Algebra 2 Readiness Summer Packet El Segundo High School

Transcription

1 Algebr Rediess Suer Pcket El Segudo High School This pcket is desiged for those who hve copleted Geoetry d will be erolled i Algebr (CP or H) i the upcoig fll seester.

2 Suer Pcket Algebr II Welcoe to Algebr II. The topics i Algebr II c be bstrct but they hve prcticl pplictios d serve s foudtio for further study i thetics d other college level thetics. Mthetics is series of buildig blocks. A studet of thetics ust hve sufficiet Algebr I skills to be proficiet i Algebr II. This Review Pcket ws prepred for studets to be ble to review teril fro Algebr I. The suer pcket is to be copleted by the first dy of school. This pcket covers ll review skills. Algebr Resources Kh Acdey Tke cotrol of your lerig by workig o the skills you choose t your ow pce.... Mth, sciece, coputer progrig, history, rt, ecooics, d ore. Algebsics hs video tutorils expliig the bsics of lgebr, equtios, rtio d proportio, bsolute vlue, polyoils, fctorig, lier equtios, rdicls, pplictios, d uch ore. Algebr-Clss.co offers help with solvig equtios, grphig equtios, writig equtios, iequlities, fuctios, expoets d ooils, polyoils, d the qudrtic equtio. It lso hs list of resources. Algebr.help cotis lessos o topics tht iclude equtios, siplifyig, fctorig, distributio, d trioils, s well s equtio clcultors d worksheets. This site lso hs extesive list of th resources d study tips. Algebr Help covers topics such s frctios, percets, decils, lgebric expressios, dditio, ultiplictio, d word probles. Ech sectio icludes expltios d exples. College-Cr.co llows studets to choose the lgebr subject they re strugglig with fro drop dow eu, select the pproprite chpter, d pick your resources. The oges will feture forul solvers, bottoless worksheets, flshcrds, quizzes, iterctive overviews, d brief lessos d study sheets. Iterctive Mthetics hs lrge sectio o lgebr, icludig ifortio o fctorig d frctios, the qudrtic equtio, expoets d rdicls, systes of equtios, trices d deterits, d iequlities. Mth Expressio hs videos, worksheets, d lessos to help you develop your lgebr skills. Mth topics iclude lgebr, expoets, syetry, frctios, esureets, gles, d ore. The site lso icludes list of useful resources. Purpleth cotis lessos with expltios o everythig fro bsolute vlue d egtive ubers to itercepts, vribles, d fctorig. I dditio, this site icludes foru tht llows studets to sk questios d receive swers, s well s list of hoework tips d guidelies. 0

3 Prt Oe: Order of Opertios Directios: Siplify ech proble i the spce provided, circlig your fil swer. Fil swer should hve ll positive expoets d be i siplest for. No decil pproxitios llowed. Properties. Groupig sybols. Expoets. Multiplictio or Divisio I order fro left to right 4. Additio or Subtrctio I order fro left to right Exple: (4 5) ( ) (4 5) ( 8) (4 5) 8 (9). (5-8) (5 - ) ( b) 6, usig 6, b 5. whe x 5 6. x x 4 whe x 7. x 5 x 4, whe 6 x 8. ) whe

4 Prt Two: Lier Equtios Directios: Solve ech proble i the spce provided, circlig your fil swer. Recll: to fid x-itercept set y=0 d to fid y-itercept set x=0. To fid equtio of lie fid slope d the use slope d poit to solve for y- itercept. Equtios of Lie Slope-itercept for: y x b Poit-slope for: y y x ) Stdrd for: Ax By C y Slope: x y x ( x Exple: Write the equtio of 4 lie tht hs slope d 9 y-itercept b. y x b Use the substitute vlues for d b d siplify 4 y x 9 4 y x 9 9. Fid the slope of the lie cotiig the poits ( 4, ) d ( 6, 4). 0. Write the equtio of lie tht hs slope 4 d psses 9 through the poit (8, - ).. Write the equtio of the lie cotiig the poits (,) d ( 5, ).. Write the equtio of the lie cotiig the poit ( 4, 6) d prllel to x y 8.. Write the equtio of the lie cotiig the poit (,56) d perpediculr to x y 8.

