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Study Guide and Review -Chapter 1 State whether each sentence is true or false . If false , replace the underlined term to make a true sentence. 1. An exponent indicates the number the base is to be multiplied by. ANSWER: True 2. A coordinate system is formed by the intersection of two number lines. ANSWER: true 3. An expression is in simplest form when it contains like terms and parentheses. ANSWER: false; not in simplest form 4. In an expression involving multiplication, the quantities being multiplied are called factors. ANSWER: true 5. In a function, there is exactly one output for each input. ANSWER: true 6. Order of operations tells us to always perform multiplication before subtraction. ANSWER: true 7. Since the product of any number and 1 is equal to the number, 1 is called the multiplicative inverse. ANSWER: false; multiplicative identity Write a verbal expression for each algebraic expression. 8. h – 7 ANSWER: the difference between h and 7 9. 3x 2 ANSWER: the product of 3 and x squared 3 10. 5 + 6m ANSWER: five more than the product of six and m cubed Write an algebraic expression for each verbal expression. 11. a number increased by 9 eSolutions Manual - Powered by Cognero ANSWER: x +9 Page 1 3 10. 5 + 6m ANSWER: Study Guide and Review -Chapter 1 five more than the product of six and m cubed Write an algebraic expression for each verbal expression. 11. a number increased by 9 ANSWER: x +9 12. two thirds of a number d to the third power ANSWER: 13. 5 less than four times a number ANSWER: 4x – 5 Evaluate each expression. 5 14. 2 ANSWER: 32 3 15. 6 ANSWER: 216 4 16. 4 ANSWER: 256 17. BOWLING Fantastic Pins Bowling Alley charges $2.50 for shoe rental plus $3.25 for each game. Write an expression representing the cost to rent shoes and bowl g games. ANSWER: 2.50 + 3.25g Evaluate each expression. 18. 24 – 4 ∙ 5 ANSWER: 4 2 19. 15 + 3 – 6 ANSWER: 18 20. 7 + 2(9 – 3) ANSWER: eSolutions 19 Manual - Powered by Cognero 21. 8 ∙ 4 – 6 ∙ 5 Page 2 2 19. 15 + 3 – 6 ANSWER: Study Guide and Review -Chapter 1 18 20. 7 + 2(9 – 3) ANSWER: 19 21. 8 ∙ 4 – 6 ∙ 5 ANSWER: 2 5 22. [(2 – 5) ÷ 9]11 ANSWER: 33 23. ANSWER: 3 Evaluate each expression if a = 4, b = 3, and c = 9. 24. c + 3a ANSWER: 21 2 25. 5b ÷ c ANSWER: 5 2 26. (a + 2bc) ÷ 7 ANSWER: 10 27. ICE CREAM The cost of a one-scoop sundae is $2.75, and the cost of a two-scoop sundae is $4.25. Write and evaluate an expression to find the total cost of 3 one-scoop sundaes and 2 two-scoop sundaes. ANSWER: 2.75(3) + 4.25(2); $16.75 Evaluate each expression using properties of numbers. Name the property used in each step. 28. 18 ∙ 3(1 ÷ 3) ANSWER: 18 ∙ 3(1 ÷ 3) = 18 ∙ (3) Substitution Multiplicative Inverse = 18 Multiplicative Identity eSolutions Manual - Powered by Cognero = 18 ∙ 1 Page 3 27. ICE CREAM The cost of a one-scoop sundae is $2.75, and the cost of a two-scoop sundae is $4.25. Write and evaluate an expression to find the total cost of 3 one-scoop sundaes and 2 two-scoop sundaes. ANSWER: Study Guide and Review -Chapter 1 2.75(3) + 4.25(2); $16.75 Evaluate each expression using properties of numbers. Name the property used in each step. 28. 