MATH 01 UNIT 1 HOMEWORK ASSIGNMENTS General Instructions You will notice that most of the homework assignments for a section have more than one part. Usuall, the part (A) questions ask for eplanations, definitions, or eamples. The purpose of these questions is to be sure ou understand the vocabular, ideas, and procedures of the section before ou go on to problems. The part (B) questions are usuall from the tetbook. If there are other parts, the ma be additional needed practice, as some of the topics in the course are not covered in the tetbook. Some of the problems in the Unit 1 Homework Assignments review prerequisite material. If ou need more review of these topics, see our instructor or go to the Math Lab for help. Do ALL our homework in our notebook or loose-leaf binder. Be sure to label each question. Be sure to read the directions ver carefull, since ou are often asked to do more than one thing in a problem. Be sure to write out all our work, since method is as important as getting the correct answer. The answers to the odd-numbered problems are in the back of the book, beginning on page A-11. The answers to the even-numbered problems and the etra questions (usuall A or C) in this handout are all included at the end of this handout. If ou have difficult with a problem, mark the problem and write a note in the margin about our difficult. In this wa, when ou go over homework in class, ou can be read with our questions. CHAPTER 1 Section 1.1 Problem Solving Steps and Strategies A. Tet: Read pages vii ii Read the "To the student" section of our tetbook. [pp. vii ii] Develop a strateg that will give ou the best opportunit to earn the grade ou hope to receive from this course. You ma consult with others [famil, learning assistants, counselors, etc.] for comments and ideas. Write a paragraph about our strateg. B. Eercises 1.1, page 7: 9 Section 1. Numeric Representations A. Tet: Read pages 8 16 Eercises 1., pages 17 19: 1, 3, 7, 9, 17, 19, 31, 33 B. Make an input-output table for the following rule. Use whole numbers from 0 to 6 as inputs. The output is more than three times the input. 1
C. 1. A tanning salon charges a $5 membership fee and $5 per visit. The cost of using the salon can be represented b the equation C5 5v, where v is the number of visits made to the salon. This information is graphed below. C Cost v Number of visits a. Use the graph to fill in the cost for the number of visits in the input-output table. Input, visits Output, Cost 0 3 8 11 b. Use the graph to estimate the cost of 5 visits: 5 visits to the salon would cost approimatel c. Use the equation to find the cost of 1 and visits: The cost of 1 visit would be The cost of visits would be The following topics will have been covered in our previous math courses and are considered review for MATH 01. If ou are having trouble with an of these concepts or problems, see our instructor or get help in the Math Lab. Word Bank: Sum Difference Product Quotient Fill in the blank for each sentence. You ma use the Word Bank above.. A is the answer to a multiplication problem. 3. A is the answer to a subtraction problem. 4. A is the answer to a division problem. 5. A is the answer to an addition problem. 6. Joe s insurance premium will decrease b 5% if he takes the Defensive Driving Course. If Joe s insurance premium is $775, how much will he save if he takes the course?
