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Algebra 2-2 Core 40 Practice Exam Follow the directions for each problem. 1. Which of the properties of real numbers is illustrated below? b ( b) = 0 [A] associative law [B] inverse law [C] distributive law [D] commutative law 2. State the property that is illustrated. (a 2b) 3c a (2b 3c) 3. Evaluate 2e 3 f for e = –3 and f = 1. [A] –2 [B] 9 [C] 5 [D] –3 1 4. Evaluate (7 5y) 3x when x when y = 5. 9 5. Simplify: 6 x 6 y xy 8 x 6 y 2 xy 2 [A] 7 x 6 y 3xy 8 [B] 9 x 6 y xy 8 [C] 7 x12 y 2 3xy 8 [D] 9 x 6 y x 2 y 2 8 6. Solve: 10x + 4 = 34 [A] 3 [B] 38 [C] 30 [D] 4 7. Solve the equation. 4(2 x 3) 6 (3 2 x) 8. The literature club is printing a storybook to raise money. The print shop charges $3 for each book, and $30 to create the film. How many books can the club print if their budget is $690? [A] 223 [B] 220 [C] 230 [D] 227 9. For 1980 through 1990, the average salary, A, (in thousands of dollars), of assistant principals at public high schools can be modeled by A = 2t + 25, where t = 0 represents 1980. Approximate a high school assistant principal’s salary in 1986. 5 10. Solve for A: B = (A 9). 8 8 B 45 8 B 67 8 B 40 8 B 72 [A] [B] [C] [D] 5 8 8 5 11. Solve for s: r 2 s 5s 7 9 12. Solve for C: F C 32 5 13. Guess and check: Which of the numbers 5, 6, or 7 is the solution of 81 = 87 – x? 14. Which of the numbers is the solution of 108 = 121 – x? [A] 12 [B] 11 [C] 13 [D] none of the above 15. Jeff earns $4.00 an hour baby-sitting. He is saving to buy a pair of in-line skates that costs $116.00. If Jeff already has $60.00 saved, how many hours must he baby-sit in order to buy the skates? 16. The length and width of the floor of a room are each 11 meters. The height is 4 meters. A spider, on the floor in a corner, sees a fly on the ceiling in the corner diagonally opposite. If the fly does not move, what is the shortest distance the spider can travel to reach the fly, to the nearest tenth of a meter? [A] 18.6 m [B] 16.1 m [C] 26.0 m [D] 19.6 m 17. Solve: 9b 11 10b 6 [A] b –17 [B] b 17 [C] b 20 [D] b = 5 5 18. Is x = a solution of the inequality 5x 4 3( x 7) ? 2 19. Solve: –6 3x 15 12 20. On a road in the city of Wilsonville, the maximum speed is 55 miles per hour and the minimum speed is 30 miles per hour. If x represents speed, which sentence best expresses this condition? [A] 55 x 30 [B] x 30 < 55 [C] 55 x 30 [D] 55 x 30 21. Solve: x 3 3 [A] x < –6 or x > 0 [B] –6 x 0 [C] x –6 or x 0 [D] –6 < x < 0 22. Solve the inequality. Then graph your solution. 2 x 3 5 1 23. For a door to meet specifications at a carpentry shop the width must be within inch of the expected width 2 1 of the door. The shop gets an order for doors that are 3 feet wide. Which of the following is an inequality that 2 expresses the range of widths for acceptable doors? 1 1 1 1 1 1 [A] x 42 [B] x 42 [C] x 3 [D] x 3 2 2 2 2 2 2 24. You have $20,000 available to invest in two stocks, A and B. Write an inequality stating the restriction on A if at least $3000 must be invested in each stock. 25. Find the range of the relation {(– 2, – 3), (1, 0), (5, – 2)}. [A] {–2, 1, 5} [B] {2, –1, –5} [C] {3, 0, 2} [D] {–3, 0, –2} 26. Determine whether the relation is a function. (4, 0), (4, 1), (5, 2), (6, 3), (6, 4) 27. Find f F 1I. f ( x) 18x G3J 2 12 x 3 HK 3 28. Graph f ( x) x 5. 4 [A] y [B] y x x [C] y [D] y x x 29. Find the slope of the line. y 10 –10 10 x –10 2 10 9 5 [A] [B] [C] [D] 5 9 10 2 7 5 30. Which line is steeper, y x 5 or y x 2 ? 4 3 31. In 1983 the pollution in a local lake was rated at 1.4 parts per million. By 1987 it had risen to 2.6 parts per million. Which of the following expresses the rate of change in parts per million from 1983 to 1987? 1 5 6 3 [A] [B] [C] [D] 4 6 5 10 32. Graph the linear equation by finding x- and y-intercepts. 3x 3y = 9 [A] y [B] y x x [C] y [D] y x x 33. Find the slope and y-intercepts of the line. 4 x 3y 36 34. Graph: 9 x 7 y 63 [A] y [B] y x x [C] y [D] y x x 35. Write the equation in slope-intercept form. Then identify the slope and y-intercept. 15x 3y 7 36. Write an equation to model the following situation. A candle is 6 in. tall and burns at a rate of 2.50 in./h. [A] y = 6 x + 2.5 [B] y = 6x – 2.5 [C] y = 2.5x+6 [D] y = –2.5x + 6 37. The variables x and y vary directly and y = –7 when x = 14. Write an equation that relates the variables. 