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1 Mth B Elementry Algebr Spring 0 Finl Em Study Guide The em is on Wednesdy, My 0 th from 7:00pm 9:0pm. You re lloed scientific clcultor nd " by 6" inde crd for notes. On your inde crd be sure to rite ny formuls you needed for ny of the problems listed. I ill not provide you ith ny formuls on the em. The Finl Em is comprehensive; hoever, not ll of the problems tht ppered in the previous ems ill pper in the finl. Use this study guide to kno hich mth concepts you need to revie. For the Finl Em, you ill need to be ble to:. Simplify epressions using the rules of eponents, including epressions ith both positive, negtive nd zero eponents. The finl nser must hve only positive eponents. 6. & 6.. Convert to nd from scientific nottion nd perform clcultions in scientific nottion. 6.. Add or subtrct to polynomils. Write the nser in descending order. 6.. Multiply to polynomils. Write the nser in descending order. 6.. Divide polynomil by monomil or binomil. If there is reminder, use pproprite nottion Fctor completely ny given polynomil using the methods lerned ) Fctor polynomil by fctoring out the GCF of ll the terms. 7. b) Fctor polynomil by grouping. 7. c) Fctor trinomil ith leding coefficient tht is one. 7. d) Fctor trinomil ith leding coefficient tht is not one. 7. e) Fctor difference of squres. Recognize tht sum of squres is prime. 7. f) Fctor using miture of these tools Solve qudrtic eqution by fctoring. * Simplify rtionl epression nd stte the vlues for hich the epression is defined Multiply or divide to rtionl epressions. Simplify the result Add or subtrct to rtionl epressions tht hve common denomintors or different denomintors. Simplify the result, if possible. 8. & 8.. Solve rtionl eqution. Remember to eliminte solutions tht mke the epression in the originl eqution undefined (mke one of the denomintors = 0) Solve n ppliction problem involving ork or involving motion (time=distnce/rte) 8.7. Simplify squre root epression by using the multipliction property of squre roots or using fctor tree nd dividing vrible eponents by. You might first need to multiply to squre root epressions nd then simplify. 9.. Add or subtrct squre root epressions. You might need to simplify terms before they cn be combined. 9.. Multiply squre root epressions by using the distributive property or the FOIL method Simplify squre root epression by using the division property of squre roots. You might first need to divide to squre root epressions nd then simplify Simply epressions ith squre root in the denomintor by rtionlizing the denomintor. You might need to simplify first Solve rdicl eqution. If the eqution hs no solution, stte so. Remember to check for etrneous solutions. (In the process of solving the rdicl eqution you might need to solve qudrtic eqution.) Solve ppliction problems involving squre roots the only problems I ill put on the em ill involve the Pythgoren Theorem Solve qudrtic eqution by using the squre root property. If possible, simplify rdicls nd rtionlize denomintors. No deciml pproimtions. *0.

2 . Solve qudrtic eqution by completing the squre. If possible, simplify rdicls nd rtionlize denomintors. No deciml pproimtions. *0.. Solve qudrtic eqution by using the qudrtic formul. If possible, simplify rdicls nd rtionlize denomintors. No deciml pproimtions. *0. *You must solve the qudrtic equtions using the indicted method in order to receive full credit.*. Solve ppliction problems involving qudrtic eqution. You ill either be given the qudrtic eqution nd you ill need to kno ho to use it to nser the question OR you ill need to come up the eqution yourself these involve the re of rectngle (pge 6 #0) or right tringle so you ill use the Pythgoren Theorem (pge 6 #). You cn solve the eqution by either fctoring or using the qudrtic formul (if the eqution doesn t fctor) 7.7, 0., nd 0.. Repeting from bove! On your inde crd be sure to rite ny formuls you needed for ny of the problems listed bove. I ill not provide you ith ny formuls on the em. Prctice Problems for the Finl To study for the finl do the folloing problems AND look t the problems tht ere on the ems (but only those similr to those listed in this hndout). The nser to the problems listed belo, even nd odd, re in the bck of the book. (For those of you ho hve the Chpter Test Prep Video cd tht cme ith the book, you cn vie it to see someone orking out ech of the problems tht re in the Chpter Tests.) Revie Eercises Chpter 6 Pge 98 #8,,, 08, 8,, Revie Eercises Chpter 7 Pge 6 #8, 8, 8, 88, 0, 0, (solve by fctoring nd pplying the Zero-Product Rule), 7, 0 Revie Eercises Chpter 8 Pge #, 8, 8, 9, 60, 80, 8, 8, 8 Revie Eercises Chpter 9 Pge 88 #, 8, 6,,, 7, 70 Also try: Pge # 8 Pge 70 #6 [nser: =7],, 7 Chpter 0 Prctice Test Pge 6 #*, 6* Also try pge 60 #*7, *, *7 *You must solve the qudrtic equtions using the method indicted. If you do not, then you ill receive miniml credit for correct nser.

