2014 Summer Assignment
AP Calculus BC
Mr. Aldea
Welcome to AP Calculus! To begin the year, it is expected that you will have a certain understanding of the material that you covered in Precalculus last year. The summer assignment will cover exactly those topics. You will need to be familiar with these ideas in order to have the best chance for success this year.
Make sure you pick up a text and sign it out with me. All of our assignments will come from the textbook, plus the additional problems at the end of this handout.
NOTE: This assignment will be checked on the first day of school and it will count as several homework assignments. Show all work and check your answers in the back of the book for odd problem exercises.
If you need to reach me during the summer, email me at .
Part One. Textbook. All of the exercises can be found in the textbook:
Calculus: Early Transcendentals/Single Variable, Ninth edition by Howard Anton.
Chapters 0 and 1. Take notes where necessary.Do the following exercises:
pp. 63-65 / Chapter 0 Review: #1, #5, #15, #27a,b,c,e, #29, #33
pp. 77 / #1-9 odd
pp. 87-88 / #1-31 odd, #32, #37, #39, #40
pp. 97-98 / #9-39 odd, #47
pp. 118-119 / #11-21 odd, #29, #31, #35
pp. 126-127 / #17-35 odd, #51
Part Two. Graphing Calculator.
A note about using your calculator
The graphing calculator is an important tool in AP Calculus. There are certain skills you should have mastered by September if you haven’t mastered them already. Use your owner’s manual to assist you with the following exercises.
For the AP exam, all answers that are approximated on a calculator must be rounded to three decimal places. You must not round off intermediate results, as this will propagate any rounding errors that may occur. Use the [2nd][Ans] feature on the calculator to preserve the intermediate answer in its original form.
Remember, the calculator only works as well as the person programming it. Order of operations is important. You must bring your understanding of graphing and the characteristics of specific functions with you to the calculator. Some notation that is OK when you write an expression or an equation by hand cannot be used on the calculator because it will give you incorrect results. Also, it is better to use too many sets of parentheses then not enough.
These exercises are designed to help you become more proficient with the use of your graphing calculator:
Set 1. Graphing.
1. Graph . Make sure your graph is complete. You may have to “play around” with the way you enter the functions into the calculator to get the complete picture.
2. Graph . Adjust the window until you can clearly see all the x- and y- intercepts.
3. Graph . By adjusting the window, determine if the function is periodic and, if so, find the period.
Set 2. Solving Equations. Find the roots of each of the following equations.
4.
5.
6.
7.
8.
Set 3. Points of Intersection. Find the points of intersection for each of the following pairs of functions. Note that
being able to find a point of intersection is NOT one of the four required features of a calculator approved for the AP exam. That doesn’t mean you cannot use the feature but it does mean that you must show the following work on the exam:
Ex. You need to find the intersections of y = sin x and y = -2x + 3 on .
You cannot go directly from those equations to a list of the ordered pairs where the graphs intersect.
What you must first do is show that you are solving the following equation: .
You may then use “solve” or some other feature that finds roots or use “intersect” and list the ordered pairs.
9. and on .
10. and
11. and
Set 4. Miscellaneous exercises.
12. Find all real zeros of the equation.
13. Consider the function . Use the calculator to determine the equation(s) of any horizontal asymptotes that may exist for the function.
14. Graph .