How to Succeed in AP Calculus¹

BHS -> Mr. Stanbrough -> AP Calculus -> AP Calculus Intro -> this page

KEEP UP WITH THE ASSIGNMENTS! Over the years, I have found that the best indicator of a student's success is whether they keep up with their assignments. Students who keep up, do well - students who don't, don't. I won't kid you - AP Calculus is a long, grueling trek, but it is essential that you KEEP UP.

REMEMBER THAT THE GOAL OF AN ASSIGNMENT IS TO UNDERSTAND THE MATERIAL - NOT JUST GET THE PROBLEMS DONE! You understand the material when you can do the problems - and get them right - BY YOURSELF. There is absolutely nothing wrong with asking questions or seeking help from your fellow students or me. Everyone will need help sooner or later in this course. However, you must have the integrity to realize that the goal of the assignment is NOT just to get the assigned problems finished and turned in! When I select problems for an assignment, I try to pick enough representative problems to provide adequate practice for the "average" student (not, believe it or not, to provide you with hours and hours of useless drudgery!). There will be times when you will need more practice than this, and you must have the courage and integrity to realize it.

TREAT ASSIGNMENTS AS "PRACTICE TESTS." Fifty percent of your score on the AP test (as well as most tests and quizzes during the year) will be determined from your solutions to free-response questions. For these problems, the correct answer counts for as little as twenty-five percent of the total score. The rest of the points are awarded on the quality of your solution to the problem. This means that if you have correct answers for all problems - with no (or disorganized, or incomplete, or unreadable) supporting work - you will fail miserably. If you have a few incorrect answers, but well-organized, complete solutions that use proper mathematical vocabulary and symbolism - you will generally do well. Use your assignments as an opportunity to practice presenting well-organized mathematical solutions to problems.

NEVER ERASE. If you hit a "dead end" and want to start over, cross out the work you don't want with a big "X" - do NOT erase it. It might turn out later to be correct! Also, if you come to me for help, the first thing that I will say is, "Let me see what you have done so far." If you tell me that you erased it, you will just have to go back and reproduce it from memory. Erasing can be a big time-waster on tests (where time is very valuable). Material that is "X"'d out will not be graded on tests - including the AP test.

READ THE BOOK. This is important in every class, but in this class the text serves as a valuable supplement to what happens in class. It is not just a place to find the homework problems. Read the book slowly, line-by-line, with a pencil and paper nearby. Pay particular attention to the illustrations and examples. Study the examples carefully. Work through them with the authors. Be sure that you know how the authors get from one step to the next.

LEARN THE VOCABULARY AND SYMBOLS. It is vitally important that we can communicate in the language of mathematics. As you read or participate in class, pay particular attention to the meaning of each new term and symbol.

UNDERSTAND THE USAGE OF AND MEMORIZE EACH NEW FORMULA. It is crucial to your success at just about everything that we will do this year. Of course, I don't mean that you need to memorize every line of the book, but when I say, "You need to know this." - I mean it! Having a calculator does not mean that you don't need to know any mathematics.

REVIEW CONSTANTLY. Lucky for you, every test and quiz is cumulative, and we will review extensively in class; therefore review is somewhat automatic. Don't hesitate to go back to review or seek help on algebra, geometry, and trigonometry skills that you may not have mastered sufficiently in earlier courses. The majority of the errors that students make on tests and quizzes are not calculus mistakes - they are algebra, geometry, and trigonometry mistakes.

TAKE GOOD NOTES DURING EACH CLASS. Good notes are essential for success in any technical field. They are essential for review - not only for tests, but also for the problems you will work that evening! Many former students have told me that their class notes made a valuable reference for them even three or four years later in college.

EVERY MINUTE OF CLASS TIME IS VALUABLE! Use the time at the beginning of class to get ready for calculus - get out your books, assignments, notebooks, pencils, etc. What questions do you have about yesterday's work? Socializing may be more pleasant than math, but the goal is to make math more pleasant, and socializing gets in the way. At the end of the discussion period, begin (or continue) the current assignment right away - what better time to get help if you get stuck? We only spend valuable class time on important topics, so take good notes constantly during class.

ORGANIZE. Your success depends on your ability to recall (or find, relearn, and then remember) concepts and techniques which were introduced earlier. If your notes and assignments are scattered about, folded inside the covers of your book, papering the bottom of your locker or the floor of your car, you're sunk.

BE READY FOR CONSTANT ASSESSMENT. We will have a major test approximately every twelve class periods during the year. Additionally, we will have a short quiz most days. Each test covers everything from the first day onward. Today's quiz is probably strikingly similar to a couple of the homework problems due yesterday.

BECOME AS SELF-SUFFICIENT AS POSSIBLE. There are many students, and just one teacher, and time is too valuable for you to just wait - stuck in neutral - for help. Look in your text and your notes for sample problems that might shed some light on your difficulty. Learn tenacity - don't just "fold" at the first sign of difficulty! Is there another way to approach the problem? You can do it!

SEEK HELP AGGRESSIVELY. Everyone, no matter how smart or proficient in math, will get "stuck" sometime this year. Perhaps there is a new concept or technique that just won't fit into place in your brain, or maybe you realize a year too late that Ms. Hoeing was right when she said "You're going to need this for Calculus!" Tenacity and self-sufficiency are great attributes, but there is going to be a quiz on this stuff tomorrow! Sometimes there just isn't time to be tenacious! Attend the morning help sessions. Ask questions in class. Get the help you need to succeed.

BECOME PROFICIENT AT USING A GRAPHING CALCULATOR. Your calculator is a valuable tool for visualizing and solving problems of all sorts. On parts of the AP exam, as well as on tests and quizzes during the year, you will be required to demonstrate your mastery of the graphing calculator as a mathematical tool. Learn to use it well. Become familiar with ALL of the ways that your calculator can be used to solve a problem.

BECOME PROFICIENT AT NOT USING YOUR GRAPHING CALCULATOR. Be aware that you may not use your calculator for all parts of the AP exam, and that some quizzes and tests will contain "No Calculator" problems. In all cases, you will be required to demonstrate your understanding of calculus. You will be required to provide symbolic (often exact) solutions for many problems, and you must be able to explain your solutions using correct mathematical symbolism and vocabulary.

COMMUNICATE. If you have a worry, complaint, suggestion, or concern of any kind let me know. I can't fix it if I don't know about it. Remember that just because a problem - or a solution - seems obvious to you, it may not be obvious to everyone. Speak up!

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