3 Mth B Finl Em Revie Nme. Simplify. (m p n) ( mp n ). Evlute. ( ). Evlute:. Simplify: ( y z ) ( yz ). Convert the folloing to stndrd form Convert the folloing to scientific nottion Divide. Leve nser in scientific nottion. ( 0 ) ( 0 ) 8. Multiply. Leve nser in scientific nottion. 7 (9 0 )(8 0 ) 9. Subtrct. (6 7) ( ) 0. Multiply. ( )( ). Multiply. ( n )( n ). Multiply. ( )

4 . Divide. 9 y 6y 7 y 8 y. Divide using long division. ( ) ( ). Fctor 6. Fctor 6 7. Fctor 9 8. Fctor y 6y 9. Solve for by fctoring. ( ) 6 0. Solve for p by fctoring. p 8p 0

5 . Multiply:. Divide: 9 6 k k k. Add: Subtrct: p p p. Solve for y. y y y y 6 6. Solve for. 6 6

6 7. Together, you nd your brother cn pint room in hours. Alone, your brother cn pint room in 6 hours. Ho long ould it tke you to pint room lone? 8. The ind is bloing t n verge of 0 miles per hour. Riding ith the ind, bicyclist cn cycle 7 miles in the sme mount of time it tkes to cycle miles ginst the ind. Wht is the cyclist s verge rte in clm ir? Let = With the ind dist time Rte Distnce rte Aginst the ind 9. Find ech indicted root. If the root is not rel number, sy so.. 00 b. 0 c. 0. Find the missing length. 0 8

7 Simplify ech epression completely. Assume ll vribles re rel, non-negtive numbers.. Multiply: 6. Multiply:. Multiply: y 6y. Rtionlize the denomintor:. Simplify: 8 b c 6. Simplify: Simplify: Add: k n k k n

8 9. Simplify: ( ) 0. Rtionlize the denomintor:. Rtionlize the denomintor:. Solve for :. Simplify.. Solve by using the squre root property: (k ). Solve by completing the squre: 6. Solve by using the qudrtic eqution: 0

9 7. Find the length nd idth of rectngle if the idth is inches less thn the length nd the re of the rectngle is 80 squre inches. Let = Then = Eqution: 8. A -ft ldder is lening ginst building. The ldder reches up the ll 7 feet more thn the distnce of the ground beteen the bottom of the ldder nd the bse of the building. Find the distnce of the ground beteen the bottom of the ldder nd the bse of the building, nd find the distnce the ldder reches up the ll. Let = Then = Eqution: (leg) (other leg) (hy potenuse) 9. A rectngle hs digonl of 7 feet. If the length of the rectngle is foot less thn tice its idth, find the dimensions of the rectngle. Let = Then = Eqution:

10 0. The eqution for the height of bll thron, from 60 foot cliff, into the ir t 6 feet per second is h ( t) 6t 6t 60, here h(t) is the height of the bll fter t seconds..) Clculte the time it tkes for the bll to be 08 feet bove the ground. 08 ft ft Eqution: height eqution t? t? b.) Clculte the seconds it tkes for the bll to hit the ground. 60 ft Eqution: height eqution 0 ft -- t?

11 Ansers: 6 9 8m n p 6 z 9 y n 9y.. 7 y. ( ) 6. ( 9)( ) 7. ( )( ) 8. ( y)( y) 9., 0. p, p.. - ( p ).. ( ) ( ) p. No solution hours 8. mph 9. 0,, not rel bc b y y k n k, k Width = inches 6., Length = inches 9. Width = 8 feet Length = feet 0.. nd seconds b.. 7 seconds 8. feet nd feet up the ll

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