Class: Date: Geometry Pre-Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. An equilateral triangle has three sides of equal length. What is the equation for the perimeter of an equilateral triangle if P = perimeter and s = length of a side? a. s = 3P b. P = 3s c. P = 3 + s d. P = 3(s + s + s) Simplify the expression. 2. 4(20 + 12) (4 3) a. 29 b. 80 c. 128 d. 92 3. 1 ( 12m + 38) 2 a. 6m + 38 c. 6m + 76 b. 24m + 19 d. 6m + 19 12 4. c 8 d 2 a. 12 cd 6 b. 5. 12 3 12 10 12 0 6. (k 2 ) 4 96c d 2 c. 12 c 8 d 2 d. a. 36 7 b. 1728 7 c. 1 d. 12 7 a. k 6 b. 2k 8 c. k 16 d. k 8 7. ( 5g 5 h 6 ) 2 (g 4 h 2 ) 4 g 26 h 20 a. 25g 26 h 20 b. c. 25g 26 h 20 d. 25g 15 h 14 25 8. Over the first five years of owning her car, Gina drove about 12,700 miles the first year, 15,478 miles the second year, 12,675 the third year, 11,850 the fourth year, and 13,075 the fifth year. a. Find the mean, median, and mode of this data. b. Explain which measure of central tendency will best predict how many miles Gina will drive in the sixth year. a. mean = 12,700; median = 13,156; no mode; the mean is the best choice because it is representative of the entire data set. b. mean = 13,156; median = 12,700; mode = 3,628; the median is the best choice because it is not skewed by the high outlier. c. mean = 13,156; median = 12,700; no mode; the mean is the best choice because it is representative of the entire data set. d. mean = 13,156; median = 12,700; no mode; the median is the best choice because it is not skewed by the high outlier. 12c 8 d 2 1
9. Make a stem-and-leaf plot for the following set of data. 1.1, 1.3, 1.8, 2.2, 2.6, 2.8, 3.1, 3.8 a. c. 1 1 means 1.1 1 0.1 means 1.01 b. d. 1 1 means 1.1 1 8 means 1.8 Write a function rule for each table. 10. Hours Worked Pay 2 $15.00 4 $30.00 6 $45.00 8 $60.00 a. p = 7.50h c. p = h + 15 b. p = 15h d. h = 7.50p 11. The cost of playing pool increases with the amount of time using the table. Identify the independent and dependent quantity in the situation. a. time using table; cost c. number of games; cost b. cost; time using table d. cost; number of players 12. Simplify 7(499) using the Distributive Property. a. 3500 b. 3493 c. 3514 d. 3486 2
Name the property the equation illustrates. 13. 8.2 + ( 8.2) = 0 a. Inverse Property of Addition b. Addition Property of 0 c. Identity Property of Addition d. Inverse Property of Multiplication Refer to the spinner below. 14. Find P(even and not shaded). 1 1 5 a. b. c. 0 d. 6 3 6 15. A cell phone company orders 500 new phones from a manufacturer. If the probability of a phone being defective is 2.6%, predict how many of the phones are likely to be defective. Round to the nearest whole number. a. 16 phones b. 13 phones c. 11 phones d. 130 phones 16. A small software company has three customer service representatives. After a week of observation, the supervisor of the customer service department determines that there is an 85% probability that a customer service representative will be on the phone with a customer at any given time. What is the probability of all three representatives being on the phone at the same time? Round to the nearest percent if necessary. a. 28% b. 72% c. 39% d. 61% 17. A basket contains 11 pieces of fruit: 4 apples, 5 oranges, and 2 bananas. Jonas takes a piece of fruit at random from the basket, and then Beth takes a piece at random. What is the probability that Jonas will get an orange and Beth will get an apple? 9 9 20 2 a. b. c. d. 10 11 121 11 Solve the equation. 18. 2 = 10 + z 3 a. 4 b. 16 c. 15 d. 5 19. 3.4 = 13.6 + ( 3.4c) + 1.7c a. 8 b. 2 c. 10 d. 4 20. 3p 1 = 5(p 1) 2(7 2p) a. 3 b. 0 c. 9 d. 10 3
