By David M. Wells, J. Douglas Faires

This is the 9th publication of difficulties and recommendations from the yank arithmetic Competitions (AMC) contests. It chronicles 325 difficulties from the 13 AMC 12 contests given within the years among 2001 and 2007. The authors have been the joint administrators of the AMC 12 and the AMC 10 competitions in the course of that period.

The difficulties have all been edited to make sure that they agree to the present variety of the AMC 12 competitions. Graphs and figures were redrawn to cause them to extra constant in shape and elegance, and the options to the issues were either edited and supplemented.

A challenge index behind the ebook classifies the issues into topic components of Algebra, mathematics, complicated Numbers, Counting, features, Geometry, Graphs, Logarithms, good judgment, quantity concept, Polynomials, chance, Sequences, facts, and Trigonometry. an issue that makes use of a mix of those parts is indexed a number of times.

The difficulties on those contests are posed by means of contributors of the mathematical neighborhood within the desire that each one secondary institution scholars may have a chance to take part in problem-solving and an enriching mathematical experience.

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**Additional resources for The Contest Problem Book IX**

**Example text**

Two examples may look the same, but the instructions may be asking you to do two different things. For example: Identify the following property: a ϩ (b ϩ c) ϭ (a ϩ b) ϩ c versus On the other hand, two different examples may have the same instructions but require you to do different things. For example: Evaluate: 2(3 Ϫ 8) versus Evaluate: 2 ϩ (3 Ϫ 8) You are asked to evaluate both expressions, but the solutions require different steps. It is a good idea to familiarize yourself with the various ways in which the same basic instructions can be worded.

In the denominator, ؊10 ؊ 10 means ؊10 ؉ (؊10). 100 ϭ ᎏᎏ Ϫ20 ϭ Ϫ5 As the example shows, the location of parentheses can make a great difference in what an example means. We will frequently emphasize the importance of reading an example carefully so that you clearly understand what it is saying and what it is asking. Properties of 0 Finally, we conclude this section with some special properties of the number 0. We are familiar with the numerical facts that 5 и 0 ϭ 0 and 11 и 0 ϭ 0. In fact, 0 times any whole number is equal to 0, and this fact extends to the negative integers as well.

Reviewing the material before doing exercises makes each solution you go through more meaningful. The better you understand the concepts underlying the exercise, the easier the material becomes and the less likely you are to confuse examples or forget steps. When reviewing the material, take the time to think about what you are reading. Try not to get frustrated if it takes you an hour to read and understand a few pages of a math text—that time will be well spent. As you read your text and your notes, think about the concepts being discussed: (a) how they relate to previous concepts covered and (b) how the examples illustrate the concepts being discussed.