аЯрЁБс>ўџ .0ўџџџ-џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџьЅСs ПpjbjbР Р (ЊkЊkp џџџџџџ]RRRRRRR––––– Ђ– "ккккккккШЪЪЪЪЪЪ,-є!XіRкккккіюRRкккюююк RкRкШf~RRRRкШю@ю.Њ:|RRШОЮЖ3П––ф ЖMATH ANALYSIS PAGE FALL 2005 DESCRIPTION Math analysis is the culmination of the College Prep Math sequence. It is intended to prepare students for three possible paths: those who will not go on to calculus but who will probably take another math course; those who will take calculus; and those who will go on to college but will not continue in mathematics. Algebra fluency and accuracy are emphasized in the course. A good deal of the course develops the concepts of calculus without focusing on the computational techniques. There is also a strong statistical component to the course. It emphasizes the analysis of models generated to explain real data such as those students are liable to meet in other college level courses, even non-science ones. A final theme is the preparation of students for more traditional mathematics courses, including learning to read a standard math textbook and more teacher-directed lessons. The primary text used for this course will be Math Analysis published by CPM Educational Program, Inc. COURSE CONTENT Calculus Concepts (not techniques) Area under a curve Area as velocity Rates of change Infinity Limits Velocity at a specific value of x (numerical derivative) Trigonometry Unit circle Radians Pythagorean identities Reciprocal identities Sum/difference identities Law of sines Law of cosines More on graphing periodic functions Laws of exponents and of logarithms Modeling Lines of best fit (some regression) Statistics 1 variable stats 2 variable stats median-median line Vectors via parametric equations Algebra techniques GOALS On successful completion of Math Analysis, students should be able to: use statistical tools to develop models of data they have collected be comfortable with graphs and equations of common families of functions understand the concepts of limits, integrals, and derivatives manipulate algebraic symbols accurately and automatically using a wide range of techniques make full use of graphing calculator, including simple programming develop facility with manipulating algebraic expressions to put them into more useful forms use trigonometric identities further develop the ability to construct convincing arguments and to support or prove assertions be able to communicate their mathematical ideas clearly using appropriate vocabulary and symbols understand the difference between conjecture and proof, including understanding the structure of them and feeling the need for them use elementary probability and statistics to solve problems use graphing and scientific calculators effectively and efficiently Communication, organization, and responsibility are important learning skills. Students will be expected to use and develop these skills with regard to their application in this class. The following are integral components to this course: Students will keep an organized three ringed binder containing the daily work from the most recent unit, tests, and other course material Students will take notes on new concepts as they encounter them Students will correct their own daily written work Students will spend a majority of class time working in study teams developing and executing the concepts covered in the course. This setting allows students to maximize their own active participation time in class as they will be able to both “talk math” and listen to others do the same GRADING SYSTEM Daily Written Work 20% Assessment 80% *, 2 3 4Cpїђђьђђ 5OJQJOJQJ5CJ OJQJ *ЇATeu~…ОЫзпі & 3 B f §ћћћљћћћљћээээээщнннннннн & F„И ЦhИ„P & F„И ЦhИ*ЇATeu~…ОЫзпі & 3 B f Š “ З Т г ќљіѓэъчфолеЭХНЕ­ЊЄœ”Œ„|tlif`]W Mўџџ Xўџџ |ўџџ …ўџџЉўџџЭўџџ  мўџџ  щўџџ  џџџ  џџџ  0џџџ  8џџџ   Dџџџ QџџџŠџџџ  ‘џџџ  šџџџ  Њџџџ  Лџџџ   Юџџџ ёџџџ ёћџџќџџwќџџєџџџ тџџџуџџџэџџџђџџџf Š “ З Т г ф ї  + , 2 z О  E   у ? \ Н  Ђ о "ћћяћууућћћсћееееееееееее & F„И ЦhИ & F„И ЦhИ & F„И ЦhИ„Pг ф ї  + , 2 z О  E   у ? \ Н  Ђ о "о34CD]oїяьщцрнзЯЧПЗЏЇŸ—‡|yqia^XUROжџџџяџџџ№џџџ ліџџљјџџњџџ  Nњџџ  њџџ    ќџџNќџџ  Šќџџ  §џџ  o§џџ  а§џџ  э§џџ  Iўџџ  Œўџџ  чўџџ  %џџџ  nџџџ   Вџџџ њџџџ у§џџф§џџї§џџўџџ+ўџџ  <ўџџ  "о34CD]opћяяяяћэћћћы & F„И ЦhИ„P opќФџџџАа/ Ар=!А"А# $ %А [4@ёџ4NormalCJOJPJQJmH <`< Heading 1$@&5CJ OJQJ8`8 Heading 2$@& 5OJQJ<`< Heading 3 $„P@& 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