"How do I prepare for the AMC contests?"

AMC Preparation

On "Goodly Maths" (Math Problems Online)

Your Numero Uno Resource for Math Problems

A common question is "How do I prepare for the AMC contests?"

Fortunately, I do have some answers.

First, you need to know what the AMC contests are, and how they are scored. The following is a brief description:

The AMC (American Mathematics Competition) contests are examinations in middle and high school mathematics. There are three levels: the AMC-8 is for students in grades 8 and below; the AMC-10 is for students in grades 10 and below; and the AMC-12 is for students in grades 12 and below.

The AMC-8 is given in the fall (usually November) and the AMC-10 and AMC-12 are given in the spring (usually February). There is only one date on which you may take the AMC-8, but there are two dates on which you may take the AMC-10 and AMC-12. These dates are usually referred to as the "A date" and the "B date", with the "A date" preceding the "B date".

The AMC contests have certain rules. They are as follows:

AMC-8 Rules and Scoring

The AMC-8 has 25 multiple-choice questions and is to be taken in 40 minutes. Calculators are allowed. The AMC-8 is scored based on the number of questions answered correctly only. There is no penalty for getting a question wrong, and each question has equal value. Thus, a student who answers 23 questions correctly receives a score of 23.

AMC-10 and AMC-12 Rules and Scoring

The AMC-10 and AMC-12 each have 25 questions, and each is to be taken in 75 minutes. Calculators are allowed. On a given date, a student is only allowed to take one contest (either the AMC-10 or AMC-12; not both). The AMC-10 is scored based on the number of questions answered correctly and the number of questions left blank. A student receives 6 points for each question answered correctly and 2.5 points for each question left blank. (Incorrect answers contribute 0 points). Thus, a student who answers 18 correctly, leaves 5 blank, and misses 2 gets 18*6 + 5*2.5 = 120.5 points. The maximum possible score is 6*25 = 150 points.

There are certain rewards for doing well on the AMC tests. For the AMC-8, a perfect score may earn you a book prize (as it did for the students who achieved perfect scores in 2002); a list of high scoring students is also available to colleges, institutions, and programs who want to attract students strong in mathematics. This may earn you an invitation to places like MathPath, a summer program for middle schoolers. The top-scoring student in each school is also awarded a special pin.
For the AMC-10 and AMC-12, a perfect score earns you recognition (your picture and name are published in a special awards book); as with the AMC-8, a list of high-scoring students is also available to colleges, institutions, etc. The top-scoring student in each school is awarded a special pin, or a bronze, silver, or gold medal, depending on how many times he or she was the top scorer. For more information on awards, visit the official Awards for the AMC page.
In addition, high scorers on the AMC-10 and AMC-12 are invited to take the American Invitational Mathematics Examination (AIME); high scoring students on this exam are invited to take the USA Mathematical Olympiad (USAMO), the premier mathematics examination for American students.

With that said, it's time to talk about the ways to prepare for the AMC.

The best thing to do to prepare is to practice by doing old AMC problems. The AMC has provided some sample questions from 2003, 2002, and 2001, which you will find by following the respective links. There are several years of old AMC problems available on this site at the AMC Archive. After that, more problems are available for purchase from the AMC; you may order by printing out the order form sheet and sending it to the address provided on the linked webpage. Of particular interest are the Contest Problem Books, which each contain between five and ten years worth of AMC exams.
Consider working on some AMC problems without a time limit, and taking some full AMC exams under the proper time limit (75 minutes). This will help you get used to taking an AMC exam under test conditions.
You may also wish to practice by doing math problems from other contests, such as MATHCOUNTS (several years of MATHCOUNTS problems are available on this site at the MATHCOUNTS Archive). Although they may have a different format, they use similar concepts and will help your problem-solving skills. Also, there are a number of problems posted on the Art of Problem Solving forums. Consider hanging around the forums there and solving some problems.

Another thing you can do to prepare is to read books devoted to improving your problem solving skills. I highly recommend The Art of Problem Solving books (by Richard Rusczyk and Sandor Lehoczky), which not only teach new techniques for solving problems (ranging from quadratic equations, the Power of a Point theorem, basic transformation geometry, and other useful topics that appear often on math contests like the AMC), but also include over 1000 problems from actual competitions. (A list of topics is available for Volume 1 and Volume 2).
Other good books include The Art and Craft of Problem Solving, by Paul Zeitz; Geometry Revisited, by Coxeter and Greitzer; and Problem-Solving Strategies, by Arthur Engel, although these books are fairly advanced and are generally useful for higher-level competitions.

One final way to prepare for the AMC exams is to learn from the experts by taking a problem solving class, such as the Art of Problem Solving Online Classes. If you take one of these, you get lessons, problems, and challenge sets. AMC-level classes include MATHCOUNTS/AMC Number Theory, MATHCOUNTS/AMC Counting, MATHCOUNTS/AMC Geometry, AMC/AIME Algebra, and AMC/AIME Trigonometry/Complex Numbers. Or, you may wish to attend a mathematics summer program, such as Canada/USA MathCamp, MathPath, PROMYS, or the Ross Program. (A more complete list is available here.)

I hope this document has given you some ideas for how to prepare for the AMC. If you have further questions, ask around on the AMC Forum or consider contacting me by e-mailing goodlymaths@netscape.net.


Good luck!