Assessment Center Elementary Algebra Study Guide for the ACCUPLACER (CPT)
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1 Assessmet Ceter Elemetr Alger Stud Guide for the ACCUPLACER (CPT) The followig smple questios re similr to the formt d cotet of questios o the Accuplcer Elemetr Alger test. Reviewig these smples will give ou good ide of how the test works d just wht mthemticl topics ou m wish to review efore tkig the test itself. Our purposes i providig ou with this iformtio re to id our memor d to help ou do our est. I. Order of opertios. 0. ( )( ) 7. ( 7 ) () 7.. II. Scietific Nottio Write the followig i Scietific Nottio.. 0,000, ,00,000,000,000,000,000 Simplif. Write swers i scietific ottio. 7. ( )( ) ( ) III. Sustitutio Fid ech vlue if,, d z.. z z. ( z) IV. Lier equtios i oe vrile Solve the followig for... Write i epded form ( )( ) z. 0. z ( ) 0 ( ) ( ) //00 0: Elemetr Alger Review.rtf
2 V. Formuls. Solve PV RT for T.. Solve for.. Solve for.. Solve h for. Solve C πr for r. VI. Word Prolems. Oe umer is more th twice other umer. The sum of the umers is. Fid the umers.. Ms. Joes ivested $,000 i two ccouts. Oe ccout ps % simple iterest d the other ps %. Her totl iterest for the er ws $,0. How much did she hve i ech ccout? How m liters of 0% solutio d % solutio must e mied to oti 0 liters of % solutio?. Sheil ought urgers d fries for her childre d some frieds. The urgers cost $.0 ech d the fries re $. ech. She ought totl of items, for totl cost of $.. How m of ech did she u? VII. Iequlities Solve d grph o the umer lie.. 7. ( ) < VIII. Epoets & polomils Simplif d write swers with positive epoets.. ( ) ( ). ( c ). 7 ( c ) 0 ( z )( z ) 7. ( )( 7) c c. ( ) 7. ( c ). z z IX. Fctorig M 00 : Elemetr Alger Review.rtf
3 X. Qudrtic Equtios ( ). r r 0 XI. Rtiol Epressios Perform the followig opertios d simplif where possile. If give equtio, solve for the vrile..... XII. Grphig Grph ech equtio o the coordite is k k k M 00 : Elemetr Alger Review.rtf
4 Sstems of Equtios Solve the followig sstems of equtios XIII. Rdicls Simplif the followig usig the rules of rdicls (rtiolize deomitors). All vriles represet positive umers I. Order of Opertios ep oets Whe workig with (),,,,,d Aswers, oe must rememer the order of the opertios. First, prethesis or epoets s oe clcultes from left to right. Secod, multiplictio or divisio s oe clcultes from the left to right. Ad fill, dditio or sutrctio s oe clcultes from left to right. 0.. ( )( ) (). -. M 00 : Elemetr Alger Review.rtf
5 II. Scietific Nottio All umers i scietific ottio hve the followig form:. 0,000, ,00,000,000,000,000, ( )( ) ( ) ( ). III.. z. ( )( ). 7 Sustitutio 0. power ozerodig it.restofumer.. 0,000,000,000,000,000,000, ,000, z ( ) z. () ( ) ()( ) ( z) [ ] ( ) 0. z ( ) 0 IV. Lier equtios i oe vrile.. ( ) ( ). ( ) ( ) V. Formuls. PV RT PV PV RT T R RT R. C r π.. ( h ) h h h h h VI. Word Prolems. Let other umer forcig Oe umer. d. Oe umer d other umer. M 00 : Elemetr Alger Review.rtf
