Mathematics 2 Problem Sets - Exeter

1 Mathematics 2 Mathematics DepartmentPhillips Exeter AcademyExeter, NHAugust 2019To the StudentContents: Members of the PEA Mathematics Department have written the material in thisbook. As you work through it, you will discover that algebra, geometry, and trigonometryhave been integrated into a mathematical whole. There is no Chapter 5, nor is there a sectionon tangents to circles. The curriculum is Problem -centered, rather than and theorems will become apparent as you work through the problems, andyou will need to keep appropriate notes for your records there are no boxes containingimportant theorems. There is no index as such, but the reference section that starts on page85 should help you recall the meanings of key words that are defined in the problems (wherethey usually appear italicized).

2 Problem solving: Approach each Problem as an exploration. Reading each question care-fully is essential, especially since definitions, highlighted in italics, are routinely insertedinto the Problem texts. It is important to make accurate diagrams. Here are a few usefulstrategies to keep in mind: create an easier Problem , use the guess-and-check technique as astarting point, work backwards, recall work on a similar Problem . It is important that youwork on each Problem when assigned, since the questions you may have about a Problem willlikely motivate class discussion the next day. Problem solving requires persistence as muchas it requires ingenuity. When you get stuck, or solve a Problem incorrectly, back up andstart over. Keep in mind that you re probably not the only one who is stuck, and that mayeven include your teacher.

3 If you have taken the time to think about a Problem , you shouldbring to class a written record of your efforts, not just a blank space in your notebook. Themethods 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 communicateideas are just as important as getting the correct : Many of the problems in this book require the use of technology (graphingcalculators, computer software, or tablet applications) in order to solve them. You areencouraged to use technology to explore, and to formulate and test conjectures. Keep thefollowing guidelines in mind: write before you calculate, so that you will have a clear recordof what you have done; be wary of rounding mid-calculation; pay attention to the degree ofaccuracy requested; and be prepared to explain your method to your classmates.

4 If you don tknow how to perform a needed action, there are many resources available online. Also, ifyou are asked to graphy= (2x 3)/(x+ 1) , for instance, the expectation is that, althoughyou might use a graphing tool to generate a picture of the curve, you should sketch thatpicture in your notebook or on the board, with correctly scaled testing:Standardized tests like the SAT, ACT, and Advanced Placementtests require calculators for certain problems, but do not allow devices with typewriter-likekeyboards or internet access. For this reason, though the PEA Mathematics Departmentpromotes the use of a variety of tools, it is still essential that students know how to use ahand-held graphing calculator to perform certain tasks. Among others, these tasks include:graphing, finding minima and maxima, creating scatter plots, regression analysis, and generalnumerical Exeter AcademyIntroductory Math Guide for New Students(For students, by students!)

5 IntroductionAnnually, approximately 300 new students enroll in a Mathematics course at PEA, andstudents arrive here from all over the world. As a new student, you will quickly come torealize the distinct methods and philosophies of teaching at Exeter . One aspect of Exeterthat often catches students unaware is the math curriculum. I encourage all new studentsto come to the math table with a clear mind. You may not grasp, understand, or even likemath at first, but you will have to be prepared for anything that comes before the fall of 2000, the new students avidly voiced a concern about the math cur-riculum. Our concern ranged from grading, to math policies, and even to the very differentteaching styles utilized in the Mathematics department. The guide that you have begunreading was written solely by students, with the intent of preparing you for the task thatyou have embarked upon.

6 This guide includes tips for survival, testimonials of how we feltwhen entering the math classroom, and aspects of math that we would have liked to haveknown, before we felt overwhelmed. Hopefully, this guide will ease your transition into mathat Exeter . Remember, Anything worth doing, is hard to do. Mr. Higgins 36. Anthony L. Riley 04 I learned a lot more by teaching myself than by being taught by someone else. One learns many ways to do different problems. Since each Problem is different,you are forced to use all aspects of math. It takes longer for new concepts to sink in .. you understand,but because it didn t sink in, it s very hard to expand with that concept. It makes me think more. The way the math books are setup( simple problems progressing to harder ones on a concept)really helps me understand the mathematical concepts.

7 When you discover or formulate a concept yourself, you remember it betterand understand the concept better than if we memorized itor the teacher just told us that the formula was xyz . HomeworkMath homework = no explanations and eight problems a night. For the most part, ithas become standard among most math teachers to give about eight problems a night; butI have even had a teacher who gave ten though two problems may not seem like a bigdeal, it can be. Since all the problems are scenarios, and often have topics that vary, theyalso range in complexity, from a simple, one-sentence question, to a full-fledged paragraphwith an eight-part answer! Don t fret though, transition to homework will come with time,similar to how you gain wisdom, as you get older. Homework can vary greatly from night tonight, so be flexible with your time this leads to another part of doing your ALL CLASSES THAT MEET FIVE TIMES A WEEK, INCLUDING Mathematics ,YOU SHOULD SPEND 50 MINUTES AT THE MAXIMUM, DOING HOMEWORK!

8 Noteacher should ever expect you to spend more time, with the large workload Exonians your hardest to concentrate, and utilize those 50 minutes as much as any explanations showing you exactly how to do your homework, how are yousupposed to do a Problem that you have absolutely no clue about? (This WILL happen!)Ask somebody in your dorm. Another person in your dorm might be in the same class, orthe same level, and it is always helpful to seek the assistance of someone in a higher levelof math. Also remember, there is a difference between homework and studying; after you rethrough with the eight problems assigned to you, go back over your work from the last fewdays.. with homework, you wouldn t get marked down if you didn t do a Problem . Going to the BoardIt is very important to go to the board to put up homework problems.

9 Usually, everyhomework Problem is put up on the board at the beginning of class, and then they arediscussed in class. If you regularly put problems up on the board, your teacher will have agood feel of where you stand in the class; a confident student will most likely be more activein participating in the thing to keep in mind is plagiarism. You can get help from almost anywhere, butmake sure that you cite your help, and that all work shown or turned in is your own, even ifsomeone else showed you how to do it. Teachers do occasionally give problems/quizzes/teststo be completed at home. You may not receive help on these assessments, unless instructedto by your teacher; it is imperative that all the work is Extra-HelpGetting help is an integral part of staying on top of the math program here at can be rather frustrating to be lost and feel you have nowhere to turn.

10 There are a fewtricks of the trade however, which ensure your safety, with this possibly overwhelmingword Problem and MeetingsThe very first place to turn for help should be your teacher. Since teachers at Exeter havemany fewer students than teachers at other schools, they are never less than eager to helpyou succeed in any way they can. You can often meet your teacher after Assembly or duringthe Lunch period. You can always call or ask a teacher for help. If there is no time duringthe day, it is always possible to check out of the dorm after your check-in time, to meet withyour teacher at their apartment, or house. It is easiest to do this on the nights that yourteacher is on duty in his/her dorm. Getting help from your teacher is the first and mostreliable source to turn to, for extra help.