Math 205 Elementary Algebra Fall 2010 Final Exam Study Guide

Transcription

1 Mth 0 Elementr Algebr Fll 00 Finl Em Stud Guide The em is on Tuesd, December th from :0m :0m. You re llowed scientific clcultor nd " b " inde crd for notes. On our inde crd be sure to write n formuls ou needed for n of the roblems listed. I will not rovide ou with n formuls on the em. The Finl Em is comrehensive; however, not ll of the roblems tht ered in the revious ems will er in the finl. Use this stud guide to know which mth concets ou need to review. Don t forget there is new mteril from chter 9. nd. on the finl em. For the Finl Em, ou will need to be ble to:. Solve liner equtions, including equtions with frctions. The solution to these equtions cn be unique solution, no solution, or ll rel numbers. Remember tht the correct finl nswer for these tes of roblems is either = #, ll rel numbers or no solution. Remember to cler our frctions multil ech term b the LCD.. Solve n liction roblem. These include but re not limited to roblems involving mone nd ercents.. Solve n liction roblem involving geometr mesurement of the sides of tringle nd the erimeter of rectngle.. Solve n liction roblem b setting u roortion nd solving tht roortion.. Solve liner inequlities nd grh the solution. The solution to these inequlities cn be unique intervl, no solution, or ll rel numbers.. Grh liner equtions in two vribles. * grh using oint nd the sloe. * grh using the - nd -intercets * grh b lotting oints 7. Find the sloe of the line given two oints or given n eqution. This includes horizontl nd verticl lines. 8. Given grh, find the sloe of the line or stte tht the sloe is undefined. 9. Write n eqution of the line in sloe-intercet form. * write n eqution given oint nd the sloe. * write n eqution given two oints. 0. Grh liner inequlities. Shde the regions tht mke the sttement true.. Solve sstem of liner equtions grhicll. This includes sstems tht hve one unique solution, no solution, or n infinite number of solutions.. Solve sstem of liner equtions b substitution or ddition. You m choose either method to solve the sstem. The sstem might hve one unique solution, no solution or n infinite number of solutions.. Solve n liction roblem involving interest, mitures, or distnce. You sw these tes of roblems twice. Once ou hd to solve using vrible (liner equtions) nd gin using vribles(sstems of equtions). You cn solve these roblems either w.. Simlif eressions using the rules of eonents, including eressions with both ositive, negtive nd zero eonents. The finl nswer must hve onl ositive eonents.. Convert numbers to nd from scientific nottion nd erform clcultions.. Add or subtrct two olnomils. Write the nswer in descending order. 7. Multil two olnomils. Write the nswer in descending order. 8. Divide olnomil b binomil. If there is reminder, use rorite nottion. 9. Fctor comletel n given olnomil using the methods lerned. ) Fctor olnomil b fctoring out the GCF of ll the terms. b) Fctor olnomil b grouing.

2 c) Fctor trinomil with leding coefficient tht is one. d) Fctor trinomil with leding coefficient tht is not one. e) Fctor difference of squres. Recognize tht sum of squres is rime. f) Fctor using miture of these tools. 0. Solve qudrtic equtions b fctoring.. Simlif rtionl eression.. Multil or divide two rtionl eressions. Simlif the result.. Add or subtrct two rtionl eressions tht hve common denomintors or different denomintors. Simlif the result, if ossible.. Simlif comle frctions. * get it into one frction over one frction, then fli nd multil the bottom frction * multil ech term b the LCD of ll the denomintors.. Solve rtionl eqution. Remember to eliminte s solutions n vlues tht mke n eression in the originl eqution undefined (mke one of the denomintors = 0).. Simlif squre root eression b using the multiliction roert of squre roots. You might first need to multil or divide two squre root eressions nd then simlif. 7. Add or subtrct rdicl eressions. You might need to simlif terms before the cn be combined. 8. Multil squre root eressions b using the distributive roert or the FOIL method. 9. Simlif squre root eression b using the division roert of squre roots. You might first need to divide two squre root eressions nd then simlif. 0. Siml eressions with squre root in the denomintor b rtionlizing the denomintor. You might need to simlif first.. Solve rdicl eqution. If the eqution hs no solution, stte so. Remember to check for etrneous solutions. (In the rocess of solving the rdicl eqution ou might need to solve qudrtic eqution.). Solve liction roblems involving squre roots the onl roblems I will ut on the em will involve the Pthgoren Theorem.. Solve qudrtic eqution b using the qudrtic formul. If ossible, simlif rdicls nd rtionlize denomintors. No deciml roimtions. *You must solve the qudrtic equtions using the indicted method in order to receive full credit.*. Solve liction roblems involving qudrtic eqution. You will either be given the qudrtic eqution nd ou will need to know how to use it to nswer the question OR ou will need to come u the eqution ourself these involve the re of rectngle, or right tringle so ou will use the Pthgoren Theorem. You cn solve the eqution b either fctoring or using the qudrtic formul (if ou don t like to fctor). Reeting from bove! On our inde crd be sure to write n formuls ou needed for n of the roblems listed bove. I will not rovide ou with n formuls on the em. Prctice Problems for the Finl To stud for the finl do the following roblems AND look t the roblems tht were on the ems (but onl those similr to those in this hndout). The nswer to the roblems listed below, (For those of ou who hve the Chter Test Pre Video cd tht cme with the book, ou cn view it to see someone working out ech of the roblems tht re in the Chter Tests.)

