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Solution Manual for Math Lit, 2nd Edition

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    I NSTRUCTOR ’ S R ESOURCE M ANUAL WITH CONTRIBUTIONS FROM R ACHEL E. J OHNSON Harry S Truman College M ATH L IT A P ATHWAY TO C OLLEGE M ATHEMATICS S ECOND E DITION Kathleen Almy Rock Valley College Heather Foes Rock Valley College

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    iii C ONTENTS Introduction ................................ ................................ ................................ ................................ .............. iv Quizzes C ycle 1 ................................ ................................ ................................ ................................ ..................... 1 C ycle 2 ................................ ................................ ................................ ................................ ..................... 6 C ycle 3 ................................ ................................ ................................ ................................ ................... 10 C ycle 4 ................................ ................................ ................................ ................................ ................... 15 Half Cycle Exams C ycle 1 ................................ ................................ ................................ ................................ ................... 20 Cycle 2 ................................ ................................ ................................ ................................ ................... 27 Cycle 3 ................................ ................................ ................................ ................................ ................... 33 Cycle 4 ................................ ................................ ................................ ................................ ................... 42 Exams C ycle 1 ................................ ................................ ................................ ................................ ................... 50 Cycle 2 ................................ ................................ ................................ ................................ ................... 66 Cycle 3 ................................ ................................ ................................ ................................ ................... 78 Cycle 4 ................................ ................................ ................................ ................................ ................... 90 Final Exam ................................ ................................ ................................ ................................ ............. 103 Answers Quizzes ................................ ................................ ................................ ................................ ................. 115 Half Cycle Exams ................................ ................................ ................................ ................................ 119 Exams ................................ ................................ ................................ ................................ ................... 127 Final Exam ................................ ................................ ................................ ................................ ........... 143

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    INTRODUCTION The Instructor’s Resource Manual is designed to complement the Math Lit, 2 nd edition instructor support package. The Annotated Instructor’s Edition and Instructor Guide provide assistance to instructors for each cycle as a whole, as well as each section. This manual provides additional assessment 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 exams Math Lit, 2 nd Edition 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 each cycle. Form A is similar to the recaps provided in the text. It includes three to four unrelated problems that assess skills, concepts, and applications from that part of the worktext. Form B takes one scenario and asks several questions about it. Often, the questions are more involved and 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 quizzes provided in MyMathLab. New to the second edition are half cycle exams. An exam is provided for the first and second halves of each cycle. Two exam forms are provided for each cycle. Forms A and B are similar in approach and emphasis. Approximately half of each exam addresses skills while the remaining half addresses concepts 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 and TestGen ® testbank, available electronically.

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    Quiz 1 Name _______________________________________ Math Lit Cycle 1, Quiz for First Half (Sections 1.1 – 1.8), Form A 1. If a lawyer bills $350/hour, how much does he make every second? How much does he make per year? Assume he works 50 hour s per week, 48 weeks per year. 2. The student to teacher ratio is 19:1 at a local school and there is a total of 500 students and 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. 7 5 9 12 + = b. 2 3 9 4  = 4. A recipe calls for 3 4 cup of sugar to make 18 cookies. How many cookies can you make with 6 cups of sugar?

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    2 Quiz Name _______________________________________ Math Lit Cycle 1, Quiz for First Half (Sections 1.1 – 1.8), Form B 1 . Throughout the course of a trip, a family travels from 865 feet above sea level to 122 feet below sea level. How many feet did the family descend? a. Choose the calculation that describes the scenario. A . 122 865 − B. 865 122 − C. 122 865 − − D. 865 ( 122) − − b. List the result. 2 . Compute the following fraction operations. a. 7 5 7 5 5 6 5 6   − − − = − − =     b. 7 5 5 6    − − =       3 . Create a data set with six different values that has an average of ‒ 1. 4. Of the 1,300 people who respo nded to a pole about coffee, 455 claimed they liked it plain. What is the relative frequency of people who drink their coffee plain?

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    Quiz 3 Name _______________________________________ Math Lit Cycle 1, Quiz for Second Half (Sections 1.9 – 1.16 ), Form A 1. John weighs 210 pounds. His goal for the new year is to lose 10% of his body weight a. How many pounds does he want to lose? b. By September, he has achieved his goal, but starts to return to his old eating habits. By the following January, he has gained 10% of the weight he was in September. How much does he weigh now? c. Over the course of the year, from the previous new year to the current one, what was his overall weight change in terms of a percent? Overall, did he gain or lose for the year? 2. Use this expression to answer the following questions: 3 4 15 x xy − + a. How many terms are in the expression? b. List the variable(s) in the expression. c. List the constant(s) in the expression. 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 nearest whole number. b. If 4 million babies were born in the U.S. last year, how many should have been born premature? Round to the nearest whole number. 4. Determine the pattern used to form the Outputs from the Inputs in the following table. Input Output 3 10 7 2 2 11 34 1 5 46

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    4 Quiz Name _______________________________________ Math Lit Cycle 1, Quiz for Second Half (Sections 1.9 – 1.16 ), Form B On average, a new car will lose 20% of its value each year. This loss of value is known as depreciation. 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 to generate the next year that would be listed in cell A3? What formula would you use to generate the next dollar value that would 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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    Quiz 5 3. Is the depreciation linear or exponential? Explain your response. 4. After 10 years, the car will be worth ________% of the value paid at the dealership when it was new. Complete the blank, rounding the value to the nearest whole percent.

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    6 Quiz Name _______________________________________ Math Lit Cycle 2, Quiz for First Half (Sections 2.1 – 2.9), Form A 1. Simplify each expression. a. ( ) ( ) 2 0 3 2 3 x x − − b. ( )( ) 2 0 3 2 3 x x − − c. ( ) 1 3 27 − 2. Evaluate 2 5 x y z − when: a. 2, 4, 1 x y z = − = − = − b. 5, 5, 1 x y z = = = − c. 2, 4, 0 x y z = − = − = 3. Simplify. a. ( ) 2 5 6 x − − b. ( )( ) 2 5 6 x − − c. ( ) 2 5 6 x − − d. 2 5 6 x − − 4. The following data set represents the number of sales each week for a 6 - week period for a salesman. Find the mean, median, and mode for the data set. Round all results to two decimal places. 2 0 6 12 4 6 Mean: Median: Mode:

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    Quiz 7 Name _______________________________________ Math Lit Cycle 2, Quiz for First Half (Sections 2.1 – 2.9), Form B 1. Find the mean of these values assuming the first 4 values each have a weight of 20% and the l ast 2 each have a weight of 10%: 5,11,13,17,22,35 2. A can of soda that is 5 inches tall and 2 .5 inches in diameter. If the can is filled 3 4 the way to the top, how much soda is in the can? 3. Rewrite each expression, using the stated property. a. ( ) 2 a b c + + associative property of addition. b. ( ) 2 a b + commutative property of multiplication. 4. Simplify. a. 2 ( 3)(2 5 6) x x x − − + b. 2 3( 4 5) (7 8) x x x − + − − 5. You thought a shirt costs $65, but your prediction was $15 less than 2 3 the actual cost of the shirt. Give an algebraic expression for this statement and solve it.

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    8 Quiz Name _______________________________________ Math Lit Cycle 2, Quiz for Second Half (Sections 2.10 – 2.17), Form A 1. A right triangular staircase has a vertical height of 13 feet and a horizontal length of 12 feet. What is the length of the staircase? 2. Solve each equation. Round results to two decimal places. a. ( ) 1.05 2 4 11.99 x + = b. ( ) 17 15 3 5 14 x x x − + = − − − 3. Solve 5 3 1 3 2 x x − − + = 4. A bag contains 3 green chips, 5 black chips, and 6 red chips. One chip is randomly drawn from the bag. Find the following probabilities: a. Drawing a green chip. b. Drawing a black chip.

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    Quiz 9 Name _______________________________________ Math Lit Cycle 2, Quiz for Second Half (Sections 2.10 – 2.17), Form B Archimedes discovered that the volume of a sphere is two - thirds the volume of the smallest cylinder that surrounds the sphere. The volume of any cylinder is given by the formula: ( ) ( ) 2 radius of cylinder height of cylinder V  = 1. Find the volume of a sphere using the relationship between a sphere and cylinder that Archimedes found and 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 the smallest cylinder that surrounds the sphere. The surface area of any cylinder is given by the formula: ( ) ( )( ) 2 2 radius of the cylinder 2 radius of the cylinder height of the cylinder SA   = + 2. Find the surface area of a sphere using the relationship between a sphere and cylinder that Archimedes found and the formula for the surface area of a cylinder.

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    10 Quiz Name _______________________________________ Math Lit Cycle 3, Quiz for First Half (Sections 3.1 – 3.8), Form A Jamie is working with his father to replace the worn shingles on their detached garage. While there will be several materials to buy, the shingles will be the most expensive material to purchase. Complete the following problems to find the cost of the shingles. Begin by finding the dimensions of one side of the roof. Then find the total area of the roof, the amount of shingles necessary, 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 the triangular 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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    Quiz 11 5. A “square” is a unit of measure in construction. It is the area contained in a 10 foot by 10 foot square. Find the number of squares, rounded up to the nearest whole number, in the total roof area. 6. It takes three bundles of shingles to cover a square. How many bundles of shingles are needed to cover the roof? 7. Each bundle costs $24.68. Compute the total cost of the shingles assuming there will be a 7.75% sales tax.