7. What is wrong with the following problem? 3 4 3 7 5 10 10 10 0 8. Answer these questions: a. Think of numbers that ou use on a regular basis. Name one that is a rational number but not an integer. Describe the situation where ou use that number. b. Eplain wh ever integer is also a rational number. c. Is zero a rational number? An integer? Sections 1.3 1.4: Verbal and Smbolic Representations A. Tet: Read pages 0-5 Eercises 1.3, pages 6-9: 1 4 all, 7, 9, 31, 33, 35 B. Tet: Read pages 9-34 Eercises 1.4, page 36: 1, 3, 37, 38, 40 C. Translate each of the following phrases into an algebraic epression. 1. The annual salar of a person who gets paid dollars per month.. The annual salar of a person who gets paid dollars per week. 3. The value in dollars of nickels. 4. The total fee for one night at a campground that charges $0 per night plus $5 per person for a group of people. 5. The monthl cost of electricit if ou use kilowatt hours each month, if the electric compan charges $0.11 for each kilowatt hour used and a monthl service charge of $.0 D. 1. Make tables for the rules in a. and b., using integer inputs from 1 to 5. Describe the output in algebraic notation. a. The output is one less than twice the input b. The output is three more than the quotient of the input and four.. Brookdale s cafeteria charges $0.5 per ounce for salad and $1.5 for a soda. The graph below shows the cost of a salad-and-soda lunch, C, given the weight of the salad, w, in ounces. 3
C Cost w Ounces of Salad a. Use the graph above to fill in the table below. Input, w, Output, C, Ounces of Salad Cost of lunch 5 9 4.00 15 b. Write the equation to calculate the cost, C, of a salad and soda lunch if we know the weight of a salad, w, in ounces. 3. James sells sub-sandwiches for $4.50 each. Let the input be n, the number of sandwiches he sells, and let the output be R, the revenue brought in b selling the subs. a. Make an input-output table using the even integers from 0 to 8 for n. b. Cop the coordinate plane, including the scale, onto our own graph paper. Then plot the points on the graph. Label our aes. c. Write the equation that relates the revenue and the number of sandwiches sold. 4
Write the input-output rule that describes each table below 4. 1 3 6 3 9 4 1 5 15 6. 1 5 8 3 11 4 14 5 17 5. 1 1 3 0 4 1 5 7. 1 4 3 0 4 5 4 Section 1.5: Visual Representations: Rectangular Coordinate Graphs NOTE: WHEN ANY HOMEWORK PROBLEM REQUIRES A GRAPH, BE SURE TO USE GRAPH PAPER. Draw a separate graph for each problem. Draw our aes with a ruler. Label each ais with the variable name and with an quantities represented. Be sure that ou mark our scale and that it is consistent (increments are equal) along that ais. If the graph is a line, draw the line with a ruler. A. Tet: Read pages 39 47 Answer these questions: 1. Wh is (, ) called an ordered pair?. How do ou find the quadrant in which an ordered pair is located? 3. How do ou find on which ais an ordered pair (a, 0) is located? 4. How do ou find on which ais an ordered pair (0, b) is located? B. Eercises 1.5, pages 48 51: 1, 3, 5, 19, 3, 33, 35, 38 a-d (figure is on page 47), 50 b, d 5
C. 1. One emploee noticed the Federal government took 7 ½ % of his pacheck for the social securit ta. Let the emploee s salar be s and the social securit ta be T. a. Complete the input-output table below. Cop our table in our notebook. Input Ordered pair Salar, s $700 $000 $500 Output Social Securit ta, T $315 $7500 b. Write the equation that relates the social securit ta, T, and the salar, s. c. Pick an appropriate scale and graph the ordered pairs from our table. d. Interpret the point (000, 150).. Make an input-output table for each of the following rules. Use the inputs given in each problem. Graph the input-output pairs that ou found. Connect our points and etend the graph beond them. You will need to scale our aes appropriatel. a. 0.11.00 Use inputs from 0 to 1000 in steps of 00 represents the number of kilowatt hours, and represents the monthl cost of using electricit. b. 100 400 Use inputs from 0 to 15 in steps of 3 Section.4: Properties of Real Numbers Applied to Simplifing Epressions A. Tet: Read pages 78 79 (Simplification of Fractions) & pages 86 9. Answer these questions. 