COURSE DESCRIPTION Date: March 2015 COURSE TITLE: AP Calculus BC (Calculus 2) Course Number: 204030A; 204030B STARS 20595100 Open to Grades: 11-12 Pre-requisite : Credit: Length of Course: AP Calculus AB (Calculus 1) and teacher recommendation 1 credit 1 year COURSE DESCRIPTION: This course follows the prescribed AP curriculum for Calculus BC. In addition to covering all of the topics from Calculus AB (limits, derivatives, and integrals), Calculus BC will include a study of vector functions, parametric equations, and polar coordinates; rigorous definitions of finite and nonexistent limits; derivatives of vector functions and parametrically defined functions; advanced techniques of integration and advanced applications of the definite integral; and sequences and series. Course provides students with an intuitive understanding of the concepts of calculus and experience with its methods and applications, and also requires additional knowledge of the theoretical tools of calculus. This course is intended to prepare students for the Advanced Placement Exam. COURSE OBJECTIVES: A. Students will understand the concept of limits and how they apply to calculus. B. Students will understand the concept of derivative as a function, slope of tangent line and rate of change. C. Students will apply derivatives to applications including optimization and related rates D. Students will understand the concept of integration as an antiderivative, limit of a Riemann sum, and area under a curve. E. Students will apply integration to applications including volumes of rotation. F. Students will find the length of a curve in the coordinate plane. G. Students will use Newton s method and Euler s method to make approximations. H. Students will find derivatives of relations defined by parametric equations and vectors. I. Students will find the length of and area under curves in a polar relationship. F. Students will examine infinite series and use tests to determine the convergence of series. COURSE MEASUREMENT: A. Students will have homework assignments to complete for a percentage of their nine weeks grades. B. Students will receive grades based on quizzes, which will count for a percentage of their nine weeks grades. C. Students will take examinations similar in style to the AP exam, which will count for a percentage of their nine weeks grade. D. Students will take a final exam which will count for 20% of their semester grade. E. Teacher will use formative assessment during class to gauge the understanding of students. COURSE OUTLINE: A. Course will follow approved course syllabus/outline from College Board. Upon establishment of the course, a syllabus will be submitted to College Board for approval. AP Calculus BC
B. The outline will be based upon the one attached to this document (beginning on page 4). LEARNING ACTIVITIES: A. Students will take notes on Calculus BC topics and examples. B. Students will participate in classroom discussions. C. Students will develop critical thinking skills regarding Calculus BC topics. D. Students will work AP-style problems in preparation for assessments and college courses STUDENT PERFORMANCE REQUIREMENTS: A. Attendance B. Note taking C. Group activities and discussion D. Assessments Daily work Tests and/or Quizzes Projects Other activities at the discretion of the teacher INSTRUCTIONAL MATERIALS INFORMATION: A. Textbook: Calculus Graphical, Numerical, Algebraic; Finney, Demana, Waits, Kennedy; Pearson Prentice Hall AP Calculus BC
STATE STANDARDS ADDRESSED: A. While the main mathematical standards and skills of Calculus BC are beyond those addressed in New Mexico State Standards, the following standards are ones that will have particular relevance to Calculus BC students: CCSS.MATH.CONTENT.HSN.RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. CCSS.MATH.CONTENT.HSN.Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. CCSS.MATH.CONTENT.HSN.VM.A.3 Solve problems involving velocity and other quantities that can be represented by vectors. CCSS.MATH.CONTENT.HSA.SSE.B.4 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. CCSS.MATH.CONTENT.HSA.CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. CCSS.MATH.CONTENT.HSA.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. CCSS.MATH.CONTENT.HSA.REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. CCSS.MATH.CONTENT.HSF.IF.B.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. CCSS.MATH.CONTENT.HSF.IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. CCSS.MATH.CONTENT.HSF.IF.C.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. CCSS.MATH.CONTENT.HSF.BF.A.1.C Compose functions. CCSS.MATH.CONTENT.HSF.TF.A.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. AP Calculus BC
AP Calculus BC
AP Calculus BC
AP Calculus BC