Solution Manual for Math Lit, 2nd Edition

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INSTRUCTOR’SRESOURCEMANUALWITH CONTRIBUTIONS FROMRACHELE.JOHNSONHarry S Truman CollegeMATHLITAPATHWAY TOCOLLEGEMATHEMATICSSECONDEDITIONKathleen AlmyRock Valley CollegeHeather FoesRock Valley College

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iiiCONTENTSIntroduction..............................................................................................................................................ivQuizzesCycle 1.....................................................................................................................................................1Cycle 2.....................................................................................................................................................6Cycle 3...................................................................................................................................................10Cycle 4...................................................................................................................................................15Half Cycle ExamsCycle 1...................................................................................................................................................20Cycle 2...................................................................................................................................................27Cycle 3...................................................................................................................................................33Cycle 4...................................................................................................................................................42ExamsCycle 1...................................................................................................................................................50Cycle 2...................................................................................................................................................66Cycle 3...................................................................................................................................................78Cycle 4...................................................................................................................................................90Final Exam.............................................................................................................................................103AnswersQuizzes.................................................................................................................................................115HalfCycle Exams................................................................................................................................119Exams...................................................................................................................................................127Final Exam...........................................................................................................................................143

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INTRODUCTIONThe Instructor’s Resource Manual is designed to complement theMath Lit,2ndedition instructorsupport package. The Annotated Instructor’s Edition and Instructor Guide provide assistance toinstructors for each cycle as a whole, as well as each section. This manual provides additionalassessment items to support instructors at the course level. The following are included:•Quizzes (Forms A and B) for each half of each cycle•Half Cycle Exams•Exams (Forms A and B) for each cycle•Final Exam•Answers to quizzes and examsMath Lit,2ndEdition uses a balanced approach to assessment, placing equal emphasis on skills,concepts and applications. Two quiz forms are provided for the first and second halves of eachcycle. Form A is similar to the recaps provided in the text. It includes three to four unrelatedproblems that assess skills, concepts, and applications from that part of the worktext. Form Btakes one scenario and asks several questions about it. Often, the questions are more involvedand difficult. This form is suitable for an individual quiz but also can be used for a group quiz.These quizzes can be used alone or in tandem with exercises and quizzesprovided inMyMathLab.New to the second edition are half cycle exams. An exam is provided for the first and secondhalves of each cycle.Two exam forms are provided for each cycle. Forms A and B are similar in approach andemphasis. Approximately half of each exam addresses skills while the remaining half addressesconcepts and applications.Answers for all quizzes and exams are included at the end of this manual.Additional course-level instructor support items include the Instructor’s Solutions Manual andTestGen®testbank, available electronically.

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Quiz1Name _______________________________________Math LitCycle 1, Quiz for First Half (Sections 1.1–1.8), Form A1.If a lawyer bills $350/hour, how much does he make every second? How much does hemake per year? Assume he works 50 hours per week, 48weeks per year.2.The student to teacher ratio is 19:1 at a local school and thereis a total of500 studentsand teachers. How many teachers and how many students are there?3.Show all your work on the following fraction operations. If the answer is larger than one,convert to a mixed number.a.75912+=b.2394=4.A recipe calls for34cup of sugar to make 18 cookies. How many cookies can you makewith 6 cups of sugar?

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2QuizName _______________________________________Math LitCycle 1, Quiz for FirstHalf (Sections 1.1–1.8), Form B1.Throughout the course of a trip, a family travels from 865 feet above sea level to122 feet below sea level. How many feet did the family descend?a.Choose the calculation that describes the scenario.A.122865−B.865122−C.122865−−D.865( 122)− −b.List the result.2.Compute the following fraction operations.a.75755656−−−= −−=b.7556−−=3.Create a data set with six differentvalues that has an average of‒1.4.Of the 1,300 people whoresponded to a pole about coffee, 455claimed they liked itplain. What is the relative frequency of people who drink their coffee plain?

