1 Honors and AP Calculus Syllabus CHS Mathematics Department Contact Information: Parents may contact me by phone, email or visiting the school. Teacher: Mr. Patrick Laughlin Email Address: patrick.laughlin@ccsd.us Phone Number: (740) 702-2287 ext. 16226 Online: http://www.chillicothe.k12.oh.us/schools/chs/ 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 AB- 265 State Course # #110600 Prerequisite: Students must have attained a B or better in Honors Advanced Mathematics and teacher approval. Elective Grade: 11-12 Weighted Grade Credit: 1 Honors Calculus AB is primarily concerned with developing the students understanding of the concepts of limits and differential 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, approximation, and applications and modeling, the course becomes a cohesive whole rather than a collection of unrelated topics. Advanced Placement Calculus AB - 264 State Course # 119930 Prerequisite: Students must have attained a B or better in Honors Calculus and teacher approval Elective Grade: 11-12 Weighted Grade Credit: 1 AP Calculus AB is a continuation of Honors Calculus. The Calculus AB course is primarily concerned with developing the students understanding of the concepts of calculus and providing experience with its methods and
2 applications. The major AP calculus AB topics are: 1) derivatives & their applications to curve analysis and to optimization; 2) the major theorems; 3) integrals & RAM s to accumulate area; and 4) using the graphing calculator as a tool to help verify/support graphs, solutions and conjectures. The course continues to emphasize a multi-representational approach to calculus. 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. Big Ideas/Purpose per Unit and Essential Questions/Concepts per Unit: 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. The Common Core Standards can be found at http://www.corestandards.org/the-standards. (Teacher Note: The Ainsworth Model suggests 1-3 Big Ideas for each Unit and 1-3 Essential Questions per Big Idea. Each Unit will vary.) 1 st Quarter (Honors): o Unit I Foundation of Calculus Big Idea #1: The Exploration of Various Functions. Essential Question #1: What are the characteristics of an exponential function? Essential Question #2: What are the characteristics of a parametric function? Essential Question #2: What are the characteristics of a logarithmic function? Big Idea #2: Identifying the characteristics of trigonometric functions. Essential Question #1: What is the domain and range of each function? Essential Question #2: Describe the importance of co-functions? Essential Question #3: What are the important trig identities? o Unit II Limits and Continuity Big Idea #1: Comparing types of problems worked on in precalculus and corresponding extensions that require calculus techniques. Essential Question #1: How are the average velocity and instantaneous velocity similar and different?
Essential Question #2: How are the tangent line and normal line similar and different? Essential Question #3: What are the characteristics of a limit? Big Idea #2: Compare the existence and properties of limits and continuity. Essential Question #1: Describe the various methods of finding the limit as x approaches a given value? Essential Question #2: How are one-sided limits used to determine continuity? Big Idea #3: Exploring rates of change and their relationship to tangent lines. Essential Question#1: How are limits used to find rates of change? Essential Question #2: Compare and contrast the tangent to a curve and the slope of a curve? Essential Question #3: How can limits find the horizontal and vertical asymptotes? 2 nd Quarter (Honors): o Unit III Derivatives Big Idea #1: Use limits to develop the definition of derivatives. Essential Question #1: What role do limits play in the foundation of calculus? Essential Question #2: What is the tangent line problem? Big Idea #2: The derivative is the instantaneous Rate of change at a given point. Essential Question #1: What are the product and quotient rules? Essential Question #2: When is the chain rule used? Essential Question #3: When should implicit differentiation be used? Big Idea #3: Calculating higher-order derivatives using multiple techniques. Essential Question #1: What is the relationship between first and second derivatives? Essential Question #2: How are velocity and acceleration related to derivatives? Essential Question #3: How is the derivative of exponential and logarithmic functions calculated? o Unit IV Application of Derivatives 3
Big Idea #1: Finding extreme values of a function. Essential Question #1: How are derivatives related to extreme values? Essential Question #2: How are Rolle s Theorem and the Mean Value Theorem utilized in extrema? Essential Question #3: Big Idea #2: The characteristics of a graph including increasing/decreasing functions and concavity. Essential Question #1: How are the intervals determined? Essential Question #2: How are extrema and points of inflection related? Essential Question #3: How is the first and second derivative test related? Big Idea #3: Utilize the first and second derivative to sketch curves. Essential Question #1: How is the first and second derivative used to help sketch a curve? Essential Question #2: How are f, f, f related? 