Calculus Applications Course Curriculum Letter - 2017-2018 Mr. Inhaber brandoninhaber@nestmk12.net mrinhaber.weebly.com Dear Student, I am looking forward to a great year in Calculus Applications. In order to be successful in this class, we will cultivate the following habits of mind together: Perseverance: We will work together and persevere even when the work is very difficult Courage: We will be courageous in our questioning, creativity, and academic risk taking Responsibility: We will be responsible work with academic integrity, be in attendance, prepared, and on time each day Engagement: We will be minds on, intellectually open, and committed to continual development of our skills in mathematical problem-solving This course is an introductory course in Calculus and covers the scope of a first year college calculus course. It is designed for seniors who have completed Precalculus and want to take a slower-paced course than Advanced Placement Calculus. Calculus provides answers to questions that cannot be solved by using, algebra, geometry, or trigonometry alone. Topics covered include functions and graphs, tangent lines, derivatives, limits and continuity, applications of differentiation and integration. These will be applied to problem solving with special emphasis on application in business and the social sciences. The course teaches students to approach calculus concepts and problems when they are represented graphically, numerically, analytically, and verbally, and to make connections among these different representations. Students will use extensively technology to help them solve problems, experiment, interpret results, and support conclusions. Students will be prepared to further study mathematics, engineering or the physical and social sciences at the collegiate level. A Final Exam will be administered in class at the end of the year. Essential Questions: Chapter 1 Linear Functions 1. How can we find the slope of a line? 2. What are different equations for a line? 3. What are parallel and perpendicular lines? 4. What is an equilibrium and how can we use it to solve problems? 5. How can we find the revenue and profit from a function? 6. How can we use least squares to find the line of best fit? Chapter 2 Nonlinear Functions 1. What do domain and range tell us about a function? 2. What can we know about the graph of a quadratic function? 3. What are the properties of polynomial and rational functions? 4. How can we solve problems using finance formulas 5. What are the properties of logarithms and exponential functions? Chapter 3 The Derivative 1. What is a limit? 2. How can we know if a limit exists? 3. What happens as x approaches infinity? 4. What does a derivative represent? 5. How does average rate of change relate to the derivative? Chapter 4 - Calculating the Derivative
1. What are different rules we can use to find derivatives? 2. What does the chain rule represent? 3. How can we find the derivative of exponential functions? 4. How can we find the derivative of logarithmic functions? Chapter 5 Graphs and the Derivative 1. How can we know when a function is increasing or decreasing? 2. What does the First Derivative Test tell us? 3. What is concavity, and how can we determine the concavity of a function? 4. What does the Second Derivative Test tell us? Chapter 6 Applications of the Derivative 1. How can we solve problems using extrema? 2. What is elasticity of demand? 3. How can we use implicit differentiation? 4. How can we solve related rates problems? 5. What are differentials? 6. How can we use linear approximations? Chapter 7 Integration 1. What are formulas for antidifferentiation? 2. What is a definite integral? 3. What is the Fundamental Theorem of Calculus? 4. How can we find the areas between two curves? 5. How can we find consumer s and producer s surplus? Chapter 8 Further Techniques and Applications of Integration 1. What is integration by parts? 2. How can we find the volume of a solid of revolution? 3. How can we find the average value of a function? 4. How can we solve problems with money flow? 5. What are improper integrals? 6. How can we calculate capital value? Chapter 9 Multivariable Calculus 1. What are partial derivatives? 2. How can we test for relative extrema? 3. How can we use Lagrange Multipliers? 4. How can we find approximations by differentials? 5. How can we find double integrals? 6. How can we use integrals to find the volume of a solid under a graph? Chapter 10 Differential Equations 1. What are differential equations? 2. What are separable differential equations? 3. How can we solve a linear first-order differential equation? 4. What is Euler s Method? Chapter 11 Probability and Calculus 1. What is a cumulative distribution function? 2. How can we find the variance of a function? 3. What does a standard deviation represent? 4. What do different types of distributions represent? 5. How can we use z-scores to analyze information? Chapter 12 Sequences and Series 1. How can we find terms in a geometric sequence? 2. How can we find the sum of a geometric series?