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Quiz3Name _______________________________________Math LitCycle 1, Quiz forSecondHalf (Sections 1.9–1.16), Form A1.John weighs 210 pounds. His goal for the new year is to lose 10% of his body weighta.How many pounds does he want to lose?b.By September, he has achieved his goal, but starts to return to his old eatinghabits. By the following January, he has gained 10% of the weight he was inSeptember. How much does he weigh now?c.Over the course of the year, from the previous new year to the current one, whatwas his overall weight change in terms of a percent? Overall, did he gain or losefor the year?2.Use this expression to answer the following questions:3415xxy−+a.How many terms are in the expression?b.List the variable(s) in the expression.c.List the constant(s) in theexpression.3.About 1 in 9 babies in the U.S. are born premature each year.a.What percent of babies in the U.S. are born premature? Round to the nearestwhole number.b.If 4 million babies were born in the U.S. last year, how many should havebeenborn premature? Round to the nearest whole number.4.Determine the pattern used to form the Outputs from the Inputs in the following table.InputOutput31072211341546

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4QuizName_______________________________________Math LitCycle 1, Quiz forSecondHalf (Sections 1.9–1.16), FormBOn average, a new car will lose 20% of its value each year. This loss of value is known asdepreciation.1.How much will the car be worth in 10 years? Consider using the table provided.2.If you want to use Excel to fill in the table above, what formula would you use togenerate the next year that would be listed in cell A3? What formula would you use togenerate the next dollar value thatwould be listed in cell B3? Note: You would use the“fill down” command after entering these formulas to complete the table.A3 =B3 =

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Quiz53.Is the depreciation linear or exponential? Explain yourresponse.4.After 10 years, the car will be worth ________% of the value paid at the dealership whenit was new. Complete the blank, rounding the value to the nearest whole percent.

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6QuizName _______________________________________Math LitCycle 2, Quiz for First Half (Sections 2.1–2.9), Form A1.Simplify each expression.a.()()20323xx−−b.()()20323xx−−c.()1327−2.Evaluate25xyz−when:a.2,4,1xyz= −= −= −b.5,5,1xyz=== −c.2,4,0xyz= −= −=3.Simplify.a.()256x−−b.()()256x−−c.()256x−−d.256x−−4.The following data set represents the number of sales each week for a 6-week periodfor a salesman. Find the mean, median, and mode for the data set. Round all resultsto two decimal places.2061246Mean:Median:Mode:

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Quiz7Name_______________________________________Math LitCycle 2, Quiz for First Half (Sections 2.1–2.9), Form B1.Find the mean of these values assuming the first 4 values each have a weight of 20%and the last 2 each have a weight of 10%: 5,11,13,17,22,352.A can of soda that is 5 inches tall and 2.5inches in diameter. If the can is filled34the way to the top, how much soda is in the can?3.Rewrite each expression, using the stated property.a.()2abc++associative property of addition.b.()2ab+commutative property of multiplication.4.Simplify.a.2(3)(256)xxx−−+b.23(45)(78)xxx−+−−5.You thought a shirt costs $65, but your prediction was $15 less than23the actual cost ofthe shirt.Give an algebraic expression for this statement and solve it.

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8QuizName _______________________________________Math LitCycle 2, Quiz for Second Half (Sections 2.10–2.17), Form A1.A right triangular staircase has a vertical height of 13 feet and a horizontal length of12 feet. What is the length of the staircase?2.Solve each equation. Round results to two decimal places.a.()1.05 2411.99x+=b.()17153514xxx−+= −−−3.Solve53132xx−−+=4.A bag contains 3 green chips, 5 black chips, and 6 red chips. One chip is randomlydrawn from the bag. Find the following probabilities:a.Drawing a green chip.b.Drawing a black chip.