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    12 Quiz Name _______________________________________ Math Lit Cycle 3, Quiz for First Half (Sections 3.1 – 3.8), Form B A mom needs to stock up on school uniforms for her son and is comparing online and in - store pricing. At a store in her town, uniforms are sold for $45 for a set (any top and any bottom). Her town has a 7.25% sales tax. At the online store, she can purchase each piece for $20 (any top or bottom). 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 the x - axis and which will be on the y - axis? 3. Is the online cost model linear? If so, state and interpret the slope and y - intercept. If not, explain why it is not linear. 4. How many uniform sets would she have to purchase to make it worth buying them online?

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    Quiz 13 Name _______________________________________ Math Lit Cycle 3, Quiz for Second Half (Sections 3.9 – 3.16), Form A 1. Factor the GCF: 3 2 15 45 30 x x y x − + − 2. Find the slope and y - intercept: 8 12 24 x y − = 3. a. Identify the initial value and the growth r ate in the exponential function: 4 1.2 x y =  b. Identify the vertex and y - intercept of the quadratic function: 2 3 30 76 y x x = − + 4. Write a 2 × 2 system of linear equations that has no solution.

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    14 Quiz Name _______________________________________ Math Lit Cycle 3, Quiz for Second Half (Sections 3.9 – 3.16), Form B 1. A ball is thrown upward at a speed of 50 feet per second and it is 6 feet in the air when it leaves the person’s hand. Answer the following questions given the following functional rep re sentation for the height ( h ) of the ball at a certain time ( t ). 2 16 50 6 h t t = − + + a. What is the highest point the ball will reach? b. When will the ball hit the ground? 2. Factor the following completely. a. 4 256 x − b. 2 2 22 84 x y xy y − − 3. The admission fee for a basketball game is $2.50 pe r student and $5.00 per adult. At a certain game 77 tickets are sold and $ 295 is collected. How many students and how many adults attended the game?

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    Quiz 15 Name _______________________________________ Math Lit Cycle 4, Quiz for First Half (Sections 4.1 – 4.6), Form A 1. 1 U.S. dollar is the same 1.050 Canadian dollars. Convert $20 U.S. to Canadian dollars using 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 1 Canadian dollar. 2. Simplify. Write answers with positive exponents. a. 2 4 6 x x − − b. ( ) 2 4 6 x x − − 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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    16 Quiz Name _______________________________________ Math Lit Cycle 4, Quiz for First Half (Sections 4.1 – 4.6), Form B Create a scale model that shows the relationship between the Earth and the Moon such that the distance between the Earth and the Moon in the model will be 1 meter. This choice of scale allows the model to fit in a classroom. Facts about the Earth and the Moon: Diameter of the Earth 12,742 km Diameter of the Moon 3474.8 km Average dista nce between the Earth and Moon 384,400 km The ratio 1 m 384,400 km compares 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 detail on the model Earth and Moon. Choose a scale that is larger than 1 meter but not so large that the model would not fit in a classroom. Use your scale to find the size of the Earth and Moon for your model.

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    Quiz 17 Name _______________________________________ Math Lit Cycle 4, Quiz for Second Half (Sections 4.7 – 4.12), Form A 1. Solve the following: a. Given y varies directly with x . If 2 y = and 1 2 x = , find the value of y when 1 x = . b. Given y varies indirectly with x . If 3 y = and 7 x = , find the value of y when 2 x = . c. Given y varies directly with x and z . If 1 y = , 6 x = , and 1 3 z = , find the value of y when 1 x = and 2 z = . 2. State the definition for each of the following. a. Function b. Domain c. Range

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    18 Quiz Name _______________________________________ Math Lit Cycle 4, Quiz for Second Half (Sections 4.7 – 4.12), Form B 1. State the vertex for each of the following and whether it is a maximum or a minimum. a. 2 ( 1) 3 y x = + − b. 2 11 y x = − + c. 2 4( 3) 6 y x = − − + 2. You a re standing 30 feet away from a building. If the angle of elevation from your feet to the top of the building is 65 ° , h ow tall is the building?

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    Quiz 19 3. State the domain and range of the function ( ) 2 3 f x x = − + .