3 Mth 0 Finl Em Review Nme Directions: Solve ech eqution.. ( r ) ( r ). z z 7 7. ( k ) (k ). ( 8) ( ) 9. Solve for d: d. Given the re formul for trezoid, find h, when A., b, nd b 7 A h( b b ) 7. A Luck-duck found two-thirds s much mone on Sturd s he did on Frid. Throughout both ds he found totl of $0. How much mone did he find on Frid?

4 8. Given the re formul for finding the erimeter of rectngle, solve forw. P L W 9. How mn liters of 0% lcohol should ou mi with 0 liters of 0% lcohol to obtin blend of 0% lcohol? 0. S ou nd our friend re 0 miles rt nd wnt to meet u with ech other. Both of ou left t the sme time, but our friend drives mh slower thn ou. You both finll meet u fter hours. How fst were ou ech going? Rte Time Distnce You Your friend. Solve the following inequlit. Grh it on the number line nd stte it in INTERVAL NOTATION.. Solve the following inequlit. Grh it on the number line nd stte it in INTERVAL NOTATION A cr rentl genc chrges $80 er week lus $0. er mile to rent cr. How mn miles cn ou trvel in one week if ou wnt to send $9?

5 . The erimeter of tringle is 8 feet. The medium side is feet longer thn the shorter side, while the longest side is twice s long s the shortest side. Wht re the mesures of ech of the three sides?. Deter mine whether the ordered ir, is solution to the eqution. Write the eqution, in sloe-intercet form, of the line tht hs sloe of nd sses through the oint (, -). 7. Find n eqution of line through the oints (-, ) nd (-, ) 8. Grh: 0

6 9. Grh 0. Solve the following liner sstem b grhing: 8 9. Solve the following liner sstem b elimintion or substitution: 8 9. A coin urse contins miture of 9 coins in qurters nd dimes. The coins hve totl vlue of $7.0. Determine the number of qurters nd number of dimes in the coin urse.

7 . With the current, ou cn row miles in hours. Aginst the sme current, ou cn onl row miles in hours. Find our rowing rte in still wter nd the rte of the current.. S ou invested twice s much mone t % simle interest rte thn ou did in n ccount ing % simle interest. At the end of the er, the two ccounts ern $0 in simle interest. How much ws invested t ech rte?. The other d I went to Stles to bu some office sulies. I bought ens nd binders, which together cost me $9.7. M friend bought of the sme ens nd of the sme binders, nd it cost her $9.00. Wht is the cost for single binder nd the cost for single en?. Evlute. 7. Evlute.

8 8. Simlif: ( z ) ( z ) 9. Simlif: m n 0. Evlute:. Convert the following to scientific nottion Convert the following to stndrd form Multil Subtrct. 7. Multil.. Multil. n n 7. Multil.

9 8. Divide Divide using long division. 0. Fctor. Fctor. Fctor 9. Fctor. Solve for w b fctoring. w(w ). Multil: w w w w w w

10 . Add: Divide: 9 k k k 8. Subtrct: 9. Solve for. 0. Solve for.

11 . Find ech indicted root. If the root is not rel number, s so.. 00 b. 0 c. 79 d.. Find the missing length. 0 8 Simlif ech eression comletel. Assume ll vribles re rel, non-negtive numbers.. Simlif: 7 8. Rtionlize the denomintor:. Rtionlize the denomintor:. Simlif: ( )

12 7. Solve b using the squre root roert: ( k ) 8. Solve b using the squre root roert: 9. Solve b using the qudrtic formul: 0. Solve b using the qudrtic formul: 0. Find the length nd width of rectngle if the width is inches less thn the length nd the re of the rectngle is 80 squre inches.. The lengths of the two legs of right tringle re consecutive integers. The hotenuse is one less thn twice the length of the shorter leg. Find the length of ech of the sides.

13 Answers:. r=-. z=. k=. =0. h=. d 7. Found $ Frid nd $ 9.. L of 0% Sturd 8. w l 0. You went mh nd our friend went 0 mh. (, ]. [-,). 80 miles. Shortest ft Medium 0 ft Longest ft. Not solution. =- 7. = (7, ). (-9, -). qurters, dimes. Your rte in still wter mh current s rte mh. $00 t %, $000 t %. Pens cost $.0 Binders cost $ z 8m n n ( ). ( 9)( ). ( )( ). ( )( ). w=, w= w w ( ) ( ) ( ) 9. No solution 0. = ,, -9, k=, k= inches b inches. Shortest ft 0., Medium ft Longest ft