Summer Math Requirement Algebra II Review For students entering Pre- Calculus Theory or Pre- Calculus Honors

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Maude McLaughlin
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1 Suer Mth Requireet Algebr II Review For studets eterig Pre- Clculus Theory or Pre- Clculus Hoors The purpose of this pcket is to esure tht studets re prepred for the quick pce of Pre- Clculus. The Topics cotied i this pcket re the core Algebr I d Algebr II cocepts tht studets ust uderstd to be successful i Pre- Clculus. There re cocepts ddressed i this pcket: A. Distce & Midpoit B. Circles C. Lier Fuctios D. Grphig Fuctios E. Fctorig F. Evlutig Fuctios G. Qudrtic Forul H. Solvig Iequlities I. Doi & Rge J. Properties of Epoets K. Squre Roots d Rtiolizig Deoitors For ech cocept listed, there is proble set tht eeds to be copleted. There re websites give below where you c go to fid eples, videos, d etr probles tht del with tht prticulr topic if you eed ssistce o workig the proble sets. If you try site d it is ot workig or o loger vilble, it is your resposibility to do serch for other site. It is suggested tht you coplete this prctice set i the few weeks prior to returig to school so tht the ifortio will be fresh. Plese brig this worksheet s well s ll of your work/solutios ON ANOTHER SHEET OF PAPER to clss with you o the FIRST DAY OF SCHOOL. You ust show your work just list of swers will ot be ccepted. We will go over the teril briefly d hve sutive ssesset (test) withi the first few weeks of school o these topics. If it hs bee few yers sice you hve hd Algebr II or if you re ucofortble with y of the topics fter copletig the proble set, it is recoeded tht you fid soe dditiol prctice fro the websites below or elsewhere thetics.co/ ALGEBRA.ht Plese eil Julie Vdiver (jvdiver@leigto.et), Kristy Eso (keso@leigto.et), Tiffy Roch (troch@leigto.et), Elie Lewis (elewis@leigto.et), or Bri Li (bli@leigto.et) f you hve y questios. We look forwrd to gret yer i PreClculus!!

2 Plese coplete the followig probles o ANOTHER SHEET OF PAPER. You should iclude the directios, proble, ll work ecessry d bo i your fil swer. These probles should be doe withi two weeks of the strt of school (plese do ot do the t the begiig of suer). Brig ll work with you to the first dy of clss. Feel free to use clcultor to check your work but plese uderstd tht the epecttio is tht you c coplete the followig without the use of clcultor. A. Distce d Midpoit Distce Forul = ( ) + ( y y ) Midpoit Forul =, Fid the distce d idpoit betwee these poits:, &,7. ( ) ( ). (, )& (, 9) + y + y B. Circles Forul of Circle: ( h) ( y k) r + = where (h, k) is the ceter d r is the rdius. Fid the stdrd for of the equtio of the specified circle:. Ceter (-, 9) Rdius =. Edpoits of the dieter (8, ), (, 8). Fid the ceter d rdius. The grph the circle: ( + ) + ( y ) = 6 C. Lier Fuctios Prllel lies hve the Se Slope Perpediculr lies hve Opposite Reciprocl Slopes y y Slope = = Stdrd for: A + By = C Slope- Itercept For: y= + b Poit- Slope for: ( y y ) = ( ) Zero slope = horizotl lie (y=#) Udefied slope = verticl lie (=#) Deterie the slope of the lie pssig through these poits., & 8,, &, ) ( ) ( ) ) ( ) ( ) Write equtio for the lie described i i the give ifortio. ) (, ) = ) (, ) = 6) (, ) = 7) (, ) ) psses through ( 6, ) d (, ) d perpediculr to + y =

3 D. Grphig Fuctios Sketch grph of the followig fuctios: (Grph pper o bck of pcket if eeded). y= 8. y. y =. y = +. ( y+ ) = ( ) = 6. y= 7. y = 8. y= 9. y = y= +. y= +. y=. ( ) E. Fctorig Fctor the followig copletely: p y y 8. 6c c 9. s. 8z 9z + +. r 6r +. w w w +. y y y F. Evlutig Fuctios Evlute the fuctio t the vlues give i, b, d c. Siplify where possible. You should hve swer for prt, b, d c for ech questio.. f ( ) =. f ( ) b. f ( ) c. f ( r ). h( ) = +. h( ) b. h ( 7) c. h( ). g( ), = +, >. g ( ) b. g ( ) c. g ( )

4 b± b c G. Qudrtic Forul Qudrtic Forul: = Solve usig the qudrtic forul. Aswers should be i siplest rdicl for o decils =. = H. Solvig Iequlities Solve d grph o uber lie.. ( + ). 7( 7) +. < 6 or >. 6< < I. Doi d Rge. Fid the doi d rge of the reltio below the deterie if the reltio is fuctio. {(,),(,),(, ),(,),(,),(,)} Deterie the doi d rge of the fuctios below:. Doi: Rge:. Doi: Rge:

5 J. Properties of Epoets Suppose d re positive itegers d d b re rel ubers. The the followig properties hold. =, ( b) = b g = + = b b = ( ) = = = = or = ( ) Siplify the followig usig properties of epoets. Mke sure ll swers coti oly positive epoets..... ( ) b b. y 6. ( ) r 7. ( ) 8. ( y ) 9. y y. y z (. ) y z y y. ( ). ( ).. ( ) y 6. ( ) K. Squre Roots d Rtiolizig Deoitors Siplify.. 88 y. Rtiolize y 7 y

6 Grph Pper for Prt D Grphig Fuctios if you wt to use it.

Calendar of first week of the school year. Monday, August 26 Full Day get books & begin Chapter 1

Calendar of first week of the school year. Monday, August 26 Full Day get books & begin Chapter 1 Gettig Strted Pcket Hoors Pre-Clculus Welcoe to Hoors Pre-Clculus. Hoors Pre-Clculus will refresh your Algebr skills, review polyoil fuctios d grphs, eplore trigooetry i depth, d give you brief itroductio