1 Honors/AP Calculus BC Syllabus CHS Mathematics Department Contact Information: Parents may contact me by phone, email or visiting the school. Teacher: Mrs. Tara Nicely Email Address: tara.nicely@ccsd.us Phone Number: (740) 702-2287 ext. 16228 Online: http://www.ccsd.us/1/home Teacher Contact Websites/Social Media: Twitter: @MrsNicely_CHS Google Classroom CHS Vision Statement: Our vision is to be a caring learning center respected for its comprehensive excellence. CHS Mission Statement: Our mission is to prepare our students to serve their communities and to commit to life-long learning Course Description and Prerequisite(s) from Course Handbook: Honors Calculus BC- 266 State Course # #119960 Prerequisite: Students must have attained a B or better in AP Calculus AB or teacher approval Elective Grade: 12 Weighted Grade Credit: 1 Honors Calculus BC is primarily concerned with developing the students understanding of the concepts of differential and integral calculus. It will provide experience with its methods and applications. The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. The connections among these representations also are important. Through the use of the unifying themes of derivatives, limits, integrals, approximation, and area, volume, surface area, applications and modeling, the course becomes a cohesive whole rather than a collection of unrelated topics. Please refer to the Summer Honors/AP Assignment Due Dates Policy on page 21.
2 Advanced Placement Calculus BC - 267 State Course # 119930 Prerequisite: Students must have attained a B or better in Honors Calculus BC and teacher approval Elective Grade: 12 Weighted Grade Credit: 1 AP Calculus BC is a continuation of Honors Calculus BC. AP Calculus BC is a second course in a single variable calculus that would be equivalent to a second semester calculus course at most colleges and universities. This course will provide a deeper understanding of the concepts of limit, continuity, derivatives, and integrals which were covered in AP Calculus AB. The major new topics covered in AP Calculus BC are Parametric, polar, and vector functions; slope fields; Euler s method; L Hopital s Rule; Improper Integrals; Logistic differentiable equations; Polynomial approximations and Series; and Taylor Series In order to receive AP credit with a 5 point on grading systems, the student must take and pay for the AP exam. If the student fails to take the exam, a 4.5 point grading scale will be applied to the course. Please refer to the Summer Honors/AP Assignment Due Dates Policy on page 21. Learning Targets: Defined below for clarity are the Unit Titles, Big Ideas of every Unit taught during this course, and the Essential Questions to be answered to better understand the Big Ideas. A student s ability to grasp and answer the Essential Questions will define whether or not he or she adequately learns and can apply the skills found in Big Ideas. This will ultimately define whether or not a student scores well on assessments given for this course.. Big Ideas and Essential Questions are derived from https://secure-media.collegeboard.org/digitalservices/pdf/ap/ap-calculus-aband-bc-course-and-exam-description-effective-fall-2016.pdf 1st Quarter (Honors) Unit I Title: Limits and Continuity Big Idea #1: Use the concept of a limit to understand the behavior of functions Essential Question #1: How are limits expressed symbolically using correct notation? Essential Question #2: How are limits expressed symbolically interpreted? Essential Question #3: How are limits of functions estimated by using a table? [SC9} Essential Question #4: How are limits of functions determined? Essential Question #5: How is the behavior of functions using limits deduced and interpreted? Big Idea #2: Understand continuity is a key property of functions that is defined using limits.
3 Essential Question #1: How are functions analyzed for intervals of continuity or points of discontinuity? Essential Question #2: How is the applicability of important calculus theorems using continuity determined? Unit II Title: Derivatives Big Idea #1: Understand the derivative of a function is defined as the limit of a difference quotient and determine derivatives using a variety of strategies. Essential Question #1: How is the derivative of a function as the limit of the difference quotient identified? Essential Question #2: How are derivatives estimated? Essential Question #3: How are derivatives calculated? Essential Question #4: How are higher order derivatives determined? 2nd Quarter (Honors) Unit III Title: Application of Derivatives Big Idea #1: Use the Mean Value Theorem to connect the behavior of a differentiable function over an interval to the behavior of the derivative of that function at a particular point in the interval. Essential Question #1: How is the Mean Value Theorem applied to describe the behavior of a function over an interval? Big Idea #2: Use and analyze a function s derivative, which is itself a function, to understand the behavior of the function Essential Question #1: How are derivatives used to analyze properties of a function? Essential Question #2: How is the connection between differentiability and continuity recognized? Big Idea #3: Understand the derivative has multiple interpretations and applications including those that involve instantaneous rates of change and can solve and interpret these problems Essential Question #1: How is the meaning of a derivative within a problem interpreted?