38. Graph: y 5x 2 [A] y [B] y x x [C] y [D] y x x 2 39. Graph the inequality in a coordinate plane. y x2 3 40. Sally wants to buy her boyfriend a bouquet for his birthday. She wants it to contain both carnations and roses. She has $27.60 to spend. Carnations cost $1.41 each and roses cost $2.33 each. Which graph below represents the possible combinations of numbers of carnations and roses Sally can afford to buy? [A] [B] roses roses carnations carnations [C] [D] roses roses carnations carnations 41. Graph the function. f ( x) x 3 42. Graph the function defined by y = x 3 . [A] y [B] y x x [C] y [D] y x x 43. The population, P (in thousands), of a town can be modeled by P 2 t 8 4 , where t = 0 represents 1990. During which two years does the town have a population of 8000? 44. Solve the system by graphing: x y = 2 y = 2 x 13 [A] y [B] y x x F , 13I G 3J 13 F, 4 I G 3J 2 H K 3 H K 3 [C] y [D] y x x b , 17g 15 b, – 3g 5 45. Is (5, –2) a solution of the system? 2x + 6y = –2 2x + y = 6 46. A rental car agency charges $19 per day plus 10 cents per mile to rent a certain car. Another agency charges $26 per day plus 7 cents per mile to rent the same car. How many miles per day will have to be driven for the cost of a car from the first agency to equal the cost of a car from the second agency? [A] 2333.33 miles per day [B] 233.33 miles per day [C] 1500 miles per day [D] 150 miles per day 47. The drama club sold 1500 tickets for the end-of-year performance. Admission prices were $12 for adults and $6 for students. The total amount collected at the box office was $15,600. How many students attended the play? 48. Solve the linear system: 4 x 4 y 4 3x 4 y – 25 49. Solve the system. 3 1 y x 4 4 3 3 y x 4 4 50. Tickets to a local movie were sold at $4.00 for adults and $2.50 for students. If 420 tickets were sold for a total of $1155.00, how many student tickets were sold? [A] 70 [B] 85 [C] 350 [D] 280 51. A group of 65 people attend a ball game. There were four times as many children as adults in the group. Write a system of equations that you could use to set up this problem, where a is the number of adults and c is the number of children in the group. Solve the system of equations for c, the number of children in the group. 52. Graph the system of linear inequalities: x –4 y –5 [A] y [B] y x x [C] y [D] y x x 53. Graph the system of inequalities: y –7 y < –4 54. Graph the system of inequalities: 4 x 5y 20 x y x 5 [A] y [B] y x x [C] y [D] y x x 55. Solve the system of equations: x + y + z = –2 2x y + z = – 9 x 2 y z = 16 [A] (5, –4, –3) [B] (–5, 4, 3) [C] (–3, –4, 5) [D] (3, 4, –5) 56. James sold magazine subscriptions with three prices: $20, $27, and $18. He sold 6 fewer of the $20 subscriptions than of the $27 subscriptions and sold a total of 31 subscriptions. If his total sales amounted to $678, how many $18 subscriptions did James sell? [A] 15 [B] 13 [C] 6 [D] 12 L7 –1 – 4 O L –9 –7 –6 O 57. If A = M P M P M –3 M –7 P 2 and B = P 8 M M 1 P 7 , find A + B. P N5 3 4 Q N –8 – 3 –1 Q L16 6 2 O L2 – 8 – 10O – [A] M – 8 P M – 6 9P M– 11 M 6 5 P P [B] M 0 3P M 5 P N 13 –5 Q N3 – Q L16 6 2O L2 – 8 – 10O – [C] M – 8 P M – 6 3P M– 11 M 6 – 5P [D] M 0 9P M 5 N 13 5P Q N3 – P Q L xO L 3OL 6O 4 1 58. Solve for x and y. 3M P2 M P M P 10 N 3Q N 0QN7 9Q 1 y 59. Don asked the players on two ski teams what new color each team uniform should be: red, blue, or green. He recorded the results in two matrices. Find the total for the two teams. R B G R B G L OP Males 1 6 7 L OQ Males 0 8 3 Females M 4 2P Females M 5 7P N Q 8 N Q 9 L 14 1 O [A] M 10 L 9 17O 9 N 9 17P [B] M 9 Q N 14 1 P 10 Q L 14 10O [C] M 1 L 10 9O 1 N 9 9P [D] M 17 Q N 17 9P 14 Q L2O – MP B 60. Given A 1 and MP 1 4 0 , find AB. MP N1Q L1 M – 2 –2 O P [A] 2 M [B] 2 M 5 1 P P N 0 3 1 Q L2 M – –8 0 O P M [C] 1 M 4 0 P P [D] not possible N1 –4 0 Q 61. Perform the matrix operations, if possible. L 5O 2 M 7P2 1 4 N Q 1 62. Student Government and the cheerleaders at a local school are ordering supplies. The supplies they need are listed below. Paint Paper Tape Student Government L12 M 14 5 O P Cheerleaders M N8 17 9 P Q If a bottle of paint costs $5, a roll of paper costs $12, and a roll of tape costs $2, which of the following shows the use of matrices to find the total cost of supplies for each group? L 14 12 [A] M 5OO L O L P 238 M 5 P P M P L 14 5O 12 12 M 17 9P 2 LO 238 MP N 17 8 9M 262 12 QP N Q MQ [B] N8 5 Q NQ 262 N 2 L 14 12 LO5 5O P MP 500 L 14 5O 12 12 [C] M 17 N 9P M12 QP [D] M 17 9P N 5 Q 2 500 8 MQ N 2 8 2 3 1 63. Evaluate the determinant of the matrix. 