Solution Manual for College Algebra with Intermediate Algebra A Blended Course

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Solution Manual for College Algebra with Intermediate Algebra A Blended Course - Page 1 preview image

ONLINETESTBANKCOLLEGEALGEBRAWITHINTERMEDIATEALGEBRAABLENDEDCOURSEJudith A. BeecherJudith A. PennaBarbara L. JohnsonIvy Tech Community College of IndianaMarvin L. BittingerIndiana University Purdue University Indianapolis

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iiiCONTENTSI.ALTERNATE TESTS, FORMS A, B, C, D, E, and F .......................................................... 1There are six alternate test forms for each chapter and the final examination. Alternate TestForms A, B, C, and D are equivalent in length and difficulty. Synthesis questions occur atthe end of the Test Forms, and are separated from the rest of the test by a solid line.Synthesis questions are meant to be more challenging than the previous test questions, likethose problems found in the last part of each exercise set in the text. The synthesisquestions have been placed at the end to make it easy to omit them if the instructor wishesto do so.Questions on Test Forms E and F are multiple choice. Effort was made to make the wronganswers as logically wrong as possible. In most cases answers were constructed to avoidstudents doing backward reasoning.This Instructor’s Online Test Bank is designed to accompanyCollege Algebra withIntermediate Algebra: A Blended CoursebyBeecher/Penna/Johnson/Bittinger.Chapter R ........................................................................................................................... R-1Chapter 1 ................................................................................................................................ 1Chapter 2 .............................................................................................................................. 25Chapter 3 .............................................................................................................................. 49Chapter 4 .............................................................................................................................. 73Chapter 5 .............................................................................................................................. 97Chapter 6 ............................................................................................................................ 121Chapter 7 ............................................................................................................................ 145Chapter 8 ............................................................................................................................ 169Chapter 9 ............................................................................................................................ 193Chapter 10 .......................................................................................................................... 221Chapter 11 .......................................................................................................................... 237Chapter 12 .......................................................................................................................... 261II.FINAL EXAMINATIONS................................................................................................. 289III.ANSWER KEYS FOR ALTERNATE TESTS, FORMS A, B, C, D, E, and F ................ 345IV.ANSWER KEYS FOR FINAL EXAMINATIONS........................................................... 390Thanks are extended to Mike Penna for producing the graphs and to Kelly Barber fortyping the manuscript.

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289YearNumber candles sold080170262364FINAL EXAMINATIONNAME_____________________________TEST FORM ACLASS_____SCORE_____GRADE________________________________________________________________________________1.Simplify:3452a b.2.Graph2xon a number line.3.Divide:682.4103.210. Write scientific notation for the answer.4.Find the union:2,3,8,11,163,5,8,12.5.Determine whether the correspondence is a function.2Mary3Jeff4AnthonyDeirdre6.Find an equation of the line parallel to423xywhichpasses through2, 5.7.The table below shows the number of candles sold at a charity’sfundraiser for 4 successive years.Use years 0 and 3 to model the data with a linear function, andthen predict the number of candles that will be sold in year 5using this function.ANSWERS1.2. See graph.3.4.5.6.7.

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290FINAL EXAMINATIONNAME_____________________________TEST FORM A___________________________________________________________________________ANSWERS8.9.10.11.12.13.14.15.16.17.18.19.20.21.22.a)b)23.a)b)24.a)b)25.a)b)Solve.8.624=−x9.0352=+−xx10.122+=+xx11.1582−>xx12.xxx4422733−=13.log8x14.438754xx15.2211212xxxxx.Solve, if possible. If there is no solution, state this. Use any method.16.262,7xyxy+=−= −17.326,25326,328xyzxyzxyz−+=−++= −−+−=18.26,2412xyxy+=+= −19.222538,616xyxy 20.Solve and write interval notation for the solution set:34214x.21.Given that2213,fxxfind:a)4 ;fb)2 .faForand31,fxxgxxfind each of the following:22.a) The domain off; b) the domain ofg.23.a);fgxb) the domain offg.24.a)/;gfxb) the domain of/gf.25.a);gfxb) the domain ofgf.

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291FINAL EXAMINATIONNAME_____________________________TEST FORM A___________________________________________________________________________26.The graph of the functionyfxis shown below on the left.No formula forfis given. Make graph of3yfx.Graph the equation.27.4yx 28.12yx 29.Graph:( )1−=xexf.ANSWERS26.See graph.27.See graph.28.See graph.29.See graph.