3. How can we use formulas to find the amount in an annuity? 4. What does a Taylor Series represent? 5. How is Newton s Method helpful? 6. How can we use L Hospital s Rule to find limits? Chapter 13 - The Trigonometric Functions 1. What is the difference between radians and degrees? 2. What do trigonometric functions represent? 3. What do the graphs of trigonometric functions look like? 4. How can we find transformations of trigonometric functions? 5. How can we find the derivatives of trigonometric functions? 6. How can we find the integrals of trigonometric functions? Materials: It is essential that the students are ready to learn by having the prior materials/tools. You should always have the following materials in class: 1. (1) Pencil case 2. (3) Pencils 3. (1) Eraser 4. (1) Pack of Color Pens or Highlighters 5. (1) Notebook or Binder with paper 6. (1) Folder 7. (1) Graph Notebook/Graph Paper 8. TI 83/84 Graphing Calculator 9. (1) Ruler or straightedge Classroom Policies: Our Code of Respect: We respect ourselves We respect each other We respect our school community Additional Resources: Please check the Web Site at mrinhaber.weebly.com for additional resources, including homework assignments and important announcements and documents. Assessments: Exams will only be given on Thursdays. Quizzes can be given on any day of the week. Attendance: Students are expected to arrive to class on time. By arriving late you disrupt the class and miss instruction. All students arriving late must sign in on the Log Book. All students arriving late to the first period class must submit the late pass generated by the CAASS system and sign in to the Log Book. Classroom Expectations: Class starts as soon as the bell rings. Students are expected to be in their seats with their notebook, pencils and calculators out. Students who arrive to class after the bell rings must provide a late pass and sign into the Log Book. A note must be provided for excused absences. Students who are excessively late or absent will be referred to the Assistant Principal and the student's guidance counselor. Grade Book: Assignments and grades will be posted on on PupilPath. Students and parents/guardians will be invited to set up separate accounts to access grades, assignments, and class supplementary materials. The Gradebook will be updated at minimum 2x per month per the attached AB Calendar. Digital Portfolio: Twice per semester, students will have a project, written assignment or major assessments uploaded to their bio page on PupilPath with its associated self-reflection and feedback. Portfolio pieces should always be pieces that have been drafted, polished, and given feedback before final submission. When possible, students will be able to choose the assessments uploaded to their portfolio.
Late or Missing Work Policy Homework: Homework is always in service of our summative assessments. Homework will be assigned on Delta Math. Except in the event of an excused absence, homework handed up to 1 week late will receive a maximum of 80%. Beyond 1 week late, the assignment will not earn more than 65%. Summative Assessments, e.g. projects: Except in the event of an excused absence, a summative assessment handed up to 1 week late will receive a maximum of 80%. Beyond 1 week late, the assignment will not earn more than 65%. Exams: Provided your absence was excused, you may schedule a make-up session within one week of your return to school. Excused absences: Students must hand in assignments the week they return to school with a signed note from their parent or guardian. It is your responsibility to complete and hand in all assignments that are due. Hall Pass Policy: You must always ask permission first before going to the bathroom. All students are required to sign in and sign out of the Log Book before taking the hall pass. The bathroom is located across from room 361 and 359. Scholastic Dishonesty: Scholastic dishonesty is an academic violation and is absolutely not tolerated. Student may be referred to the Dean and appropriate action will be taken. School Tone: Please keep cell phones on silent mode and in your backpack. Cell phones can only be taken out when instructed by the teacher. The first offense is a warning. Second offense will result in a phone call home. Tutoring Hours: Mr. Inhaber is available for tutoring on Wednesdays from 2:45 3:45 pm. If you are unable to attend at this time, please request a tutoring time through email. Item Formative Assessments: Classwork, Class Participation & Quizzes There will be classwork assignments that will be graded. There will also be a grade given for the amount that you participate in class. This includes being a productive and respectful member of the classroom community. There will be quizzes to assess your progress in specific units. Homework: Most nights you will have short assignments. I will grade them and return them within one week. If you are absent, you must makeup the homework within two weeks. Late homeworks will receive partial credit. Three missing homeworks will result in a phone call home. Summative Assessments: Exams & Projects We will have exams on Thursdays. These will always be announced at least one week in advance. We will review in class for exams. If you are absent on the day of an exam, you must make it up as soon as possible. Please be advised that students must be currently passing all of their classes in order to participate in special events/sports games/club activities. Reflective Practices: Summative Assessment Reflections, Unit Reflections, Self-Reflection Practices Students will be given the opportunity to reflect on their progress and mastery of the material. This will help students to focus on what they need to learn and to succeed. Total 100% Grade Breakdown 50% 10% 30% 10% Midterm: The midterm exam will be based on all the material that you learned in the semester. 15% of Semester Grade*
Contract for Learning After reading this curriculum letter, please share it with your parents, then complete and sign the contract for learning below. Both student and parent / guardian need to sign. I will collect all signed contracts on Monday, September 11. The signed contract will count as your first homework grade. Students: I have read the Course Curriculum Letter for Pre-Calculus Applications and fully understand the course expectations. I agree to cultivate the habits of mind described in the Curriculum Letter and fulfill the requirements of the Pre-Calculus Applications curriculum to the best of my ability. Student Name: Signature: Email Address: Students please check one: [ ] I already have a PupilPath Parent account and understand how to login and check my child s grades [ ] I do not have a PupilPath account and need registration / login instructions [ ] I have a PupilPath account but cannot login. I need directions for resetting my account. Parents/Guardians: I have read the Course Curriculum Letter for Pre-Calculus Applications and fully understand the course expectations. Parent/Guardian Name: Signature: Phone Number: Email Address: Parents please check one: [ ] I already have a PupilPath Parent account and understand how to login and check my child s grades [ ] I do not have a PupilPath account and need registration / login instructions [ ] I have a PupilPath account but cannot login. I need directions for resetting my account