4 1 3 5 5 2 [A] 10 [B] –18 [C] –10 [D] 18 10 7 64. Evaluate the determinant of the matrix. 5 12 65. Use Cramer’s Rule to solve for x: R 5y = 6 3 Sx 3y = 1 Tx 3 13 5 23 7 [A] [B] [C] [D] 24 8 24 8 66. Find the coefficient matrix and evaluate its determinant. R 8x 5y 7 S x 7y 4 T 12 67. Find the inverse of L 7O 4 M 8P . N Q 9 68. Use the inverse of the matrix A = L2 – 1O decode the message –9, –5, 54, 17, 24, 3. – M 1P to N Q 3 1 = A 8 = H 15 = O 22 = V 2 = B 9 = I 16 = P 23 = W 3 = C 10 = J 17 = Q 24 = X 4 = D 11 = K 18 = R 25 = Y 5 = E 12 = L 19 = S 26 = Z 6 = F 13 = M 20 = T 7 = G 14 = N 21 = U [A] CIRCLE [B] DEGREE [C] MEDIAN [D] FACTOR 69. Graph: y 4 x 2 x 1 [A] y [B] y x x [C] y [D] y x x 70. Find the vertex of the parabola and determine if it opens up or down. y 7 8 x 2 x 2 b b g g 71. Write in standard form and graph: y – 2 x 3 x 4 [A] y –2 x 2 – 14 x – 24 [B] y –2 x 2 14 x 24 y y x x [C] y –24 x 2 – 14 x – 2 [D] – 2 y x 2 7 x 12 y y x x 72. Graph: y 2 x 2 x 2 73. The surface area of a cube is 380 square inches. How long is each edge? (Round to two decimal places.) x x x 74. Solve by factoring: x 2 18x 81 0 75. A restaurant’s aquarium is destroyed in an earthquake. The insurance company is willing to replace the aquarium with one of the same dimensions. The owner can only remember that the diagonal of the front was 68 inches, the length was 28 inches more than the height of the front, and the depths was the same as the height of the front. Find the dimensions of the aquarium. [A] 61 in. 33 in. 33 in. [B] 59 in. 31 in. 31 in. [C] 58 in. 30 in. 30 in. [D] 60 in. 32 in. 32 in. 76. Find the x-intercepts of the graph of y = x 2 2 x 15 . [A] –2, 3 [B] 3, –5 y y x x [C] 2, –3 [D] –3, 5 y y x x 77. Find the zeros of the equation. x 2 2 x 15 = y 78. Solve for x: 6 x 2 = 24 [A] 2 [B] 12 [C] 144 [D] 18 1 2 79. Solve the equation. x 1 33 3 80. The distance, d (in meters), travelled by a falling object is given by the equation d 4.9t 2 , where t is the time in seconds. From what height was the object originally dropped if it took 5.27 seconds to hit the ground? Round answers to the nearest whole number. [A] 666 meters [B] 25.81 meters [C] 136 meters [D] 27.76 meters 81. Solve: (6 x 4) 2 = 77 4 77 4 + 77 4 77 4 + 77 [A] , [B] , 12 12 6 6 – 4 77 – 4 + 77 – 4 77 – 4 + 77 [C] , [D] , 6 6 12 12 82. Write the expression as a complex number in standard form. (1 i ) (8 3i ) 5 83. Write the expression as a complex number in standard form. 1 i 8 5i 84. Write the expression as a complex number in standard form. 6 4i 17 1 17 31 7 31 7 1 [A] i [B] i [C] i [D] i 5 10 5 10 13 26 13 26 85. Find the absolute value of the complex number. 2 5 i [A] 29 [B] 21 [C] 4.58 [D] 5.39 86. Solve by completing the square: x 2 6x 40 = 0 [A] 10, 4 [B] 10, –4 [C] –10, –4 [D] –10, 4 87. Solve by completing the square: 7 x 2 28x 21 0 4 2 88. Write the quadratic equation in vertex form: y x 40x 294 3 89. Find the maximum value of the quadratic equation: y 2 x 2 24 x 87 [A] max = –129 [B] max = 6 [C] max = –87 [D] max = –15 90. Solve by the quadratic formula: x 2 5x 1 = 0 5 21 5 21 – 5 29 – 5 29 [A] , [B] , 2 2 2 2 5 29 5 29 – 5 21 – 5 21 [C] , [D] , 2 2 2 2 91. State the discriminant of the quadratic. 3x 2 4 x 4 0 92. A rock is thrown from the top of a tall building. The distance, in feet, between the rock and the ground t seconds after it is thrown is given by d 16t 2 2t 405 . How long after the rock is thrown is it 300 feet from the ground? 21 5 29 7 [A] sec [B] sec [C] sec [D] sec 8 2 8 2 93. Graph: y > x 2 5x 6 94. Which is the graph of y 1 3x x 2 ? [A] y [B] y x x [C] y [D] y x x 95. Solve the inequality algebraically: ( x 5)(9 x 8) 0 96. An arrow shot into the air is 144t 4.9t 2 meters above the ground t seconds after it is released. During what period(s) of time is the arrow below 68.6 meters? Round your answer to the nearest .01 second. [A] 14 x 1539 seconds . [B] x 0.48 and x 28.90 seconds [C] x 14 and x 1539 seconds . [D] 0.48 x 28.90 seconds F 6 I5 b 97. Simplify: G9 J G J G J H K c ch 98. Simplify: xy 3 5 [A] x 5 y 3 [B] x 6 y15 [C] x 6 y 8 [D] x 5 y15 99. According to figures from 1995, the population of the United Kingdom is 58,295,119. The land mass of the United Kingdom is 94,251 square miles. If the land mass of the United Kingdom is divided evenly amongst the population, how many people live in each square mile? [A] 61.85 [B] 0.16 [C] 618.5 [D] 0.0016 100. Evaluate the polynomial when d = 5: 7d 3 6d 2 5d 12 bg 101. Use synthetic substitution to evaluate f c 9c3 2c2 5c 7 when c = 2. bg [A] f c 64 bg [B] f c 49 bg [C] f c 75 bg [D] f c 67 102. Graph: y = x 6 [A] y [B] y x x [C] y [D] y x x 103. Decide whether the function is a polynomial function. If it is, state its degree, type, and leading coefficients. f ( x) x 4 x 2 3x 7. 104. Multiply: ( x 4)( x 2 x 4) [A] x 3 x 2 16 [B] x 3 5x 2 8x 16 [C] x 3 3x 2 8x 16 [D] x 3 5x 2 16 105. The sides of a rectangle have lengths x 9 and widths x 5 . Which equation below describes the perimeter, P, of the rectangle in terms of x? [A] P = x 2 14 x 45 [B] P = 4 x 8 [C] P = x 2 4 x 45 D] P = x 4 106. Factor: 9 y 2 25 [A] (3y 5)(3y 5) [B] (3y 5)(3y 5) [C] (3y 5)(3y 5) [D] (9 y 1)( y 25) 107. Solve: x 3 6x 2 = 0 [A] 0, –6 [B] 6, –7 [C] 6, –6 [D] 0, 6 108. Find all real-number solutions. x 3 9 x 2 27 x 27 0 109. Divide: ( x 3 5x 3 ) ( x 3 ) 21 45 [A] x 2 2 x 6 – [B] x 2 3x 14 – x3 x3 27 14 [C] x 2 2 x 9 + [D] x 2 3x 4 + x3 x3 c h b g 110. A rectangle has an area of x 3 x 2 10 x 8 square meters, and a width of x 4 meters. Find its length. c h [A] x 2 x 10 meters c h [B] x 2 3x 10 meters c h [C] x 2 3x 2 meters c h [D] x 2 x 2 meters 111. Estimate the real zeros of the function graphed below. y 10 –10 10 x –10 [A] 12, 1, 3, 5 [B] 1, 3, 5 [C] –5, –3, –1 [D] 12 112. Find all real zeros of the function. g ( x) 2 x 3 x 2 6 x 3 113. For 1985 through 1996, the number, C (in thousands), of videos rented each year in Moose Jaw can be modeled by C = 0.079( t 3 2t 2 31t 600 ), where t = 0 represents 1990. During which year are 99.4 thousand movies projected to be rented? [A] 2002 [B] 1996 [C] 1994 [D] 1997 114. Write a polynomial function that has the zeros 2, –2, and –1 and has a leading coefficient of 1. Then graph the function to show that 2, –2, and –1 are solutions. [A] y y = x3 x2 4x 4 x [B] y y = x3 x2 4x 4 x [C] y y = 2x2 2x 1 x [D] y y = x2 x 2 x 115. Solve for x: x 4 12 x 2 11 = 0 116. Evaluate: 12961/ 4 1 1 [A] [B] 6 [C] [D] 36 36 6 117. Use a calculator to evaluate 9 1/ 3 to three decimal places. 118. Evaluate the expression using a calculator. Round the result to three decimal places when appropriate. 3 128 [A] 23 4 [B] 163 8 [C] 43 2 [D] 43 8 5 119. Evaluate 1540 to three decimal places using a calculator. 120. The volume of a sphere can be given by the formula V = 418879r 3 . You have to design a spherical . container that will hold a volume of 55 cubic inches. What should the radius of your container be? [A] 2.36 in. [B] 2.49 in. [C] 3.62 in. [D] 13.13 in. 495/ 6 121. Simplify: 491/ 3 FI v 122. Simplify: G J 25 3/ 5 HK w 15 123. The surface area of a baseball is 23.75 in 2 . The surface area of a softball is 53.78 in 2 . Find the ratio of the 4 volumes of a baseball to a softball. Surface Area = 4 r 2 and Volume = r 3 . 3 [A] 0.665 [B] 0.293 [C] 0.442 [D] 0.193 124. Let f ( x ) 1 x 2 and g( x) 1 x . Find f ( x) g( x) . 125. Sara bought 3 fish. Every month the number of fish she has doubles. After m months she will have F fish, where F 3 2 m . How many fish will Sara have after 3 months if she keeps all of them and the fish stay healthy? [A] 24 [B] 216 [C] 30 [D] 11 126. Find an equation for the inverse of the relation y = 5x 2 . x2 5x 2 x2 [A] y = [B] y = [C] y = [D] y = 2 x 5 5 5 5 127. Are f and g inverses of each other? bg 2 1 f x x , g x x 3 2 bg 2 3 3 4 128. Sketch the graph of the function. Is the inverse of f(x) a function? f ( x ) 2 x 2 129. Describe how to obtain the graph of y x 3 3 from the graph of y x. 130. Graph: f(x) = 3 x3 2 [A] y [B] y x x [C] y [D] y x x 131. Refer to the function g( x) 1 x 3 . What is the range of g(x)? 