AP Calculus-AB 2016/2017 Dr. Mike Hall Greene County Tech High School Text: Calculus: Graphical, Numeric, Algebraic by Finney, Demana, Waits, Kennedy, Bressoud, 5 th Ed. Student learning outcomes for AP Calculus: Students will be able to: Work with functions represented in a variety of ways and understand the connections among these representations. Understand the meaning of the derivative in terms of a rate of change and local linear approximation, and use derivatives to solve a variety of problems. Understand the relationship between the derivative and the definite integral. Communicate mathematics both orally and in well-written sentences to explain solutions to problems. Model a written description of a physical situation with a function, a differential equation, or an integral. Use technology to help solve problems, experiment, interpret results, and verify conclusions. Determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement. Develop an appreciation of calculus as a coherent body of knowledge Success in AP Calculus: I encourage each of you to explore and discover mathematics throughout the course. In my past experience, I have found that students who are comfortable with graphing calculators often ask questions based on their own investigations that allow them to see mathematics from a graphical perspective that reiterate numerical and analytical calculus concepts. One key component of learning and understanding calculus is cooperative learning. Students will sit in groups of two or three and assist each other in learning by acting as peer-mentors. Throughout the course, we will use previous AP Calculus AB Exam questions (both Multiple Choice and Free Response) as a means to create a dialog among students so that they may communicate an understanding of calculus. We will do this verbally and written with an emphasis on student explanations and justifications of solutions. These problems allow me to review student understanding of overarching concepts while also allowing students to discover their own deficiencies in understanding. In addition, all student assignments require them to include justifications of their work in multiple representations, including symbolical and graphical representations that accompany complete written sentences explaining their processes and solutions. Grading Policy: Tests 40% Quizzes 30% Homework/Classwork 15% Projects 15% Late and Make-Up Work Policy: All students are expected to complete every assignment on time. With that said, it is understandable that occasionally there are times when students simply cannot complete an assignment. If work must be submitted late, then it will be accepted for half credit for no more than three school days after the original due date. Please come speak with me if you have extenuating circumstances. The lowest two class/homework grades during each quarter will be dropped. Cell Phone Policy: In general, this is a cell phone free classroom. In the event of inappropriate use of a cell phone or other electronic/wireless device, the device will be detained and held until the end of the school day.
Additional Assistance: Students may receive additional assistance with the course daily during the enrichment hour/8 th period. Supplies: Homework: Calculators: Each student is expected to have (1) writing utensils; (2) Class notebook with loose-leaf paper to take notes In order to do well in AP Calculus, you need to complete the homework problems on a daily basis. I encourage you to discuss problems with a classmate, but you should write each solution on your own. Don t procrastinate with homework assignments We will use Texas Instruments nspire handheld calculators in class regularly. Therefore, you will also want to have a graphing calculator. We have a classroom set of TI-nSpire handhelds for your use. We will use the calculator daily in a variety of ways including: Conduct explorations. Graph functions within arbitrary windows. Solve equations numerically. Analyze and interpret results. Justify and explain results of graphs and equations. AP Calculus Exam: All students completing the course are expected to take the AP Calculus AB exam on May 5, 2017 Academic Accommodations: Communication: I have been informed of all students with document academic accommodations. I look forward to working with you to ensure your success. Please communicate with me either yourself, through your parent/guardian, or through the school counselor to inform me of your specific needs. I am very flexible and want every child to have the opportunity to succeed. For your convenience, I have created a blog (http://drhallgct.weebly.com) that allows you to keep up with weekly assignments, access online learning resources, and follow along when you miss class. I want each of you to know that my door is always open when I am not in class. If you need to discuss anything with me outside of class time, please feel free to contact me. Contact Information: Email: mike.hall@gctsd.k12.ar.us GCT High School Phone: (870) 215 4460 Calculus Free-Friday: This year we are doing something a little different each Friday. We are going to read two at least two books during the year that should be a great read and a nice break from calculus. This will be a relaxed environment, but still counts as a grade. For each semester, you will have a project that is related books we have read. I prefer you to purchase the books, but if not there may be a pdf available. Fall Into the Wild (Jon Krakauer) Spring TBA