18 ∙ 3(1 ÷ 3) ANSWER: 18 ∙ 3(1 ÷ 3) Substitution = 18 ∙ (3) Multiplicative Inverse Multiplicative Identity = 18 ∙ 1 = 18 29. ANSWER: Substitution Substitution Multiplicative Inverse 2 30. (16 – 4 ) + 9 ANSWER: 2 (16 – 4 ) + 9 = 16 – 16 + 9 =0 +9 =9 Substitution Additive Inverse Additive Identity 31. ANSWER: Substitution Substitution Multiplicative Inverse Multiplicative Identity Substitution 32. 18 + 41 + 32 + 9 ANSWER: 18 + 41 + 32 + 9 = 18 + 32 + 41 + 9 eSolutions Manual - Powered by Cognero Commutative (+) Page 4 Substitution Multiplicative Inverse Multiplicative Identity Substitution Study Guide and Review -Chapter 1 32. 18 + 41 + 32 + 9 ANSWER: 18 + 41 + 32 + 9 = 18 + 32 + 41 + 9 = (18 + 32) + (41 + 9) = 50 + 50 = 100 Commutative (+) Associative (+) Substitution Substitution 33. ANSWER: Commutative (+) Associative (+) Substitution Substitution 34. 8 ∙ 0.5 ∙ 5 ANSWER: 8 ∙ 0.5 ∙ 5 = 8 ∙ 5 ∙ 0.5 = (8 ∙ 5) ∙ 0.5 = 40 ∙ 0.5 = 20 Commutative (×) Associative (×) Substitution Substitution 35. 5.3 + 2.8 + 3.7 + 6.2 ANSWER: Commutative (+) Associative (+) Substitution Substitution 36. SCHOOL SUPPLIES Monica needs to purchase a binder, a textbook, a calculator, and a workbook for her algebra class. The binder costs $9.25, the textbook $32.50, the calculator $18.75, and the workbook $15.00. Find the total cost for Monica’s algebra supplies. ANSWER: $75.50 eSolutions Manual - Powered by Cognero Use the Distributive Property to rewrite each expression. Then evaluate. 37. (2 + 3)6 Page 5 Commutative (+) Associative (+) Substitution Study Guide and Review -Chapter 1 Substitution 36. SCHOOL SUPPLIES Monica needs to purchase a binder, a textbook, a calculator, and a workbook for her algebra class. The binder costs $9.25, the textbook $32.50, the calculator $18.75, and the workbook $15.00. Find the total cost for Monica’s algebra supplies. ANSWER: $75.50 Use the Distributive Property to rewrite each expression. Then evaluate. 37. (2 + 3)6 ANSWER: 2(6) + 3(6); 30 38. 5(18 + 12) ANSWER: 5(18) + 5(12); 150 39. 8(6 – 2) ANSWER: 8(6) – 8(2); 32 40. (11 – 4)3 ANSWER: 11(3) – 4(3); 21 41. –2(5 – 3) ANSWER: –2(5) – (–2)(3); –4 42. (8 – 3)4 ANSWER: 8(4) – 3(4); 20 Rewrite each expression using the Distributive Property. Then simplify. 43. 3(x + 2) ANSWER: 3(x) + 3(2); 3x + 6 44. (m + 8)4 ANSWER: m(4) + 8(4); 4m + 32 45. 6(d − 3) ANSWER: 6(d) – 6(3); 6d – 18 eSolutions 46. –4(5Manual – 2t) - Powered by Cognero ANSWER: Page 6 45. 6(d − 3) ANSWER: Study Guide and Review -Chapter 1 6(d) – 6(3); 6d – 18 46. –4(5 – 2t) ANSWER: –4(5) – (–4)(2t); –20 + 8t 47. (9y – 6)(–3) ANSWER: (9y)(–3) – (6)(–3); –27y + 18 48. –6(4z + 3) ANSWER: –6(4z) + (–6)(3); –24z – 18 49. TUTORING Write and evaluate an expression for the number of tutoring lessons Mrs. Green gives in 4 weeks. ANSWER: 4(3 + 5 + 4); 48 Find the solution set of each equation if the replacement sets are x: {1, 3, 5, 7, 9} and y: {6, 8, 10, 12, 14} 50. y – 9 = 3 ANSWER: {12} 51. 14 + x = 21 ANSWER: {7} 52. 4y = 32 ANSWER: {8} 53. 3x – 11 = 16 ANSWER: {9} 54. ANSWER: {6} eSolutions Manual - Powered by Cognero 55. 2(x – 1) = 8 ANSWER: Page 7 53. 3x – 11 = 16 ANSWER: Study Guide and Review -Chapter 1 {9} 54. ANSWER: {6} 55. 