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    20 Half Cycle Exam Name _______________________________________ Math Lit Cycle 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 these 120 cars , 28 are both blue and silver, and 55 are just blue . a. Draw a Venn diagram to represent this information. Write numbers in each section to indicate how many cars are in that particular category. b. How many cars are silver but not blue ? c. How many cars are neither blue nor silver ? 2. 70% of the entering freshman class will need housing their first year, 5 6 of those freshman wil l choose to live in the dorms. What fraction of freshman will choose to live in the dorms? 3. Plot each of the following ordered pairs as points on the grid. Label each point with its letter. List the quadrant (by Roman numeral) or axis to describe the location of each point. Axis or quadrant A (3, 1) ___________ B (0, 5) ___________ C ( – 2, – 9) ___________ D (1, 0) ___________ E ( – 4, 2) ___________

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    Half Cycle Exam 21 4. 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 saving money? 5. Perform each of the fraction operations and write your answers in simplest form. Show all the work. Use your calculator only to check. a. 5 7 9 15 + = b. 1 4 1 9 3 - ¸ = c . 4 5 3 6 - = d . 4 3 3 9 4 × = 6. Simplify each of the following. a. 8 2 - - = 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) average on q uizzes? 8. Find the mean of these numbers: – 15, – 9, – 5, – 1, 3, 7

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    22 Half Cycle Exam 9 . Find the midpoint of the line segment that connects 5 , 2 9 æ ö - ç ÷ è ø and 2 , 1 . 3 æ ö ç ÷ è ø 10. A dog is born weighin g 12 ounces at birth and after one year weighs 13 pounds. What is the dog’s growth rate per day? 11. For each situation, write a computation and find the result. Interpret your answer. a. Joe is $400 in credit card debt and decides to buy a TV for $250 using the same card. How much credit card debt does he have in total? b. If it is 35 degrees Fahrenheit when you go to bed at night and 7 degrees Fahrenheit below zero when you wake up the following morning, what is the change in temperature?

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    Half Cycle Exam 23 Name _______________________________________ Math Lit Cycle 1, Half Cycle Exam, Second Half (Sections 1.9 – 1. 16 ) 1. Ms. Andrew’s English class has th e following grade distribution. Complete the table and create a pie chart for to show how grades are distributed in Ms. Andrew’s class. Round to the nearest who le percent. Category Points Percentage Central Angle Homework 8 5 Quizzes 6 5 Tests 1 20 Final Exam 100

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    24 Half Cycle Exam 2. Consider the following data on the years of experience and salaries for employees of a small business. Create a scatter plot and use a smooth curve to model the data. Experience (years) 0 1 3 3 5 7 9 9 14 Salary (dollars) 36,000 36,500 47,000 51,000 52,000 60,000 62,000 67,000 78,000 3. If you’re driving 65 mph and you look out the side window for 5 seconds, how many feet have 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 Exam 25 5. a. Write an expression that ha s at least four terms. One of the terms should have more than two factors. b. Write an equation that has at least 2 terms on each side. At least two terms should have a negative coefficient. 6. Determine the pattern in the following sequence and write an expression for the n th term. 2 4 8 16 , , , ,... 4 7 10 13 7. A rectangular yard has dimension s of 11 ft by 19 ft. The homeowner wants to i ncrease each dimension by 15%. a. Find the original 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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    26 Half Cycle Exam 8. Fill in the blanks. 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 sequence s as ari thmetic, geometric or neither? If the sequ ence is arithmetic or geometric , write an expression for the n th term. a. – 3, – 4, – 6, – 9, – 13, … b. 5, 10, 20, 40, 80, … 11. Determine if the change shown in the table is li near, exponential, or neither. If it is linear o r exponential, explain why and write a function that models the data. x y 0 22 1 16 2 10 3 4 4 – 2 5 – 8

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    Half Cycle Exam 27 Name _______________________________________ Math Lit Cycle 2 , Half Cycle Exam, Firs t Half (Sections 2.1 – 2.9 ) 1. Your grade in a class is entirely based on exams and quizzes. Given the following scores, if each quiz represent s 5% of your grade, each exam represent s 15% of you r grade, and the final exam represents 30% of your grade, what is your overall grade in the class? Category Grades (each out of 100%) Quizzes 88, 76, 92, 95, 68, 81, 76, 74 Exams 71, 83 Final Exam 85 2. Find the mean, median, and mode for the data set of ages of patients at the doctor ’ s office on a given day. 12, 33, 21, 55, 61, 30, 21, 18 Mean: Median: Mode: 3. Simplify. Write answers with positive exponents. a. ( ) 2 4 5 x - b. 3 8 6 10 35 m n m n c. 0 7 (3 ) 2 x x - - × d. 2 7 (2 ) 9 x x y - e. ( ) 6 1/3 125 x

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