1. a. How do ou distinguish factors from terms? b. Using the number 3 and the variable onl, write an epression with factors. c. Using the number 3 and the variable onl, write an epression with terms.. How do ou recognize like terms? 3. Give an eample of two like terms. 4. Give an eample of two terms that are not like, but that contain the same variable(s). 5. a. Write the commutative propert of multiplication using variables and. b. Write the commutative propert of addition using variables and. c. How are these two properties similar? d. Give an eample to show that subtraction is not commutative. 6. a. Write the associative propert of addition using variables,, and z. b. Give an eample of this propert using integers. 7. a. Write the distributive propert using the variables,, and z. b. Give an eample of this propert using integers. 6
8. Can the distributive propert be used to rewrite the epression abc? B. Eercises.3, page 84: 3, 5. Eercises.4, pages 94 96: 9, 11, 13, 17, 5, 31, 35, 39, 45, 49, 51, 5, 61. C. Simplif b using the Distributive Propert to remove parentheses and then combine like terms: a b a b 1. 4. 3w5w 1. 15 7 5. 14 75 3 5 3. 15 7 6. 6d 5 c d c 5 Section.3 Part I: Fractions & Order of Operations A. Read pages 77 84. Answer these questions. 1. Write the rule for the order of operations.. a. Evaluate ( 3 5) b using the rule for the order of operations. b. Evaluate 3 5 b using the rule for the order of operations. c. Is ( 3 5) equal to 3 5? Eplain wh or wh not. B. Eercises.3, pages 84 86: 33 43 odd, 51 57 odd C. Evaluate each epression using the given values of the variables. 1. 5 = 3, = 4 5. 5 3 = 5. 3. 3 = 1 = 3 7. 4. = 3 6. 8. 3 = 4, = 4 9 = 16 = 1 D. Evaluate each equation for the given values of ; complete the input-output table; and graph the ordered pairs and connect the points with a curve on our own graph paper. Cop each table into our notebook. 1. 1 7 14 7
. 1 3 1 1 0 1 3. 10 1 0 1 4. 3 6 3 1 ½ 1/10 Solving Equations Part I CHAPTER 3 A. Tet: Read pages 18-154. Answer these questions. 1. What is an equation?. What is meant b a solution to an equation? 3. Eplain how to check a solution to an equation. 8
4. Eplain how the addition propert of equations can be used to solve 5 13. 5. Eplain how the multiplication propert of equations can be used to solve 14. 6. For the equation + 1 = 4, we sa that = 3 is a solution. How would ou check this? 7. If ou solve an equation and our solution does not check, what does that mean and what should ou do? 8. Eplain how to solve m + b = n for from a table for = m + b. Assume that the number n appears in the table. 9. Eplain how to solve m + b = n for from a graph of = m + b. Assume that the number n appears on the vertical ais. B. Eercises 3.1, pages 133-135: 11, 13, 15, 17, 31, 35. Eercises 3., pages 146-149: 1, 3, 9, 11. Eercises 3.3, pages 155-156: 7, 15, 33, 37, 41, 49. C. Additional Problems: For problems 1-3, use ONLY the table to solve each equation. 1.. = 38 46 3 176 130 1 84 0 38 1 8 54 3 100 = 0.5 0.75 1 0.5 0.5 3 0 4 0.5 5 0.5 6 0.75 7 1 a. 38 46 = 54 b. 38 46 = 176 c. 38 46 = 84 a. 0.5 0.75 = 0 b. 0.5 0.75 = 0.5 c. 0.5 0.75 = 1 d. Eplain how ou could use the table to approimate the solution to 0.5 0.75 = 0.3. 9