21. Which properties of equality justify steps c and f? a. 23 = 11 4x b. 23 = 11 + ( 4x) c. 23 + 11 = 11 + ( 4x) + 11 d. 23 + 11 = 11 + 11 + ( 4x) e. 34 = 4x f. 34 4 = 4x 4 g. 8.5 = x a. Subtraction Property of Equality; Multiplication Property of Equality b. Addition Property of Equality; Division Property of Equality c. Addition Property of Equality; Subtraction Property of Equality d. Multiplication Property of Equality; Division Property of Equality 22. Write the conversion factor for converting meters to centimeters. a. 100 cm 1 m b. 10 m 1 cm c. 100 m 1 cm d. 100 cm 10 m Solve the proportion. 23. 2 10 = 11 x a. 55 b. 2.2 c. 110 d. 1.8 24. A tree casts a shadow 10 ft long. A boy standing next to the tree casts a shadow 2.5 ft. long. The triangle shown for the tree and its shadow is similar to the triangle shown for the boy and his shadow. If the boy is 5 ft. tall, how tall is the tree? a. 18 ft b. 12.5 ft c. 15 ft d. 20 ft 4
25. Carlos and Maria drove a total of 258 miles in 5 hours. Carlos drove the first part of the trip and averaged 53 miles per hour. Maria drove the remainder of the trip and averaged 51 miles per hour. For approximately how many hours did Maria drive? Round your answer to the nearest tenth if necessary. a. 3.5 hours b. 2.5 hours c. 1.8 hours d. 1.5 hours 26. The circulation of a newsletter decreased from 5200 to 3140. Find the percent of decrease in circulation to the nearest percent. a. 66% b. 40% c. 166% d. 6% 27. You measure the width of a doorway and find that it is 0.93 m wide. Find the greatest possible error of your measurement. a. 0.05 m b. 0.005 m c. 0.01 m d. 0.001 m 28. Simplify 1.69. a. 1.33 b. 1.3 c. 0.845 d. 13 29. Between what two consecutive integers is 151? a. 11 and 12 b. 14 and 15 c. 12 and 13 d. 9 and 10 30. A scuba diver has a taut rope connecting the dive boat to an anchor on the ocean floor. The rope is 140 feet long and the water is 40 feet deep. To the nearest tenth of a foot, how far is the anchor from a point directly below the boat? a. 145.6 ft b. 9,000 ft c. 18,000 ft d. 134.2 ft Determine whether the given lengths can be sides of a right triangle. 31. 18 m, 24 m, 30 m a. no b. yes 32. ABC has coordinates of A( 8, 8), B(4, 2), and C(2, 2). Find the coordinates of its image after a dilation centered at the origin with a scale factor of 1.5. a. A( 12, 12), B(6, 3), C(3, 3) c. A( 5.33, 5.33), B(2.67, 1.33), C(1.33, 1.33) b. A( 8, 8), B(4, 2), C(2, 2) d. A( 12, 8), B(6, 2), C(3, 2) Write the inequality in words. 33. 3n < 52 a. fifty-two less than three times n b. Three times n is less than fifty-two. c. Three times n is less than or equal to fifty-two. d. Three times n is greater than fifty-two. Solve the inequality. 34. q + 12 2(q 22) > 0 a. q < 32 b. q > 32 c. q > 56 d. q < 56 35. 12x 3x + 11 > 4x (17 9x) a. x > 7 b. x < 7 c. x < 14 11 d. x > 14 11 5
36. Alexandria wants to go hiking on Saturday. She will consider these conditions when she chooses which of several parks to visit: She wants to hike for 2 hours. She wants to spend no more than 6 hours away from home. She can average 65 miles per hour to and from the park. Write and solve an inequality to find possible distances from Alexandria s home to a park that satisfies the conditions. a. 2 + 65 d 6; d 16 miles c. 2 + d 6; d 260 miles 65 b. 6 + d 65 2; d 392 miles d. 2 + d 6; d 392 miles 65 Write a compound inequality that represents each situation. Graph your solution. 37. all real numbers that are greater than 6 but less than 6 a. 6 x 6 c. 6 < x < 6 b. 6 < x < 6 d. 6 < x 6 Write an inequality for the situation. 38. all real numbers y that are less than 4 or greater than 9 a. 4 < y < 9 c. y < 4 or y > 9 b. y < 4 or y ³ 9 d. y < 9 or y > 4 Solve the equation. If there is no solution, write no solution. 39. 2 n 12 = 16 a. n = 14 or n = 14 c. no solution b. n = 26 or n = 30 d. n = 14 40. The ideal width of a safety belt strap for a certain automobile is 5 cm. An actual width can vary by at most 0.35 cm. Write an absolute value inequality for the range of acceptable widths. a. w + 5 0.35 c. w + 0.35 5 b. w 0.35 5 d. w 5 0.35 6