132. The sales of a certain product after an initial release can be found by the equation s 14 7t 45 , where s represents the total sales and t represents the time in weeks after release. How many weeks will pass before the product sells about 200 units? Round your answer to the nearest week. 133. A certain gas will escape from a storage tank according to the formula e 170 p , where e represents the amount escaping per minute in gallons, and p represents the pressure in pounds per square inch. What is the pressure on the gas when about 250 gallons per minute are escaping? Round your answer to the nearest tenth. [A] 20.5 lb/in. 2 [B] 2.2 lb/in. 2 [C] 0.7 lb/in. 2 [D] 1.5 lb/in. 2 134. Solve the equation. Check for extraneous solutions. 3 x 5 –5 [A] 130 [B] –120 [C] 30 [D] –120, 130 135. The velocity of sound in air is given by the equation v = 20 273 t where v is the velocity in meters per second and t is the temperature in degrees Celsius. Find the temperature when the velocity of sound in air is 348 meters per second. Round the answer to the nearest degree. [A] –14°C [B] 22°C [C] 6°C [D] none of these 136. Graph f ( x) = 2 e x . [A] y [B] y 10 10 –10 10 x –10 10 x –10 –10 [C] y [D] y 10 10 –10 10 x –10 10 x –10 –10 137. Is f ( x) 7e 2t an example of exponential growth or decay? 138. If $5000 is invested at a rate of 7% compounded continuously, find the balance in the account after 2 years. Use the formula A Pert . [A] $5724.50 [B] $5751.37 [C] $36945.28 [D] $6168.39 139. Evaluate: log 3 9 1 1 [A] [B] 6 [C] 2 [D] 2 6 140. Evaluate without using a calculator. log 7 343 141. Graph: y log 4 x [A] y [B] y x x [C] y [D] y x x 142. Express as a single logarithm: logb 6 logb 45 [A] logb 645 FI GJ 6 [D] logb (6 45) [B] logb 270 [C] log b HK 45 143. Expand the expression. log 4 3x 1 y 3 144. Use the formula R log10 I , where R is the measurement of the Richter scale and I is the intensity, to find the Richter scale measurement of an earthquake with intensity 120,000,000. [A] 8.0792 [B] 0.80792 [C] 18.603 [D] 1.8603 145. Solve for x correct to four decimal places: e–4 x = 58 . 1 146. Solve: = 273x5 9 13 1 17 [A] [B] [C] 1 [D] 9 3 9 147. Solve the equation. 60.2 x 3 7 148. It takes a train 7 h to get from Capital City to Johnson City when it travels 55 mi/h. How long would it take the train to go the same distance when it travels 77 mi/h? 7 5 [A] 5 h [B] h [C] h [D] 11 h 5 7 149. The variable z varies jointly with the product of x and y. z = 3.6 when x = 8 and y = 90. Find an equation that relates the variables. 150. The wattage rating of an appliance, W, varies jointly as the square of the current, I, and the resistance, R. If the wattage is 4.5 watts when the current is 0.3 ampere and the resistance is 50 ohms, find the wattage when the current is 0.2 ampere and the resistance is 100 ohms. [A] 40 watts [B] 20 watts [C] 2000 watts [D] 4 watts n 2 2n 24 151. Simplify the rational expression. 2 n 11n 28 n6 n6 n6 n4 [A] [B] [C] [D] n7 n4 n7 n7 2x 3 x2 4x 3 152. Multiply and simplify. ( x 3) 2 4x2 9 9 2 153. The length of a rectangle is m, while its width is m. Which of the following is true? y4 y 18 18 [A] perimeter: m [B] area: m2 y ( y 4) y( y 4) 11y 8 36 [C] perimeter: m [D] area: m2 y ( y 4) y( y 4) 11 1 154. Add: + 6( x 4) 6( x 4) 4 1 155. Add: + x2 x2 5x 6 5 5x 6 5 [A] [B] [C] [D] 5 x2 x2 4 x 4 2 4 1 + 156. Simplify: 5 3 2 + 7 85 63 7 [A] [B] [C] 5355 [D] 63 85 55 4 2 157. Simplify the complex fraction. x 3 3 5 x3 x2 36 158. Solve: x6 x6 [A] {6} [B] {–6, 6} [C] {–6} [D] 4x 8 159. Is x = –2 a solution of 1 ? x2 x2 160. The number of in-line skates sold between 1982 and 1991 can be modeled by the equation 1375 1 I = + x . The number of roller skates sold during the same period can be modeled by 4 4 11,835 3 S = – x , where x is the year. Use a graph to determine what year sales of in-line skates will exceed 7 7 sales of roller skates. [A] 1985 [B] 1987 [C] 1986 [D] 1984 161. Find the distance between the points (5, 8) and (5, 5) . [A] 23 [B] 10 [C] 13 [D] 3 162. Write the standard form of the equation of the parabola with its vertex at (0, 0) and directrix y –4 . 1 [A] x 2 16 y [B] y 16 x 2 [C] y 2 x [D] x –4 y 2 16 163. Identify the focus and directrix of the parabola given by y 2 4 x. 164. In a factory, a parabolic mirror to be used in a searchlight was placed on the floor. It measured 40 cm tall and 80 cm wide. Find an equation of the parabola. 80 cm 40 cm 165. Graph: 3x 2 3 y 2 = 75 166. The pool at a park is circular. You want to find the equation of the circle that is the boundary of the pool. Find the equation if the area of the pool is 900 square feet and (0, 0) represents the center of the pool. 167. Graph: 9 x 2 y 2 = 9 [A] y [B] y x x [C] y [D] y x x x2 y2 168. Sketch the graph of 1. 4 16 169. A skating park has a track shaped like an ellipse. If the length of the track is 80 m and the width of the track is 44 m, find the equation of the ellipse. x2 y2 170. Graph: 1 9 25 [A] y [B] y x x [C] y [D] y x x bg b g bg b g 171. Write the equation of the hyperbola with vertices at 2, 0 and 2, 0 and foci at 8, 0 and 8, 0 . 172. Find the center and radius of x 2 y 2 8 x 6 y 9 0. [A] center (4, 3); r = 4 [B] center (4, 3); r = 16 [C] center (–4, –3); r = 16 [D] center (–4, –3); r = 4 173. Find an equation of the hyperbola with vertices at (–3, 2) and (3, 2) and foci at (–5, 2), (5, 2). 174. Classify the conic section as a circle, an ellipse, a hyperbola, or a parabola. 144 x 2 64 64 y 2 [A] hyperbola [B] circle [C] parabola [D] ellipse 175. Classify the conic section as a circle, an ellipse, a hyperbola, or a parabola. x 2 9 y 3x 7 0 x 2 y 2 16 176. Solve: x y 4 [A] {(0, 0), (4, 4 )} [B] {(4, 4 ), ( 4 , 4 )} [C] {(0, 4 ), ( 4 , 0)} [D] {(0, 4), (4, 0)} 177. Solve the system by substitution: 3x 4 y 10 y 2 x 3 178. The cost, C, of manufacturing and selling x units of a product is C 23x 73 , and the corresponding revenue, R, is R x 2 35 . Find the break-even value of x. [A] 4 [B] 31 [C] 31 and 4 [D] 27 179. Find the first four terms of the sequence tn n(3n 7) . 180. Find the first four terms of the sequence tn n(6n 2) . [A] 4, 20, 48, 88 [B] 4, 20, 46, 84 [C] 6, 2, 0, –2 [D] 6, 22, 52, 94 181. Write the series with summation notation. 2 5 8 11 . . . 182. Find the common difference of the arithmetic sequence. 3 7 , 1, , 6, . . . 2 2 183. Find the sum of the first 14 terms of the arithmetic series. – 13 8 3 2 . . . [A] 268 [B] 273 [C] 278 [D] 546 1 1 184. Write a rule for the nth term of the arithmetic sequence with a1 and the common difference of . 2 6 185. Evaluate the sum. F I G J 30 2 i4 H K i 1 3 186. The number of lilies a large nursery can sell each day after April 1 is modeled by a sequence whose general term is an = 1700 75n , where n is the number of days after April 1. Find the number of lilies that can be sold on April 5th, 6th, and 7th. [A] 1250, 1325, 1250 [B] 1400, 1325, 1250 [C] 1325, 1250, 1175 [D] 1475, 1400, 1325 187. The distance (in feet) that a free-falling body falls in each second, starting with the first second, is given by the arithmetic progression 21, 63, 105, 147, . . . . Find the distance that the body falls in the 7th second. 188. Give the first four terms of the geometric sequence for which a1 = 4 and r 3. 4 4 4 [A] 4, 12, 36, 108 [B] 4 , , , 3 9 27 [C] 12, 36, 108, 324 [D] 7, 10, 13, 16 189. Find the common ratio of the geometric sequence. 2, –8, 32, –128, . . . 64 128 190. Write a rule for the nth term of the geometric sequence. 48, 32, , , ... 3 9 191. In a financial deal, you are promised $700 the first day and each day after that you will receive 65% of the previous day’s amount. When one day’s amount drops below $1, you stop getting paid from that day on. What day is the first day you would receive no payment and what is your total income? [A] 17th day; $1997.26 total income [B] 16th day; $1999.39 total income [C] 17th day; $1997.97 total income [D] 21st day; $1997.97 total income 192. A lunch menu consists of 6 different sandwiches, 4 different soups, and 4 different drinks. How many choices are there for ordering a sandwich, a bowl of soup, and a drink? 193. Eleven people are entered in a race. If there are no ties, in how many ways can the first two places come out? [A] 6 [B] 220 [C] 78 [D] 110 9! 194. Evaluate the factorial expression. 4! [A] 362,880 [B] 0 [C] 24 [D] 15,120 195. Find the number of permutations. 