Welcome to Precalculus !

1. Welcome to Precalculus! Mr. Ueland 1st Period Rm156

2. Today in Precalculus • Prayer • Introductions • Distribute books • Go over the class syllabus • Look at a “typical" day • Get started!

3. Books • They’re what we have. Math is scheduled for a curriculum update next year. • Record your book # and condition (from amazon.com): • Good: A copy that has been read, but remains in clean condition. All pages are intact, and the cover is intact (including dust cover, if applicable). The spine may show signs of wear. Pages can include limited notes and highlighting, and the copy can include "From the library of" labels. • Acceptable: A readable copy. All pages are intact, and the cover is intact (the dust cover may be missing). Pages can include considerable notes--in pen or highlighter--but the notes cannot obscure the text. • Unacceptable: Moldy, badly stained, or unclean copies are not acceptable, nor are copies with missing pages or obscured text. Books that are distributed for promotional use only are prohibited. This includes advance reading copies (ARCs) and uncorrected proof copies.

4. Precalculus is discovery “A great discovery solves a great problem, but there is a grain of discovery in the solution of any problem. Your problem may be modest, but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery.” – George Polya (1887-1985), a well-decorated mathematician and former professor at Stanford

5. Discover but don’t depend on BOB1 "BOB doesn’t come to school on test days.” – Mr. Ueland, has a well-decorated office, knows a professor at Stanford 1 “Back of the Book”

6. Course Description This is a fast paced, calculus prep course designed for college-bound students. Course topics include college algebra, advanced trigonometry, and analytic geometry of two and three dimensions. Students experience a thorough analysis of all elementary functions and curve-sketching. Selected discrete mathematics topics including normal probability distributions, non-linear regression, and hypothesis testing are explored. Practice with proofs such as mathematical induction are included. Experience with graphing calculators is incorporated. uh oh!

7. Prerequisites Successful completion of Algebra 2 (with a B or better) or teacher permission.

8. REQUIRED MATERIALS • a graphing calculator (minimum: TI-84, Casio FX-9750G or equivalent) • pencils, a quality eraser • textbook: PreCalculus, Sixth Edition, by Demana, Waits et al, 2004, Addison Wesley. Textbooks MUST be covered by a thick paper (grocery bag type) cover.

9. GRADING POLICY • Letter grades are determined by performance on assignments and evaluations. Equal weight is placed on each. Letter grades are determined according to Horizon Christian’s accepted grading scale (90s =A, 80s = B, etc.).

10. GRADING POLICY • HOMEWORK (50%) – Assignments are a key part of this course. I expect every student to attempt to solve every problem I assign. To be scored, each paper must be legible and properly headed. Assignments will be scored on a 5 point basis as follows (assumes ALL are attempted): • 80-100% correct 5 pts • 60-79% correct 4 pts • 40-69% correct 3 pts • 0-39% correct 2 pts • Less than 19% correct 1 pt

11. “Properly headed” Homework

12. GRADING POLICY • TESTS and QUIZZES (50%) – We will have unit tests at the completion of each unit. Test dates will normally be announced about a week in advance. Three forms of each unit test will be used: • The A form is a pre-test and is assigned as homework • The B form is the test itself, scored on a 100 pt basis. • The C form is an optional make-up test. Students may increase their unit test score by 5 pts or to an 80, whichever is higher by achieving a score at least that high on the take-home C form.

13. GRADING POLICY • We will have brief “pop” quizzes occasionally (about once a week). These serve at least two purposes: as a check for basic understanding (new terms, the example or introductory problems in a new section, etc.), and on attendance. Pop quizzes missed due to an absence may not be made up.

14. GRADING POLICY • FINAL EXAM (10%) – There will be a comprehensive, multiple-choice final exam at the end of each semester. It will be integrated into the Tests and Quizzes grade.

15. OTHER POLICIES • TARDIES: Please don’t be. We start class when the bell rings, often with a demonstration of some sort. Please be in your seat and ready to go. You will ALWAYS be marked tardy and reported to the office if you're not in the class when the bell rings. Please have the courtesy not to enter the classroom when we’re praying. • LATE WORK: Late assignments will be reduced 20% (1 pt). No assignments will be accepted after the unit test has been given. • MISSED WORK: If you have an excused absence, you may have an additional day after you return for every day you missed to get your work up to date. It is your responsibility to make arrangements for this. If your absence is for an extended period of time, please contact me so that I can get assignments to you (email is excellent for this). It is your responsibility to find out what you missed and get it in to me when it is due. This information will be available on Gradelink. Missed tests and labs must be made-up within the same time frame and on your own time or in a work group. See me to schedule this. Missed pop quizzes may not be made up.