For problem 3, solve each equation using the given graph. 3. a. b. c. 1 0.6 5 5 1 0.6 5 5 5 1 0. 5 d. Estimate the solution to 1 0.8 5 5 4. Sam, a part-time salesperson at the Silver Car Agenc, is paid $500 in salar ever month along with a 5% commission on the sales he makes. Let be the amount of sales Sam makes in a month and let be the total amount of mone he earns in a month. a. Write an equation (input-output rule) that gives the total amount of mone he earns in terms of the sales he makes. b. Make an input-output table using the sales amount ranging from 0 to $10,000 in steps of 000s. c. Graph the ordered pairs ou found in part b. Connect with a line. d. Use the graph or the table ou made to solve the following equations: i) 500 + 0.05 = 600 ii) 500 + 0.05 = 700 iii) Estimate using the graph: 500 + 0.05 = 750 D. Review Simplif the following epressions. 1. 3( ) ( 4). 4( ) ( ) 1 8 3 3. 4. 45 5. 3 1 5( ) 10
Solving Equations Part II Section 3. A. Answer these questions. 1. What is the difference between the graphs of linear and nonlinear equations?. How do ou identif a linear equation (either one-variable or two-variable)? 3. How can ou identif the independent (or input) variable in an application? 4. What phrases in a word problem tell us that its equation ma contain parentheses? 5. Does ever equation have eactl one solution? Eplain our answer. B. Problems: For problems 1-4, use the table or graph to solve the equations. 1. 1 3 17 10 0 9 1 8 1 3 18 4 55 9 a. 3 9 10 b. 3 9 18 c. 3 9 8 d. Use the table to approimate the solution to 3 9 0.. a. When what is the value? b. c. d. Estimate the solutions to 11
3. The graph of 5 is shown below. Complete the accompaning table, then use the table and the graph to solve the equations that follow. Y X Y 5 0 4 1 1 6 3 8 4 a. 5 3 b. 5 1 c. 5 d. 5 8 e. 5 Eplain. 1
1 ( ) 4 4. The graph of is shown below. Use the graph to complete the inputoutput table for inputs the integers from to 4. Then use the table and graph to solve the equations that follow. Y X a. b. c. 1 ( ) 4 4 1 ( ) 4 1 ( ) 4 4 1 d. ( ) 4 5 For problems 5 7, use the properties of equalit to solve the equation. Check our solution. 3 4 1 5 5. 6. (m 3) 5m 5 7. 14 16 3(a 1) C. Eercises 3.1, page 133: 5 Eercises 3., pages 146-149: 13, 15. Section 3.4 A. Tet: Read pages 157-16. B. Eercises 3.4, pages 164-167: 9, 11, 1, 17, 18, 19. 13
SOLUTIONS Section 1. B. Input Output 0 1 5 8 3 11 4 14 5 17 6 0 C. 1. a. v, visits C,Cost 0 5 3 40 8 65 11 80 b. $50 c. $30 for 1 visit, $35 for visits. product 3. difference 4. quotient 5. sum 6. $38.75 7. The denominators should not be added. The denominator should be 10. 8. a. Answers var. b. Ever integer is also a rational number because ever integer can be written as a fraction with a denominator of 1. c. Zero is both a rational number and an integer. Zero is an integer because the integers include all the whole numbers beginning with 0. Zero is a rational number both because it is an integer and because it can be written as a fraction, for eample 0 1. Sections 1.3 1.4 A.. 700; 7 4. 97; 3 B. 38. a. = 5; = 0.04n b. $5 c. $80 d. $6 e. $0.0 f. The fee would be $5 because the transfer is between $0 and $15. g. The fee is $5 for both transfers. The input has to cover all possible balance transfer amounts. 40. 4 tables, 10 chairs; 0 tables, 4 chairs. The number of chairs is two more than twice the number of tables. C. 1. 1. 5 3. 0.05 4. 0 + 5 5. 0.11 +.0 D. 1. a. 1 1 1 3 3 5 4 7 5 9 b.. a. 3 4 1 1 3 4 1 3 3 3 3 4 4 4 5 1 4 4 Input, w, Ounces of Salad b. C0.5w 1.5 Output, C, Cost of lunch 5.50 9 3.50 11 4.00 15 5.00 14
3. a. Input n = number of sandwiches R Output, R = revenue 0 0 9 4 18 6 7 8 36 b. c. R 4.50n 4. 3 5. 3 6. 3 7. 6 Section 1.5 A. 1. (, ) is called an ordered pair because the first number in the pair is the -coordinate, which gives the horizontal distance from the vertical ais, and the second number is the -coordinate, which gives the vertical distance from the horizontal ais.. The signs of the numbers in the pair tell ou the quadrant; (+, +) is in Quadrant 1, (, +) is in Quadrant, (, ) is in Quadrant 3, and (+, ) is in Quadrant 4. 3. In (a, 0), the second number is 0, so there is no vertical movement and the point is on the -ais. 4. In (0, b), the first number is 0, so there is no horizontal movement and the point is on the -ais. B. 38. a. (1000,40) b. $500 is the credit limit. c. $100 at I d. $50 at H. 50. b. A(,-5); B(-,-5) d. A(3,4); B(5,) C. n 1. a. 3900 3600 3300 3000 700 400 Input Salar, s 3 6 Output Social Securit ta, T 9 1 15 Ordered pair $700 $5.50 (700, 5.50) $000 $150 (000, 150) $500 $187.50 (500, 187.50) 400 $315 (400, 315) $7500 $56.50 (7500, 56.50) b. T.075s c. T d. If ou earn $000, the Social Securit ta is $150.. a. 100 + 400 0 400 3 700 6 3000 9 3300 1 3600 15 3900 s 15