Course Planner and Schedule Functions (Two weeks) Graphs, Models, Linear Models, Rates of Change, Fitting Models to data Limits (Three weeks) 1. Local Linearity 2. Limits 3. Continuity 4. Infinite Limits CBL Ball Toss Lab (see Student Activity 1, below) Graphing the Derivative of a Function (see Student Activity 2) Differentiation (Four weeks) 1. Derivatives and Tangent Lines 2. The Derivative Function 3. Interpretations of the Derivative 4. The Second Derivative 5. Powers and Polynomials 6. The Exponential Function 7. The Product and Quotient Rules 8. The Chain Rule 9. The Trigonometric Functions 10. Applications of the Chain Rule and Related Rates 11. Implicit Functions 12. Linear Approximation and the Derivative 13. Using Local Linearity to Find Limits Applications of the Derivative (Five weeks) 1. Using First and Second Derivatives 2. Families of Curves 3. Optimization and Modeling 4. Theorems About Continuous and Differentiable Functions Integration (Five weeks) 1. Area and Definite Integrals Riemann Sums, left, right, and mid-point 2. The Mean Value Theorem for Integrals and the Average Value of a Function 3. The Fundamental Theorem of Calculus, Parts I & II 4. Integration by Substitution Pattern Recognition, Change of Variables for Definite Integrals, Integration of Odd and Even Functions 5. Trapezoid Approach for finding Area 6. Trigonometric Integrals 7. Trigonometric Substitution Rate/Flow Project Exploring the Fundamental Theorem of Calculus Logarithmic, Exponential, and Other Transcendental Functions (Four weeks) 1. Inverse Functions Derivative of an Inverse Function 2. Derivatives and Integration of natural log and exponential functions 3. Inverse Trig Functions - Derivatives of inverse Trig Functions 4. Integrals Involving Inverse Trig Functions 5. l Hôspital s Rule Applications of the Definite Integral (Three Weeks) 1. Areas and Volumes 2. Applications to Geometry 3. Volumes of Solids of Revolution The Disk Method and Exploring Volume by Cross Sections Differential Equations (Three Weeks) 1. Slope fields 2. Differential Equations: Growth and Decay Models 3. Separation of Variables 4. First-Order Differential Equations
Week Dates Sections Homework Aug 15 19 1.1, 1.2, 1.3: Functions 1 Graphing Calculators 2 Aug 22 26 1.5: Inverse Functions and Logarithms 1.6: Trigonometric Functions Chapter 1 Quest 3 Aug 29 Sept 2 2.1: Rates of Change and Limits, Finding Limits Graphically and Numerically 2.2: Infinite Limits 4 Sept 6 9 2.3: Continuity/One-sided limits 2.4: Rates of Change, Tangent Lines 5 Sept 12 16 Chapter 2 Test 3.1: Derivatives and the Tangent Line 6 Sept 19 23 3.2: Differentiability 3.3: Rules for Differentiation 3.4: Velocity and Other Rates of Change 7 Sept 26 30 3.5: Derivatives of Trigonometric Functions Chapter 3 Test 8 Oct 3 7 4.1: Chain Rule 4.2: Implicit Derivatives 9 Oct 10 14 4.3: Derivatives of Inverse Trigonometric Functions 10 Oct 17 21 4.4: Derivatives of Exponential and Logarithmic Functions Chapter 4 Test 11 Oct 24 28 9.2: Indeterminate Forms and L Hôpital s Rule 5.1: Extreme Values of Functions 5.2: Mean Value Theorem 12 Oct 31 Nov 4 5.3:!, f and the graph of f 13 Nov 7 11 5.4: Modeling and Optimization 14 Nov 14 18 5.5: Linearization and Newton s Method 5.6: Related Rates Chapter 5 Test 15 Nov 28 Dec 2 6.1: Estimating with Finite Sums (Riemann Sums) 6.5: Trapezoidal Rule 6.2: Definite Integrals 16 Dec 5 9 6.3: Definite Integrals and Antiderivatives 6.4: Fundamental Theorem of Calculus 17 Dec 12 16 Chapter 6 Test 18 Jan 5 6 7.2: Antiderivatives by Substitution 19 Jan 9 13 7.3: Antiderivatives by Parts 20 Jan 16 20 7.4: Exponential Growth/Decay 21 Jan 23 27 7.1: Slope Fields and Euler s Method First-Order Differential Equations 22 Jan 30 Feb 3 Chapter 7 Test 25 Feb 6 10 8.1: Accumulation and Net Change 26 Feb 13 17 8.2: Area Between Two Curves 27 Feb 20 24 8.3: Volumes: The Disk Method and Washer Method 28 Feb 27 Mar 3 Project #2 29 Mar 6 10 Project #2 Presentations 30 Mar 13 18 Chapter 8 Test 31 Mar 27 Mar 31 AP Review: Non-calculator multiple choice 32 Apr 3 7 AP Review: Multiple choice AP Review: Free Response 33 Apr 10 14 AP Review: Mock Exam Problem Set AP Review: Free Response Problem Set 34 Apr 17 21 AP Review: Area/Volume (MC) AP Review: Area/Volume (FR) 35 Apr 24 28 AP Review: Slope fields/differential Equations AP Review: FTC-Accumulations AP Review: Calc & Non-Calc MC Problem Set AP Review: Calc & Non-Calc FR Problem Set 36 May 2 6 AP EXAM-May 5
Greene County Tech 9 Week Off-Campus Lunch and Semester Test Exemption Guidelines First and Third Nine Weeks: Greene County Tech High School students will have the opportunity to qualify for an off-campus lunch during the 1 st and 3 rd nine week periods given the following criteria: Attendance A student may not have more than two absences in the 1 st and 3 rd nine weeks. School activity will not count against your off-campus lunch Students have 48 hours to document a professional absence. If not documented, the absence will be considered a non-professional absence. Doctors, court, or funeral excuses (professional notes) will NOT count against days missed Discipline No ISS/OSS during the 1 st and 3 rd nine weeks No Bus Suspension during the first and third nine weeks. Second and Fourth Nine Weeks: Greene County Tech High School students may qualify for semester test exemptions during the 2 nd and 4 th nine week periods given the following criteria: Grades Must have a C average for the semester. Absences Only four non-professional absences will be allowed in each class period during the entire SEMESTER. You may save all 4 absences to use the 4 prior days to semester exams. Doctors, court, or funeral excuses (professional notes) will NOT count against the student s exemption. Students have 48 hours to document a professional absence. If not documented, the absence will be considered a non-professional absence. School Activities will not count against a student s eligibility for qualifying for exemptions. Discipline - No ISS/OSS during the 2 nd or 4 th nine weeks. No Bus Suspension during the 2 nd or 4 th nine weeks. Fines/Fees All fines and fees must be paid in full (i.e. library, lunch, books, etc.) for the current semester. ***Administration meeting resulted in allowing pre-ap and AP students the ability to qualify for semester test exemptions.