6 . Let the dollrs i the ccout pig % iterest The,,000 the dollrs i the ccout pig %. The iterest dollrs re clculted multiplig the totl dollrs i the ccout the iterest rte. Hece:.0 the iterest ered the first ccout.0 (,000 ) the iterest ered the secod ccout. Addig up ll the iterest,.0.0(,000 ),0. Solvig, 7,00. So, Ms. Joes hs $7,00 i the ccout pig % iterest d $,00 i the ccout pig % iterest. Use the followig uckets: 0 % 0 - % 0 liters % From the digrm, we get the equtio:.. (0 ) 0(.) d the swer is liters t 0% d liters t %.. Let the umer of urgers d the umer of fries. To get the totl mout of moe spet, multipl the umer of items the cost of the item..0 the totl dollrs spet o urgers d. ( ) the totl dollrs spet o fries. The equtio is:.0. ( ).. Solvig the equtio,. Hece, she ought urgers d fries. VII. Iequlities Solve iequlities the sme s equtios with oe eceptio. Whe oth sides re multiplied or divided egtive umer, rememer to switch the directio of the iequlit < - - < - - < >. - VIII. Epoets & Polomils -. Add like terms: ( ) ( ). c ( c ) c c 7 ( c ) c 0 0 ( z )( z ) ( ) z z z ( c ) ( ) c c c ( z) ( z ) ( z )( z ) z z 7. 0 z M 00 : Elemetr Alger Review.rtf
7 c c c c 0. ( ) ( )( ) IX. Fctorig Steps to fctorig:. Alws fctor out the Gretest Commo Fctor (If possile).. Fctor the first d third term. Figure out the middle term.. ( )( ). ( )( ) ( )( ), Differece of two squres. Sum of two squres requires the comple umer sstem to fctor. Not fctorle.. ( ) ( )( ) ( )( )( ). Differece of two cues: ( )( ) ( )( ) 7. ( ). Let d d use the formul to get : 7 X. Qudrtic Equtios Steps:. Get zero o oe side of the equls. Fctor Set ech fctor to zero. Solve for our vrile If ou cot fctor the equtio d the qudrtic is i the form c 0, the use the qudrtic formul. ± c. 0 ( )( ) 0 0 or 0 or -., ( - )( ) 0 or.,. The solutio is give elow: ( ) 0 ( - )( ) 0 or - 0. ± M 00 7: Elemetr Alger Review.rtf
8 M 00 : Elemetr Alger Review.rtf XI. Rtiol Epressios. Need to fid commo deomitor (fctor deomitors to see wht ou eed), dd, d the reduce (if possile) t the ver ed.. This prolem uses the sme techique s ove. Be creful of the sutrctio. To multipl frctios, fctor d ccel first efore multiplig.. Divisio is the sme process with oe etr step (ivert & multipl): c d d c. Oe other hit:. Fctor d Reduce to get.. Fid the Lowest commo deomitor (LCD) for ll frctios (), the multipl the umertor d deomitor the LCD. 7. Aihilte the deomitors multiplig oth sides of the equtio the LCD [ ], solve the resultig, frctioless equtio, d check swers i the origil equtio to isure tht the deomitors re ot zero. or Sice these swers do ot mke the deomitor zero i the origil equtio, the re the solutio. k -. -
9 XII. Grphig... M 00 : Elemetr Alger Review.rtf
10 .. 7. XIII. Sstems of Equtios The followig re dimesiol lier equtios. Ech equtio represets lie tht c e grphed o the coordite ple. The ultimte solutio to sstem of equtios is for the lies to itersect i o poit such s questio # d #. Questio # hs two equtios d oe is multiple of the other. Hece, oth formuls grph the sme lie mkig the solutio ifiite, { }. The lst possiilit is i questio # If ou grph the lies i questio #, ou will see tht the re prllel d do ot cross. This sstem hs o solutio (The solutio is the empt set.).. The swer is d. The work is elow.., Multipl - - Now, sustitutig ito the first equtio () M 00 : Elemetr Alger Review.rtf This documet is used with permissio grted Aims Commuit College,
11 M 00 : Elemetr Alger Review.rtf This documet is used with permissio grted Aims Commuit College, XIV. Rdicls Thik of the ide ( ide ) s door perso. If it is two, the two ideticl fctors iside ecome oe outside. Also, rememer these properties: Worked out elow
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