical, and verbal representations and demonstrate connections among them. CR2e The course provides opportunities for students to build notational fluency. CR2f The course provides opportunities for students to communicate mathematical ideas in words, both orally and in writing. See pages 2, 3, and 5 CR3a Students have access to graphing calculators. See page 1 CR3b Students have opportunities to use calculators to solve problems. See pages 1, 2, 4, and 5 CR3c Students have opportunities to use a graphing calculator to explore and interpret calculus concepts. See pages 1, 2, 4, and 5 CR4 Students and teachers have access to a college-level calculus textbook. See page 1 Updated Jan, 2017 ii
Course Overview AP Calculus AB Syllabus Mrs. Denzin The overall goal of this course is to help students understand and apply the three big ideas of AB Calculus: limits, derivatives, and integrals and the Fundamental We will investigate and analyze course topics using equations, graphs, tables, and words, with a particular emphasis on a conceptual understanding of calculus. This class is designed to place special emphasis on mathematical practices for AP Calculus: reasoning with definitions and theorems, connecting concepts, implementing algebraic/computational processes, connecting multiple representations, building notational fluency, and communicating mathematics orally and in well-written sentences. Technology Requirement Students will need a handheld graphing calculator every day. You may use any AP-approved calculator, or you may checkout a TI-84 from Mrs. Denzin for the entire year. You are encouraged to use your own device as appropriate for classwork and projects. [CR3a] [CR3a] Students have access to graphing calculators. Textbook Larson, Ron and Bruce H. Edwards. AP Edition Calculus. California: Brooks/Cole, Cengage Learning, 2010 [CR4] [CR4] Students and teachers have access to a college-level calculus textbook Course Expectations Attendance is extremely important as all students are expected to actively participate in daily large and small group discussions as we explore the big ideas of limits, derivatives, integrals and the Fundamental Quarter and semester grades will be determined by Homework: 5% of the quarter grade o A sampling of assigned homework problems will be collected daily. Feedback will be given on the mathematical accuracy and of calculus reasoning. Weekly timed quizzes: 25% of the quarter grade o Each quiz will consist of 5 multiple choice questions Quizzes may require the use of a graphing calculator or you may be required to complete the quiz without a calculator. [CR3b] [CR3c] Tests: 70% of the quarter grade o Each test will be divided into calculator and non-calculator sections that are timed in accordance to the timing of the AP exam. [CR3b] [CR3c] [CR3b] Students have opportunities to use calculators to solve problems Additional Resources AP Calculus AB Google Classroom is set up which will contain PDF versions of all notes and handouts. Daily assignments will be posted. Mrs. D s AP Calculus AB Class Facebook page is set up for discussion of questions on specific homework problems and/or concepts as well as a place to provide helpful links for online applications, study guides, videos, and AP review sources. 1
AP Calculus AB Course Outline Limits and Continuity (Chapter 1) [CR1a] 1.1 A Preview of Calculus 1.2 Finding Limits Graphically and Numerically 1.3 Evaluating Limits Analytically 1.4 Continuity and One-Sided Limits 1.5 Infinite Limits 3.5 Limits at Infinity [CR1a] The course is structured around the enduring understandings within Big Idea 1: Limits. Sample Activity: The Four Ways of Exploring Limits Limits will be examined numerically by using the table feature on their graphing calculator. Second limits will be determined analytically by algebraically manipulating expressions into a form in which the limit can be determined. Third, limits will be found by graphing the function of the graphing calculator. Finally, students will use verbal descriptions of functions to sketch a graph of the function described. In all four instances a complete sentence description will be required of the discontinuity observed and how they are able to prove that their description of the discontinuity is accurate. [CR2c] [CR2d] [CR2f] [CR3b] [CR3c] [CR3b] Students have opportunities to use calculators to solve problems Differentiation (Chapter 2) [CR1b] 2.1 The Derivative and the Tangent Line Problem 2.2 Basic Differentiation Rules and Rates of Change 2.3 Product and Quotient Rules and Higher-Order Derivatives 2.4 The Chain Rule 5.5 Implicit Differentiation 2.6 Related Rates Sample Activity: Balloon Change Students will complete the Balloon Change activity in which they will measure the changes of a balloon following each puff of air the put into the balloon. They will collect their data in a table and calculate the rate of change in circumference, radius, volume, and surface area. Each set of data will then be graphed and compared so that conclusions can be drawn about the related rates of volume, circumference, and surface area with the radius. [CR2b] [CR2c] [CR2d] [CR2e] [CR2f] 2
Applications of Differentiation (Chapter 3) [CR1b] 3.1 Extrema on an Interval 3.2 Rolle s Theorem and the Mean Value Theorem 3.3 Increasing and Decreasing Functions and the First Derivative Test 3.4 Concavity and the Second Derivative Test 3.6 A Summary of Curve Sketching 3.7 Optimization Problems 3.8 Differentials Sample Activity: f, f, f Matching Students will work in a group of 3. They will be given 50 cards. There will be 10 cards which contain a verbal description of the functions, 10 cards which will contain the equations of the functions, 10 cards which will contain the graphs of the functions, 10 cards which contain the first derivative graph of the functions, and 10 cards which contain the second derivative graph of the functions. Students will have to match each description to its equation, graph, first derivative graph, and second derivative graph. [CR2b] [CR2d] Integration (Chapter 4) [CR1c: integration] 4.1 Antiderivatives and Indefinite Integration 4.2 Area 4.3 Riemann Sums and Definite Integrals 4.4 The Fundamental Theorem of Calculus (Parts I and II) 4.5 Integration by Substitution 4.6 Numeric Integration Sample Activities: Riemann Sums and Hand Turkeys Students will complete the Riemann Sums and Hand Turkey activity. After tracing their hands on a piece of graph paper students are asked to find the area of their handprint. After a few minutes of individual work time, students will get into groups and share their approach with their group members. After a few more minutes groups will be asked to present their method for determining the area of a handprint. Through the exploration students will discover left-hand, right-hand and midpoint Riemann summations. [CR2b] [CR2c] [CR2d] [CR2e] [CR2f] 3
Fundamental Theorem of Calculus Desmos Activity Students will work through the Fundamental Theorem of Calculus Part 1 Desmos Activity to get a better understanding of how a variable bound affects the evaluation of an integral and to make the connection between the general Fundamental Theorem of Calculus ( g( x) f (t) dt b specific Fundamental Theorem of Calculus ( (x) a f dx F b F a a x ) and the ) [CR2a] [CR2b] [CR2c] [CR2d] [CR2e] [CR3b] [CR3c] [CR2a] The course provides opportunities for students to reason with definitions and theorems [CR3b] Students have opportunities to use calculators to solve problems Logarithmic, Exponential, and Other Transcendental Functions (Chapter 5) [CR1b] [CR1c] 5.1 The Natural Logarithmic Function: Differentiation 5.2 The Natural Logarithmic Function: Integration 5.3 Inverse Functions 5.4 Exponential Functions: Differentiation and Integration 5.5 Bases Other Than e and Applications 5.6 Inverse Trigonometric Functions: Differentiation 5.7 Inverse Trigonometric Functions: Integration Differential Equations (Chapter 6) [CR1b] [CR1c] 6.1 Slope Fields 6.2 Differential Equations: Growth and Decay 6.3 Separation of Variables Slope Field Card Match Activity: Similar to the f, f, f matching activity described on page 3, students will be placed into groups of 3 and given 30 cards to match. 10 cards will have slope fields on them, 10 will have differential equations, and 10 will have verbal descriptions. [CR2b] [CR2d] 4
Applications of Integration (Chapter 7) [CR1c] 7.1 Area of a Region Between Two Curves 7.2 Volume: The Disk (and Washer) Method Eating Volumes Activities: Student groups will be given half an orange and a knife. Through teacher directed instructions, students will explore how the volume of their orange can be calculated through the sum of the semicircle slices they make which will lead to the discovery and a verbal description of the Disk Method of finding the volume of a solid of a revolution. After learning the Disk and Washer methods (~2 class periods later), we will perform a similar activity using Hostess/Little Debbie cupcakes in order to discover and describe how we can use known cross sections to also find the volume of a solid. [CR2b] [CR2c] [CR2d] [CR2e] [CR2f] AP Review [CR1a] [CR1b] [CR1c] 8.1 Basic Integration Rules 8.7 Indeterminate Form and L Hopital s Rule Past multiple choice and free response problems [CR1a] The course is structured around the enduring understandings within Big Idea 1: Limits. Sample Activity: Practice AP Exams Multiple AP practice exams will be given. We discuss solutions together. Students will work on their verbal, analytical, graphical, and numeric proof. We will dissect how points can be earned and lost on the free response questions [CR2a] [CR2b] [CR2c] [CR2d] [CR2e] [CR2f] [CR3b] [CR3c] [CR2a] The course provides opportunities for students to reason with definitions and theorems [CR3b] Students have opportunities to use calculators to solve problems. 5