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292FINAL EXAMINATIONNAME_____________________________TEST FORM A___________________________________________________________________________ANSWERS30.See graph.31.See graph.32.See graph.33.a)b)c)d)e)f) See graph.30.Make a graph of22.xy+< −31.Graph242fxx.Label all the asymptotes andany intercepts.32.Graph2212149xy.33.For the graph of the function()2245,fxxx=++a) find the vertex;b) find the axis of symmetry;c) state whether there is amaximum or minimum valueand find that value;d) find the range;e) determine the intervals on whichthe function is increasing,decreasing, and constant;f) graph the function.

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293FINAL EXAMINATIONNAME_____________________________TEST FORM A___________________________________________________________________________34.Graph:3x .35.Find the asymptotes of the hyperbola given by2245100xy.36.Find the center and the radius of a circle given by22810230.xxyy++−−=37.Determine whether the graph of5yx=is symmetric withrespect to thex-axis, they-axis, and/or the origin.38.Find the maximum value and minimum value of15Fxy=+subject to5,326,0,10.xyxyxy+≥−≤≥≤39.For43235642,fxxxxxwhat does Descartes’ ruleof signs tell you about:a) the number of positive real zeros,b) the number of negative real zeros?40.Suppose that a polynomial function of degree 5 with rationalcoefficients hasi−−3and,52,as zeros. Find the otherzeros..ANSWERS34.See graph.35.36.37.38.39.a)b)40.

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294FINAL EXAMINATIONNAME_____________________________TEST FORM A___________________________________________________________________________ANSWERS41.42.43.44.45.46.47.48.49.50.51.52.53.54.55.UseA=−701213,B=−5432for Exercises 41 and 42.41.FindBA, if possible.42.FindB1−, if possible.43.Evaluate the determinant.210321543−−−Perform the indicated operations and simplify.44.22643xyxyxyxy45.332532623xxxxx 46.238x47.31848.2223104xxxx49.22329562739xxxxxx50.Multiply:325ii.51. Divide:432322xxxx.52.Use the laws of exponents to simplify. Write answers withpositive exponents.1/ 23/82/5ab.Factor.53.2151416nn54.222444aabbc55.Find the formula for the inverse of5 ,xfxxif possible.

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295FINAL EXAMINATIONNAME_____________________________TEST FORM A___________________________________________________________________________56.Find an equation of variation in whichyvaries directly asx, and0.8y=when6.x=57.Given that5000.02logand7925.112log==bb, find6logb.58.The population of a bacteria culture doubled in 6 hr. What wasthe exponential growth rate?59.You are taking a history course in which there will be 4 tests,each worth 100 points. You have scores of 84, 71, and 79. Youmust have a total of at least 320 points in order to get a B.What scores on the last test will give you at least a B?60.An airplane flew 4 hr with a 25-mph tailwind and returned in 4.5 hragainst the same wind. How fast can the plane fly in still air?61.In a right triangle with legs5 and7ab, find hypotenusec.Give an exact answer and an approximation to three decimalplaces.62.Amount of an Annuity. To create a college fund, a parent makesa sequence of 15 yearly deposits of $3000 each in a savingsaccount on which interest is compounded annually at 4.5%.Find the amount of the annuity.63.How many license plates can be formed using three lettersfollowed by 3 digits?64.Card Drawing. Suppose we draw a card from a well-shuffleddeck of 52 cards. What is the probability of drawing a king ora two?65.The 1st term of an arithmetic sequence is3−and the 13th termis 6. Find the 8th term.66.Evaluate: 51132kkk.67.If1142, and21, find.nnaaaa+= −=−ANSWERS56.57.58.59.60.61.62.63.64.65.66.67.

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296FINAL EXAMINATIONNAME_____________________________TEST FORM A___________________________________________________________________________ANSWERS68.69.70.71.72.68.Use mathematical induction to prove that for every naturalnumbern,481241 .nn n    69.Find:103.C70.The graph of the functiongxis shown at the right.The graph of21fxgxis which of the following?A.B.C.D._______________________________________________________71.Find the domain of2−xx.72.If()6,4−is on the graph of( )xfy=, what point do you knowis on the graph of()2−xf?