16. OTHER POLICIES • EXTRA CREDIT WORK: There will be some extra credit nuggets sprinkled throughout this course (often on exams). Take advantage when they’re offered. There are no other opportunities. • ACADEMIC HONESTY: I expect no problems here, but I want to be explicit. Each student in this course will do their own work, every day, all term. If you get stuck on an assignment, you may seek a tip from me, a classmate, or the solution guide if allowed, BUT your work must be your own (Prov. 4:25-27, 2 Cor. 8:21). This is intuitive to everybody in some situations (in an exam, for instance), but in other situations elements of our culture may have soiled our consciences some. Any honor violations will be dealt with swiftly and firmly according to the student handbook. Credit is never awarded for work found to be dishonorable (zero). • HELP!: If you need help for any reason, please come see me! I highly recommend attending the group help session held before school prior to each unit test. If you need individual help, PLEASE ASK. I am often available before school.

17. Other ways to contact me: cell: 541.806.2101 (before 10 please) email: hueland@horizonchristianschool.org or hal@julieueland.com (I check both)

19. Acknowledgement of Receipt • Please take the syllabus home to review with your parents and have one sign and return the Acknowledgement to me tomorrow.

20. Schedule of a typical day • 8:00 – Announcements • 8:05 – Brief devotion and prayer • 8:10 – Correct HW in class (usually, although I also sometimes collect it) • 8:15 – Work any problems that were troublesome • 8:25 – Lesson on new material • 8:35 – Work time • 8:50 – Dismissal

21. Questions? • Let’s begin!

22. Preface:The “Rule of Four” • Algebraic methods (ex. solving a system of equations by elimination) • Numerical methods (ex. ramming in 10 sets of coordinates and getting a best fit line) • Graphical methods (ex. Solving a system of equations by graphing and finding an intersection) • Verbal methods (EVERYBODY’s favorite – “story problems”)

23. Using graphers • TI keystrokes are assumed, so it will be a bit easier if you use a TI rather than a Casio • Some moderately helpful TI programs are downloadable from http://www.aw-bc.com/demana6e/ti.html (note 6th edition, this is different than listed in the text) • TI-84 guidebook is available online: http://education.ti.com/downloads/guidebooks/graphing/84p/TI84Plus_guidebook_EN.pdf

24. P.1: Real Numbers • A real number can be written as a decimal (ex. –8, 2.333, e, π ) • Natural numbers are counting numbers (1,2,3, …) • Whole numbers include zero (0,1,2,3,…) • Integers include negatives (…,–2,–1,0,1,2,…) • Rational numbers can be written as a ratio of 2 integers (2/3, 57/1037)

26. How to say it • A vertical bar in set notation is read as “such that.” • ex. is read “the set of numbers a over b such that a and b are integers and b does not equal zero.”

27. Bounded intervals and the number line • Closed interval: [a,b] – (includes a and b) • Open interval: (a,b) – (does NOT include a or b) • Half interval: [a,b) – includes a, does not include b) • Example 1: Give interval notation: Ans: [–2,4) • Example 2: Give inequality notation for the above. Ans:

28. Special case • Infinity is always an open interval (how could you ever bound it?)

29. Properties of Algebra • Commutative (order) property: • Associative (grouping) property: • Distributive (spreading) property: • Identity property: • Inverse property:

30. Properties of exponents

31. Properties of exponents

32. Examples ANYTHING to the zero power is one

33. Examples 2

34. Scientific Notation • Any positive number can be written in scientific notation • The coefficient or (decimal part) has a units digit followed by a decimal • The base of the exponent is always 10 • The exponent may be either positive or negative • Ex: 65,000,000 =

35. Using Scientific Notation: Adding & Subtracting mentally • When adding or subtracting numbers expressed as scientific notation, convert all to the highest exponent and add or subtract the coefficients: • Why would you choose –2 rather than –4?

36. Using Scientific Notation: Multiplying and dividing mentally • When multiplying or dividing numbers expressed as scientific notation, multiply or divide the coefficients, add or subtract the exponents and simplify back to correct form:

37. Using Scientific Notation: Multiplying and dividing mentally • Converting numbers with many zeros to scientific notation simplifies calculations. For example: Restate in form given

38. Using Scientific Notation: on your grapher Use parentheses to ensure correct order of operations • Enter scientific notation numbers with the [EE] or [EXP] key: The [EE] button is [2nd][,] The calculator displays:

39. Assignment • P.1, 1-73 eoo (every other odd, i.e. 1,5,9,13…) • “Group Activities” (i.e. #45) may be done with a neighbor or individually. • Due Thursday at the start of class.