Licol Ld Commuity College Plcemet d Testig Office Elemetry Algebr Study Guide for the ACCUPLACER (CPT) A totl of questios re dmiistered i this test. The first type ivolves opertios with itegers d rtiol umbers, d icludes computtio with itegers d egtive rtiols, the use of bsolute vlues, d orderig. A secod type ivolves opertios with lgebric epressios usig evlutio of simple formuls d epressios, d ddig d subtrctig moomils d polyomils. Questios ivolve multiplyig d dividig moomils d polyomils, the evlutio of positive rtiol roots d epoets, simplifyig lgebric frctios, d fctorig. The third type of questio ivolves the solutio of equtios, iequlities, word problems, solvig lier equtios d iequlities, the solutio of qudrtic equtios by fctorig, solvig verbl problems preseted i lgebric cotet, icludig geometric resoig d grphig, d the trsltio of writte phrses ito lgebric epressios. Suggestio: Use this study guide i cojuctio with the videos t www.khcdemy.org I. Order of opertios. 0. ( )( ) 7. ( 7 ) 7. 7. 0... 7. 7. II. Scietific Nottio Write the followig i Scietific Nottio.. 0,000,000. 0.0000000000000. 0,00,000,000,000,000,000 Write i epded form...0 0..0 0.. 0 Simplify. Write swers i scietific ottio. 7.. ( 0 )( 0 ) ( 0 ) 0. 0 0. (. 0 )( 0 ) 0 Referece: Creted by Fculty t Aims Commuity College, Greeley, CO
III. Substitutio Fid ech vlue if. yz z. y. ( y z), y, d IV. Lier equtios i oe vrible Solve the followig for... z. z. y. y. 0. z ( ) 0 ( ) ( ) V. Formuls y. Solve PV RT for T.. Solve for y.. Solve y for.. Solve y h for.. Solve C πr for r. VI. Word Problems. Oe umber is more th twice other umber. The sum of the umbers is. Fid the umbers.. 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 be mied to obti 0 liters of % solutio?. Sheil bought burgers d fries for her childre d some frieds. The burgers cost $.0 ech d the fries re $. ech. She bought totl of items, for totl cost of $.0. How my of ech did she buy? VII. Iequlities Solve d grph o the umber lie.. 7. ( ) <. ( ) ( ) VIII. Epoets & polyomils Simplify d write swers with positive epoets.. ( ) ( ) ( b c ). 7 ( b c ) 0. ( y z )( y z ). 7. 7. ( )( 7) b c. bc b c. ( ). y z y z Referece: Creted by Fculty t Aims Commuity College, Greeley, CO
IX. Fctorig.... y. 7 7. y y.. X. Qudrtic Equtios. 0. 0. 0. 0. ( ). r r 0 XI. Rtiol Epressios Perform the followig opertios d simplify where possible. If give equtio, solve for the vrible. y.. y.... XII. Grphig Grph ech equtio o the coordite is.. y.. y y. 7... k k k 7. y y 7. y. Referece: Creted by Fculty t Aims Commuity College, Greeley, CO
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 vribles represet positive umbers.. ( 0).... y 0. 7 7.. I. Order of Opertios ep oets Whe workig with,,,,,d Aswers, oe must remember 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 subtrctio s oe clcultes from left to right. 0.. ( )( ) ( ). 7. 00.. 7. 7 0 7 7.. - 0. Referece: Creted by Fculty t Aims Commuity College, Greeley, CO
II. Scietific Nottio All umbers i scietific ottio hve the followig form:. 0,000,000. 0. 0.0000000000000. 0. 0,00,000,000,000,000,000.0 0 7.. 0. ( 0 )( 0 ) 0 0 ( 0 ) ( 0 ) 0 0. 0 0 0 0 (. 0 )( 0 ). 0 7 0 0 0. 0 0 power ozerodig it.restofumber 0.. 0,000,000,000,000,000,000,000. 00,000,000. 0.00000000. 0 0 III.. yz.. Substitutio z ( ) z. y ( ) 0 y ( ) ( y z) [ ] ( ) ( 0) 0. y z ( ) ( ) 0 IV. Lier equtios i oe vrible.. ( ) ( ) ( ).. ( ) ( ) 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 Referece: Creted by Fculty t Aims Commuity College, Greeley, CO