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Quiz9Name _______________________________________Math LitCycle 2, Quiz for Second Half (Sections 2.10–2.17), Form BArchimedes discovered that the volume of a sphere is two-thirds thevolume of the smallestcylinder that surrounds the sphere.The volume of any cylinder is given by the formula:() ()2radius of cylinderheight of cylinderV=1.Find the volume of a sphere using the relationship between a sphere and cylinder thatArchimedes foundand the formula for the volume of a cylinder.Archimedes also discovered that the surface area of a sphere is two-thirds the surface area of thesmallest cylinder that surrounds the sphere.The surface area of any cylinder is given by the formula:()()()22radius of the cylinder2radius of the cylinderheight of the cylinderSA=+2.Find the surface area of a sphere using the relationship between a sphere and cylinder thatArchimedes found and the formula for the surface area of a cylinder.

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10QuizName _______________________________________Math LitCycle 3, Quiz for First Half (Sections 3.1–3.8), Form AJamie is working with his father to replace the worn shingles on their detached garage. Whilethere will be several materials to buy, theshingles will be the most expensive material topurchase. Complete the following problems to find the cost of the shingles. Begin by finding thedimensions of one side of the roof. Then find the total area of the roof, the amount of shinglesnecessary, and their total cost.1.The roof has a 4:12 slope, meaning there are 4 units of rise for every 12 units of run.Slope relationship in roof:Use the slope relationship and the dimensions of the garage to find the height,h, of thetriangular end of the garage.2.Find the length,l, of the slant of the roof.3.Find the area of one side of the roof.4.Find the total area of the roof.

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Quiz115.A “square” is a unit of measure in construction. It is the area contained in a 10 foot by 10foot square. Find the number of squares, rounded up to thenearest whole number, in thetotal roof area.6.It takes three bundles of shingles to cover a square. How many bundles of shingles areneeded to cover the roof?7.Each bundle costs $24.68. Compute the total cost of the shinglesassuming there will be a7.75% sales tax.

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12QuizName _______________________________________Math LitCycle 3, Quiz for First Half (Sections 3.1–3.8), Form BA mom needs to stock up on school uniforms for herson and is comparing online and in-storepricing. At a store in her town, uniforms are sold for $45 for a set (any top and any bottom).Hertown has a 7.25% sales tax. At the online store, she can purchase each piece for $20 (any top orbottom). There is no sales tax and just a flat rate shipping of $9.99.1.Write a cost model for the cost of a uniform set (includes 2 pieces) at the online store.Use meaningful variables and define them.2.If we were to graph the model from #1, which variable will be on thex-axis and whichwill be on they-axis?3.Is the online cost model linear? If so, state and interpret the slope andy-intercept. If not,explain why it is not linear.4.How many uniform sets would she have to purchase to make it worth buying themonline?

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Quiz13Name _______________________________________Math LitCycle 3, Quiz for Second Half (Sections 3.9–3.16), Form A1.Factor the GCF:32154530xx yx−+−2.Find the slope andy-intercept:81224xy−=3.a.Identify the initial value and the growth rate in the exponential function:4 1.2xy=b.Identify the vertex andy-intercept of the quadratic function:233076yxx=−+4.Write a 2×2 system of linear equations that has no solution.

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14QuizName _______________________________________Math LitCycle 3, Quiz for Second Half (Sections 3.9–3.16), Form B1.A ball is thrown upward at a speed of 50 feet per secondand it is 6 feet in the air when itleaves the person’s hand. Answer the following questions given the following functionalrepresentation for the height (h) of the ball at a certain time (t).216506htt= −++a.What is the highest point the ball will reach?b.When will the ball hit the ground?2.Factor the followingcompletely.a.4256x−b.222284x yxyy−−3.The admissionfee for a basketball game is $2.50 per student and $5.00 per adult.At a certain game 77 tickets are sold and $295is collected. How many studentsand how many adults attended the game?

