TAILIEUCHUNG - Mathematics 2: Mathematics Department Phillips Exeter Academy

You will use the numbers in the table to work out how to get the card into your volunteer’s favourite number position. Suppose their favourite number is 17. First of all, take away 1 to work out how many cards you will need on top by the end of the trick – here it will be 1 . Now you need to work out how to make 1 using the numbers in the table. You will need the 1, the and the 9 (1 + + 9 = 1 ). The table tells that in the first recombination, you must. | Mathematics 2 Mathematics Department Phillips Exeter Academy Exeter NH August 2012 To the Student Contents Members of the PEA Mathematics Department have written the material in this book. As you work through it you will discover that algebra geometry and trigonometry have been integrated into a mathematical whole. There is no Chapter 5 nor is there a section on tangents to circles. The curriculum is problem-centered rather than topic-centered. Techniques and theorems will become apparent as you work through the problems and you will need to keep appropriate notes for your records there are no boxes containing important theorems. There is no index as such but the reference section that starts on page 201 should help you recall the meanings of key words that are defined in the problems where they usually appear italicized . Comments on problem-solving You should approach each problem as an exploration. Reading each question carefully is essential especially since definitions highlighted in italics are routinely inserted into the problem texts. It is important to make accurate diagrams whenever appropriate. Useful strategies to keep in mind are create an easier problem guess and check work backwards and recall a similar problem. It is important that you work on each problem when assigned since the questions you may have about a problem will likely motivate class discussion the next day. Problem-solving requires persistence as much as it requires ingenuity. When you get stuck or solve a problem incorrectly back up and start over. Keep in mind that you re probably not the only one who is stuck and that may even include your teacher. If you have taken the time to think about a problem you should bring to class a written record of your efforts not just a blank space in your notebook. The methods that you use to solve a problem the corrections that you make in your approach the means by which you test the validity of your solutions and your ability to communicate ideas .

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