Westchester Community College Elementary Algebra Study Guide for the ACCUPLACER

Transcription

1 Westchester Commuity College Elemetry Alger Study Guide for the ACCUPLACER Courtesy of Aims Commuity College The followig smple questios re similr to the formt d cotet of questios o the Accuplcer Elemetry Alger test. Reviewig these smples will give you good ide of how the test works d just wht mthemticl topics you my wish to review efore tkig the test itself. Our purposes i providig you with this iformtio re to id your memory d to help you do your est. I. Order of opertios.. 0. ( )( ) II. Scietific Nottio Write the followig i Scietific Nottio.. 0,000, ,00,000,000,000,000,000 Write i epded form Simplify. Write swers i scietific ottio. 7.. ( 0 )( 0 ) ( 0 ) III. Sustitutio (. 0 )( 0 ) 0 Fid ech vlue if, y, d. yz z. y. ( y z) z... z y y z IV. Lier equtios i oe vrile Solve the followig for ( ) 0 ( ) ( )

2 V. Formuls. Solve PV RT for T. y. Solve for y.. Solve y for.. Solve y 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 pys % simple iterest d the other pys %. Her totl iterest for the yer ws $,0. How much did she hve i ech ccout?. How my 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 $.0. How my of ech did she uy? VII. Iequlities Solve d grph o the umer lie.. 7. ( ) <. ( ) ( ) VIII. Epoets & polyomils Simplify d write swers with positive epoets.. ( ) ( ). ( c ). 7 ( c ) 0. ( y z )( y z ) ( )( 7) c c c. ( ). y z y z IX. Fctorig.... y y y..

3 X. Qudrtic Equtios ( ) r r 0 XI Rtiol Epressios Perform the followig opertios d simplify where possile. If give equtio, solve for the vrile y y k k k 7 XII. Grphig Grph ech equtio o the coordite is.. y.. y. y. y. y 7. y

4 XIII. Systems of Equtios Solve the followig systems of equtios.. y y. y 0 y. y y 7. y y XIV. Rdicls Simplify the followig usig the rules of rdicls (rtiolize deomitors). All vriles represet positive umers.. ( 0 ).... y 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 filly, dditio or sutrctio s oe clcultes from left to right. 0.. ( )( )

5 II. Scietific Nottio All umers i scietific ottio hve the followig form:. 0,000, ,00,000,000,000,000, ( 0 )( 0 ) 0 0 ( 0 ) ( 0 ) III.. yz.... y (. 0 )( 0 ) Sustitutio ,000,000 power ozerodig it.restofum er 0.. 0,000,000,000,000,000,000, z ( ) y ( ) 0 ( y z ) [ ] ( ) ( 0 ) 0 z y ( ) z ( ) ( ) 0 0 IV. Lier equtios i oe vrile.... ( ) ( ) ( ) ( ) V. Formuls. PV RT PV PV RT T R RT R. y y y y y. C r π. y y. ( h ) y y h y h h h h

6 VI. Word Prolems. Let other umer forcig Oe umer. d 0. Oe umer d other umer 0.. Let the dollrs i the ccout pyig % iterest The,,000 the dollrs i the ccout pyig %. The iterest dollrs re clculted y multiplyig the totl dollrs i the ccout y the iterest rte. Hece:.0 the iterest ered y the first ccout.0 (,000 ) the iterest ered y the secod ccout. Addig up ll the iterest,.0.0(,000 ),0. Solvig, 7,00. So, Ms. Joes hs $7,00 i the ccout pyig % iterest d $0,00 i the ccout pyig % 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 moey spet, multiply the umer of items y the cost of the item..0 the totl dollrs spet o urgers d. ( ) the totl dollrs spet o fries. The equtio is:.0. ( ).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 y egtive umer, rememer to switch the directio of the iequlity ( ) < < - - < > -. VIII. Epoets & Polyomils -. Add like terms: ( ) 0 0 c ( c ) c c. 7 ( c ) c 0. 0 y z y z y y z z y z c c c c y z y z y z y z y z y z ( )( 7) c c c c 0. ( ) ( )( ) y z

7 IX. Fctorig Steps to fctorig:. Alwys 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 system to fctor. Not fctorle... y y y y y y y. Differece of two cues: get : ( )( ) 7. ( 7 y ). ( ) X. Qudrtic Equtios. Let d d use the formul to Steps:. Get zero o oe side of the equls. Fctor. Set ech fctor to zero. Solve for your vrile If you c ot 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. ±

8 XI. Rtiol Epressios. Need to fid commo deomitor (fctor deomitors to see wht you eed), dd, d the reduce (if possile) t the very ed. 0. This prolem uses the sme techique s ove. Be creful of the sutrctio. 0. To multiply frctios, fctor d ccel first efore multiplyig.. Divisio is the sme process with oe etr step (ivert & multiply): c d d c. Oe other hit: (Cotiues o et pge). Fctor d Reduce to get.. Fid the Lowest commo deomitor (LCD) for ll frctios (y), the multiply the umertor d deomitor y the LCD. y y y y y y y y 7. Aihilte the deomitors y multiplyig oth sides of the equtio y 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, they re the solutio.. k -. -

9 XII. Grphig. y -.. y. y. y. y

10 7. y XIII. Systems of Equtios The followig re dimesiol lier equtios. Ech equtio represets lie tht c e grphed o the coordite ple. The ultimte solutio to system 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 possiility is i questio #. If you grph the lies i questio #, you will see tht they re prllel d do ot cross. This system hs o solutio.. The swer is d y. The work is elow. y y y., y Multiply y - - y y Now,sustitutig itothe first equtio XIV. Rdicls Thik of the ide ( ide outside. Also, rememer these properties: ) s door perso. If it is two, the two ideticl fctors iside ecome oe. ( )( 0 ) y y y y y y y y y y. Worked out elow ( ). ( )( ) 0 0 7