41. Lena makes home deliveries of groceries for a supermarket. Her only stops after she leaves the supermarket are at traffic lights and the homes where she makes the deliveries. The graph shows her distance from the store on her first trip for the day. What is the greatest possible number of stops she made at traffic lights? a. 3 b. 4 c. 9 d. 5 42. Evaluate f(x) = 1 x for x = 4. 3 a. 1 1 1 3 b. c. 3 12 4 d. 12 43. Write a function rule that gives the total cost c(p) of p pounds of sugar if each pound costs $0.59. a. c(p) = 59p c. c(p) = p + 0.59 b. c(p) = p 0.59 d. c(p) = 0.59p Find the constant of variation k for the direct variation. 44. 3x + 5y = 0 a. k = 3 5 b. k = 5 c. k = 3 5 d. k = 5 3 45. The distance a spring will stretch varies directly with how much weight is attached to the spring. If a spring stretches 9 inches with 100 pounds attached, how far will it stretch with 90 pounds attached? Round to the nearest tenth of an inch. a. 8.9 in. b. 10 in. c. 8.1 in. d. 9.1 in. 46. Suppose that y varies inversely with x. Write an equation for the inverse variation. y = 6 when x = 8 a. y = x b. y = 2x c. x = y d. y = 48 48 2 x 7
Do the data in the table represent a direct variation or an inverse variation? Write an equation to model the data in the table. 47. x 2 4 8 12 y 6 3 3 2 1 a. direct variation; y = 12x c. direct variation; y = 12 x b. inverse variation; xy = 12 d. inverse variation; y x = 12 Use inductive reasoning to describe the pattern. Then find the next two numbers in the pattern. 48. 9, 4, 1, 6,... a. add 5 to the previous term; 11, 16 b. multiply the previous term by 5; 30, 150 c. subtract 5 from the previous term; 1, 4 d. multiply the previous term by 5; 11, 150 Find the common difference of the arithmetic sequence. 49. 5, 5.3, 5.6, 5.9,... a. 0.3 b. 1.1 c. 1.1 d. 10.3 Determine whether the function rule models discrete or continuous data. 50. A movie store sells DVDs for $15 each. The function C(d) = 15d relates the total cost of movies to the number purchased d. a. discrete b. continuous 8
The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation. 51. Time (hours) Distance (miles) 4 260 6 390 8 520 10 650 a. 10; Your car travels for 10 hours. b. 260; Your car travels 260 miles. c. 65 ; Your car travels 65 miles every 1 hour. 1 d. 1 ; Your car travels 65 miles every 1 hour. 65 52. A student finds the slope of the line between (14, 1) and (18, 17). She writes 1 17. What mistake did she 18 14 make? a. She should have added the values, not subtracted them. b. She used y-values where she should have used x-values. c. She mixed up the x- and y-values. d. She did not keep the order of the points the same in the numerator and the denominator. Find the slope and y-intercept of the line. 53. y = 4 3 x 3 a. 3; 4 3 b. 3; 4 3 c. 3 4 ; 3 d. 4 3 ; 3 9
54. Use the slope and y-intercept to graph the equation. y = 3 4 x 3 a. c. b. d. Find the x- and y-intercept of the line. 55. 2x + 3y = 18 a. x-intercept is 18; y-intercept is 18. c. x-intercept is 2; y-intercept is 3. b. x-intercept is 6; y-intercept is 9. d. x-intercept is 9; y-intercept is 6. 56. The grocery store sells kumquats for $4.25 a pound and Asian pears for $2.25 a pound. Write an equation in standard form for the weights of kumquats k and Asian pears p that a customer could buy with $18. a. 4.25k + 2.25p = 18 c. 4.25k = 2.25p + 18 b. 4.25p + 2.25k = 18 d. 4.25 + 2.25 = k 10
Graph the equation. 57. y 3 = (x + 5) a. c. b. d. 11
Is the relationship shown by the data linear? If so, model the data with an equation. 58. x y 9 2 5 7 1 12 3 17 a. The relationship is linear; y + 2 = 4 (x + 9). 5 b. The relationship is linear; y + 9 = 4 (x + 2). 5 c. The relationship is not linear. d. The relationship is linear; y + 2 = 5 (x + 9). 4 Are the graphs of the lines in the pair parallel? Explain. 59. y = 1 6 x + 8 2x + 12y = 11 a. Yes, since the slopes are the same and the y-intercepts are the same. b. No, since the y-intercepts are different. c. Yes, since the slopes are the same and the y-intercepts are different. d. No, since the slopes are different. Write the equation of a line that is perpendicular to the given line and that passes through the given point. 60. 4x 12y = 2; (10, 1) a. y = 3x + 29 c. y = 3x + 29 b. y = 1 3 x + 29 d. y = 1 3 x + 7 12
61. A balloon is released from the top of a building. The graph shows the height of the balloon over time. a. What does the slope and y-intercept reveal about the situation? b. For a similar situation, the slope is 35 and the y-intercept is 550. What can you conclude? a. The balloon starts at a height of 500 ft, and rises at a rate of 100 ft; the balloon starts at a height of 550 ft, and rises at a rate of 35 ft. b. The balloon starts at a height of 500 ft, and rises at a rate of 100 ft; the balloon starts at a height of 35 ft, and rises at a rate of 550 ft. c. The balloon starts at a height of 100 ft, and rises at a rate of 500 ft; the balloon starts at a height of 550 ft, and rises at a rate of 35 ft. d. The balloon starts at a height of 100 ft, and rises at a rate of 500 ft; the balloon starts at a height of 35 ft, and rises at a rate of 550 ft. 13
62. Solve the following system of equations by graphing. 4x + 3y = 12 2x + 3y = 18 a. c. b. d. Graph each system. Tell whether the system has no solution, one solution, or infinitely many solutions. 63. y = x + 4 y 4 = x a. infinitely many solutions b. no solutions c. one solution Solve the system of equations using substitution. 64. y = 2x + 3 y = 3x + 1 a. ( 2, 1) b. ( 1, 2) c. (2, 7) d. ( 2, 5) 14
Solve the system using elimination. 65. 3x y = 28 3x + y = 14 a. (8, 4) b. ( 7, 7) c. (7, 7) d. ( 4, 8) 66. 3x 4y = 9 3x + 2y = 9 a. (3, 9) b. ( 27, 9) c. ( 3, 6) d. ( 9, 9) 67. An ice skating arena charges an admission fee for each child plus a rental fee for each pair of ice skates. John paid the admission fees for his six nephews and rented five pairs of ice skates. He was charged $32.00. Juanita paid the admission fees for her seven grandchildren and rented five pairs of ice skates. She was charged $35.25. What is the admission fee? What is the rental fee for a pair of skates? a. admission fee: $3.25 c. admission fee: $3.00 68. skate rental fee: $2.50 b. admission fee: $3.50 skate rental fee: $3.00 Write the linear inequality shown in the graph. skate rental fee: $2.00 d. admission fee: $4.00 skate rental fee: $3.50 a. y 3x + 4 b. y 3x + 4 c. y 3x 4 d. y 3x 4 15
69. A doctor s office schedules 10-minute and 20-minute appointments. The doctor also makes hospital rounds for four hours each weekday. a. Suppose the doctor limits these activities to, at most, 30 hours per week. Write an inequality to represent the number of each type of office visit she may have in a week. Let x represent the number of 10-minute appointments and y the number of 20-minute appointments. b. Graph the inequality. c. Is (63, 30) a solution of the inequality? 16
a. 10x + 20y 600 yes b. 10x + 20y 600 no c. 20x + 10y 600 no 17
d. 20x + 10y 600 yes Write a system of inequalities for the graph. 70. a. y x 2 y 3x 6 b. y x + 3 y 2x 6 c. y x 2 y 3x 6 d. y x + 3 y 2x 6 71. Chase scored 14 points on Monday, and he doubled his score each day thereafter. How many points did he score on Thursday? a. 224 points b. 112 points c. 56 points d. 42 points 72. 9 10 4 Write the number in standard notation. a. 9,000 b. 90 4 c. 90,000 d. 360 18
73. Radio signals travel at a rate of 3 10 8 meters per second. How many seconds will it take for a radio signal to travel from a satellite to the surface of the Earth if the satellite is orbiting at a height of 3.6 10 7 meters? a. 8.3 seconds c. 1.08 10 16 seconds b. 1.2 10 1 seconds d. 10.8 10 15 seconds Find the common ratio of the sequence. 74. 2, 10, 50, 250,... a. 5 b. 12 c. 75. Which function is greater at the given value? y = 2 x or y = x 2 at x = 9 a. 2 x b. x 2 1 5 d. 12 Find the balance in the account. 76. $3,800 principal earning 2%, compounded quarterly, after 7 years a. $4,369.52 c. $64,926.56 b. $4,365.01 d. $108,528.00 77. A boat costs $11,850 and decreases in value by 10% per year. How much will the boat be worth after 8 years? a. $5,101.04 b. $11,770.00 c. $4,590.93 d. $25,401.53 Find the degree of the monomial. 78. 6x 8 y 5 a. 5 b. 6 c. 13 d. 8 79. Write the perimeter of the figure. a. 9x + 7x b. 11x + 3x + 2 c. 14x + 2 d. 14x 19
Simplify the product. 80. 2n(n 2 + 3n + 4) a. 2n 3 + 6n 2 + 8n c. 2n 3 + 6n + 8 b. 2n 3 + 3n + 4 d. n 2 + 5n + 4 Factor the polynomial. 81. 2x 3 + 4x 2 + 8x a. 2x(x 2 + 2x + 4) c. x(2x 2 + 4x + 8) b. 2x(x + 2)(x + 4) d. 2x 3 + 4x 2 + 8x Simplify the product using FOIL. 82. (3x 7)(3x 5) a. 9x 2 + 6x + 35 c. 9x 2 36x 35 b. 9x 2 + 36x + 35 d. 9x 2 36x + 35 83. Simplify using the horizontal method. (2n 2 + 4n + 4)(4n 5) a. 8n 3 + 26n 2 36n 20 c. 8n 3 + 4n 2 6n 20 b. 8n 3 + 6n 2 4n 20 d. 8n 3 6n 2 + 36n 20 84. Both figures are squares. Find the area of the UNSHADED region. Write your answer in standard form. a. 2x 2 + 10x + 25 c. 10x + 25 b. x 2 + 8x + 25 d. x 2 + 10x + 25 Find the product. 85. (4p 6)(4p + 6) a. 16p 2 36 c. 16p 2 + 48p + 36 b. 16p 2 48p 36 d. 16p 2 + 36 20
Factor the expression. 86. d 2 + 10d + 9 a. (d + 9)(d 1) c. (d 9)(d 1) b. (d 9)(d + 1) d. (d + 9)(d + 1) 87. 15x 2 16xy+ 4y 2 a. (3x 2y)(5x + 2y) c. (3x + 2y)(5x 2y) b. (3x 2y)(5x 2y) d. (3x + 2y)(5x + 2y) 88. 16m 2 24mn + 9n 2 a. (4m 3n)(4m + 3n) c. (4m 3n) 2 b. (16m 3n)(m + 3n) d. (4m + 3n) 2 89. r 2 49 a. (r 7)(r + 7) c. (r 7)(r 7) b. (r + 7)(r + 7) d. (r 7)(r + 9) 90. 50k 3 40k 2 + 75k 60 a. 5(2k 2 3)(5k + 4) c. (2k 2 + 15)(5k 20) b. (10k 2 3)(25k + 4) d. 5(2k 2 + 3)(5k 4) Factor by grouping. 91. 21m 2 29m 10 a. (7m 2)(3m 5) c. (7m + 2)(3m 5) b. (7m + 2)(3m + 5) d. (7m 2)(3m + 5) 92. Identify the vertex of the graph. Tell whether it is a minimum or maximum. a. (0, 1); minimum c. (0, 1); maximum b. ( 1, 0); maximum d. ( 1, 0); minimum 21
93. If an object is dropped from a height of 38 feet, the function h(t) = 16t 2 + 38 gives the height of the object after t seconds. Graph the function. a. c. b. d. 94. A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function h = 16t 2 + 36t + 9. a. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. b. What is the ball s maximum height? a. 1.13 s; 69.75 ft b. 1.13 s; 29.25 ft c. 1.13 s; 31.5 ft d. 2.25 s; 9 ft 22
95. Graph f(x) 2x 2 + 4x. a. c. b. d. 23
96. Solve x 2 + 2 = 6 by graphing the related function. a. c. b. There are two solutions: 2 and 2. d. There are two solutions: 2 and 2. There are two solutions: ± 8. There are no real number solutions. 97. x 2 + 20 = 4 Solve the equation using square roots. a. 24 c. ± 24 b. 4 d. no real number solutions Solve the equation by factoring. 98. 6x 2 17x + 13 = 20x 2 32 5 a. 3, 9 b. 5 2 2, 9 7 c. 5 2, 9 7 d. 5 3, 9 2 24