Pre-Calc Unit 1 Lesson 1

Transcription

1 Pre-Calc Unit 1 Lesson 1 The Number System and Set Theory Learning Goal: IWBAT write subsets of the rational, real, and complex number system using set notation and apply set operations on sets of numbers. Homework: Number System Worksheet """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" Do Now: a) Name as many different types of numbers you can think of. b) What is the difference between rational and irrational numbers?

2 Mathematical Terminology & Notation In mathematics, different types of numbers are grouped or organized together and given names. First we need to establish basic terms. {a, b, c} : set, a finite or infinite group of elements : the null set or the empty set : element, an object in a set : subset, a portion of a set or a set within a set In the diagram, A is a subset of B or A B

3 Complex and Real Numbers C Complex number set Any number of the form Ex:,,,,,, R Real number set a + bi 5 4i π Any number with no imaginary part π Ex:,,,,,

4 Rational and Irrational Numbers Q Rational number set Can be written as a fraction, repeating or terminating decimal Ex:,,, R\Q - Irrational number set Numbers that cannot be written as a fraction, repeating, or terminating decimal. 13 π 3.7 Ex:,,, 0.3 e

5 Natural Numbers and Integers Z Integer number set Positive and negative counting numbers Ex:,,, N Natural number set Positive counting numbers Ex:,,

6 Number System Diagrams

7 Set Notation Set notation uses brackets { } Description Method Describes the numbers in the set through words Ex: {prime numbers} Set-Builder Notation Describes set of numbers through a condition Ex: {x x is an even positive integer} Roster Method Lists the numbers numerically Ex: {2, 3, 5} Inequality Notation Similar to the set-builder notation, but uses inequalities instead of words. Ex: {x -5 x < 1}

8 Interval Notation Interval notation uses open or closed parenthesis. Intervals represent all real numbers between two numbers. Open parenthesis ( ) end value is not included in the solution. Closed parenthesis [ ] end value is part of the solution. Positive infinity + graph goes on forever to the right Negative infinity - Graph goes on forever to the left

9 Examples of Set & Interval Notation Ex #1: For solving 2x + 5 = 17 Solution Set = {6}, Which notation? Set Notation Ex #2: 2x + 5 > 17 Inequality Notation: x > 7 Set Notation: {x x is an integer greater than 7} Interval Notation: (7, + )

10 Set & Interval Notation Below are methods for writing a set of numbers in set and interval notation. Let a be a real number. Set Notation {x x > a} {x x a} {x x < a} {x x a} Interval Notation (a, + ) [a, + ) (-, a) (-, a]

11 Set Operations I : intersection of two sets; the elements that both sets have in common {1, 2} {1, 2} = {1, 2}. {1, 2} {2, 3} = {2}. U : union of two sets; the elements of both sets combined {1, 2} {1, 2} = {1, 2}. {1, 2} {2, 3} = {1, 2, 3}. {1, 2, 3} {3, 4, 5} = {1, 2, 3, 4, 5}

12 Examples of Set Operations Find the union or intersections of the following sets. 1.) {x x 4} I {x 1< x 9} 2.) {x x < 5} U {x x 7} 3.) (2,13) I[7, 25) 4.) [ 5,13) U ( 7,10)

13 Pre-Calc Unit 1 Lesson 2 Set Theory and Operations Learning Goal: IWBAT apply set operations such as union, intersection, and relative complement on sets of numbers. Homework: Union and Intersection of Sets Worksheet (ODD) """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" Do Now: a) b) c) ( 5, 0) U ( 7,15] ( 5, 0) I ( 7,15] ( 5, 0) \ ( 7,15]

14 Set Operations Practice Work on the even problems in the practice worksheet. For HW you will work on the odd problems in the practice worksheet.

15 Pre-Calc Unit 1 Lesson 3 Set Theory and Operations Learning Goal: IWBAT determine whether a number set is closed under addition, subtraction, multiplication, and division. Homework: Pre-Calculus by Sullivan pg. 122 #1 5 """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" Do Now: find domain of the following a) b) "x"5%

16 Station 1: Domain Restrictions Direc/ons:%Inpartners,competetofindthedomainofthefunc5onsalgebraically usingyourknowledgeofdomainrestric5ons.youwillplayagainsteachotherina gameofpre"calc5c"tac"toe. Atthetopoftheworksheet,youwillfindathreebythreegridwithsolu5onsto theproblemsbelow.thesearethespacesyouwillmarkaseither X or O. Bothplayersagreetoworkonthesameproblemforacertainamountof5me. Whoeversolvestheproblemcorrectlygetstoplacetheirmarkonthechart.If bothplayerssolvetheproblemcorrectly,thenneitherplayerplacesamarkon thechart.beforemovingontothenextproblem,bothpartnersshould understandandagreeuponthefinalanswerwithvalidreasoning.thefirstplayer toreachthreemarkingsinarowordiagonalwinsthegame. Ifyoufinishthegameearly,switchpartnersinyourgroupandplayagain.

17 Station 2: Domain & Range of Graphs Direc/ons:%Asagroup,worktogethertofindthedomainandrangeoffunc5ons graphically.selectonememberofthegrouptoaccessthesocra5veproblemson theiripad.instruc5onstoaccessthesocra5veproblemsarebelow.onceyou entersocra5ve,taketurnssolvingeachproblemby thinkingoutloud. Askyour groupforassistanceifyouareunsureaboutyoursolu5ontotheproblem. Followtheinstruc5onsbelowtoaccessthedomain&rangeproblemson Socra5ve. 1. GototheSocra5veApponyouriPad.IfyoudonothavetheSocra5veApp,enter StudentLogin. 2. EnterRoomName:Rivera201% 3. Typeeverygroupmember sname:firstnameandini5alleweroflastname 4. Answereachques5onandclick Submit tomoveontothenextques5on.

18 Station 3: Set Operations Direc/ons:%Asagroup,worktogethertocreateaposterthatexplainstheunion, intersec5on,andrela5vecomplementsofsetsusingavenndiagram.includea real"lifeormathema5calexampleofaunion,intersec5on,andcomplementof twosets. Ex:LetAbethesetofESATstudentscurrentlyenrolledinPre"CalculusandB bethesetofesatstudentscurrentlyenrolledinchemistry.theunionof setsaandbwillbethesetofallstudentstakingpre"calculusorchemistry. A\ercomple5ngtheposter,prac5cefindingtheunionandintersec5onofsetsin theworksheet.

19 Station 4: Complex Number System Direc/ons:%Ingroups,worktogethertocompletetheworksheetonthecomplex numbersystem.