4 Essential Question #2: How are problems involving the slope of a tangent line solved? Essential Question #3: How are problems involving optimization, rectilinear motion, and planar motion solved? Unit IV Title: Definite Integrals Big Idea #1: Recognize and understand antidifferentiation is the inverse process of differentiation Essential Question #1: How are antiderivatives of basic functions recognized? Big Idea #2: Understand and interpret the definite integral of a function over an interval is the limit of a Riemann sum over that interval and can calculate it using a variety of strategies Essential Question #1: How is the definite integral as the limit of a Riemann sum interpreted? Essential Question #2: How is the limit of a Riemann sum expressed in integral notation? Essential Question #3: How is a definite integral approximated? Essential Question #4: How is a definite integral calculated using areas and properties of definite integrals? Big Idea #3: Understand the Fundamental Theorem of Calculus, which has two distinct formulations, connects differentiation and integration and use it to calculate and evaluate problems Essential Question #1: How are functions defined by an integral analyzed? Essential Question #2: How are antiderivatives calculated? Essential Question #3: How are definite integrals evaluated? END OF COURSE EXAM 3rd Quarter (AP) Unit V Title: Differential Equations Big Idea #1: Understand antidifferentiation is an underlying concept involved in solving separable differential equations. Understand solving separable differential equations involves determining a function or relation given its rate of change. Apply this knowledge to find and analyze solutions
5 4th Quarter (AP) Essential Question #1: How are differential equations analyzed to obtain general and specific solutions? Essential Question #2: How are differential equations from problems in context interpreted, created and solved? Essential Question #3: How is Euler s method used to approximate a solution or a point on a solution curve? Unit VI Title: Application of Integration and Improper Integrals Big Idea #1: Understand and apply the definite integral of a function over an interval is a mathematical tool with many interpretations and applications involving accumulations Essential Question #1: How is the meaning of a definite integral within a problem interpreted? Essential Question #2: How are definite integrals applied to problems involving the average value of a function? Essential Question #3: How are definite integrals applied to problems involving motion? Essential Question #4: How are definite integrals applied to problems involving area, volume, and length of a curve? Essential Question #5: How is the definite integral used to solve problems in various contexts? Essential Question #6: How is an improper integral found and shown that it diverges? Unit VII Title: Polynomial Approximations and Series Big Idea #1: Understand and determine when the sum of an infinite number of real numbers may converge Essential Question #1: How is a series determined to converge or diverge? Essential Question #2: How is the sum of a series determined or estimated? Big Idea #2: Understand a function can be represented by an associated power series over the interval of convergence for the power series and use this to determine functions Essential Question #1: How are Taylor polynomials constructed and used? Essential Question #2: How is a power function representing a given function written?
6 Essential Question #3: How is the radius and interval of convergence of a power series determined? Unit VIII Title: Parametric, Vector, and Polar Functions Big Idea #1: Determine, apply and solve parametric AP Exam May END OF COURSE EXAM functions and vectors in the plane Essential Question #1: How can methods for calculating derivatives of real-valued functions be extended to vector-valued functions and parametric functions? Essential Question #2: How are derivatives used to determine velocity, speed, and acceleration for a particle moving along curves given by parametric and vector-valued functions? Essential Question #3: How are the definite integral used to determine displacement, distance, and position of a particle moving along a curve given by parametric or vector-valued functions? Essential Question #4: How is the length of a planar curve defined by a function or by a parametrically defined curve calculated using a definite integral? Big Idea #2: Determine, apply and solve polar functions Essential Question #1: How can methods for calculating derivatives of real-valued functions be extended to functions in polar coordinates? Essential Question #2: How does a curve given by a polar equation r=f(theta), derivatives of r, x, and y with respect to Theta and first and second derivatives of y with respect to x can provide information about the curve? Essential Question #3: How are areas bounded by polar curves calculated with definite integrals? Course Material: Google Chromebook 3-ring Binder with Dividers Loose Leaf College Ruled Paper Pencils Graph Paper Graphing Calculator (TI-84+ is recommended)