5 Prt Three: Rules of Expoets Directios: Siplify ech proble i the spce provided, circlig your fil swer. Fil swer should hve ll positive expoets. Exple: ) ( ) ( ) ( ) ( x 5. 0 xy y x ) 4 ( x 8. 5 v u z xy z y x Properties b b 0,, 0, 0 b b b

6 Prt Four: Siplifyig Rdicls Directios: Siplify ech proble i the spce provided, circlig your fil swer. Fil swer should hve ll positive expoets d be rtiolized. No decil pproxitios llowed. Properties b b b b or x x Exple: x x BE CAREFUL: b b b b b b 4

7 Prt Five: Siplifyig Polyoils Directios: Siplify ech proble i the spce provided, circlig your fil swer. Fil swer should hve ll positive expoets d be i siplest for. No decil pproxitios llowed. Properties c( x y) cx cy ( b)( c d) c d bc bd Exple: (4x 7x ) (x 4x 4x x 7x x x x 4 5x ) 5x ) 7x 5x ) 9. (7x y) (x 5 y) 0. 7x (x 9). ( x y) (x y). ( x 4)(x 9). 7(x 0x) 4x 4. x 0x 4( x 7) 5. (x 5)(x ) 6. ( x y)(x y) 5

8 Prt Six: Fctorig Directios: Fctor ech proble copletely i the spce provided, circlig your fil swer. Recll: if ot fctorble, it is prie. Strtegies. GCF. Differece of Squres ( b)( b) b. Trioils: fctors of c tht dd up to b 4. Su d Differece b b ( b) 5. Groupig b b ( b ) Exple: b 5b 8 ( b 5b 6) ( b )( b ) 7. x 6x 5 8. x x 6 9. x 8x 4x x 6 4. x 7x 4 4. x x 5 4 0x 44. x x 8x 6

9 Prt Six: Solvig Directios: Solve ech proble copletely i the spce provided, circlig your fil swer. Recll: For qudrtics you y eed the zeroproduct property if b 0, the 0 or b 0. Strtegies. Fctor out GCF (if oe exists).. Qudrtic fctor, copletig the squre or qudrtic forul. b b 4c x. Cubic try to fctor by groupig. 4. Absolute vlue equtios : b b c or b c 5. Rdicl equtios rise ech side to the root. c 45. ( x 7) 5 x 8 x 47. ( x 4)(9x ) x x x x x x 5. 4x x x 5 7

10 Prt Seve: Systes of Equtios Directios: Solve ech proble copletely i the spce provided, circlig your fil swer. Methods. Grphig.. Substitutio. Eliitio. 54. x y 9x 8y y x 6x y y x 7.5y 5x 5 Prt Eight: Systes of Iequlities Directios: Solve ech syste of iequlities by grphig. Methods Grph both iequlities o the se coordite ple d their itersectio (overlppig regio) is the solutio. < d > re dotted lies, d re solid lie. 57. y x y x 58. y x x y 6 8

11 Prt Nie: Bsic Geoetry d Trigooetry Set Oe: Set Two:

12 Solutios Prt Oe: Order of Opertios.) 68.).) ) 4 5.) Oops 6.) 8 7.) ½ 8.) Prt Two: Lier Equtios 9.) " 0.) y =.) y = x +.) y = x +.) y = Prt Three: Rules of Expoets 4.) 5.) 7x y 6.) - 7.) 64x 9 " 8.) " 9.) " " 0.) "# "#.) " Prt Four: Siplifyig Rdicls.) 0 7.) " 4.) 7 5.) ) - 7.) 5x 8.) 5 Prt Five: Siplifyig Polyoils 9.) 4x 7y 0.) x.) -x.) 6x 9x 6.) x + 66x 4.) x + 6x ) 6x 9x + 0x 5 6.) -6x + 5xy y Prt Six: Fctorig 7.) (x + 5)(x + ) 8.) (x + )(x ) 9.) x(x + 4)(x + ) 40.) 4( 6) 4.) 6(x + )(x ) 4.) (x )(x + 4) 4.) x (x + )(x + ) 44.) (x + )(x + )(x ) Prt Six(): Solvig 45.) 46.) 4 47.), ) -4, 49.) -7, 5 5.) -, 5.) x > ½ 5.) 6 50.) ± Prt Seve: Systes of Equtios 54.) ( ", ) 55.) No solutio 56.) Ifiite solutios Prt Eight: Systes of Iequlities

13 57.) 58.)

14 Prt Nie: Bsic Geoetry d Trigooetry Set Oe:

15 Set Two: