AP Calculus AB Syllabus Rampart High School Facilitator: Lyn Osburne Course Overview Within RHS, there are two primary objectives for the Advanced Placement Calculus AB class. The first objective is to insure that students are prepared to take the AP Exam in May. The second objective is to insure that students leave the halls of RHS prepared for success in future math courses. The AP Calculus AB Course Description encompasses all topics and subtopics, as identified in the AP College Board Calculus Topic Outline and Course Description, including but not limited to: Students working with functions, graphs and limits, inclusive of working with functions numerically, graphically, analytically, and when represented verbally. Students working with derivatives. Students working with integrals. Students mastering their explanations of solutions to problems and the rationale for problem-solving strategies and reasonable solutions, using complete, written sentences as well as oral explanations/arguments. Students mastering the use of graphing calculators for solving problems, experimenting with problem-solving strategies, and to interpret results and/or support conclusions. Throughout the course the primary textbook is Calculus: Early Transcendentals Eighth Edition, by Howard Anton, Irl Bivens, and Stephen Davis. Additional supporting materials are used as found on the internet, and through the ebook Calculus, by College Preparatory Mathematics (CPM). Cooperative learning and best practices in study-team strategies are implemented throughout the class, beginning on the first day of school. Students also are encouraged to work together and form study groups outside of class. Thus, students discuss and communicate openly the calculus topics learned and problem-solving strategies used as a normal facet of their learning venue.
Course Planner Chapter 1: Prerequisites for Calculus (2-3 weeks on block schedule with 5-6 88- minute classes concluding with one day/class for the unit assessment cooperative learning and team strategies developed concurrently including student-driven instructional approaches with these review topics) Real Numbers, Intervals, and Inequalities Absolute Value Coordinate Planes and Lines Distance, Circles, and Quadratic Equations Trigonometry Review Properties of Functions Chapter 2: Limits and Continuity (2 weeks on block schedule with 5 88-minute classes concluding with one day/class for the unit assessment each day beginning with openended critical thinking problem to ignite learning and exploration, often carrying solution into end of class, or beginning of the next class) Finding Limits Intuitively Computing Limits Limits at Infinity Continuity Continuity and Limits of Trigonometric Functions Chapter 3: The Derivative (3.5-4 weeks on block schedule with 10-11 88-minute classes concluding with one day/class for the unit assessment each day beginning with open-ended critical thinking problem to ignite learning and exploration, often carrying solution into end of class, or beginning of the next class The Definition of the Derivative o Relating the graphs of f(x) and the derivative of f(x) o When does the derivative not exist? The Derivative at a Point Equations of Tangent Lines Product Rule and Quotient Rule Derivatives of the Trigonometric Functions Chain Rule Implicit Differentiation Related Rate Problems Linear Approximations and Differentials
Chapter 4: The Derivatives of Exponential, Logarithmic, and Inverse Trigonometric Functions (3.5-4 weeks on block schedule with 10-11 88-minute classes concluding with one day/class for the unit assessment each day groups highlight problems and strategies used to find derivatives, thus explaining multiple approaches to their peers, as well as taking questions and justifying solutions regular/normal routines established so that each week every person in the class has a minimum of one opportunity to lead the whole-group discussion) Exponential and Logarithmic Functions Derivatives of Logarithmic Functions Derivatives of Inverse Functions Derivatives of Exponential Functions L Hopital s Rule and Indeterminate Forms Derivatives of the Inverse Trigonometric Functions Chapter 5: The Derivative in Graphing and Applications (Part 1) (2-3 weeks on block schedule with 5-7 88-minute classes concluding with one day/class for the unit assessment each day beginning with open-ended critical thinking problem to ignite learning and exploration, often carrying solution into end of class, or beginning of the next class) Analysis of Functions: Increase, Decrease, and Concavity Analysis of Functions: Relative Extrema, Critical Points Absolute Maxima and Minima End of the first semester Chapter 5: The Derivative in Graphing and Applications (Part 2) (2-3 weeks on block schedule with 5-7 88-minute classes concluding with one day/class for the unit assessment each day beginning with open-ended critical thinking problem to ignite learning and exploration, often carrying solution into end of class, or beginning of the next class) Applied Maximum and Minimum Problems Newton s Method Mean Value Theorem Motion Along a Line: Velocity, Acceleration, Distance Traveled Chapter 6: Integration (3.5-4 weeks on block schedule with 10-11 88-minute classes concluding with one day/class for the unit assessment each day groups highlight problems and strategies used to find derivatives, thus explaining multiple approaches to their peers, as well as taking questions and justifying solutions regular/normal