3 rd Quarter (AP): o Unit V Definite Integrals Big Idea #1: The connection between Differentialtion and Antidifferentiation. Essential Question #1: How is an indefinite integration related to antidifferentiation? Essential Question #2: What is the relationship between differentiation and integration? Big Idea #2: Areas estimated by Finite Sums. Essential Question #1: How are Riemann Sums calculated? Essential Question #2: What is the relationship between Reimann and definite integration? Essential Question #3 How is calculating the trapezoidal sum related to Riemann Sums/ Big Idea #3: The Importance of the Fundamental Theorem of Calculus. Essential Question #1: How does it help computing integration? Essential Question #2: How does integration by substitution help solve various functions? Essential Question #3: Explain numerical integration. o Unit VI Differential Equations Big Idea #1: Utilizing Slope Fields and Euler s Method. 4
5 Essential Question #1: When are slope utilized? Essential Question #2: Does Euler s Method give exact solutions? Essential Question #3: How substitution used in integration? Big Idea #2: Exploring Exponential Growth and Decay. Essential Question #1: What is the formula? Essential Question #2: How are decay and growth similar and different? Big Idea #3: Separation of Variables Essential Question #1: What types of equations can be solved by separation of variables? Essential Question #2: How can you recognize and solve homogeneous equations? 4 th Quarter (AP): o Unit VII Application of Integration Big Idea #1: Calculating Integrals as net change and area. Essential Question #1: What is the general strategy Essential Question #2: How is the area changed when it is moved from above the x-axis to below? Big Idea #2: Calculating Volumes using Integration Essential Question #1: How is the volume calculated by rotation? Essential Question #2: What is the technique for finding volume by know cross sections? Big Idea #3: L Hopital s Rule Essential Question #1: How can this be used to solve earlier limits? Essential Question #2: How are partial fractions used in finding limits? o AP EXAM May 5, 2015 o Unit VIII Intoduction to BC topics Big Idea #1: Series Essential Question #1: What are Power Series? Essential Question #2: What is a Taylor Series? END OF COURSE EXAM Textbook: Finney, Demana, Waits and Kennedy (2012). Calculus- Graphical, Numerical, Algebraic. 4 th ed. Pearson. Course Expectations 1.) Be punctual Class Rules
6 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 Procedure 1.) Students will write and perform Bell ringer, write the essential question(s), and get materials ready the first 5 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 turn in work at the appropriate time and place 4.) Students will clean up after themselves as well as their group members 5.) Students will remain seated in their assigned seat unless otherwise given permission 6.) Students are responsible for getting their make-up work after an absence 7.) Students are responsible for scheduling make-up tests and quizzes with the teacher 8.) Students are responsible for all resources provided to them, until collected. Course Material Binder/Notebook Pencils Graphing Calculator is suggested (TI-84+, TI-89, TI Inspire are recommended) Grading: Unit Exams 50% Assessments (Including: Quizzes, Essays, Labs, and Projects) 30% Homework 10% Class work 10% End of Course Exam is 20% of a student s final grade. Grading Scale The grading scale for Chillicothe High School can be found in the student handbook.
7 Late Work: Late work will be subject to the board adopted policy on assignments that are turned in late (to be reviewed in class). 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 Foundations of Calculus Week 1: Exponential and Parametric Functions and Logarithm Week 2: Trig Functions, Rate of Change and Limits Unit I Summative Assessment Unit II Limits and Continuity Week 3: Infinite Limits, Continuity Week 4: Tangent Lines and Rates of Change Unit II Summative Assessment Unit III Derivatives Week 5-6: Derivative and Differentiability Weeks 6-7: Rules for Differentiation and Velocity, Rates of Change Unit III Summative Assessment Unit IV Applications of Derivatives Week 8: Derivatives of Trig Function Weeks 9: Chain Rule Implicit Differentiation Unit IV Summative Assessment Part 1 2nd 9 Weeks (Honors): Week 1: Derivative of Inverse Trig, Exponential and Logarithmic Week 2: Extreme Value, Mean Value Thm Week 3-4: Optimization and Related Rates Unit IV Summative Assessment Unit V Title: Definite Integration Week 5-6: Estimating with Finite Sums, Definite Integrals Week 7-9: Antiderivatives and FTC Unit V Summative Assessment 3rd 9 Weeks (AP):
8 Unit VI Differential Equations Week 1-2: Antidifferentiation and Slope Fields Week 3: Integration by Substituion Week 4-5 Exponential Growth and Decay, Numerical Methods Unit VI Summative Assessment Unit VII Application Of Integration Week 6: Integration as Net Change Week 7-9: Areas and Volumes in a Plane 4th 9 Weeks (AP): Week 1: l Hopital s Rule Unit VII Summative Assessment Week 2-6 Review for AP Exams including practice exams END OF COURSE EXAM May 5, 2015 AP EXAM Unit VIII Intro to BC Topics Week 8 Improper Integrals, Power and Taylor Series 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 decision-making 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.
9 CHS Honors and AP Calculus 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: