Name: Class: Date: ID: A Review for Final Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Give two ways to write the algebraic expression z 28 in words. a. the quotient of 28 and z 28 divided by z c. the quotient of z and 28 z divided by 28 b. z subtracted from 28 z less than 28 d. the product of z and 28 z times 28 2. Ramona s class has collected 98 cans in a food drive. They plan to sort the cans into y bags, with an equal number of cans in each bag. Write an expression to show how many cans there will be in each bag. a. 98 y c. 98y b. 98 + y d. 98 y 3. Julia has saved 34 sand dollars and wants to give them away equally to x friends. Write an expression to show how many sand dollars each of Julia s friends will receive. Then, find the total number of sand dollars each of Julia s friends will get if Julia gives them to 2 friends. a. 34x; 17 sand dollars c. 34 x; 32 sand dollars 34 b. ; 17 sand dollars d. 34 + x; 32 sand dollars x 4. Evaluate the expression 2a + b for a = 9 and b = 6. a. 24 c. 30 b. 21 d. 17 5. The highest temperature recorded in the town of Westgate this summer was 90ºF. Last winter, the lowest temperature recorded was 1ºF. Find the difference between these extremes. a. 91ºF c. 89ºF b. 89ºF d. 91ºF 6. Simplify 3 3. a. 0 c. 27 b. 9 d. 27 7. Write 9 as a power of the base 3. 9 a. c. 3 9 3 b. 3 2 d. 2 3 8. The area of a square garden is 202 square meters. Estimate the side length of the garden. a. 12 m c. 14 m b. 17 m d. 16 m 81 9. Write all classifications that apply to the real number. 4 a. rational number, terminating decimal, integer, whole number, natural number b. rational number, terminating decimal c. irrational number, integer d. irrational number 1
10. Give two ways to write the algebraic expression 30t in words. a. t more than 30 t added to 30 c. 30 groups of t 30 times t b. t subtracted from 30 t less than 30 d. the quotient of 30 and t 30 divided by t 11. Simplify 4 3 + 8 4 ( 1 5). a. 60 c. 22 b. 70 d. 12 12. Simplify the expression 8 + 2 2 4 + 13 19. a. 31 c. 12 b. 3 d. 9 13. Simplify by combining like terms. 8t 3 + 9y + 7t 3 2y t 2 a. t 3 + 11y t 2 c. 15t 3 + 7y t 2 b. 56t 3 18y t 2 d. 14t 3 + 7y 14. Name the quadrant where the point ( 2, 1) is located. a. Quadrant I c. Quadrant IV b. Quadrant III d. Quadrant II 15. Solve 45b + 27 43b = 35. a. b = 4 c. b = 2 b. b = 2 d. b = 4 16. Taylor needs to take a taxi to get to the movies. The taxi charges $2.50 for the first mile, and then $1.50 for each mile after that. If the total charge is $8.50, then how far was Taylor s taxi ride to the movie? a. 4 miles c. 5 miles b. 3.4 miles d. 5.7 miles 2
17. Create a table of ordered pairs for the function y = 2x 2 2 using the values x = 2, 1, 0, 1, and 2. Graph the ordered pairs and describe the shape of the graph. x y (x, y) 2 9 ( 2, 9) a. 1 2 ( 1, 2) 0 1 (0, 1) 1 0 (1, 0) 2 7 (2, 7) The points form an S shape. x y (x, y) 2 5 ( 2, 5) b. 1 3 ( 1, 3) 0 1 (0, 1) 1 1 (1, 1) 2 3 (2, 3) The points form a straight line. x y (x, y) 2 3 ( 2, 3) c. 1 1 ( 1, 1) 0 1 (0, 1) 1 1 (1, 1) 2 3 (2, 3) The points form a V shape. x y (x, y) 2 6 ( 2, 6) d. 1 0 ( 1, 0) 0 2 (0, 2) 1 0 (1, 0) 2 6 (2, 6) The points form a U shape. 3
18. A startup software company s total investment for the first two years is $26,394. Write and solve an equation to find the investment for the second year if the first year s investment is $13,205. a. 13,205 + x = 26,394 The investment for the second year is $13,197. b. 13,205 + x = 26,394 The investment for the second year is $13,189. c. 13,205 + x = 26,394 The investment for the second year is $39,599. d. 13,205 + x = 26,394 The investment for the second year is $26,394. 19. Solve 46q 34 = 51q 99. a. q = 65 c. q = 13 b. q = 13 d. q = 65 20. Solve c + 7 2c = 2 3c. a. c = 2 1 2 c. c = 2 1 4 b. c = 1 1 4 d. c = 4 1 2 21. Solve 8g + 3 + 3g = 10 5g 7. Tell whether the equation has infinitely many solutions or no solutions. a. Only one solution c. Infinitely many solutions b. Two solutions d. No solutions 22. Solve 4x z = y for x. a. x = y z 4 c. x = y + z 4 b. x = y 4 + z d. x = y + z 4 23. Ramon drives his car 150 miles in 3 hours. Find the unit rate. a. Ramon drives 50 miles per hour. b. Ramon drives 1 mile per 50 hours. c. Ramon drives 30 miles per hour. d. Ramon drives 150 miles per 3 hours. 24. The local school sponsored a mini-marathon and supplied 84 gallons of water per hour for the runners. What is the amount of water in quarts per hour? a. 21 qt/h c. 336 qt/h b. 672 qt/h d. 168 qt/h 25. Solve the proportion 1 6 = x 24. a. x = 4 c. x = 5 b. x = 0.01 d. x = 144 26. An architect built a scale model of a shopping mall. On the model, a circular fountain is 54 inches tall and 49.5 inches in diameter. If the actual fountain is to be 12 feet tall, what is its diameter? a. 11 ft c. 13.1 ft b. 12 ft d. 7.5 ft 4
27. Find the value of MN if AB = 9 cm, BC = 7.2 cm, and LM = 12 cm. ABCD LMNO a. 9.6 cm c. 5.4 cm b. 10 cm d. 10.2 cm 28. Find 65% of 105. a. 161.54 c. 6825 b. 67.65 d. 68.25 29. 86 is 11% of what number? If necessary, round your answer to the nearest hundredth. a. 7.82 c. 9.46 b. 0.13 d. 781.82 30. According to the United States Census Bureau, the United States population was projected to be 293,655,404 people on July 1, 2004. The two most populous states were California, with a population of 35,893,799, and Texas, with a population of 22,490,022. About what percent of the United States population lived in California or Texas? Round your answer to the nearest percent. a. 8% c. 20% b. 12% d. 37% 31. Adam works part time as a salesperson for an electronics store. He earns $7.75 per hour plus a percent commission on all of his sales. Last week Adam worked 19 hours and earned a gross income of $354.25. Find Adam s percent commission if his total sales for the week were $3,600. If necessary, round your answer to the nearest hundredth of a percent. a. 0.06% c. 5.75% b. 7.25% d. 1.04% 32. Felix is a waiter. He waits on a table of 4 whose bill comes to $100.17. If Felix receives a 15% tip, approximately how much will he receive? a. $15.00 c. $14.55 b. $115.00 d. $5.00 33. Find the result when 105 is decreased by 80%. a. 189 c. 84 b. 21 d. 25 34. Describe the solutions of 6 + m > 2 in words. a. The value of m is a number less than 8. b. The value of m is a number greater than or equal to 7. c. The value of m is a number equal to 7 d. The value of m is a number greater than 8. 5
35. Solve the inequality t 7 < 1.5 and graph the solutions. a. t < 8.5 b. t < 8.5 c. t < 5.5 d. t < 5.5 36. Solve the inequality w 2 2 and graph the solutions. a. w 4 b. w 4 c. w 4 d. w 4 37. Mrs. Williams is deciding between two field trips for her class. The Science Center charges $75 plus $6 per student. The Dino Discovery Museum simply charges $9 per student. For how many students will the Science Center charge less than the Dino Discovery Museum? a. 72 or fewer students c. More than 25 students b. Fewer than 25 students d. 72 or more students 38. Solve 1.5 1.25x 0.5 0.75x. a. 4 x c. x 8 b. x 0.09 d. x 4 6
39. Solve the inequality w + 3 > 4 and graph the solutions. a. w < 7 b. w > 1 c. w > 7 d. w < 1 40. Solve the inequality and graph the solution. 3x + 2.5x 1.5(x + 4) a. x 3 b. x 3 c. x 3 d. x 3 41. Write the compound inequality shown by the graph. a. x 5 AND x > 3 c. x 5 OR x > 3 b. x 3 AND x > 5 d. x < 5 OR x > 3 7
42. Give the domain and range of the relation. x y 4 9 10 21 0 0 1 1 a. D: { 1, 0, 4, 10}; R: { 1, 0, 9, 21} c. D: { 1, 0, 9, 21}; R: { 1, 0, 4, 10} b. D: { 1, 4, 10}; R: { 1, 9, 21} d. D: {4, 10, 1, 9, 21, 1}; R: {0} 43. Solve and graph the solutions of the compound inequality 1 < 3x 2 10. a. 1 < x AND x < 4 b. 1 x AND x 4 c. 1 < x AND x 4 d. 1 > x AND x 4 44. Solve and graph the compound inequality. s + 2 < 4 OR 3 + s 6.5 a. s < 2 OR s < 9.5 b. s < 2 OR s 9.5 c. s < 2 OR s < 9.5 d. s < 2 OR s 9.5 8
45. Give the domain and range of the relation. a. D: 0 x 7; R: 1 y 7 c. D: 2 x 6; R: 4 y 7 b. D: 1 x 6; R: 1 y 7 d. D: 1 x 7; R: 1 y 6 46. Determine a relationship between the x- and y-values. Write an equation. x 1 2 3 4 y 6 7 8 9 a. y = x + 5 c. y = x + 4 b. y = 5x + 1 d. y = x + 5 47. Give the domain and range of the relation. Tell whether the relation is a function. x y 0 4 0 0 1 1 2 4 a. D: { 4, 0, 1, 4}; R: {0, 1, 2} The relation is not a function. b. D: {0, 1, 2}; R: { 4, 0, 1, 4} The relation is not a function. c. D: {0, 1, 2}; R: { 4, 0, 1, 4} The relation is a function. d. D: { 4, 0, 1, 4}; R: {0, 1, 2} The relation is a function. 48. Identify the independent and dependent variables in the situation. As Kyoko works more hours, her total pay increases. a. Independent: hours worked; Dependent: total pay b. Independent: total pay; Dependent: hours worked 49. A video club costs $25 to join. Each video that is rented costs $2.50. Let v represent the number of videos. Identify the independent and dependent variables. Then, write a rule in function notation for the situation. a. Independent: total cost; Dependent: videos rented; f(v) = 25v 2.5 b. Independent: videos rented; Dependent: total cost; f(v) = 2.5v 25 c. Independent: videos rented; Dependent: total cost; f(v) = 2.5v + 25 d. Independent: videos rented; Dependent: total cost; f(v) = 25v + 2.5 9
50. Which situation is best represented by the graph? a. A swimmer starts at a steady pace, slows down to a stop, and then starts up swimming again, but at a slower pace than when she first started. b. After a ball is thrown into the air, it falls back to the ground and bounces. c. An airplane starts slowly on the runway, and then quickly takes off before finding a nice cruising speed. d. A car starts on flat ground and drives quickly up a hill, and then it keeps driving. 51. Which situation best describes a positive correlation? a. The amount of gasoline in a car and how far the car has traveled b. The temperature on Tuesdays c. The size of a sundae and the amount of calories it contains d. The size of a snowball and how long it has been melting 52. Determine whether the sequence appears to be an arithmetic sequence. If so, find the common difference and the next three terms in the sequence. 5, 11, 16, 20, 27,... a. Yes; common difference 7; next three terms are 34, 41, 48 b. Yes; common difference 5; next three terms are 32, 37, 42 c. Not an arithmetic sequence d. Yes; common difference 6; next three terms are 21, 15, 9 53. Find the 20th term in the arithmetic sequence 9, 8, 7, 6, 5,... a. 11 c. 19 b. 29 d. 10 10
54. Temperature changes throughout the hours of a day. Early in the morning, temperature increases slowly. At noon, the temperature rises sharply. During the afternoon, the temperature stays the same for several hours. As night falls, the temperature decreases slightly. Choose the graph that best represents this situation. a. c. b. d. 11
55. Graph the function y = x 2 2. a. c. b. d. 56. Write an equation in slope-intercept form for the line that passes through (7, 7) and (2, 4). a. y = 5 x + 14 c. y = 3 x + 5 3 5 5 14 b. y = 3 x + 14 d. y = 3 x + 14 5 5 5 5 57. Write an equation in slope-intercept form of the line with slope 7 that contains the point (3, 4). a. y = 7x 4 c. y = 7x + 3 b. y = 7x 21 d. y = 7x 25 12
58. Lionel observes that traffic is getting worse and it s taking him longer to get to work. He records once a week the following data for several weeks. Graph a scatter plot using the given data. Week 1 2 3 4 5 6 7 8 Time 8.3 9.1 8.9 9.7 10.5 9.3 9.1 10.9 (min) a. c. b. d. 59. Identify the lines that are perpendicular: y = 2; y = 1 x + 3; x = 2; y + 3 = 5 x + 2 5 a. y = 2 and x = 2 are perpendicular. b. None of the lines are perpendicular. c. y = 1 5 x + 3 and y + 3 = 5 ( x + 2) are perpendicular. d. y = 2 and x = 2 are perpendicular; y = 1 5 perpendicular. x + 3 and y + 3 = 5 ( x + 2 ) are 13
60. Describe the correlation illustrated by the scatter plot. a. positive correlation c. cannot determine b. negative correlation d. no correlation 61. Sylvie is going on vacation. She has already driven 48 miles in one hour. Her average speed for the rest of the trip is 59 miles per hour. How far will Sylvie have driven 6 hours later? a. 343 miles c. 402 miles b. 288 miles d. 354 miles 62. Tell whether the set of ordered pairs {(1, 5), (2, 7), (3, 6), (4, 9)} satisfies a linear function. Explain. a. No; there is a constant change in x that corresponds to a constant change in y. b. Yes; there is no constant change in x that corresponds to a constant change in y. c. No; there is no constant change in x that corresponds to a constant change in y. d. Yes; there is a constant change in x that corresponds to a constant change in y. 63. Find the x- and y-intercepts. a. x-intercept: 2, y-intercept: 5 c. x-intercept: 2, y-intercept: 5 b. x-intercept: 5, y-intercept: 2 d. x-intercept: 2, y-intercept: 5 14
64. Find the x- and y-intercepts of 2x 2y = 6. a. x-intercept: 2, y-intercept: 3 c. x-intercept: 3, y-intercept: 1 2 b. x-intercept: 2, y-intercept: 1 2 d. x-intercept: 3, y-intercept: 3 65. Use intercepts to graph the line described by the equation 2x + 2y = 16. a. x-intercept: 13 21, y-intercept: c. x-intercept: 13, y-intercept: 8 2 2 2 b. x-intercept: 8, y-intercept: 21 2 d. x-intercept: 8, y-intercept: 8 66. Find the slope of the line that contains (3, 1) and (2, 7). a. 8 5 c. 1 6 b. 6 d. 67. Find the slope of the line described by 3x + 2y = 6. a. 2 3 c. b. 3 2 d. 2 3 5 8 3 2 15
68. Find the slope of the line. a. 3 5 c. 2 5 b. 5 3 d. 5 3 69. Tell whether the equation 5x + y = 4 represents a direct variation. If so, identify the constant of variation. a. Not a direct variation. c. Direct variation, k = 4 b. Direct variation; k = 5 d. Direct variation, k = 1 5 70. Tell whether the relation is a direct variation. Explain. x 8 6 4 y 72 54 36 a. This is a direct variation, because it can be written as y = 1 9 x, where k = 1 9. b. This is not a direct variation, because it cannot be written in the form y = kx. c. This is a direct variation, because it can be written as xy = 9, where k = 0. d. This is a direct variation, because it can be written as y = 9x, where k = 9. 71. Write the equation that describes the line with slope = 1 and y-intercept = 1 in slope-intercept form. a. y = x 1 c. y = x + 1 b. x + y = 1 d. x = y 1 72. Write the equation that describes the line in slope-intercept form. slope = 3, point (1, 4) is on the line a. y = 3x + 7 c. y = 3x 7 b. y = 3x + 4 d. y = 3x + 1 16
73. The cost to fill a car s tank with gas and get a car wash is a linear function of the capacity of the tank. The costs of a fill-up and a car wash for three different customers are shown in the table. Write an equation for the function in slope-intercept form. Then, find the cost of a fill-up and a car wash for a customer with a truck whose tank size is 22 gallons. Tank size (gal) (x) Total cost ($) f(x) 10 24.75 16 37.35 17 39.45 a. f(x) = 2.00x + 4.00; Cost for truck = $48.00 b. f(x) = 2.10x + 3.75; Cost for truck = $49.95 c. f(x) = 1.90x + 3.25; Cost for truck = $45.05 d. f(x) = 0.48x + 1.79; Cost for truck = $12.35 74. At a summer camp there is one counselor for every 8 campers. Write a direct variation equation for the number of campers, y, that there are for x counselors. Then graph. a. y = 8x + 8 c. y = 8x b. y = 8x d. y = x 8 17
75. Graph the line with the slope 3 and y-intercept 1. 2 a. c. b. d. 76. The equations of four lines are given. Identify which lines are parallel. Line 1: y = 5x 7 Line 2: y + 6 = 1 (x 2) 5 Line 3: y = 2x 3 Line 4: x 1 2 y = 3 a. Lines 2 and 3 are parallel. c. Lines 3 and 4 are parallel. b. Lines 1 and 3 are parallel. d. All four lines are parallel. 77. Write an equation in slope-intercept form for the line parallel to y = 2x 9 that passes through the point (1, 9). a. y = 2x 7 c. y = 1 2 x 9 b. y = 1 2 x 19 2 d. y = 2x 3 18
78. Write the equation x + 3y = 12 in slope-intercept form. Then graph the line described by the equation. a. y = 1 3 x 4 c. y = 1 3 x 4 b. y = 1 3 x 4 d. y = 1 3 x 4 79. Write an equation in point-slope form for the line that has a slope of 7 and contains the point (1, 2). a. y + 2 = 7(x 1) c. y 2 = 7(x + 1) b. y + 1 = 7(x 2) d. x 1 = 7(y + 2) Numeric Response 80. A car rental company increases daily rental fees 15% in the summer to cover increased fuel costs. They then have a 25% off promotion for the fall. If a car rented for $36.00 per day before the summer, what would the per-day rental cost be during the fall promotion? 19
Review for Final Answer Section MULTIPLE CHOICE 1. ANS: C The operation means divided by or quotient. z 28: the quotient of z and 28 z divided by 28 PTS: 1 2. ANS: D y represents the number of bags. Think: How many groups of 98 are in y? 98 y PTS: 1 3. ANS: B The expression 34 x Evaluate 34 x 34 2 = 17 for x = 2. models the number of sand dollars each of Julia s friends will receive. If Julia gives 34 sand dollars to 2 friends, each friend will get 17 sand dollars. PTS: 1 4. ANS: A Substitute 9 for a and 6 for b. 2a + b = 2(9) + 6 Simplify. Remember: 2a means 2 times a. 2(9) + 6 = 24 PTS: 1 5. ANS: A Subtract the negative temperature from the positive temperature to calculate the difference in the two readings. PTS: 1 1
6. ANS: D The exponent tells the number of times to multiply the base number by itself. The negative sign in front of the expression multiplies the expression by 1. Multiply 3 by itself 3 times, and then multiply your answer by 1. PTS: 1 7. ANS: B The number given as a base should be multiplied by itself a certain number of times in order to represent the value of the whole number given. The product of two 3 s is 9. PTS: 1 8. ANS: C 202 is between 196 and 225. Since 202 is closer to 196, the best estimate for the side length is 14 m. PTS: 1 9. ANS: B A rational number can be written as a fraction. Rational numbers include integers, fractions, terminating decimals, and repeating decimals. An irrational number cannot be expressed as either a terminating decimal or repeating decimal. PTS: 1 10. ANS: C The operation means times, multiplied by, product, or each groups of. 30t: 30 groups of t 30 times t PTS: 1 11. ANS: B Use the order of operations: 1. Perform operations in parentheses. 2. Evaluate powers. 3. Multiply or divide from left to right. 4. Add or subtract from left to right. PTS: 1 STA: 9.1.4 12. ANS: D First, simplify the numerator of the fraction, and then divide the numerator by the denominator. Next, subtract the terms in the absolute value, and then find the absolute value. 8 + 4 + 6 = 12 4 4 + 6 Finally, add the two terms. 3 + 6 = 9 PTS: 1 STA: 9.1.4 2
13. ANS: C 8t 3 + 9y + 7t 3 2y t 2 (8t 3 + 7t 3 ) + (9y 2y) t 2 Group like terms. 15t 3 + 7y t 2 Add or subtract the coefficients. PTS: 1 STA: 9.4.11 14. ANS: B If both x and y are positive, the point is in Quadrant I. If x is negative and y is positive, the point is in Quadrant II. If both x and y are negative, the point is in Quadrant III. If x is positive and y is negative, the point is in Quadrant IV. PTS: 1 STA: 9.4.3 15. ANS: A 45b + 27 43b = 35 45b 43b + 27 = 35 Use the Commutative Property of Addition. 2b + 27 = 35 Combine like terms. 27 27 Since 27 is added to 2b, subtract 27 from both sides to undo the addition. 2b = 8 2b 2 = 8 Since b is multiplied by 2, divide both sides by 2 to undo the 2 multiplication. b = 4 PTS: 1 STA: 9.4.4 3
16. ANS: C Let d be the distance (in miles) to the movies, then d 1 is the number of miles after the first mile. So a formula for the total charge could be first mile + (d 1) rate after first = total charge charge mile 2.50 + (d 1) 1.50 = 8.50 Subtract 2.50 from each side. (d 1) 1.50 = 8.50 2.50 (d 1) 1.50 = 6 Divide both sides by 1.50. (d 1) = 6 1.50 (d 1) = 4 Add 1 to both sides. d = 4 + 1 d = 5 PTS: 1 STA: 9.4.3 17. ANS: D Make a table to find values of (x, y) for y = 2x 2 2. x y (x, y) 2 2( 2) 2 2 = 6 ( 2, 6) 1 2( 1) 2 2 = 0 ( 1, 0) 0 2(0) 2 2 = 2 (0, 2) 1 2(1) 2 2 = 0 (1, 0) 2 2(2) 2 2 = 6 (2, 6) The points form a U shape. PTS: 1 STA: 9.4.2 4
18. ANS: B First year investment Ê ËÁ $ ˆ Added to Second year investment Ê ËÁ $ ˆ is 26,394 b + x = 26,394 b + x = 26,394 13,205 + x = 26,394 13,205 13,205 x = 13,189 Write an equation to represent the relationship. Substitute 13,205 for b. Since 13,205 is added to x, subtract 13,205 from both sides to undo the addition. The investment for the second year is $13,189. PTS: 1 STA: 9.4.2 19. ANS: C 46q 34 = 51q 99 46q 46q To collect the variable terms on one side, subtract 46q from both sides. 34 = 5q 99 Since 99 is subtracted from 5q, add 99 to both sides to undo the subtraction. +99 +99 65 = 5q 65 5 = 5q 5 13 = q Since q is multiplied by 5, divide both sides by 5 to undo the multiplication. PTS: 1 STA: 9.4.4 20. ANS: A c + 7 2c = 2 3c (c 2c) + 7 = 2 3c Combine like terms. Add to undo the subtraction. Or subtract to undo the addition. c + 7 = 2 3c Then, divide to undo the multiplication. c = 2 1 2 PTS: 1 STA: 9.4.4 21. ANS: C Combine like terms on each side of the equation before collecting variable terms on one side. If you get an equation that is always true, the original equation is an identity, and it has infinitely many solutions. If you get a false equation, the original equation is a contradiction, and it has no solutions. PTS: 1 STA: 9.4.5 5
22. ANS: D 4x z = y 4x 4 x +z +z = y + z 4 = y + z 4 Add z to both sides. Divide both sides by 4. PTS: 1 STA: 9.4.3 23. ANS: A 150 miles 3 hours 50 miles 1 hour = = x x 1 hour 50 miles The unit rate is. 1 hour Ramon drives 50 miles per hour. Write a proportion to find an equivalent ratio with a second quantity of 1. Divide on the left side to find x. PTS: 1 STA: 9.2.1 24. ANS: C 84 gal 4 qt To convert the first quantity in a rate, multiply by a 1 hr 1 gal conversion factor with that unit in the first quantity. 336 quarts per hour PTS: 1 STA: 9.2.5 25. ANS: A 1 6 = x 24 1 ( 24) = 6 ( x) Use cross products. 1 ( 24) = 6 ( x) Divide both sides by 6. 6 6 4 = x PTS: 1 STA: 9.2.4 6
26. ANS: A model height actual height 54 in. 49.5 in. = 12 ft x x(54) = 12(49.5) x = 11 54 in. 12 ft Write the scale as a fraction. Let x be the actual diameter. Use cross products to solve. PTS: 1 STA: 9.3.2 27. ANS: A A corresponds to L, B corresponds to M, C corresponds to N, and D corresponds to O. 9 12 = 7.2 AB x LM = BC MN 9 ( x) = 12 ( 7.2) Use cross products. 9 ( x) 12 = ( 7.2 ) Since x is multiplied by 9, divide both sides by 9 to undo the 9 9 multiplication. x = 9.6 MN is 9.6 cm. PTS: 1 STA: 9.3.2 28. ANS: D Method 1 Use a proportion. part whole = percent Use the percent proportion. 100 x 105 = 65 Let x represent the part. 100 100x = 105 ( 65) Find the cross products. 100x 105 = ( 65 ) Since x is multiplied by 100, divide both sides by 100 to 100 100 undo the multiplication. x = 68.25 65% of 105 is 68.25. Method 2 Use an equation. x = 65% of 105 Write an equation. Let x represent the part. x = 0.65 ( 105) Write the percent as a decimal and multiply. x = 68.25 65% of 105 is 68.25. PTS: 1 STA: 9.1.4 7
29. ANS: D Method 1 Use a proportion. part whole = percent 100 86 x = 11 100 11x = 86(100) 11x 11 = 86(100) 11 x = 781.82 Use the percent proportion. Let x represent the whole. Find the cross products. Since x is multiplied by 11, divide both sides by 11 to undo the multiplication. 11% of 86 is 781.82. Method 2 Use an equation. 86 = 11 of x Write an equation. Let x represent the whole. 86 = 0.11x Write the percent as a decimal. 86 0.11 = 0.11x Since x is multiplied by 0.11, divide both sides by 0.11 to 0.11 undo the multiplication. 781.82 = x 11% of 86 is 781.82. PTS: 1 STA: 9.1.4 30. ANS: C total in Texas + total in California total population = 22,490,022 + 35,893,799 293, 655, 404 0.198 20% PTS: 1 STA: 9.1.4 8
31. ANS: C Write the formula for gross income. gross income = (income number of hours) + commission Write the formula for commission. gross income = (income number of hours) + % of total sales 354.25 = (7.75 19) + x of 3,600 Substitute value given in the problem. Let x represent the percent commission. 354.25 = ( 147.25) + x(3,600) Multiply 354.25 ( 147.25) = x(3,600) Subtract. (354.25 147.25) = x(3,600) Since x is multiplied by 3,600, divide both sides by 3,600 3,600 3,600 to undo the multiplication. 0.0575 = x The answer is a decimal. 5.75% = x Write the decimal as a percent. Adam s percent commission is 5.75%. PTS: 1 STA: 9.1.4 32. ANS: A Round $100.17 to $100.00. 15% = 10% + 5% 10% of $100 = $10.00 5% of $100 = $5.00 $10.00 + $5.00 = $15.00 PTS: 1 STA: 9.1.4 33. ANS: B To find the amount of decrease, multiply 105 by 0.8. Then, subtract the decrease from 105 to find the result of the decrease. PTS: 1 STA: 9.1.4 34. ANS: D Test values of m that are positive, negative, and 0. When the value of m is a number greater than 8, the value of 6 + m is less than 2. When the value of m is 8, the value of 6 + m is equal to 2. When the value of m is a number less than 8, the value of 6 + m is greater than 2. It appears that the solutions of 6 + m > 2 are numbers greater than 8. PTS: 1 STA: 9.4.6 9
35. ANS: D t 7 < 1.5 + 7 + 7 Add 7 on both sides to isolate t. t < 5.5 Use a solid circle when the value is included in the graph, such as with or. Use an empty circle when the value is not included, such as with > or <. PTS: 1 STA: 9.4.4 36. ANS: D w 2 2 ( 2) w 2 2( 2) Multiply both sides by 2 to isolate w. When you multiply by a negative number, reverse the inequality symbol. w 4 Use a solid circle when the value is included in the graph, such as with or. Use an empty circle when the value is not included, such as with > or <. PTS: 1 STA: 9.4.6 37. ANS: C Science Center fee plus $6 per student is less than $12 per student $75 + $6 + s < $9 + s 75 + 6s < 9s 6s 6s 75 < 3s 75 < 3s 3 3 25 < s If 25 < s, then s > 25. The Science Center charges less if there are more than 25 students. PTS: 1 STA: 9.4.6 10
38. ANS: A 1.5 1.25x 0.5 0.75x 1.5 0.5 0.75x + 1.25x Combine like terms. 2 0.5x Simplify. 4 x Divide both sides by 0.5. PTS: 1 STA: 9.4.6 39. ANS: D Use inverse operations to undo the operations in the inequality one at a time. w + 3 > 4 w < 1 Use a solid circle when the value is included in the graph, such as with or. Use an empty circle when the value is not included, such as with > or <. PTS: 1 STA: 9.4.6 40. ANS: B On the left side, combine the two terms. On the right side, distribute 1.5. 3x + 2.5x 1.5(x + 4) 0.5x 1.5x + 6 Subtract the 1.5x from both sides of the inequality. 2x 6 Divide both sides of the inequality by 2. Reverse the inequality symbol. x 3 PTS: 1 STA: 9.4.6 41. ANS: C x 5 OR x > 3 The numbers to the left of 5 are shaded. A solid circle is used. This part of the inequality uses. The shaded area is not between two numbers so the compound inequality uses OR. The numbers to the right of 3 are shaded. An empty circle is used. This part of the inequality uses >. PTS: 1 STA: 9.4.2 11
42. ANS: A The domain is the set of all x-values. The range is the set of all y-values. PTS: 1 STA: 9.4.1 43. ANS: C 1 < 3x 2 AND 3x 2 10 Write the compound inequality using AND. 3 < 3x 3x 12 Solve each simple inequality. 3 < 3x 3 3 1 < x AND x 4 3x 12 3 3 Divide to undo the multiplication. First, graph the solutions of each simple inequality. Then, graph the intersection by finding where the two graphs overlap. PTS: 1 STA: 9.4.6 44. ANS: D First solve each simple inequality to obtain s < 2 OR s 9.5. The graph of the compound inequality is the union of the graph of s < 2 and the graph of s 9.5. Find the union by combining the two regions. PTS: 1 STA: 9.4.2 45. ANS: B The domain is the set of all x-values. The graph goes from 1 to 6 on the x-axis, so D: 1 x 6. The range is the set of all y-values. The graph goes from 1 to 7 on the y-axis, so R: 1 y 7. PTS: 1 STA: 9.4.1 46. ANS: A The correct equation is y = x + 5. x 1 2 3 4 x + 5 6 7 8 9 PTS: 1 STA: 9.4.1 47. ANS: B A function is a special type of relation that pairs each x-value with exactly one y-value. If the same x-value has more than one y-value, then the relation is not a function. PTS: 1 STA: 9.4.1 48. ANS: A The value of the dependent variable depends on the value of the independent variable. In this situation, the total amount Kyoko is paid depends on the number of hours she works, so hours worked is the independent variable and total pay is the dependent variable. PTS: 1 STA: 9.4.1 12
49. ANS: C The total cost of the membership depends on the number of videos rented, so the total cost is the dependent variable and videos rented is the independent variable. With a membership fee of $25 and each video costing $2.50, the total cost of renting videos as a member of the club is f(v) = 2.5v + 25. PTS: 1 STA: 9.4.2 50. ANS: A The speed starts with a horizontal line, which means the speed is the same at the start. Next, the speed gets slower and slower until it reaches 0, which means the speed decreases until it stops. Then, the speed continues with another horizontal line that lower than the first horizontal line. This means the speed increases and continues at a constant speed, which is slower than the first speed. So the graph could represent the situation where a swimmer starts at a steady pace, slows down to a stop, and then starts up swimming again, but at a slower pace than when she first started. PTS: 1 STA: 9.4.2 51. ANS: C Situation The size of a sundae and the amount of calories it contains The temperature on Tuesdays The amount of gasoline in a car and how far the car has traveled The size of a snowball and how long it has been melting Type of correlation Positive correlation No correlation Negative correlation Negative correlation PTS: 1 STA: 9.5.6 52. ANS: C For a sequence to be an arithmetic sequence, each number subtracted from the one before it should result in a common difference. This is not an arithmetic sequence because the differences between the terms are not all the same. PTS: 1 STA: 9.5.1 13
53. ANS: D Find a specific term from a given sequence by using the equation a n = a 1 + (n 1)d, where: a n = your result a 1 = the initial term of the sequence n = the number in the sequence you want to calculate d = the common difference between the terms n is given in the problem, a 1 is the first term in the sequence, and d is the difference between adjacent terms. PTS: 1 STA: 9.5.1 54. ANS: D Only graph D contains the required features in the correct order. Key phrases Segment should be... Shown in increases slowly slanting upward all graphs rises sharply slanting upward more steeply graphs B, C, and D stays the same horizontal graphs B and D (also in graphs A and C, but out of order) decreases slightly slanting downward graphs A and D PTS: 1 STA: 9.4.2 14
55. ANS: C Step 1: Choose several values of x and generate ordered pairs. x y = x 2 2 y 2 ( 2) 2 2 6 1 ( 1) 2 2 3 0 (0) 2 2 2 1 (1) 2 2 3 2 (2) 2 2 6 Step 2: Plot enough points to see a pattern. Step 3: Draw a curve through all the points to show all the ordered pairs that satisfy the function. PTS: 1 STA: 9.4.10 56. ANS: B Calculate the slope of the line through the two points by using the equation m = y 2 y 1 x 2 x 1. Then substitute that value along with the coordinates of one of the given points into the equation y = mx + b to find b. PTS: 1 STA: 9.4.8 57. ANS: D First, write the equation in point-slope form. y y 1 = m(x x 1 ) y ( 4) = 7[x (3)] Next, solve the equation for y. y + 4 = 7(x 3) y + 4 = 7x 21 y = 7x 25 PTS: 1 STA: 9.4.8 15
58. ANS: B Use the table to make ordered pairs. Plot the ordered pairs to make a scatter plot. PTS: 1 STA: 9.5.2 59. ANS: D y = 2 is horizontal, and x = 2 is vertical. These lines are perpendicular. Check if the product of the slopes of the other two lines is 1. y = 1 x + 3 has slope = 1. y + 3 = 5 ( x + 2 ) has slope = 5. 5 5 Ê 5 1 ˆ 5 ËÁ = 1 The product of the slopes is 1, so these two lines are also perpendicular. PTS: 1 STA: 9.4.8 60. ANS: D A scatter plot with a positive correlation has a slope that rises from left to right. A scatter plot with a negative correlation has a slope that falls from left to right. A scatter plot with no correlation, in general, neither rises nor falls as it moves from left to right. PTS: 1 STA: 9.5.2 61. ANS: C Since you want to find the distance for 6 hours later, you need to find the 7th term of the sequence. So, n = 7. a n = a 1 + (n 1)d Write the rule to find the nth term. a n = 48 + (7 1)(59) Substitute 48 for a 1, 59 for d, and 7 for n. a n = 402 Sylvie will have traveled 402 miles. Simplify. PTS: 1 STA: 9.5.1 62. ANS: C In a linear function, a constant change in x means a constant change in y. x y 1 5 + 1 2 7 2 + 1 3 6 + 1 NOT a constant change in y + 1 4 9 3 PTS: 1 STA: 9.4.3 63. ANS: A The graph intersects the x-axis at ( 2, 0). The x-intercept is 2. The graph intersects the y-axis at (0, 5). The y-intercept is 5. PTS: 1 STA: 9.4.4 16
64. ANS: D To find the x-intercept, replace y with 0 and solve for x; to find the y-intercept, replace x with 0 and solve for y. x-intercept 2x 2(0) = 6 2x = 6 x = 6 2 x = 3 y-intercept 2(0) 2y = 6 2y = 6 y = 6 2 y = 3 PTS: 1 STA: 9.4.4 65. ANS: D To find the x-intercept, let y = 0 and solve for x; to find the y-intercept, let x = 0 and solve for y. Then, plot the intercepts and draw a line connecting them. PTS: 1 STA: 9.4.3 66. ANS: B m = y y Use the slope formula. 2 1 x 2 x 1 (7) (1) Substitute (3, 1) for (x m = 1, y 1 ) and (2, 7) for (x 2, y 2 ). (2) (3) m = 6 1 = 6 Simplify. PTS: 1 STA: 9.4.14 67. ANS: B Find the x-intercept by substituting x = 0 into the equation. Find the y-intercept by substituting y = 0 into the equation. Use the two intercept points and the slope formula, m = y 2 y 1 x 2 x 1, to calculate the slope. PTS: 1 STA: 9.4.6 68. ANS: B To find the slope, use the coordinates of two points on the line. Starting at one point, count the units down (negative units) or up (positive units) and to the right (positive units) or to the left (negative units) to arrive at the other point. The units up or down are the rise. The units to the right or to the left are the run. Write a fraction with the rise in the numerator and the run in the denominator. Simplify the fraction. PTS: 1 STA: 9.4.14 17
69. ANS: A An equation is a direct variation if it can be written in the form y = kx, where k is the constant of variation. 5x + y = 4 y = 5x 4 y = 5x 4 This is not a direct variation, because it cannot be written in the form y = kx. PTS: 1 STA: 9.4.13 70. ANS: D Write an equation in the form y = kx where k is the constant of variation. y = 9x Find y x 72 8 for each ordered pair. = 9; 54 6 = 9; 36 4 = 9 This is a direct variation, because y x is the same for each ordered pair. 9 is the constant of variation. PTS: 1 STA: 9.4.13 71. ANS: A The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Substituting 1 for the slope and 1 for the y-intercept gives y = x 1. PTS: 1 STA: 9.4.6 72. ANS: A If you are given the slope and one point, you can find the y-intercept by substituting for m, x, and y in the equation y = mx + b. Then, solve for b. 4 = 3(1) + b 4 = 3 + b 7 = b So, the equation of the line in slope-intercept form is y = 3x + 7. PTS: 1 STA: 9.4.6 18
73. ANS: B Use any two points to find the slope. m = y 2 y 1 x 2 x 1 = 37.35 24.75 16 10 = 12.60 6 = 2.10 To find an equation, substitute the slope and any ordered pair from the table into the point-slope form. Then solve for y to put the equation into slope-intercept form. y y 1 = m(x x 1 ) y 24.75 = 2.10(x 10) y 24.75 = 2.10x 21.00 y = 2.10x + 3.75 To find the cost for the truck, substitute the truck s tank size for x and simplify. y = 2.10x + 3.75 y = 2.10(22) + 3.75 y = 49.95 The cost for the truck is $49.95. PTS: 1 STA: 9.4.8 74. ANS: C Choose several x-values and make a table of ordered pairs. Then, graph the ordered pairs and connect them with a line. x y = 8x (x, y) 0 y = 8(0) (0, 0) 1 y = 8(1) (0, 8) 2 y = 8(2) (0, 16) PTS: 1 STA: 9.4.13 19
75. ANS: B Plot the y-intercept 1 on the graph at (0, 1). The slope is 3, so from the y-intercept, rise 3 units and 2 run 2 units. Plot another point. Connect the points to graph the line. PTS: 1 STA: 9.4.8 76. ANS: C Write all the equations in slope-intercept form (y = mx + b). The equations that have the same slope but different y-intercepts are parallel lines. PTS: 1 STA: 9.4.8 77. ANS: A Parallel lines have the same slope. Since the given line has a slope of 2, the parallel line has a slope of 2. y y 1 = m(x x 1 ) Use the point-slope form to write an equation. y ( 9) = 2(x (1)) Substitute 2 for m and (1, 9) for (x 1, y 1 ). y = 2x 7 Distribute 2 on the right side. Add 9 to both sides. PTS: 1 STA: 9.4.8 20
78. ANS: D y = 1 x 4 3 m = 1, b = 4 3 Plot (0, 4). Count 1 up and 3 right, and plot another point. Draw a line connecting the two points. PTS: 1 STA: 9.4.6 79. ANS: A Substitute the point and slope into the point-slope form y y 1 = m(x x 1 ), where m represents the slope and (x 1, y 1 ) represents a point on the line. PTS: 1 STA: 9.4.8 NUMERIC RESPONSE 80. ANS: $31.05 PTS: 1 STA: 9.4.4 21