Welcome to Honors AP Calculus AB at Metamora High School! Dear Students and Parents,

Mathematics is a discipline that constantly builds on previous knowledge. Students entering AP

Calculus AB will be expected to recall and apply the material that they learned in previous courses. Calculus is

the most challenging class offered by the Mathematics Department. It can also be the most rewarding. During

this course you will be asked to look at functions in a whole new way. To help prepare you for the course

ahead, this packet has been provided. Included in this packet you will find:

General Information

Additional resources can be found on my class page on the school Web site.

There is also a link to my class wiki contained on my class page (username: redbirds, password:

redbirds)

On the wiki there is a ton of resources to help you through the class (including a solutions manual to

help you with the summer packet problems)

Calculus is tough, but you can conquer it! I am always happy to help, and if you are ever struggling,

just ask for help!!!

As an AP Calculus AB student, you have been given the privilege of being issued your textbook prior to

the end of the school year to help you as you prepare for the year ahead. You are expected to take good care

of this textbook. Any lost or damaged book will need to be replaced, at a cost of the book, which is currently

$126.00. If you should happen to lose this packet, you can email me a request for an electronic copy at the

email address below.

Please spend some time looking over these materials before attending class on August 17th. There will

be a 50 point test over this included material on Tuesday, August 22nd. If you have any questions,

contact me at estone@mths.us. If you happen to lose this packet, you can find it on the class wiki, the math

department Web page, or in the Guidance office.

Have a wonderful summer (okay so giving you a packet of math problems, probably not your idea of wonderful, but it will be worth it in the end, trust me)! Mr. Stone

Chapter 1 Prerequisites for Calculus Assignments Note: The problem sets will indicate when not to use a graphing calculator by having a grey

circle around the number. Problem Sets are assigned from the Exercises section not the Quick

Review section. Please follow these instructions accordingly as quizzes and tests in Honors AP

Calculus AB will almost always have two parts: no calculator allowed and graphing calculator

permitted.

AP Calculus with an approved Graphing Calculator Packet

Section 1.1 Lines p.9 #3-36 by threes, 37, 41

Section 1.2 Functions and Graphs p.19 #3-33 by threes, 35, 36, 39, 42, 45, 51, 55, 61

Section 1.3 Exponential Functions p.26 #3-21 by threes, 23-27, 32, 36

AP Preparation: Sections 1.1-1.3 p.28 #1-4

Section 1.5 Functions and Logarithms p.43 #3-24 by threes, 33, 36, 39, 48

Section 1.6 Trig Functions p.51 #3-15 by threes (#12a only), 27, 28, 29, 32, 33, 36, 59

AP Preparation: Sections 1.4-1.6 p.54 #1-4

Chapter 1 Review Exercises p.55 #3-42 by threes, 55-65 odd

Chapter 1 Prerequisites for Calculus: Class Schedule Note: These sections are an independent review (meaning your teacher will not be lecturing on any of these

topics) of previously learned material. You are responsible for completing these problems either on your own or

within a study group. I will provide time each class period for a question/answer session according to the

schedule below. There will not be enough class time to complete all assignments. Please be prepared

with questions each day.

Schedule for Honors AP Calculus Chapter 1 Thursday, August 17th – Questions/Answers over Sections 1.1 and 1.2 Friday, August 18th – Questions/Answers over Section 1.3, 1.5, and 1.6 Monday, August 21st – Questions/Answers over Chapter 1 Review Exercises Tuesday, August 22nd - HOMEWORK DUE FOR COMPLETION GRADE, Chapter 1 Test

Calculus is used in every branch of the physical sciences, actuarial science, computer science, statistics, engineering, economics, business, medicine, demography, and in other fields wherever a problem can be mathematically modeled and an optimal solution is desired. It allows one to go from (non-constant) rates of change to the total change or vice versa, and many times in studying a problem we know one and are trying to find the other.

Graphs you need to know:

DO’S AND DON’TS AP CALCULUS AB

*NEVER use the word “it” on a free response question. (Ex: “f’ is increasing” or “ f” changes from positive to negative”) *Don’t hand compute if it’s a calculator question. Just show your setup otherwise you are wasting your time. *Do not truncate points of intersection. Name points of intersection, then store. Integrate using stored values. *Don’t assume values on a graph except those given or determined by a correct equation. *Don’t round in the middle of a problem. *Don’t ever verify/justify by just saying “My calculator said…” Your calculator doesn’t talk! *DON’T FORGET UNITS ON ANSWERS for free response or YOU WILL LOSE THE ANSWER POINT! *Don’t leave BALD ANSWERS. Bald answers get nothing, you must show calculus support. ******************************************************************************************** *MUST show ALL candidates for Absolute max/min. Use the candidate test. *Must describe the test, not just name it. (Ex: “By the 1st deriv. test, a relative max. exists because the sign of the 1st derivative changes from + to –“; not “a relative max. because of the 1st deriv. test”.) *Must find the y value if asked for “a maximum or minimum” or a “maximum value or minimum value”. *Change limits if using u-sub. Otherwise you need to put everything back in terms of x. *Do show all work. If you make a jump – the grader may or may not accept it. *Do complete whatever parts you can. * CALCULATOR CAUTIONS: YOU MAY: Draw a graph

Solve equations (find points of intersection / zeroes); write the set up/equations first

Calculate numerical derivative Calculate numerical integral YOU MAY NOT: Find a max. / min. Determine concavity or POI

Determine intervals of increasing / decreasing Determine domain / range Regression equation in any way *Incomplete graphs lead to problem (adjust calculator to given window if there is one). *Information given in the stem of a problem must be needed for something. Mark on graph if given one. * Know how to do derivatives by hand. *Know how to do a derivative of an inverse. *Graders will not look in other parts for an answer. *Graders are forbidden to look at anything you X out. You must try to erase the X if you change your mind. *If you write 2 possible answers and expect the grader to choose, they will grade both, average the scores, and truncate the result. *When solving differential equations, use the initial condition early on. *When taking a square root, check for which solution (+ or -) you need. *If asked to explain what an integral means, you need 3 things: what it finds, units, and interval (limits of integration). *For trapezoids, you need to set up, but not solve. If you solve wrong you lose the credit. Draw a picture to help. *A sign chart will not earn points. *When asked to “Explain why there must be…”, you will use one of the following theorems:

MVT (must be differentiable and continuous) Rolle’s Thm (must be differentiable and continuous) IVT (continuous, but not necessarily differentiable) EVT (continuous, but not necessarily differentiable) *When asked to “Justify”, you must use words: “Since there is a change in ______ at x= _______ from _____ to ______ then there is a _______ at ______.

Try using unit analysis to set up integral applications

Look for FTC Part 2 Problems, i.e. given Acceleration, need to find V(5), etc

Look for Separable Differential Equation problems

Under/Over Estimates with RAM, Trap Rule – connect to increasing/decreasing functions