Welcome To AP Calculus BC! - Erie High School

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Welcome to AP Calculus BC!Erie High SchoolAnna PanakhyoPanakhyo [email protected] to AP Calculus:AP Calculus is a rigorous course in which we will be covering all topics included on the APCalculus BC Course Exam (more information alculus-bc). This course will cover theconcepts of Calculus AB and the additional topics of Calculus BC, therefore we will have a verybusy year! The major textbook is the 10th edition of Larson Calculus of a Single Variable APEdition. My goal is to prepare you to do well on the AP exam, but also to become betterproblem solvers, critical thinkers and further develop your study skills. All of these arecrucial for the transition into college.All students are expected to take the AP exam at the end of the year. The cost was 93.00 forthe 2016 exam. The AP exams are graded on a scale from 1 to 5. A score of 3 (qualified) mayor may not earn you credit at colleges you are interested in. You will need to check with yourparticular college of interest to see what score you will need to be given credit. The APCalculus BC exam will give you a AP Calculus AB sub-score, which may give you credit forCalculus 1 at your college. You will also get an AP Calculus BC score, which may give youcredit for Calculus 2 at your college. Some colleges and programs may require you to re-takeCalculus 1 and 2 at their school. The exposure here will be helpful, but you never know whattopic your college/school will want you to know.We will be using graphing calculators in this course and you can use graphing calculators onpart of the AP Exam. The calculator I use and recommend is a TI-84. You are expected tobring your calculator everyday to class whether we use it that day or not. You are expectedto know how to use certain functions of the graphing calculator including finding theintersection of two functions, finding the maximum and minimum of a function, usingSOLVER to solve equations, fitting a window of a graph, changing graphing settings, andadjusting a table. If you need help using or learning these functions I will be availableThursday, May 19 after school for a graphing calculator training. I highly suggest anyone whodoes not know how to use these functions of the graphing calculator come to the calculatortraining as there is very little time in class to teach these graphing calculator functions.Additionally, I suggest you get an AP Calculus review book to supplement the practice in classand from our textbook. On Schoology (schoology.svvsd.org), I will have a list of books that Isuggest. This is not a requirement, but HIGHLY recommended.Schoology (schoology.svvsd.org) will be used for the class webiste. On Schoology, I will postcalendars, homework assignments, study aides, online resources and important information.Class notes will be posted on the website and students will be expected to print notes beforeclass. The website is schoology.svvsd.org.Summer Homework:In order to get through all of the material by May, you have been assigned a summerassignment. In this assignment you will be reviewing concepts from previous math courses,practicing graphing using your calculator, and introducing yourself to the course material.This summer assignment will count for a major portion of your semester homework grade;therefore, this is not an optional assignment. Your summer assignment will be due the first1

day of class. Students who do not, or cannot complete this assignment should definitely askthemselves if they should be taking AP Calculus BC.I suggest you complete the assignment in parts over the summer to avoid cramming theentire assignment until August. All of these problems were chosen to help students reviewand prepare over the summer, as well as familiarize you with the AP exam. Students areencouraged to work together, but any final work must be that of the individual student. Youare encouraged to review and use your notes from previous math courses to help with theassignment.Legibility and understandability are important. If your work is illegible, I cannot find youranswer, or there is not support (work) for your answer, you will receive not credit for theproblem. You can use your calculator to complete the summer homework, but please keep inmind that more than half of the AP exam is non-calculator. Therefore, do not rely too much onyour calculator.Schoology:You will be added to a Schoology (schoology.svvsd.org) course for the summer. Most likelythis will be a different Schoology course than we will use during the school year. I will use thisSchoology site to share important information and resources throughout the summer. Therewill also be a discussion board where you can post questions for your peers and the teacherthroughout the summer. It is an expectation that you check Schoology on a regular basis overthe summer.Calculus Readiness Test for student who have NOT taken Calculus AB:Please use the Fresno State University Calculus Readiness placement-exams/calc-readiness.html) toprepare for the upcoming year of calculus. There are two practice test available, and you willget immediate feedback. The problems on this readiness test are similar to the summerhomework. This readiness test can help you determine any pre-requisite skills you need torevisit.Calc Camp:Calc Camp will be August 1-4 in T109 from 1-3 pm.August 1- Reviewing Precalculus skills and calculator tipsAugust 2- Continued review of Pre-Calculus skills and limitsAugust 3- Limits and DerivativesAugust 4- Parametric EquationsAll students in Calculus BC are highly recommended to attend the August 4th session, asparametric equations may not have been covered in your Pre-Calculus class and will beincluded in Calculus BC.Calc Camp is not required, but highly suggested.Other Online xhttps://www.wolframalpha.com/2

