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1、.Honors AP Calculus AB Name_Thrill-a-Minute Summer Opportunity 2010Textbook #_ Your summer assignment is to basically have the review packet (a review of Algebra 2 / Trig. and Pre-Calculus), Chapter 1, and 2.1-2.2 (all of which you learned from Mr. Kozeny) of the Calculus book mastered by the time s
2、chool begins in the fall (this includes working problems from the book and the attached worksheets). You are to do this by preparing a packet of the homework assigned below, which will exhibit your efforts related to the chapter. The homework packet will be due on the first day of class. Work all in
3、dicated problems and as many more as you need to work in order to fully understand each topic presented. Neatly show your work on all the problems assigned. Your homework grade will be based partially on quality completion, and partially on correct answers. Much of the two chapters is very readable,
4、 IF YOU READ IT! Read everything slowly and with great care. Much of what you read will be review and should be well within your grasp. At all cost, give everything an honest attempt. I suggest you begin working by August 1st (at the latest) and continue to do about two sections or worksheets per da
5、y. That way you wont be laboring on it all summer and you wont have to cram in the last few days before school starts. Dont procrastinate. Lets get the year off to a flying start (then we can find its related rate)! It will be expected that you have a good working knowledge of your graphing utility
6、including max-min, intersect, zero, window. You will do quite a bit of “analysis” of graphs in calculus where you work exclusively with the graph of the function without ever knowing or needing to know the definition of that function. This may be new to you. To prepare I suggest you look at each gra
7、ph as an opportunity to synthesize what you know about it, i.e. domain, range, zeros, asymptotes, max-min, whether increasing or decreasing and on what intervals. Have fun doing this work - make it good - anything worth doing is worth doing well. BE WARNED: this assignment will be worth points and w
8、e will take a test on this on the third or fourth day of class. This will set the stage for your calculus grade (test and homework combined 130 points), so DO NOT skimp on the effort. Be thoughtful about every step and use this opportunity to become familiar with your authors style of presentation.S
9、o, here it is. The assignment youve been waiting for:1. Complete ALL problems on the Worksheets (see further instructions next page)2. Complete the following problems from Chapter 1 and 2 in your text:Section 1.1: A Preview of Calculus p. 47: 1-6 allSection 1.2: Finding Limits Graphically and Numeri
10、cally p. 54-57: 3,11- 17 odd20,21,23,29,32,34,35,40,55,56,57Section 1.3: Evaluating Limits Analytically p. 67-69:9,13,28,37,44,50,53,58,60,69,77,87,89,91Section 1.4: Continuity and One-Sided Limits p. 78-81: 12,16,21,30,31,46,50,59,60,79,84,100Section 1.5: Infinite Limits p. 88-90: 13,17,22,26,36,41
11、,50,62Section 2.1: The Derivative and the Tangent Line Problem p. 103-106 : 16,21,23,26,34,37-40all,42,57,71,74,82,89,95,96Section 2.2: Basic Differentiation Rules and Rates of Change pp. 115-118:9,21,26,29,32,44,52,55,62,63,91,94,97,103,106 Thank you for your efforts and I look forward to a fun and
12、 rigorous year of Calculus. Never forgetthere is no rest in the quest for Calculus knowledge!AP Calculus Summer Homework Worksheet InstructionsGoing into AP Calculus, there are certain skills that have been taught to you over the previous years that we assume you have. IF you do not have these skill
13、s, you will find that you will consistently get problems incorrect next year even though you understand the Calculus concepts. It is frustrating for students when they are tripped up by the algebra and not the Calculus. This summer packet is intended for you to brush up and possibly relearn these to
14、pics.We assume you have basic skills in algebra. Being able to solve equations, work with algebraic expressions, and basic factoring, for example, should now be a part of you. So only the topics I see that students consistently do not have down in their basic skill set are included here. These are s
15、ills that are used continually in AP Calculus.On the following 8 pages, you have 15 problem sets. Each problem should be done in the space provided and all work should be shown. DO NOT rely on the calculator to think for you. Half of your AP exam next year is no calculator, so use pencil, paper and
16、brain techniques to solve these problems. We will definitely work a lot with the calculator next year, but these sets should be done without it (except, possibly, to check you answers). Realize that certain concepts are interrelated. Domain, for example, may require you to be expert at working with
17、inequalities. Solving quadratic equations may involve techniques used in solving fractional equations. If you have questions, a good website for algebra review topics is . Otherwise, Google search a topic and lots of sites will pop up. I will be in my room the 3 days before school starts too if you
18、want to stop by for help.Topic 1: Fractional and Negative Exponents Simplify using only positive Exponents 1. 2. 3. 4. 5. 6. Topic 2: DomainFind the domain of the following functions1. 2.3. 4. 5. 6. Topic 3: Solving inequalities (absolute value)Write the following absolute value expressions as piece
19、wise expressions1. 2. Solve the following absolute value inequalities3. 4. 5. Topic 4: Solving inequalities (quadratic)Write the following absolute value expressions as piecewise expressions1. 2. Solve the following by factoring and making appropriate sign charts to check the critical points.3. 4. 5
20、. Topic 5: Special FactorizationFactor Completely 1. 2. 3. 4. 5. Topic 6: Function TransformationIf, describe in words what the following would do to the graph of f(x):1.) 2.) 3.) 4.) 5.) 6.)Here is f(x): Now graph the following based on f(x)7.) 8.) 9.) 10.) 11.) 12.) Topic 7: Factor theorem (over m
21、ethod/synthetic division)Use the over method and synthetic division to factor the polynomial (x). Then solve (x) =01.) 2.) 3.) Topic 8: Even and Odd functionsShow work to determine if the relation is even, odd, or neither.1.) 2.)3.) 4.)5.) 6.)Topic 9: Solving quadratic equations and quadratic formulaSolve each equation (show your work).1.) 2.)3.)4.) 5.) 6.)Topic 10: Asymptotes For each function, find the equations of both the vertical asymptote(s) and horizontal asymptotes (if
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