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By Charles T. Salkind, James M. Earl

The yearly highschool contests were backed considering that 1950 via the Mathematical organization of the United States and the Society of Actuaries, and extra lately by means of Mu Alpha Theta (1965), the nationwide Council of lecturers of arithmetic (1967) and the Casualty Actuarial Society (1971). difficulties from the contests through the interval 1950-1960 are released in quantity five of the hot Mathematical Library, and people for 1961-1965 are released in quantity 17. the recent Mathematical Library will proceed to post those contest difficulties from time-to-time; the current quantity comprises these from the interval 1966-1972. The questions have been compiled by way of Professor C.T. Salkind until eventually his dying, and because 1968 via Professor J.M. Earl, who died on November 25, 1972 after filing difficulties for the 1973 contest. Professors Earl and Salkind additionally ready the strategies for the competition difficulties. In getting ready this and the sooner Contest challenge Books the editors of the NML have elevated those options and additional substitute ideas.

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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.

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