If you have any questions, you can contact me over the summer atpanakhyo [email protected] I will be out of town part of the summer, but generally check thise-mail every 2-3 days. Please send me a brief e-mail introducing yourself and so I have a wayof contacting you over the summer.I am looking forward to an exciting year in AP Calculus BC next year and getting to know allof you!Have a good summer and see you in the fall,Anna PanakhyoSummer Homework Part 1: Kahn Academy1. Go to kahnacademy.com2. Create an account with your school e-mail address.3. Once you log-in, you will see your name in the upper right corner. Click on the arrow nextto your name. Click on “Profile.”3

4. Your Dashboard will now be open. Click on “Coaches.”5. Under “Add a Coach,” enter the AP Calculus BC 2016-2017 code . You will nowbe part of the course and Ms. Panakhyo can recommend you the following skills for youpractice. It is suggested that you practice the skills in this order, as they may not be in thisorder on your screen. This is the most logical order. There are 20 skills you must practice. Finding limits numerically One sided limits from graphs Two-sided limits from graphs Two sided limits using algebra Continuity Limits at infinity where f(x) is unbounded The formal and alternate form of the derivative Recognizing slope of curves Graphs of functions and their derivative Visualizing derivatives Power rule (basic) Special derivatives Chain rule on two functions Product Rule Quotient Rule Application of derivatives: tangent and normal lines Application of derivatives: motion along a line Extreme values from graphs Concavity and the second derivative Local linearizationYou are not limited to only practicing these skills. You are welcome to practice additionalCalculus skills as well. These will be the skills I will check for in August.4

6. On the Dashboard bar, click on “Progress.” Then click on “Coach Recommendations.” Atfirst you will see a grey/empty box under the “Mastery Status” column. Once you answer 5questions in a row correctly you will reach the “Practiced” level. You will need to meet the atleast the “Practiced” level for these 20 skills by the first day of school. Every so often you willget a Mastery Mission, where you can move up a level or reach the Mastery level. Completethese Mastery Missions.7. For each skill, you will complete the exercises indicated with a star on the timeline on theleft side of the screen. For the exercises, you can get a hint by clicking the “I’d like a hint.”You can also watch a video pertaining to the question’s topic. If this is a new topic or conceptfor you, I suggest you watch the videos and tutorials before the exercise indicated by anarrow on the timeline on the left-side of the screen.8. If it has been a while since you logged into Kahn Academy to check your progress, makesure on your Progress screen on the top right of the chart you change “Activity from” to“Last 30 days” or “All time.” The automatic default is “Last 7 days.”5

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Summer Homework Part 2: Problem SetYou will find an attached problem set that reviews limits, derivatives and applications. Theseproblems are due the first day of class. Use your notes from previous math classes andCalculus AB to help you complete these problems. You may also work with others, butremember each person must turn in their own work. All work must be shown. If you use acalculator, you must set-up the problem on your paper and indicate what the calculatorproduced.NOTE: Problems with an asterisks (**) are required for students who have taken APCalculus AB. Students who have not taken AP Calculus AB may need to research how tocomplete theses problems. These problems are not required for students who have not takenAP Calculus AB, but recommended to try.For #1-17, consider the graph of f below.1) lim 𝑓(𝑥) 9) lim 𝑓(𝑥) 2) lim 𝑓(𝑥) 10)3) lim 𝑓(𝑥) 11)4) lim 𝑓(𝑥) 12) lim 𝑓(𝑥) 5) lim 𝑓(𝑥) 13)6) lim 𝑓(𝑥) 14)7) lim 𝑓(𝑥) 15) 𝑓 2 8) lim 𝑓(𝑥) 16) 𝑓 3 &' &- & .- .' . /' /lim 𝑓(𝑥) 0'lim 𝑓(𝑥) 0 0lim 𝑓(𝑥) 1lim 𝑓(𝑥) '1 /-7