b. 0.11 +.00 0.00 00 4.00 400 46.00 600 68.00 800 90.00 1000 11.00 C. 1. 3a + b. 7 + 1 3. 8 + 16 4. w 1 5. 31 175 6. 4d 3c Section.3 Part One A. 1. Complete grouped operations, then eponents, then (working left to right) multiplication and/or division followed b addition and subtraction (left to right).. a. 35 8 64 C. b. 3 5 95 34 c. Not equal because of the order of operations. Section.4 A. 1. a. Factors are multiplied; terms are added. b. Answers var. 3 c. Answers var. 3 +. Variables and eponents are identical. 3. eample: and 3 4. eample: and 5. a. b. c. Similar both involve two numbers and changing the order has no effect on the answer. d. Eample: 3 = 1 but 3 = 1, so 3 3 z z 6. a. ( ) b. (1 ) 3 33 6 and 1 ( ) 15 6 so, 1 3 1 ( 3) 7. a. z z b. 3 4 7 14 and 3 4 6 8 14, 3 4 3 4 8. No B. 5. a. 3 b. c. 4 d. 3 e. 3 1. 3. 4 3. 9 4. 9 5. 60 6. ½ 7. 6 8. 1 4 D. 1. 0 1 1 7 3 14 4 16
. 1 3 1 3 1 0.5 0 1 1 1.5 5 4. 3 Y 6 ½ 3 1 3 1 3 ½ 6 1/10 30 3. 10 6 1 9 0 10 1 9 6 Solving Equations Part I A 1. An equation is a statement of equalit.. A solution is a value of the variable that makes the equation true. 3. To check a proposed solution, substitute that value for the variable and evaluate each side separatel to determine if the resulting equation is true. 4. B adding 5 to both sides of the equation, ou have an equivalent equation that is solved for the variable. 5. B dividing both sides of the equation b, ou have an equivalent equation that is solved for the variable. 6. To check the solution = 3, ou substitute 3 and obtain the equation 3 + 1 = 4. Because this is a true equation, the solution checks. 7. If our solution does not check, look for an error either in the steps used in the solution or in the steps used in the check. 8. Look at the column, and see where n appears. Look to the left to see which value(s) of give(s) n. This/these values of is/are the solution(s). 9. Look up or down to find n on the -ais, then draw a horizontal line right and left (from n) to see where the graph of the equation meets this line. The value(s) of where the meet is/are the solution(s). C 1. a. = b. = 3 17
c. = 1. a. = 3 b. = 1 c. = 7 d. 0.3 is between 0.5 and 0.5, so the solution lies somewhere between = 4 and = 5, probabl closer to 4. 3. a. = b. = 1 c. = 0 d. 0.5 4. a. = 500 +.05 b. (Sales, $) (Salar, $) 0 500 000 600 4000 700 6000 800 8000 900 10000 1000 c. d. i) = 000 ii) = 4000 iii) = 5000 D 1. 5 +. 5 + 6 3. 1 4. 8 40 5. 1 Solving Equations Part II (Section 3.) A. 1. The graph of a linear equation is a line. The graph of a non-linear equation is not a line; it ma be a curve, a V, or another shape.. A linear equation has no eponents other than 1, no absolute value, and no root applied to the variable. The variable is not in the denominator of a fraction. 3. The independent variable can be determined on its own, without being calculated. The dependent variable is calculated or derived from the independent variable. 4. Amount over, in ecess of, additional, after the first, "the sum of", the difference between" might tell ou to use parentheses. 5. No. Linear equations have one solution. Non-linear equations can have no solution, one solution, or more than one solution. B. 1. a. = 1 b. = 3 c. = 1 d.. a. b. = 1, c. =, 1 d. = 0, 1.7, 1.7 3. X 5 0 4 1 1 1 6 3 8 4 3 a. = 4 b. = 4 c. = 1 d. = 3 e. No solution. The value of is never negative, since we are taking the principal (positive) square root. 4. X 4 1 0.5 0 1 3.5 4 3 3.5 4 a. =, 6 b. = 0, 4 c. = d. No solution. 5. = 1 6. m = 7. a = 1 6 Solving Equations Part II (Section 3.4) B. 1. = 18. = 4 18