To: AP Calculus AB Students and Parents From: Carly Kelly (formerly Fabris)

The AP Course AP Calculus AB is a college level course covering material traditionally taught in the first semester of college calculus. The course topics are listed on the College Board website: http://apcentral.collegeboard.com/apc/public/courses/descriptions/index.html

The Prerequisite Summer Assignment Students need a strong foundation to be ready for the rigorous work required throughout the term. Completing the prerequisite summer assignment should prepare you for the material that will be discussed and taught in this course. This assignment consists of material studied during Algebra II and PreCalculus and students should anticipate working approximately 10 hours to complete it properly.

In preparation for the AP test students need to begin showing all work with logical steps. Do not list only an answer. Work neatly from left to right or in a vertical manner moving to the right if you do not have enough room in the provided space. You work must be an organized fashion.

Using my Website as a Resource You will find some useful ‘tools’ that are posted on my website that will include:

A “Toolkit of Functions”. You should be familiar with each of the graphs found here. A formula and identities section. These are for your reference and do not need to be memorized at this time.

A unit circle template with which to practice your unit circle.

A list of skills that you will need for AP Calculus.

To access my website please visit http://www.lcps.org/Domain/16448 or go to www.pfhs.org, click on Staff, scroll and click on Carly Fabris, click on AP Calculus AB.

Calculators Students enrolled in AP Calculus AB will be using a graphic calculator throughout the course. A graphic calculator is required on the AP Examination. A list of acceptable calculators is available on the College Board website.

Acknowledgement of Receiving the Summer Assignment The following information acknowledges receipt of the packet and an understanding that completion of this prerequisite packet is a requirement for the AB Calculus course. The packet is due on the first day of class. This assignment will be for a grade in the course and a test over the preliminary material may likely occur at the end of the first week of school. Before the first day of school, you must email me at Carly.Fabris@lcps.org the following showing that you have received the summer assignment:

Subject heading must be your full name. Grade level you will be in the first day of the 2016-2017 school year. Your favorite part of a math class as well as your least favorite part of a math class. Your parent’s email address. Why decided to take this class. Something unique about yourself and any school activities, clubs, sports, etc. that you are a part of.

I anticipate a motivating and challenging year. Calculus is a stimulating and exciting field of mathematics and I look forward to sharing my excitement with you. I will be there to help and support you. Be prepared to do your share as well.

Carly Kelly

Name: Block:

Your first opportunity to demonstrate your capabilities and resourcefulness in AB Calculus is through the completion of this assignment; which will help you maintain/improve your skills for the start of the school year.

Work on as much of these on your own as you can. If you do not understand a topic get together with a friend, ask your teacher or “google” the topic.

There is enough room for you to show your work in the space provided for each question. If you require more space then you must state “See Attached.”

Be sure all problems are neatly organized and all writing is legible. Points will be deducted if your work is illegible. Round all answers when necessary to three decimal places.

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.

Non-Calculator

1. Simplify 7 9

5 6.

x

x Express your answer using a single radical.

2. Factor the following expression completely: 3 26 17 5x x x

3. Find the equation of the line through the points 2,7 and 3,5 in point-slope form.

4. Rewrite the expression 5log 3x into an equivalent expression using only natural logarithms

5. Let 23 and 1.f x x g x x Compute ,g f x then state the domain of ,g f x in

interval notation.

6. Let 3 7

.2

xf x

x

Find 1 ,f x

the inverse of .f x

7. Find an equation for the parabola whose vertex is (2,–5) and passes through (4,7). Express your answer

in the standard form for a quadratic.

8. Which of the following could represent a complete graph of 3,f x ax x where a is a real number?

Explanation for why you chose your answer:

9. Find a degree 3 polynomial with zeros –2, 1, and 5 and going through the point (0, –3).

10. The graph of 32 xy a for 1a is best represented by which graph?

Explanation for why you chose your answer:

11. Describe the transformations that can be used to transform the graph of log x to a graph of

4log 2 3.f x x Be sure to use proper mathematical vocabulary.

12. Simplify: csc tan sin cos .x x x x Your answer should be in terms of only sin or cos .x x

13. Find the exact value of 1 17cos cos .

5

If not possible, explain why.

14. Graph the piecewise function on the given axes.

2 2 1

2 1

3 4 1 2

x x

f x x

x x

15. Solve the equation 22sin cos cosx x x algebraically.

16. Find all the exact solutions to 22sin 3sin 2 0x x on the interval 0,2 .

17. For the function graphed below, evaluate 3

lim .x

f x

Give reason for your answer.

18. Given the equation 2 23 ,xe y solve for y.

19. Describe the end behaviors of 2

2

2.

5 9 2

xf x

x x

Also state the Domain of the function.

20. Find the domain of 5

.2

x

x

Express your answer in interval notation.

21. Using Descarte’s Rule determine the amount of possible positive and/or negative zeros the function

6 5 3 23 5 4 1.f x x x x x x Explain how you were able to determine the amount of possible roots.

Calculator Active

22. Arturo invests $2700 in a savings account that pay 9% interest, compounded quarterly. If there are

no other transactions, when will his balance reach $4550? Round to three decimal places.

23. Determine the range of: 2 413 20 3 .f x x x x Also, find the maximum and minimum points

24. Three sides of a fence and an existing wall form a rectangular enclosure. The total length of a fence

used for the three sides is 240 feet. Let x be the length of two sides perpendicular to the wall as shown

in the figure below.

a) Write an equation of area A of the enclosure as a function of x for the rectangular area as shown

in the above figure.

b) Find value(s) of x for which the area is 25500 .ft Round your answers to three decimal places.

x x

Existing Wall

y

of .f x Round your answers to three decimal places.

25. Solve the equation 4 3 5 4x x algebraically. Then use your calculator to find the solution(s).

Give a brief explanation of the steps you did on your calculator in order to obtain your solution.

Brief Explanation:

26. The table shows average salaries for employees of Mediocre Tool, Inc. Find a linear regression

equation for the data. Then use that equation to estimate the average salary in 2008. (Use 0x for

1975, and express your values to the nearest thousandth).

27. The number of elk after t years in a state park is modeled by the function 0.03

1216.

1 75 tP t

e

a) What was the initial population of elk?

b) After how many years will the number of elk be 250?

28. Solve the system of equations graphically, accurate to the nearest thousandth. Sketch and label your

solution on the axes provided.

2 2

102 5

1

3

x y

y x

Year Average Salary ($) 1975 15,642

1980 16,580

1985 17,409

1990 19,150

1995 20,491

2000 21,925

Equation:

Estimated Salary in 2008:

29. Two students are 180 feet apart on opposite sides of a telephone pole. The angles of elevation from the

students to the top of the pole are 35 and 23 . Find the height of the telephone pole.

30. Find the points of intersection of 2 2 4x y and 2 2 4 4 4.x y x y Graph the system on given axes.