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297FINAL EXAMINATIONNAME_____________________________TEST FORM BCLASS_____SCORE_____GRADE________________________________________________________________________________1.Evaluate43xyxwhen3 and8xy .2.Simplify:5 57xy.3.Convert to scientific notation: 0.0543.4.Write interval notation for85xx.5.Find the distance between3.4and 7.6.6.Is the graph at right a graphof a function?7.Determine whether the pair of lines are parallel, perpendicular,or neither.236,328.xyxy 8.The table below shows the number of trips over 50 mi made for4 successive years.Use years 1 and 3 to model the data with a linear function, andthen predict the number of trips over 50 mi in year 6 using thisfunction.ANSWERS1.2.3.4.5.6.7.8.Year,xNumber of trips over 50 mi,T020122230332

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298FINAL EXAMINATIONNAME_____________________________TEST FORM B___________________________________________________________________________ANSWERS9.10.11.12.13.14.15.16.17.18.19.20.21.a)b)Solve.9.2111235=−+−+xxx10.082=−−nn11.2460xx12.6475x13.xx36162=−14.1.0ln=x15.737x 16.431259xandx17.279xx. Give exact solutions and approximate solutions tothree decimal places.Solve, if possible. If there is no solution, state this. Use any method.18.1275=−yx,19.823−=+−zyx,61410−=+−yx10834−=+−−zyx,1342=++zyx20.Solve:312=+yx,16−=xy.21.a) Solve by graphing:42,3.yxxyb) Classify the system as consistentor inconsistent and the equationsas dependent or independent.

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299FINAL EXAMINATIONNAME_____________________________TEST FORM B___________________________________________________________________________For( )3−=xxfand( )12+=xxg, find each of the following:22.a) The domain off; b) the domain ofg.23.a)()( )xgf−; b) the domain ofgf−.24.a)()( )xfg/; b) the domain offg/.25.a)()( )xfg; b) the domain offg.26.Write an equation for a function that has the shape ofxy=,but shifted left 2 units and up 4 units.Graph the equation.27.421−=xy28.12−−=xy29.Graph:( )2+=xexf.ANSWERS22.a)b)23.a)b)24.a)b)25.a)b)26.27.See graph.28.See graph.29.See graph.

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300FINAL EXAMINATIONNAME_____________________________TEST FORM B___________________________________________________________________________ANSWERS30.See graph.31.See graph.32.See graph.33.See graph.34.30.Graph the system of equations and find the coordinates of anypoints of intersection.53,423−≥≥−xyyx31.Graph:3yx.32.Graph:()()1924122=−−+yx.33.Graph :xxy23+−=.34.Determine if the graph of the equation in Exercise 33 issymmetric with respect to thex-axis, they-axis, and the origin.

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301FINAL EXAMINATIONNAME_____________________________TEST FORM B___________________________________________________________________________35.For the graph of the function( )xxxf42+−=,a) find the vertex;b) find the axis of symmetry;c) state whether there is amaximum or minimum valueand find that value;d) find the range;e) determine the intervals on whichthe function is increasing,decreasing, and constant;f) graph the function.36.Find the center and the radius of the circle given by02912822=−++−yyxx.37.Find a rational function that has vertical asymptotes of3=xand6−=x, andy-intercept()2,0.38.Maximizing Profit. Bruce’s Bakery prepares cakes and muffins.In a given week, 200 products can be prepared of which 50cakes and 70 dozen muffins are required by regular customers.Each dozen muffins represents one product as muffins are onlysold in packages of one dozen. The profit on a cake is $2andon a package of muffins is $50.1. How many of each shouldthe bakery make to maximize profit? What is the maximumprofit?39.For( )4632235−+−=xxxxf, what does Descartes’ rule ofsigns tell you about:a) the number of positive real zeros;b) the number of negative real zeros?40.Use the intermediate value theorem to determine whether( )243+−=xxxfhas a real zero between0and1−, ifpossible. Show your work. If it is not possible to make adetermination using this method, state this.UseA=−−824251,B=−−5432for Exercises 41 and 42.41.FindAB, if possible.42.FindB1−, if possible.ANSWERS35.a)b)c)d)e)f) See graph.36.37.38.39.a)b)40.41.42.

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