7 The graphing calculator is used to help students develop an intuitive feel for concepts before they are approached through typical algebraic techniques. We use the calculator as a tool to illustrate ideas and make discoveries about functions in Calculus. The four required functionalities of graphing technology are: 1. Finding a root 2. Sketching a function in a specified window 3. Approximating the derivative at a point using numerical methods 4. Approximating the value of a definite integral using numerical methods Students are also required to make connections between the graphs of functions and their analysis, and conclusions about the behavior of functions when using a graphing calculator Many of the discovery lessons rely heavily on the use of the graphing calculator. The calculator helps students develop a visual understanding of the material that they would not otherwise have. My students use the TI-84 graphing calculator almost every day in class for explorations (such as experimenting to discover the power rule for derivatives or exploring the graphs of f and its derivative to discover relationships between them) and in assignments to analyze functions and justify solutions. For example, the students use the calculator to approximate the values of derivatives and definite integrals obtained through analytical means in order to verify that the answers are reasonable. [SC11, SC12 & SC13] However, many homework problems and about half of the problems on quizzes and tests are done without the use of the graphing calculator. Because the AP Exam is half calculator and half non-calculator, I feel that it is very important for students to have practice working problems both ways. We spend time in class talking about the types of questions that they must know how to solve with their calculators and the types of questions that they must know how to solve without their calculators. We also discuss the techniques needed to use the calculator most efficiently (storing functions in the y = screen, storing values that will be used later in the problem, etc.). Textbook: Finney, Demana, Waits, and Kennedy (2012). Calculus Graphical, Numerical, Algebraic. 4 th ed. Pearson Supplemental Textbook(s): Electronic Resources: Google Classroom GeoGebra https://www.geogebra.org/ National Library of Virtual Manipulatives http://nlvm.usu.edu/ NCTM Illuminations http://illuminations.nctm.org/ Purplemath http://www.purplemath.com/modules/index.htm
8 College Board https://apstudent.collegeboard.org/apcourse/ap-calculusab http://online.math.uh.edu/apcalculus/ http://www.calculus.org/ Course Expectations: Rule of Four I give my students many opportunities to work problems presented in a variety of ways: graphical, numerical, analytical, and verbal. Most of the problems in my primary textbook are written with an analytical representation, so I frequently supplement these problems with ones that utilize a graph or tabular data. I also often ask students to work in groups or to come to the board for oral explanations to give them the opportunity to communicate their reasoning in spoken words. [SC9] Justification of Answers I ask my students to justify their answers on homework, quizzes, and tests, and I require that they write the justifications in sentences. We talk a lot about the amount of work they need to show and the correct way to justify their work on various types of problems. [SC10] (The Commentary on the Instructions for the Free-Response Section 5 of the AP Calculus Exams on AP Central is very helpful in showing examples of correct justifications.) C2-The course teaches all topics associated with Functions, Graphs, and Limits; Derivatives; and Integrals as delineated in the Calculus AB Topic Outline in the AP Calculus Course Description. C3-The course provides students with the opportunity to work with functions represented in a variety of ways graphically, numerically, analytically, and verbally and emphasizes the connections among these representations. C4-The course teaches students how to communicate mathematics and explain solutions to problems both verbally and in written sentences. C5-The course teaches students how to use graphing calculators to help solve problems, experiment, interpret results, and support conclusions The Mathematical Practices for AP Calculus will be a major focus of this course. They include: MPAC 1: Reasoning with definitions and theorems MPAC 2: Connecting concepts MPAC 3: Implementing algebraic/computational processes MPAC 4: Connecting multiple representations
9 MPAC 5: Building notational fluency MPAC 6: Communicating Class Rules 1. Be punctual 2. Be prepared for class 3. Be respectful towards teachers/staff, class members, school property, etc. 4. Be honest 5. Be observant of all class, school, and district rules and policies 6. Be positive Class Procedures 1. Students will perform the Bell Ringer, review the Essential Question(s), and get materials ready the first 3 minutes of class 2. Students will request permission from the teacher, get their agenda signed, and sign out on the back of the door to leave the classroom for any reason 3. Students will be expected to be WELL PREPARED FOR AND TAKE AN ACTIVE ROLE in class sessions. IF YOU DO NOT UNDERSTAND SOMETHING, ASK! It is preferable that you speak up and are wrong than for you not to speak at all. 4. Students will have their Chromebook, pencil, and paper every day. 5. Students will turn in work at the appropriate time and place 6. Students will clean up after themselves as well as their group members 7. Students will remain seated in their assigned seat unless otherwise given permission 8. Students are responsible for getting their make-up work after an absence 9. Students are responsible for scheduling make-up tests and quizzes with the teacher or will be assigned to SHARP. Grading: Unit Exams 50% Assessments (Including: Quizzes, Essays, Labs, and Projects) 30% Class work/homework 20% End of Course Exam is 20% of a student s final grade.