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Quiz15Name _______________________________________Math LitCycle 4, Quiz for First Half (Sections 4.1–4.6), Form A1.1 U.S. dollar is the same 1.050 Canadian dollars. Convert $20 U.S. to Canadian dollarsusing each of the following methods. Round each result to two decimal places.a.Use a proportion.b.Use dimensional analysis with the fact relating the two currencies above.c.Use dimensional analysis with this fact: 0.953 U.S. dollars is the same as 1Canadian dollar.2.Simplify. Write answers with positive exponents.a.246xx−−b.()246xx−−3.Another salesman has 8 sales every week of the 6-week period. Find the mean, median,mode, and standard deviation of his sales numbers.Mean:Median:Mode:Standard deviation:

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16QuizName _______________________________________Math LitCycle 4, Quiz for First Half (Sections 4.1–4.6), Form BCreate a scale model that shows the relationship between the Earth and the Moon such that thedistance between the Earth and the Moon in the model will be 1 meter. This choice of scaleallows the model to fit in a classroom.Facts about the Earth and the Moon:Diameter of the Earth12,742 kmDiameter of the Moon3474.8 kmAverage distance between the Earth and Moon384,400 kmThe ratio1 m384,400 kmcompares the model measurement to the actual measurement.1.Using the ratio and facts above, find the diameter of the Earth in the model.List the answer rounded to the nearest whole millimeter.2.Using the ratio and facts above, find the diameter of the Moon in the model.List the answer rounded to the nearest whole millimeter.3.Choose objects that can be used in the model to represent the Earth and the Moon.Use the measurements you found in #1 and #2 and the ruler below.4.The choice of scale of 1 meter creates a very small model, making it difficult to see detailon the model Earth and Moon.Choose a scale that is larger than 1 meter but not so largethat the model would not fit in a classroom. Use your scale to find the size of the Earthand Moon for your model.

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Quiz17Name _______________________________________Math LitCycle 4, Quiz for Second Half (Sections 4.7–4.12), Form A1.Solve the following:a.Givenyvaries directly withx. If2y=and12x=,find the value ofywhen1x=.b.Givenyvaries indirectly withx. If3y=and7x=,find the value ofywhen2x=.c.Givenyvaries directly withxandz. If1y=,6x=, and13z=,find the value ofywhen1x=and2z=.2.State the definition for each of the following.a.Functionb.Domainc.Range

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18QuizName _______________________________________Math LitCycle 4, Quiz for Second Half (Sections 4.7–4.12), Form B1.State the vertex for each of the following and whether it is a maximum or a minimum.a.2(1)3yx=+−b.211yx= −+c.24(3)6yx= −−+2.You are standing 30 feetaway from a building. If the angle of elevation from your feetto the top of the building is65°, how tall is the building?

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Quiz193.State the domain and range of the function( )23fxx=−+.

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20Half Cycle ExamName _______________________________________Math LitCycle 1,Half Cycle Exam, First Half(Sections 1.1–1.8)1.At a car dealership that has 400 cars on the lot, 120 are blue or silver. Of these120cars,28are bothblue and silver, and 55 arejustblue.a.Draw a Venn diagram to represent this information. Write numbers in eachsection to indicate how manycarsare in that particular category.b.How manycarsaresilverbut notblue?c.How manycars are neither blue nor silver?2.70%of the entering freshman class willneed housing their first year,56of thosefreshman will choose to live in the dorms.What fraction of freshman will choose to livein the dorms?3.Plot each of the followingordered pairs as points on thegrid. Label each point with itsletter. List the quadrant (byRoman numeral) or axis todescribe the location of eachpoint.Axis or quadrantA(3, 1)___________B(0, 5)___________C(–2,–9)___________D(1, 0)___________E(–4, 2)___________

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Half Cycle Exam214.During a recent survey, 758 out of 1,320 people were concerned about saving money.What is the likelihood that someone chosen at random will not be concerned about savingmoney?5.Perform each of the fraction operations and writeyour answers in simplest form. Showall the work. Use your calculator only to check.a.57915+=b.14193-¸=c.4536-=d.43394×=6.Simplify each of thefollowing.a.82--=b.16-=7.Suppose a student received a 6,8,8 on their first three quizzes each worth 10 points.What would they have to receive on the fourth quiz to have a B (8 out of 10)averageonquizzes?8.Find the mean of these numbers:–15,–9,–5,–1, 3, 7

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22Half Cycle Exam9.Find the midpoint of the line segment that connects5 , 29æö-ç÷èøand2 , 1 .3æöç÷èø10.A dog is born weighing 12 ounces at birth and after oneyear weighs 13 pounds.What is the dog’s growth rate per day?11.For each situation, write a computation andfind the result.Interpret your answer.a.Joe is$400 in credit card debt and decides to buy a TVfor $250 using the samecard.How much credit card debt does he have in total?b.If it is 35degrees Fahrenheit when you go to bed at night and 7 degreesFahrenheit below zero when you wake up the following morning, what is thechange in temperature?

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Half Cycle Exam23Name _______________________________________Math LitCycle 1,Half Cycle Exam,Second Half (Sections 1.9–1.16)1.Ms. Andrew’sEnglishclass has the following grade distribution.Complete the table andcreate a pie chart for to show how grades are distributed in Ms. Andrew’s class.Round tothe nearest wholepercent.CategoryPointsPercentageCentral AngleHomework85Quizzes65Tests120Final Exam100

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24Half Cycle Exam2.Consider the following data on the years of experience and salaries foremployees of asmall business.Create a scatter plot and use a smooth curve to model the data.Experience(years)0133579914Salary(dollars)36,00036,50047,00051,00052,00060,00062,00067,00078,0003.If you’re driving 65mph and you look out the side window for 5 seconds, howmany feethave you driven in that time?Round to the nearest foot.4.You have a starting salary of $52,000. You receive a 3.5% raise every year.a.How much will your salary be after 4 years?b.What is the percent change in your salary?

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Half Cycle Exam255.a.Write an expression that has at least four terms.One of the terms should havemore than two factors.b.Write an equation that has at least 2 terms on each side. At least two terms shouldhave a negative coefficient.6.Determine the pattern in the following sequence and write an expression for thenth term.24816,,,,...47 10 137.A rectangular yard has dimensionsof 11ft by19ft. The homeowner wants to increaseeach dimension by 15%.a.Find theoriginal area and perimeter of the yard.b.Find the area and perimeter of the yard after a 15% increase in each dimension.c.By what percent will the area increase?d.By what percent will the perimeter increase?

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26Half Cycle Exam8.Fill in theblanks.a. ____________________ reasoning is used to form conjectures.b.____________________reasoning is used to prove conjectures.9.Create an example of each of the following.a.A monomial with degree 1.b.A trinomial with degree 5.c.Binomial with at least one fractional coefficient and degree 6.10.Is the following sequences asarithmetic, geometric or neither?If the sequence isarithmetic or geometric, write an expression for thenth term.a.–3,–4,–6,–9,–13, …b.5, 10, 20, 40, 80, …11.Determine if the change shown in the table is linear, exponential, or neither.If it is linearorexponential, explain why and write a function that models the data.xy022116210344–25–8

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Half Cycle Exam27Name _______________________________________Math LitCycle 2, Half Cycle Exam, First Half (Sections 2.1–2.9)1.Your grade inaclass is entirelybased on exams and quizzes.Given the following scores,ifeachquiz represents5% of your grade,eachexam represents15% of yourgrade, andthe final exam represents 30% of your grade, what is your overall grade in the class?CategoryGrades(each out of 100%)Quizzes88,76,92,95,68,81,76,74Exams71,83Final Exam852.Find the mean, median, and mode for the data set of ages of patients at the doctor’s officeon a given day.12,33,21,55,61,30,21,18Mean:Median:Mode:3.Simplify. Write answers with positive exponents.a.()245x-b.3861035m nm nc.07(3 )2xx--×d.27(2 )9xx y-e.()6 1/3125x

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