2(x – 1) = 8 ANSWER: {5} Solve each equation. 56. a = 24 – 7(3) ANSWER: 3 2 57. z = 63 ÷ (3 – 2) ANSWER: 9 58. AGE Shandra’s age is four more than three times Sherita’s age. Write an equation for Shandra’s age. Then solve the equation if Sherita’s is 3 years old. ANSWER: 3K + 4 = E; 13 Express each relation as a table, a graph, and a mapping. Then determine the domain and range. 59. {(1, 3), (2, 4), (3, 5), (4, 6)} ANSWER: D = {1, 2, 3, 4} R = {3, 4, 5, 6} 60. {(–1, 1), (0, –2), (3, 1), (4, –1)} ANSWER: eSolutions Manual - Powered by Cognero Page 8 Study D Guide = {1, 2,and 3, 4}Review R = {3,-Chapter 4, 5, 6} 1 60. {(–1, 1), (0, –2), (3, 1), (4, –1)} ANSWER: D = {–1, 0, 3, 4} R = {–2, –1, 1} 61. {(–2, 4), (–1, 3), (0, 2), (–1, 2)} ANSWER: Express the relation shown in each table, mapping, or graph as a set of ordered pairs. 62. ANSWER: {(5, 3), (3, –1), (1, 2), (–1, 0)} eSolutions Manual - Powered by Cognero Page 9 Study Guide and Review -Chapter 1 Express the relation shown in each table, mapping, or graph as a set of ordered pairs. 62. ANSWER: {(5, 3), (3, –1), (1, 2), (–1, 0)} 63. ANSWER: {(–2, –2), (0, –3), (2, –2), (2, 0), (4, –1)} 64. GARDENING On average, 7 plants grow for every 10 seeds of a certain type planted. Make a table to show the relation between seeds planted and plants growing for 50, 100, 150, and 200 seeds. Then state the domain and range and graph the relation. ANSWER: Determine whether each relation is a function. eSolutions Manual - Powered by Cognero Page 10 Study Guide and Review -Chapter 1 Determine whether each relation is a function. 65. ANSWER: function 66. ANSWER: function 67. {(8, 4), (6, 3), (4, 2), (2, 1), (6, 0)} ANSWER: not a function 2 If f (x) = 2x + 4 and g(x) = x – 3, find each value. 68. f (–3) ANSWER: –2 69. g(2) ANSWER: 1 70. f (0) ANSWER: 4 71. g(–4) ANSWER: 13 72. f (m + 2) ANSWER: 2m + 8 73. g(3p ) eSolutions Manual - Powered by Cognero ANSWER: 2 9p – 3 Page 11 72. f (m + 2) ANSWER: Study Guide and Review -Chapter 1 2m + 8 73. g(3p ) ANSWER: 2 9p – 3 74. GRADES A teacher claims that the relationship between number of hours studied for a test and test score can be described by g(x) = 45 + 9x, where x represents the number of hours studied. Graph this function. ANSWER: 75. Identify the function graphed as linear or nonlinear. Then estimate and interpret the intercepts of the graph, any symmetry, where the function is positive, negative, increasing, and decreasing, the x-coordinate of any relative extrema, and the end behavior of the graph. ANSWER: Nonlinear; the graph intersects the y-axis at about (0, 56), so the y-intercept is about 56. This means that about 56,000 U.S. patents were granted in 1980. The graph has no symmetry. The graph does not intersect the x-axis, so there is no xintercept. This means that in no year were 0 patents granted. The function is positive for all values of x, so the number of patents will always have a positive value. The function is increasing for all values of x. The y-intercept is a relative minimum, so the number of patents granted was at its lowest in 1980. As x increases, y increases. As x decreases, y decreases. eSolutions Manual - Powered by Cognero Page 12