10 Grading Scale: The grading scale for Chillicothe High School can be found in the student handbook or online at http://www.chillicothe.k12.oh.us/1/content2/studenthandboook Late Work: Late work will be subject to the board adopted policy on assignments that are turned in late (to be reviewed in class). Information can be viewed on-line at http://www.chillicothe.k12.oh.us/1/content2/studenthandboook CHS TENTATIVE Course Schedule This is an overview of what will be covered in this course at CHS for this school year. Although, I would like to follow this plan verbatim this years tentative schedule is subject to change (at the teachers discretion). 1st 9 Weeks (Honors): Week 1: Beginning of the Year Pre-Assessment Exam Unit I Title: Limits and Continuity Week 1: 2.1 Rates of Change and Limits 2.2 Limits Involving Infinity Formative Assessment Week 2 2.3 Continuity 2.4 Rates of Change and Tangent Lines Formative Assessment Unit I Summative Assessment Unit II Title: Derivatives Week 3-4: 3.1 Derivative of a Function 3.2 Differentiability 3.3 Rules for Differentiation 3.4 Velocity and Other Rates of Change 3.5 Derivatives of Trigonometric Functions Formative Assessment Week 5-6: 3.6 Chain Rule 3.7 Implicit Differentiation 3.8 Derivatives of Inverse Trigonometric Functions 3.9 Derivatives of exponential and Logarithmic functions Formative Assessment Unit II Summative Assessment Unit III Title: Application of Derivatives Week 7-8: 4.1 Extreme Values of Functions
11 4.2 Mean Value Theorem 4.3 Connecting f and f with the graph of f Formative Assessment Week 8-9: 4.4 Modeling and Optimization 4.5 Linearization and Newton s Method 4.6 Related Rates Formative Assessment Unit III Summative Assessment 2nd 9 Weeks (Honors): Unit IV Title: Definite Integrals Week 1: 5.1 Estimating with Finite Sums 5.2 Definite Integrals Formative Assessment Week 2-3: 5.3 Definite Integrals and Antiderivatives 5.4 Fundamental Theorem of Calculus 5.5 Trapezoid Rule Formative Assessment Unit IV Summative Assessment Unit V Title: Differential Equations Week 3-4: 6.1 Slope Fields 6.2 Antidifferentiation by Substitution 6.3 Antidifferentiation by Parts Formative Assessment Week 5: 6.4 Exponential Growth and Decay 6.5 Logistic Growth Formative Assessment Unit V Summative Assessment Unit VI Title: Application of Integration and Improper Integrals Week 6-7: 7.1 Integral As Net Change 7.2 Areas in the Plane 7.3 Volumes 7.4 Lengths of Curves 7.5 Applications from Science and Statistics Formative Assessment Week 8-9: 8.1 Sequences 8.2 L Hopital s Rule
12 8.3 Relative Rates of Growth 8.4 Improper Integrals Formative Assessment Unit VI Summative Assessment END OF COURSE EXAM 3 rd 9 Weeks (AP) : Week 1: Unit VII Title: Polynomial Approximations and Series Week 1-2: 9.1 Power Series 9.2 Taylor Series Formative Assessment Week 3-5: 9.3 Taylor s Theorem 9.4 Radius of Convergence 9.5 Testing Convergence at Endpoints Formative Assessment Unit VII Summative Assessment Unit VIII Title: Parametric, Vector, and Polar Functions Week 6-7: 10.1 Parametric Functions 10.2 Vectors in the Plane Formative Assessment Week 8-9: 10.3 Polar Functions Formative Assessment Unit VIII Summative Assessment 4 th 9 Weeks (AP) (AP): Week 1-6: Review and Practice for the AP Exam AP Calculus Exam May 9, 2017 Week 7-9: Project END OF COURSE EXAM Performance Based Section: Writing Assignments/Exams/Presentations/Technology One or more of the End of Unit Exams may be Performance Based. According to the Ohio Department of Education, Performance Based Assessments (PBA) provides authentic ways for students to demonstrate and apply their understanding of the content and skills within the standards. The performance based assessments will provide formative and summative information to inform instructional decisionmaking and help students move forward on their trajectory of learning. Some examples of Performance Based Assessments include but are not limited to portfolios, experiments, group projects, demonstrations, essays, and presentations.
13 CHS Honors/AP Calculus BC Course Syllabus After you have reviewed the preceding packet of information with your parent(s) or guardian(s), please sign this sheet and return it to me so that I can verify you understand what I expect out of each and every one of my students. Student Name (please print): Student Signature: Parent/Guardian Name (please print): Parent/Guardian Signature: Date: