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IB HL AP/BC Calculus Summer Assignment Dear IB HL AP/BC Calculus students, The summer assignment is a mixture of review problems and some very challenging IB problems. Do not wait until the last minute to attempt these. On the website from which you downloaded this summer packet, there is also an IB HL Math Formula Packet. I recommend that you use this as it will help you with some of the formulas you may not remember. This is good number of problems for you to work on this summer. It is not meant to be busy work. On the contrary, it is to keep your minds fresh and sharp during the summer break so that when you come back in September, you will hit the ground running or at least at a very brisk walking pace. The IB HL AP/BC Calculus course is particularly difficult in terms of the quantity and depth of the material. The quantity of letters in the title should give you an indication of that. The course you are about to take is difficult for many reasons. First of all, the material itself is challenging. Secondly, we are covering the BC AP Curriculum and the HL Mathematics curriculum. Both curriculums are difficult and, although there is some overlap, the curriculums differ in their focus and content. Thirdly, many of you will also be taking the AP Statistics course to cover some of the Paper 3 topics for the IB math test. Lastly, it is more than likely that you are taking other challenging courses and have afterschool commitments with extra-curricular activities, which are also important. I don’t think I need to mention the demands of the college admissions process. All of these things require time and effort so you will have to learn to be as efficient as possible and work to your potential. Plan ahead. Develop a personalized strategy. Although I will encourage you to work with each other as much as possible on certain assignments, your academic strategy may not be the same as the other people in the class. What has worked for you in the past may work for you again and it may not. Adapt. Find Balance. Improvise. Overcome. Persevere. Words to think about as you go through the year. I am not saying all this to discourage you as much as I want you to be prepared. The class is challenging but it is also extremely rewarding. Also, I am here to help you get through those challenges as much as I can. Please use me as a resource. The course will demand a lot of you and I would expect, in turn, that you will demand a lot of your teacher. Work through the problems a little at a time. Some of them are challenging. I encourage you to work with each other as much as possible on this assignment. If you have any questions you can e-mail me [email protected] or use the blog on my personal webpage (See next page). 1. (5 points) You will go to my webpage and sign onto my e-mail distribution list for IB HL Calculus 2010. The password until august 1 is carlsagan. The password will change on august 1 to feynman. http://teachersites.schoolworld.com/webpages/NMessare/
There are three ways to sign up for the e-mail distribution list. a) click on the small envelope at the top of the screen that is just to the right of “My Message Board” b) click on the hyperlink towards the bottom of the webpage. c) copy the hyperlink into your web browser. http://www.myteacherpages.com/webpages/NMessare/contact.cfm This is important as I will be distributing information regularly to you using e-mail once the school year commences. Here is what this years webpage looks like. Obviously, it will be different next year and I will have a different schedule.
2. If you have questions on the assignment please use the blog that is on the webpage for the IB. http://teachersites.schoolworld.com/webpages/NMessare/myblog.cfm Along the top, in the top right corner of my webpage you see the words “My Blog.” Select this and then select IB/HL Calculus Blog for Summer Packet. Choose comment to post a question. Don’t forget to write the problem number down. I will check my e-mail and the blog daily so you should get a response back within a day.
a) You will receive an extra credit point on your first quiz for posting a solution to one of the problems.
b) You will get an additional extra credit point for a correct solution. Don’t forget to include your name. If your solution is correct I will post a comment to let you know that it is correct. If you post a solution and it is incorrect, you or someone else may continue to post possible solutions until we get one that is correct.
Note: maximum of 2 extra credit points for this assignment. Here are the problems. Write your answers in problem order and put them in a three-ring binder or heavy duty folder with your name on it. You will turn this problem set binder in and it will be returned to you the next day after I have checked to see what you have done. Answers will be posted on my website the day you turn the packet in on the first day of school. The problems are not easy and are IB problems taken from actual tests or IB resources. They will take a while to do and in some cases you may not be able to figure them out right away. Welcome to IB HL math problems. Some of the solutions are not obvious and you may not see the path to a solution until you get near the end of the problem solving process. You will get better at this throughout the year as you work on these kinds of problems. You may post questions and possible solutions on the blog for our website.
You will have a quiz on some randomly selected problems at the end of the first full week of school when our class meets. Remember that you will get 1 extra credit point for posting a solution to one of these problems and an additional extra credit point when you post a correct solution. (2 points maximum)
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(a) Find the first and second derivative of the function ( ) 32 −= xxf using the limit method of finding the derivative. (b) Hence find the slope of the tangent line at the x value x = 2. (c) Hence, find the equation of the tangent line at x = 2. (d) Find the value of x and y when the slope of the tangent line is
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