10 P6 196. You own 9 sweaters and are taking 4 on vacation. In how many ways can you choose 4 sweaters from the 9? [A] 362,880 [B] 36 [C] 126 [D] 504 197. A four-person committee is chosen at random from a group of 15 people. How many different committees are possible? 198. Expand ( p 2q ) 4 . [A] p 4 8 p 3q 24 p 2 q 2 32 pq 3 16q 4 [B] p 4 2 p 3q 2 p 2 q 2 2 pq 3 2q 4 [C] p 4 8 p 3q 12 p 2 q 2 8 pq 3 2q 4 [D] p 4 2 p 3q 4 p 2 q 2 8 pq 3 16q 4 b 199. Expand A 2 B . g4 200. A card is drawn from a standard deck of playing cards. Find the probability that it is not a face card (J, Q, or K) or an ace. 201. A student fails to study for a 9 question true/false test. What is the probability that the student gets 6 questions correct? 3 945 21 21 [A] [B] [C] [D] 256 2048 128 256 202. Half of a circle is inside a square and half is outside, as shown. If a point is selected at random inside the square, find the probability that the point is also inside the circle. r 2r Reference: [1.1.2.11] [1] [B] Reference: [1.1.2.16] [2] Associative property of addition Reference: [1.2.1.19] [3] [D] Reference: [1.2.1.28] [4] 96 Reference: [1.2.2.37] [5] [A] Reference: [1.3.1.40] [6] [A] Reference: [1.3.1.45] 5 [7] x 2 Reference: [1.3.2.49] [8] [B] Reference: [1.3.2.51] [9] $37,000 Reference: [1.4.1.58] [10] [A] Reference: [1.4.1.60] 7 [11] s 2 r 5 Reference: [1.4.2.63] 5 [12] C ( F 32) 9 Reference: [1.5.1.65] [13] 6 Reference: [1.5.1.66] [14] [C] Reference: [1.5.2.72] [15] 14 hours Reference: [1.5.2.76] [16] [A] Reference: [1.6.1.79] [17] [A] Reference: [1.6.1.83] [18] No Reference: [1.6.2.87] [19] 3 x 9 Reference: [1.6.2.89] [20] [C] Reference: [1.7.1.91] [21] [C] Reference: [1.7.1.95] [22] 1 x 4 –2 –1 0 1 2 3 4 5 6 x Reference: [1.7.2.98] [23] [A] Reference: [1.7.2.101] [24] 3,000 A 17,000 Reference: [2.1.1.2] [25] [D] Reference: [2.1.1.6] [26] It is not. Reference: [2.1.2.10] [27] 3 Reference: [2.1.2.13] [28] [A] Reference: [2.2.1.17] [29] [B] Reference: [2.2.1.24] 7 [30] y x 5 4 Reference: [2.2.2.28] [31] [D] Reference: [2.3.1.31] [32] [A] Reference: [2.3.1.34] 4 [33] slope ; y-intercept = (0, –12) 3 Reference: [2.3.2.42] [34] [D] Reference: [2.4.1.48] 7 7 [35] y 5x ; Slope: 5; y-intercept: (0, ) 3 3 Reference: [2.4.1.55] [36] [D] Reference: [2.4.2.63] 1 [37] y x 2 Reference: [2.6.1.75] [38] [A] Reference: [2.6.1.82] [39] y 5 4 3 1 –3 –2 –1 1 2 x Reference: [2.6.2.88] [40] [C] Reference: [2.8.1.109] [41] f(x ) 5 4 1 –6 –5 –4 –3 –2 x –1 Reference: [2.8.1.113] [42] [D] Reference: [2.8.2.122] [43] 1996, 2000 Reference: [3.1.1.4] [44] [D] Reference: [3.1.1.11] [45] No Reference: [3.1.2.17] [46] [B] Reference: [3.1.2.19] [47] 400 Reference: [3.2.1.23] [48] (–3, –4) Reference: [3.2.1.29] 2F I G J , 1 [49] 3H K 4 Reference: [3.2.2.36] [50] [C] Reference: [3.2.2.39] [51] Sample Acceptable Response: a c = 65 c = 4a by substitution: a 4a = 65 5a 65 = 5 5 a = 13 c = 4(13) = 52 children Reference: [3.3.1.42] [52] [A] Reference: [3.3.1.47] [53] y 10 –10 10 x –10 Reference: [3.3.2.59] [54] [A] Reference: [3.6.1.78] [55] [A] Reference: [3.6.2.83] [56] [B] Reference: [4.1.1.4] [57] [B] Reference: [4.1.1.10] [58] x = 4, y = 2 Reference: [4.1.2.19] [59] [C] Reference: [4.2.1.21] [60] [C] Reference: [4.2.1.25] [61] Not possible Reference: [4.2.2.29] [62] [A] Reference: [4.3.1.35] [63] [A] Reference: [4.3.1.38] [64] 155 Reference: [4.3.2.48] [65] [C] Reference: [4.3.2.52] [66] L O 8 5 M P , 8 –5 = 116 N Q 12 7 12 7 Reference: [4.4.1.67] L M 8 7 O P [67] M M 31 9 31 4P P N 31 31Q Reference: [4.4.2.71] [68] [D] Reference: [5.1.1.4] [69] [B] Reference: [5.1.1.8] [70] Vertex: (–2, 15); Opens down Reference: [5.1.1.17] [71] [A] Reference: [5.1.1.22] [72] y 10 –10 10 x –10 Reference: [5.1.2.24] [73] 7.96 in. Reference: [5.2.1.30] [74] 9 Reference: [5.2.1.34] [75] [D] Reference: [5.2.2.38] [76] [D] Reference: [5.2.2.39] [77] –5, 3 Reference: [5.3.1.45] [78] [A] Reference: [5.3.1.50] [79] 4 6 Reference: [5.3.2.55] [80] [C] Reference: [5.4.1.62] [81] [C] Reference: [5.4.1.71] [82] 7 2i Reference: [5.4.1.82] 5 5 [83] i 2 2 Reference: [5.4.1.87] [84] [C] Reference: [5.4.2.93] [85] [D] Reference: [5.5.1.100] [86] [D] Reference: [5.5.1.108] [87] x = –1 and –3 Reference: [5.5.2.113] 4 b g [88] y x 15 6 3 2 vertex = (15, –6) Reference: [5.5.2.115] [89] [D] Reference: [5.6.1.120] [90] [A] Reference: [5.6.1.129] [91] –32 Reference: [5.6.2.135] [92] [B] Reference: [5.7.1.138] [93] y 10 –10 10 x –10 Reference: [5.7.1.143] [94] [D] Reference: [5.7.2.147] F G [95] – , 8O P 5, g H 9Q Reference: [5.7.2.149] [96] [B] Reference: [6.1.1.2] b 30 [97] 45 c Reference: [6.1.1.6] [98] [D] Reference: [6.1.2.16] [99] [C] Reference: [6.2.1.18] [100] 688 Reference: [6.2.1.20] [101] [D] Reference: [6.2.2.22] [102] [C] Reference: [6.2.2.27] [103] The function is a quartic polynomial with degree 4 and leading coefficient 1. Reference: [6.3.1.40] [104] [B] Reference: [6.3.2.47] [105] [B] Reference: [6.4.1.50] [106] [A] Reference: [6.4.2.60] [107] [D] Reference: [6.4.2.63] [108] 3 Reference: [6.5.1.66] [109] [B] Reference: [6.5.2.80] [110] [C] Reference: [6.6.1.82] [111] [C] Reference: [6.6.1.84] 1 [112] , 3 2 Reference: [6.6.2.86] [113] [D] Reference: [6.7.1.90] [114] [B] Reference: [6.7.2.97] [115] 1, 11 Reference: [7.1.1.3] [116] [C] Reference: [7.1.1.10] [117] 0.481 Reference: [7.1.1.13] [118] [C] Reference: [7.1.1.17] [119] 4.340 Reference: [7.1.2.21] [120] [A] Reference: [7.2.1.28] [121] 7 Reference: [7.2.1.34] v 15 [122] 9 w Reference: [7.2.2.38] [123] [B] Reference: [7.3.1.39] [124] x 2 x Reference: [7.3.2.44] [125] [A] Reference: [7.4.1.47] [126] [C] Reference: [7.4.1.58] [127] No Reference: [7.4.2.63] [128] No f(x ) 3 1 –3 1 3 x –2 –3 Reference: [7.5.1.65] [129] You move the graph left 3 units and down 3 units. Reference: [7.5.1.69] [130] [A] Reference: [7.5.1.74] [131] g( x) 1 Reference: [7.5.2.79] [132] 18 weeks Reference: [7.5.2.80] [133] [B] Reference: [7.6.1.84] [134] [B] Reference: [7.6.2.90] [135] [D] Reference: [8.3.1.28] [136] [B] Reference: [8.3.1.35] [137] Decay Reference: [8.3.2.42] [138] [B] Reference: [8.4.1.44] [139] [C] Reference: [8.4.1.50] [140] 3 Reference: [8.4.2.55] [141] [D] Reference: [8.5.1.63] [142] [B] Reference: [8.5.1.68] [143] log4 3 log 4 x 3 log4 y Reference: [8.5.2.73] [144] [A] Reference: [8.6.1.76] [145] –0.4395 Reference: [8.6.2.80] [146] [A] Reference: [8.6.2.84] [147] x = –6.425 Reference: [9.1.1.4] [148] [A] Reference: [9.1.2.10] 1 [149] z xy 200 Reference: [9.1.2.13] [150] [D] Reference: [9.4.1.28] [151] [A] Reference: [9.4.1.36] x 1 [152] ( x 3)(2 x 3) Reference: [9.4.2.44] [153] [B] Reference: [9.5.1.47] 2 [154] x4 Reference: [9.5.1.48] [155] [C] Reference: [9.5.2.53] [156] [B] Reference: [9.5.2.56] 2( x 3) [157] 15 Reference: [9.6.1.63] [158] [A] Reference: [9.6.1.68] [159] It is not. Reference: [9.6.2.73] [160] [A] Reference: [10.1.1.1] [161] [D] Reference: [10.2.1.10] [162] [A] Reference: [10.2.1.18] [163] Directrix: x = 1 Focus: (–1, 0) Reference: [10.2.2.24] 1 2 [164] Answers may vary. Sample answer: y x 40 40 Reference: [10.3.1.27] [165] y 10 –10 10 x –10 Reference: [10.3.2.35] 900 [166] x 2 y 2 = Reference: [10.4.1.38] [167] [C] Reference: [10.4.1.43] y [168] 6 –6 –4 4 6 x –6 Reference: [10.4.2.46] x2 y2 [169] + = 1 1600 484 Reference: [10.5.1.48] [170] [A] Reference: [10.5.1.53] x2 y2 [171] 1 4 60 Reference: [10.6.1.61] [172] [D] Reference: [10.6.1.68] [173] x2 b g y2 2 1 9 16 Reference: [10.6.2.74] [174] [D] Reference: [10.6.2.80] [175] Parabola Reference: [10.7.1.86] [176] [D] Reference: [10.7.1.87] [177] ( 2 , 1 ) Reference: [10.7.2.88] [178] [D] Reference: [11.1.1.1] [179] –4, –2, 6, 20 Reference: [11.1.1.2] [180] [A] Reference: [11.1.2.6] a f [181] 3i 1 i 1 Reference: [11.2.1.11] 5 [182] 2 Reference: [11.2.1.16] [183] [B] Reference: [11.2.1.22] 1 1 [184] an n 6 3 Reference: [11.2.1.29] [185] 430 Reference: [11.2.2.33] [186] [B] Reference: [11.2.2.34] [187] 273 ft Reference: [11.3.1.37] [188] [A] Reference: [11.3.1.45] [189] –4 Reference: [11.3.1.52] [190] an 48 FI GJ 2 n 1 HK3 Reference: [11.3.2.59] [191] [C] Reference: [12.1.1.3] [192] 96 Reference: [12.1.1.5] [193] [D] Reference: [12.1.2.9] [194] [D] Reference: [12.1.2.12] [195] 151,200 Reference: [12.2.1.20] [196] [C] Reference: [12.2.1.25] [197] 1365 Reference: [12.2.2.29] [198] [A] Reference: [12.2.2.33] [199] A4 8 A3 B 24 A2 B2 32 AB3 16B4 Reference: [12.3.1.39] 36 9 [200] 52 13 Reference: [12.3.1.44] [201] [C] Reference: [12.3.2.52] [202] 8 Department of Education Core 40 Website http://doe.state.in.us/core40eca/welcome.html

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