Evaluate the following limits algebraically: '417) lim 521)18) lim (2𝑥 / 3𝑥 4) 22) 4 '4 619)20)lim '/lim : -/ 5 '46'& 5 - '. '& 5 '; 23)24). 5 -6 lim '1 4' / '& lim cos 𝑥 1lim '1lim/ 56 5 '; '/ 5 - '1 &' 𝑥 / 𝑎/ 𝑥 𝑖𝑓 𝑥 24 2𝑥 / 𝑖𝑓 𝑥 2a) Find the lim 𝑓 𝑥25) **Let 𝑓 𝑥 /'b) Find the lim 𝑓 𝑥 /-c) Find all values of a that make f continuous at 2. Justify your answer.Find the derivative of the following526) 𝑓 𝑥 𝑥 'E33) **𝑓 𝑥 27) 𝑓 𝑥 𝑥 & 𝑥 / 2𝑥34) 𝑓 𝑥 28) **𝑓 𝑥 5𝑒 329) 𝑓 𝑥 30) 𝑓 𝑥 31) 𝑓 𝑥 :𝑥JK 5 L'& 35) 𝑓 𝑥 sin 𝑥 cos 𝑥36) 𝑓 𝑥 𝑥 / cos 𝑥4H37) 𝑓 𝑥 2 cot 𝑥 𝑥 sec 𝑥 I 5 -0 -&38) **𝑓 𝑥 𝑥 & 14HH 32) **𝑓 𝑥 𝑥 / 𝑒 39) **𝑓 𝑥 𝑥 / 7𝑥8

40) ** If 𝑓 𝑥 𝑥 / 2𝑒 , find the value of 𝑓′(1)41) If 𝑓 𝑥 2𝑥 / 𝑥 & , find 𝑓′(𝑥), 𝑓′′(𝑥), and 𝑓′′′(𝑥)42) Find the slope of the tangent line to the graph of 𝑔 𝑥 𝑥 / 4 at the point (1, 3).&43) Find the equation of the tangent line to the hyperbola 𝑦 at the point (3, 1). 44) ** FindVW45) ** FindVWV V by implicit differentiation: 𝑥 / 𝑦 / 25by implicit differentiation: 𝑥 / 𝑥𝑦 𝑦 & 89

46) ** A particle moves according to a law of motion 𝑠 𝑓 𝑡 𝑡 & 12𝑡 / 36𝑡, 𝑡 0, wheret is measure in seconds and s in meters.a) Find the average velocity on the interval [2, 7].b) Find the velocity at time t.c) What is the velocity after 3 seconds?d) When is the particle at rest?e) Find the total distance traveled during the first 8 seconds.f) Find the acceleration at time t.g) Find the acceleration after 3 seconds.10

47) Suppose that a function f and its first derivative have the following values at 𝑥 0 and𝑥 1.𝑥𝑓(𝑥)𝑓′(𝑥)019 3 24Find the first derivative of the following functions at the given values at x. a) 3𝑓 𝑥 , 𝑥 1d),𝑥 1 b) 𝑥𝑓 𝑥 , 𝑥 1c) 𝑥 / 𝑓 𝑥 , 𝑥 1e) 5 -/,𝑥 0f) 𝑓 𝑥 𝑓(𝑥), 𝑥 048) The accompanying figure shows thegraph of the derivative of a function f. Thedomain of f is the closed interval [-3, 3].a) For what values of x in the openinterval (-3, 3) does f have a relativeminimum? Justify your answer.b) For what values of x in the openinterval (-3, 3) does f have a relativemaximum? Justify your answer.c) ** For what values of x is the graph off concave up? Justify your answer.d) ** Suppose 𝑓 3 0. Sketch a possible graph of f on the domain [-3, 3].11