VI. Word Problems. Let other umber forcig Oe umber. d 0. Oe umber d other umber 0.. Let the dollrs i the ccout pyig % iterest The,,000 the dollrs i the ccout pyig %. The iterest dollrs re clculted by multiplyig the totl dollrs i the ccout by the iterest rte. Hece:.0 the iterest ered by the first ccout.0 (,000 ) the iterest ered by 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 buckets: 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 umber of burgers d the umber of fries. To get the totl mout of moey spet, multiply the umber of items by the cost of the item..0 the totl dollrs spet o burgers d. ( ) the totl dollrs spet o fries. The equtio is:.0. ( ).0. Solvig the equtio,. Hece, she bought burgers d fries. VII. Iequlities Solve iequlities the sme s equtios with oe eceptio. Whe both sides re multiplied or divided by egtive umber, remember to switch the directio of the iequlity. 0. 7-7 7 7 0. ( ) < -0 - < - - < > -. - VIII. Epoets & Polyomils. Add like terms: 0 0 b c ( b c ) b c b c. 7 ( b c ) b c 0 0. b c y z y z y y z z y z. 7 0 0 ( b c ) ( ) b c b c. 0 0 0 y z ( y z) ( y z ) ( y z )( y z ) y z y z. 7. ( )( 7) 7 0 0 7 Referece: Creted by Fculty t Aims Commuity College, Greeley, CO
. b c bc ( ) b c b c 0 b. ( ) ( )( ) 0 0 0 IX. Fctorig Steps to fctorig:. Alwys fctor out the Gretest Commo Fctor (If possible).. Fctor the first d third term.. Figure out the middle term.. ( )( ). ( )( ), Differece of two squres. Sum of two squres requires the comple. umber system to fctor. Not fctorble.. y ( y ) ( y )( y ) ( y)( y)( y ). Differece of two cubes: b ( b)( b b ) get : ( )( ) 7 y. 7.. Let d b d use the formul to X. Qudrtic Equtios Steps:. Get zero o oe side of the equls. Fctor. Set ech fctor to zero. Solve for your vrible If you cot fctor the equtio d the qudrtic is i the form b c 0, the use the qudrtic formul. b ± b c. 0 ( )( ) 0 0 or 0 or -., -. 0 0 0 0 0 ( - )( ) 0 or.,. The solutio is give below: ( ) 0 ( - )( ) 0 or - 0. ± 7 Referece: Creted by Fculty t Aims Commuity College, Greeley, CO
Referece: Creted by Fculty t Aims Commuity College, Greeley, CO XI. Rtiol Epressios. Need to fid commo deomitor (fctor deomitors to see wht you eed), dd, d the reduce (if possible) t the very ed. 0. This problem uses the sme techique s bove. Be creful of the subtrctio. 0. To multiply frctios, fctor d ccel first before multiplyig.. Divisio is the sme process with oe etr step (ivert & multiply): c d b d c b. 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 by the LCD. y y y y y y y y 7. Aihilte the deomitors by multiplyig both sides of the equtio by the LCD [ ], solve the resultig, frctioless equtio, d check swers i the origil equtio to isure tht the deomitors re ot zero. or 0 0 - - - - Sice these swers do ot mke the deomitor zero i the origil equtio, they re the solutio.. k -. -
XII. Grphig. y -.. y y.. y. y Referece: Creted by Fculty t Aims Commuity College, Greeley, CO
7. y XIII. Systems of Equtios The followig re dimesiol lier equtios. Ech equtio represets lie tht c be 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, both formuls grph the sme lie mkig the solutio ifiite. The lst possibility 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 below. y y y Multiply by - - y., y y Now, substitutig ito the first equtio ( ) XIV. Rdicls Thik of the ide ( ide outside. Also, remember these properties:. ( )( 0 ) 0.... ) s door perso. If it is two, the two ideticl fctors iside become oe b b b 0 0 0 0 y y y y y y y y y y b. Worked out below. 7 7 7 0 7. ( ). ( )( ) 0 0 7 0 Referece: Creted by Fculty t Aims Commuity College, Greeley, CO
Elemetry Algebr Cotet Ares of ACCUPLACER Recommedtio: Use the videos t Kh Acdemy (www.khcdemy.org) with these cotet res for dditiol preprtio Itegers d Rtiols Orderig Opertios with siged umbers Absolute vlue Algebric Epressios Evlutig formuls d other lgebric epressios Additio d subtrctio of moomils d polyomils Multiplictio of moomils d polyomils Positive rtiol roots d epoets Squrig biomil Fctorig differece of squres Fctorig b c over the itegers Fctorig polyomils tht re ot qudrtics Opertios with lgebric frctios ivolvig dditio, subtrctio, multiplictio & divisio Divisio of moomils d polyomils icludig simplifictio of lgebric frctios Equtios, Iequlities, d Word Problems Solvig lier equtios d iequlities Systems of lier equtios Qudrtic equtios solutio by fctorig Trsltig writte phrses or seteces ito lgebric epressios or equtios Solvig verbl problems i lgebric cotet icludig geometric resoig Grphig Referece: Creted by Fculty t Aims Commuity College, Greeley, CO