routines established so that each week every person in the class has a minimum of one opportunity to lead the whole-group discussion) The Indefinite Integral Integration by Substitution Riemann Sums The Definite Integral The Fundamental Theorem of Calculus Average Value Motion Along a Line Using Integration Evaluating the Definite Integral with Substitution Chapter 7: Applications of the Definite Integral (3 weeks on block schedule with 6 8 88-minute classes concluding with one day/class for the unit assessment, in addition to instructional times, students will complete multiple free-response released AP questions using AP grading rubrics) Area Between Curves Volumes by Disks and Washers Volumes by other Cross Sections: Semicircles, Squares, Equilateral Triangles Numerical Integration: Trapezoidal Rule Chapter 9: Differential Equations (2-3 weeks on block schedule with 5-6 88-minute classes concluding with one day/class for the unit assessment, in addition to instructional times, students will continue to complete free-response released AP questions using AP grading rubrics as well as practice multiple-choice released questions) Solving Differential Equations by Separation of Variables Slope Fields Exponential Growth and Decay Student Evaluation The 18 week in-progress grade each semester is calculated such that assessment scores comprise 85% and homework and in-class activities comprise 15%.. The overall semester grade is calculated such that 80% of the grade is from the in-progress grades while the semester exam accounts for 20%. In the first semester there are five chapter tests and in the second semester there are four chapter tests. The final exam in the second semester is a released AP Exam. And yes, the final exam is in addition to the actual AP Exam.
Beginning with Chapter 4, at the completion of a unit the students will work through a few free-response questions from previous AP Exams. The scoring guidelines for these questions are discussed in class so that students understand what is expected when they present their solutions. The free-response questions allow students the opportunity to work with functions described graphically, numerically, analytically, and verbally. At this point in the course, free-response questions will be included in each chapter test. Graphing Calculators All students are expected to have their own graphing calculator. The TI-83 plus is the recommended calculator. The graphing calculator is NOT allowed for tests in the first semester of the class. In the second semester students will use a calculator on each chapter test. As a pre-requisite, students know how to use the calculator to perform certain operations. Throughout the spring semester, students enhance and hone their skills to include graphing function in specified windows, finding the zeros of functions, finding intersection points between two functions, evaluating definite integrals, and evaluating derivatives at given values. Although the graphing calculator is a tool to help students solve problems and interpret results, students also refine their abilities to communicate the reasoning behind solutions found with the calculator. Preparing for the AP Exam Pending unforeseen events, there will be 2-3 weeks devoted to AP Exam preparation and practice; inclusive of a complete 3-hour mock exam. During this time, students will work on multiple choice problems as well as free-response questions. The cooperative learning environment remains constant throughout the year so students will continue to dialogue with others, explaining solutions and problem-solving strategies. In addition, the AP grading rubrics will be incorporated into discussions and peer evaluations in order to increase the richness of students conversations. Student Activity Example Motion Along a Line Let s(t)= sin (2t) be the position function of a particle moving along a coordinate line, where s is in meters and t is in seconds. a) Find the velocity function and the acceleration function.
b) Complete the table showing the position, velocity, and acceleration to two decimal places at times t= 1, 2, 3, 4, and 5. Time Position Velocity Acceleration t =1 t =2 t =3 t =4 t =5 c) At each of the times in part b, determine the direction (left or right) the particle is moving. d) At each of the times in part b, determine whether the particle is speeding up or slowing down. e) Use the appropriate graphs to determine the time intervals (from t =0 to t =5) on which the particle is speeding up and on which it is slowing down. Use the calculate zero function when analyzing the graphs.