AP CALCULUS AB ~  er Work and List of Topical Understandings~ Revere High Math Department

1. Intro-1 AP CALCULUS AB ~er Work and List of Topical Understandings~ Revere High Math Department • As instructors of AP Calculus, we have extremely high expectations of students • taking our courses. As stated in the district program planning guide, we expect a • certain level of independence to be demonstrated by anyone taking AP Calculus. • Your first opportunity to demonstrate your capabilities and resourcefulness to us • is through this summer work packet which will help you maintain/improve your • skills. This packet is a requirement for all AP Calculus students and is due on the • three different assigned dates. If it is not completed on the assigned dates, you may • not be allowed to attend the AP Calculus class starting in late August. Work on • as much of this packet on your own as you can, then get together with a friend, • e-mail one of the teachers or “google” the topic to find an appropriate solution. • SHOW US YOUR BEST WORK. • Requirements • The following are guidelines for completing the summer work packet… • There are many questions you must complete. You must show us all of your quality work. There is enough room for you to show your work in the packet. • Be sure all problems are neatly organized and all writing is legible. • In the event that you are unsure how to perform functions on your calculator, you may need to read through your calculator manual to understand the necessary syntax or keystrokes. You must be familiar with certain built-in calculator functions such as finding maximum and minimum values, intersection points, and zeros of a function. You will also need to be able to do regression analysis on your calculators.

2. We expect you to come in with certain understandings that are • prerequisite to Calculus. A list of these topical understandings is below. • Please be familiar with all of these and ready to apply them to a higher level. • Topical understandings within summer work… • Factoring • Zeros/roots/x-intercepts of rational and polynomial functions • Unit Circle • Composite function and notation • Limits of functions • Solving trigonometric equations • Trigonometry Identities • Conic shapes and their equations • Domain/Range • Interpreting and comprehending word problems • Regression analysis • Graphing, simplifying expressions, and solving equations of • The following types: trigonometric, rational, piecewise, logarithmic, exponential, polynomial/power, radical, polar, and parametric. Intro-2 Finally, we suggest not waiting until the last moment to begin working on this packet. If you spread it out, you will most likely retain the information much better. Once again this is due, completed with quality, on the dates indicated inside this package. It is your ticket into the class. NO TICKET…NO SEAT!! Best of luck and if you have Any questions, feel free to contact us. We really hope you are showing all you work. Do not skip steps. Please be extremely neat. The secret in successfully learning calculus is to approach each step in solving a problem with caution. Label all answers when it is required. Helpful web-sites http://www.coolmath.com/precalculus-review-calculus-intro/index.html http://www.youtube.com/user/khanacademy http://www.kutasoftware.com/free.html http://www.algebra-class.com/algebra-cheat-sheet.html http://www.ecalc.com/math-help/ http://regentsprep.org/REgents/math/ALGEBRA/math-ALGEBRA.htm First impressions are lasting impressions…impress us!! If I have seen farther than others it is because I have stood on the shoulders of giants.

3. Intro-3 TWO Mr Cifuni and Ms Szymanski will be available to give hints and answers to the questions that you might be having difficult doing. Email address: cszymanski29@comcast.net Email address: geraldcifuni@comcast.net If you feel the need to, Mr Cifuni or Ms Szymanski can schedule class meeting(s) at the high school, the public library, or some place else. You just have to let us know if and when you would like to Meet. Good Luck and Welcome to Advanced Placement Calculus!

4. Intro-4 How to Succeed In AP Calculus How to succeed in Mathematics By being prepared for class each day - with homework complete and all required materials. Reason - puts us in position to succeed. By taking notes – write all teacher notes and practice problems done in class in your notebook. Reason – writing things down helps us to remember them and gives us examples to use if we have trouble doing homework. It also helps to keep us focused in class. By asking questions to help gain understanding. Reason - we need to ask questions when we do not understand – it leads to learning. By answering questions. Reason - helps to check our understanding and make sure we are on the right track. By doing the problems the way the teacher does them. Reason - this way works. Doing problems this way will result in the correct answers. By reviewing your notes each night. Reason - reviewing helps us to determine if we really understand the process and helps us identify the questions we need to ask. By doing homework each night. Reason - practicing a skill helps us to become better. It also helps us to determine if we really understand the process and helps us identify the questions we need to ask. (Math is not a spectator sport. We learn math by doing it ourselves. To improve, we need to practice.) By practicing problems for quizzes/tests. Reason - practice helps make us better and more confident. We need to be our best on quiz/test days. By seeking help when it is needed. Reason - it is important to keep up. New lessons build on previous lessons. By having a positive attitude. Attitude by Charles Swindoll "The longer I live, the more I realize the impact of attitude on life. Attitude to me, is more important than facts. it is more important than the past, than education, than money, than circumstances, than failures, than successes, than what other people think or say or do. it is more important than appearance, giftedness, or skill. it will make or break a company . . . a church . . . a home. The remarkable thing is we have a choice every day regarding the attitude we will embrace for that day. We cannot change our past . . . we cannot change the fact that people will act in a certain way. We cannot change the inevitable. The only thing we can do is play on the one string we have, and that is our attitude. . . I am convinced that live is 10% what happens to me and 90% how I react to it. And so it is with you . . . we are in charge of our attitudes." Daily Check List I am prepared for class I am in my desk when the bell rings I have my homework finished and out for review I have a “I want to learn” Attitude I participate in “my” learning I am listening when others are talking I ask questions to help me understand I do “my” best - My success in My success Study Skills (from a poster in the guidance office at CCC) • Pay Attention in Class • Take good notes • Keep an organized notebook for each subject • Know the purpose of each assignment • Ask questions in class • Review, Review, Review It can help you retain 80% of the information • Plan a definite time and place for studying each day • Study for awhile and take short breaks • Don’t cram for hours the night before a test Study a little bit each day • Think positive • Do your best

5. Intro-5 How Your Summer Assignment Will Be Graded. The Rubric is shown below:

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10. Of2011 1 Time Due: Before 1:00 pm 27

11. Page 1 Summer Assignment 1 Ex1: During as camping trip in North Bay, a couple went one-third of the way by boat, 10 miles by foot, and one sixth of the way by horse. How long was the trip? Identify the question: Set up an equation: Solve the equation: Check the solution: Ex 2: The manual for your car suggests using gasoline that is 89 octane. In order to save money, you decide to use some 87 octane and some 93 octane in combination with the 89 octane currently in your tank in order to have an approximate 89 octane mixture. Assuming you have 1 gallon of 89 octane remaining in your tank (your tank capacity is 16 gallons), how many gallons of 87 and 93 octane should be used to fill up your tank to achieve a mixture of 89 octane? Identify the question: Set up an equation: Solve the equation: Check the solution:

12. Page 2 Summer Assignment 1 Ex3: It takes eight hours to fly from Orlando to London and 9.5 hours to return. If an airplane averages 550 mph in still air, what is the average rate of the wind blowing in the direction from Orlando to London? Assume the wind speed for both legs of the trip. Identify the question: Set up an equation: Solve the equation: Check the solution: Ex4: From 1999 to 2001 the price of Abercrombie & Fitch’s (ANF) stock was approximately give by P = 0.2t2 – 5.6t + 50.2, where P is the price of stock in dollars, t is in months, and t=1 corresponds January 1999. When was the value of the stock worth $30? Identify the question: Set up an equation: Solve the equation: Check the solution:

13. Page 3 Summer Assignment 1 Ex5: Solving Rational Equations: Solve the equation: Ex6: Solving an Equation Involving a Radical: Solve the equation: Ex7: Solving an Equation Quadratic in Form with Negative Exponents: Find the solutions to the equation: Ex8: Solving an Equation Quadratic in Form with Negative Exponents: Find the solutions to the equation:

14. Page 4 Summer Assignment 1 Ex9: Solving a Quadratic Absolute Value Equation Solve the equation: Ex10: Solving a Linear Inequality Solve and graph the inequality: Ex 11: Two car rental companies have advertised weekly specials on full-size cars. Hertz is advertising an $80 rental fee plus an additional $.10 per mile. Thrifty is advertising $60 and $.20 per mile. How many miles must you drive for the rental car from Hertz to be the better deal? Ex12: Finding the Center and Radius of a circle by Completing the Square Solve the center and radius of the circle with the equation

15. Page 5 Summer Assignment 1 Ex13: Finding an Equation of a Line That is Perpendicular to Another Line Find the equation of the line that passes through the point (3,0) and is perpendicular to the line y = 3x + 1. Ex14: Evaluating Functions Sums For the given function H(x) = x2 + 2x (a.) H(x+1) (b) H(x) + H(1) Ex15: Evaluating the Difference Quotient For the function

16. Page 6 Summer Assignment 1 Ex16: Determine Whether a Function Is Even, Odd, or Neither. (c) (a) (b) Ex17: Determine Average Rate of Change. Key: The slope of the secant line is used to represent the average rate of change of a function. Find the average rate of change of f(x) = x4 from x = -1 to x= 0. Ex18: Graphing Piecewise-Defined Functions. Graph the piecewise-defined function, and state the domain, range, and interval when the function is increasing, decreasing, or constant. You must graph piecewise function here! { G(x) = Ex19: Sketching the Graph of a Function Using Both Shifts and Reflections. Sketch the graph of the function You must graph function here!

17. Dog Pen House Page 7 Summer Assignment 1 Ex20: Determine a Composite Function. (c) (a) (b) Ex21: Determine the Domain of a Composite Function. Given the function and , determine f g and state its domain. Ex22: Determine the Inverse Function. The function is a one-to-one function. Find its inverse Ex23: Determine the Inverse Function. You have just bought a puppy and want to fence in an area in the backyard for her. You buy 100 linear feet of fence from Home Depot and have decided to make a rectangular fenced-in area using the back of your house as one side. Determine the dimensions of the rectangular pen that will maximize the area in which your puppy may roam. What is the maximum area of the rectangular pen? Do you know why dogs do not go to heaven?

18. Page 8 Summer Assignment 1 Ex24: Identifying Polynomial and Their Degrees. (a) (b) (c) (c) (d) (e) Ex25: Identify the Real Zero’s of a Polynomial Function. Find the zeros of the polynomial function Ex26: Long Division of Polynomial with “Missing” Terms. Ex27: Synthetic Division by Divide by Divide

19. Page 9 Summer Assignment 1 Ex28: Find Slant Asymptotes Determine the slant asymptote of the rational function Ex29: Graphing Rational Function with a Hole in the Graph Graph the rational function . Find the domain, x and y intercept, asymptotes, and hole . Ex30: Graphing Rational Function with a Hole in the Graph Find the exact value of (a) (b) (c)

20. Page 10 Summer Assignment 1 Ex31: Application of Logarithms The magnitude of an earthquake is measured using the Richter scale. Where M= is the magnitude E is the seismic energy released by the earthquake (in joules) E0 is the energy released by a reference earthquake E0= 104.4 joules On October 17, 1989, just moments before game 3 of the World Series between the Qakland A’s and the San Francisco Giants was about to start - with 60,000 fans in Candlestick Park – a devastating earthquake erupted. Parts of interstates and bridges collapsed and President George W Bush declared the area a disaster zone. The earthquake released approximately 1.12 x 1015 joules. Calculate the magnitude of the earthquake using the Richter scale. Ex32: Combining Logarithmic Expressions into a Single Logarithm Write the expression as a single logarithm. Ex33: Expanding Logarithmic Expressions into a Sum or Difference of Logarithms Write the expression as a sum and difference of logarithms. Ex34: Solving a Simple Logarithmic Equation Solve the equation

21. Page 11 Summer Assignment 1 Ex35: Calculating How Many Years It Will Take for Money to Double. Recall the compound continuous interest formula: You save $1,000 from a summer job and put it in a CD earning 5% compounding continuously. How many years will it take for your money to double? Round to the nearest year. Ex36: Calculating World Population Projections. The world population is the total number of humans on Earth at a given time. In 2000 the world population was 6.1 billion and in 2005 the world population was 6.5 billion. Find the annual growth rate and determine what year the population will reach 9 billion.