Accuplacer Elementary Algebra Study Guide

Transcription

1 Testig Ceter Studet Suess Ceter Aupler Elemetry Alger Study Guide The followig smple questios re similr to the formt d otet of questios o the Aupler Elemetry Alger test. Reviewig these smples will give you good ide of how the test works d just wht mthemtil topis 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 II. Sietifi Nottio Write the followig i Sietifi Nottio.. 0,000, ,00,000,000,000,000,000 Write i epded form Simplify. Write swers i sietifi ottio. 7.. III Sustitutio Fid eh vlue if, y, d. yz z. y. y z IV. Lier equtios i oe vrile Solve the followig for... z y.0 0 z. y z 0 7//0 elemetry lger[].do

2 V. Formuls. Solve PV RT for T. y. Solve for y.. Solve y = + for.. Solve y h for.. Solve C r for r. VI. Word Prolems. Oe umer is more th twie other umer. The sum of the umers is. Fid the umers.. Ms. Joes ivested $,000 i two outs. Oe out pys % simple iterest d the other pys %. Her totl iterest for the yer ws $,0. How muh did she hve i eh out?. How my liters of 0% solutio d % solutio must e mied to oti 0 liters of % solutio?. Sheil ought urgers d fries for her hildre d some frieds. The urgers ost $.0 eh d the fries re $. eh. She ought totl of items, for totl ost of $.0. How my of eh did she uy? VII. Iequlities Solve d grph o the umer lie VIII. Epoets & polyomils Simplify d write swers with positive epoets y z y z y z y z IX. Ftorig.. y y y.. 7//0 elemetry lger[].do

3 X. Qudrti 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 eh equtio o the oordite is.. y.. y. y. y. y 7. y 7//0 elemetry lger[].do

4 XIII. Systems of Equtios Solve the followig systems of equtios.. y y. y 0 y. y y 7. y y XIV. Rdils Simplify the followig usig the rules of rdils (rtiolize deomitors). All vriles represet positive umers y I. Order of Opertios Whe workig with,or epoets,,,,d Aswers, oe must rememer the order of the opertios. First, prethesis or epoets s oe lultes from left to right. Seod, multiplitio or divisio s oe lultes from the left to right. Ad filly, dditio or sutrtio s oe lultes from left to right //0 elemetry lger[].do

5 II. Sietifi Nottio All umers i sietifi ottio hve the followig form: o-zero digit. rest of umer 0 power.. 0,000, ,000,000,000,000,000,000, ,000,000. 0,00,000,000,000,000, III. Sustitutio. yz.. z y 0 y z 0 0 z. y. y z 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. y y. h y y h y h h h h 7//0 elemetry lger[].do

6 VI. Word Prolems. Let = other umer forig + = Oe umer. + + = d = 0. Oe umer = d other umer = 0.. Let = the dollrs i the out pyig % iterest The,,000 = the dollrs i the out pyig %. The iterest dollrs re lulted y multiplyig the totl dollrs i the out y the iterest rte. Hee:.0 = the iterest ered y the first out.0 (,000 ) = the iterest ered y the seod out. Addig up ll the iterest,.0 +.0(,000 ) =,0. Solvig, = 7,00. So, Ms. Joes hs $7,00 i the out pyig % iterest d $0,00 i the out pyig % iterest.. Use the followig ukets: 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 ost 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, =. Hee, she ought urgers d fries. VII. Iequlities Solve iequlities the sme s equtios with oe eeptio. Whe oth sides re multiplied or divided y egtive umer, rememer to swith the diretio of the iequlity VIII. Epoets & Polyomils -. Add like terms: y z y z y y z z y z //0 elemetry lger[].do y z. y z y z y z y z y z y z

7 IX. Ftorig Steps to ftorig:. Alwys ftor out the Gretest Commo Ftor (If possile).. Ftor the first d third term.. Figure out the middle term..., Differee of two squres. Sum of two squres requires the omple umer system to ftor. Not ftorle... y y y y y y y. Differee of two ues: 7.. Let = d = d use the formul to get : 7y. X. Qudrti Equtios Steps:. Get zero o oe side of the equls. Ftor. Set eh ftor to zero. Solve for your vrile If you ot ftor the equtio d the qudrti is i the form 0, the use the qudrti formul or 0 or -., or.,. The solutio is give elow: 0-0 or //0 7 elemetry lger[].do

8 7//0 elemetry lger[].do XI. Rtiol Epressios. Need to fid ommo deomitor (ftor deomitors to see wht you eed), dd, d the redue (if possile) t the very ed. 0. This prolem uses the sme tehique s ove. Be reful of the sutrtio. 0. To multiply frtios, ftor d el first efore multiplyig.. Divisio is the sme proess with oe etr step (ivert & multiply): d d. Oe other hit: (Cotiues o et pge). Ftor d Redue to get.. Fid the Lowest ommo deomitor (LCD) for ll frtios (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, frtioless equtio, d hek swers i the origil equtio to isure tht the deomitors re ot zero. or Sie 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 7//0 elemetry lger[].do

10 7. y XIII. Systems of Equtios The followig re dimesiol lier equtios. Eh equtio represets lie tht e grphed o the oordite ple. The ultimte solutio to system of equtios is for the lies to iterset i o poit suh s questio # d #. Questio # hs two equtios d oe is multiple of the other. Hee, 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 ross. This system hs o solutio.. The swer is = d y =. The work is elow. y y y. =, y = Multiply y - - y y Now,sustituti gitothefirst equtio XIV. Rdils Thik of the ide ( ide Also, rememer these properties: ) s door perso. If it is two, the two idetil ftors iside eome oe outside y y y y y y y y y y. Worked out elow //0 0 elemetry lger[].do