VIEWS: 115 PAGES: 11 POSTED ON: 8/10/2011 Public Domain
Advanced Algebra – Honors - Semester Exam 2010-2011 Semester grades will be computed as follows: 40% - 1st quarter percentage 40% - 2nd quarter percentage 20% - Semester Exam percentage The semester exam will consist of two independent parts: Part I – 32 multiple choice questions – no calculator – 50 minutes Part II – 28 multiple choice questions – calculator required – 40 minutes As this is a timed exam, NO additional time will be given on either part. In addition, students may not begin Part II of the exam until 50 minutes have passed. The 60 questions will be based upon the seven units studied this semester: Chapter 1A – 9 questions Chapter 9 – 9 questions Chapter 10 – 7 questions Chapter 1B – 8 questions Chapter 2 – 10 questions Families of Graphs – 5 questions Chapter 3 – 12 questions Note: Some questions DO crossover between units. There will be NO new material on the semester exam. Only the sections of each unit covered during the semester will be on the exam. Students may write on the exam; however, the Mastery Manager form will become the official document of your answers. Any writings on the exam will not contribute or detract from your grade. No additional time will be given for students to transfer their answers to the Mastery Manager form. Ample room will be given for students to work out problems on the exam. Therefore, the use of any additional paper will not be permitted. The attached review is intended to review the mathematics of all topics covered this semester. Students should not assume that the questions will be “like those on the review”. Answers to all 100 questions will be distributed on the last day of class before the semester exam. In addition to this review packet, students should review all POW‟s from the semester. Students have the original problems, their answers, and step by step solutions to each question. Advanced Algebra Honors – Semester Review Name ________________________________ Part I – No Calculator (32 questions – 50 minutes) 1. Which of the following represents a solution to x 8 2x 3 x 8 I. x = –2 II. x = 2 III. x = 0 A. I only B. II only C. III only D. I and III only E. II and III only 2. Given f x x 2 and g x 6 2x , evaluate f g 2 . A. 6 B. 2 C. –2 D. –6 E. –14 3. Given f x x 2 2x and g x 2x 3 evaluate f g x . A. 4x2 8x 3 B. 2x2 4x 3 C. 2x3 x2 6x D. 3x2 x E. 4x2 2x 3 x3 4. Which of the following represents the inverse of f(x) if f x ? 2 3 A. f 1 x 2x C. f 1 x 2x 6 D. f 1 x 2x 3 E. f 1 x x 2 B. f 1 x 2 x3 5. Three lines are represented below by two points which lie on each line. Which lines are perpendicular? I. (7, 3) and (2, 1) II. (10, 6), (0, 10) III. (6, 11) and (4, 6) A. I and II B. I and III C. II and III D. all are perpendicular E. none of these 6. Which of the following best represents the graph of h(x) below? A. h x x 2 B. h x ln x 1 C. h x x 2 D. h x ln x 1 E. h x ln x 1 7. Which of the following represents the equation of the line passing through (2, 5) and (3, 7)? 1 1 A. y 3 2 x 7 B. y 5 2 x 2 C. y 7 2 x 3 D. y 7 x 3 E. y 5 x 2 2 2 8. Which of the following represents the equation of the line passing through (7, 1) and (6, 4)? A. y 3x 22 B. y 3x 20 C. y 3x 22 D. y 3x 4 E. y 3x 4 9. If f x 4x 3, evaluate f 3x . A. 43x – 9 B. 3x – 3 C. 12x – 3 D. 12x – 9 E. 3x – 9 10. Which of the following best represents a solution to 3x 4 5x 8 A. , 6 B. , 6 C. 6, D. 6, E. 6, 6 x 2y 3 11. Which of the following is a correct computation to solve ? 3x 4y 5 1 2 3 4 2 3 1 1 3 3 1 4 2 3 1 3 3 A. B. C. 2 2 4 5 D. 2 3 1 5 E. 3 4 5 3 1 5 2 4 5 12. A total of $100,000 is placed into two mutual funds. The first fund earns 10% and the second fund earns 15% interest each year. The total interest earned in one year was $5000. Which of the following represents a system of equations which will yield the amount invested at each rate? 10x 15y 100000 x y 100000 A. B. x y 5000 10x 15y 5000 x y 100000 0.10x 0.15y 100000 C. D. 0.10x 0.15y 5000 E. 0.10x 0.15y 5000 x y 5000 13. Which of the lines below have a slope of zero? I. y 2x 3 II. x 4 III. y = 7 A. I only B. II only C. III only D. II and III only E. I, II and III only 3 2 14. Evaluate 1 1 A. 1 B. 6 C. –1 D. 7 E. –5 15. Which of the following best represents the graph of m(x) below? 1 A. m x 1 3 D. m x 2 x2 x 3 1 E. m x 1 B. m x 2 3 x3 x 2 2 1 C. m x 2 x 3 2 16. Which of the following best represents the equation of the line which passes through (2, 4) and (7, -6) A. y 4 2 x 2 B. y 4 2 x 2 C. y 6 2 x 7 D. y 6 2 x 7 E. y 6 2 x 7 2x 3 x 1 17. If f x what is the value of f(3) + f(-3)? 3x 5 x 1 A. 0 B. –12 C. –18 D. –11 E. –13 18. Rewrite 3 x 4 using interval notation A. 3, 4 B. 3, 4 C. 4, 3 D. 3, 4 E. 4, 3 19. Which of the following relationships is a function? I. Domain Range II. x 2 y 2 4 III. {(2, 4), (3, 5), (4, 6), (7, 9)} 2 3 -1 4 0 5 3 A. I only B. II only C. III only D. I and III only E. I, II, and III 20. Which of the following is equivalent to x 0 ? A. x B. 0x C. 1 D. 0 E. 90 21. Which of the lines below have a slope which is undefined? I. y 2x 3 II. x 4 III. y = 7 A. I only B. II only C. III only D. II and III only E. I, II and III only x 2 5x 6 22. Which of the following values of x is not an element of the domain of f x ? x2 4x 3 I. 1 II. 2 III. 3 A. I only B. II only C. III only D. I and II only E. I and III only 23. Which of the following represents x3 y3 in factored form? A. x y x2 xy y2 B. x y x2 xy y2 C. x y x2 2xy y2 D. x y x2 2xy y2 E. x y x2 xy y2 24. A student loan for college is given in two parts….one part is at 8% interest and the second part is at 12% interest. If the total of the student loan is $20000, and if $232 in interest must be paid after the first year, set up the system of equations necessary to find the amount of each part of the loan. x y 20000 x y 232 A. B. 8x 12y 232 0.08x 0.12y 20000 x y 232 x y 20000 0.08x 0.12y 232 C. D. E. 8x 12y 20000 0.0096(x y) 232 x y 20000 5 2 25. Evaluate 3 7 A. 32 B. 11 C. 29 D. –11 E. –29 26. Which of the following functions could be called a constant function? 2x 1 A. f x 2x 3 B. f x 3 C. f x x 2 6 D. f x x3 E. f x x3 1 2 3 27. Which of the following is a correct second column expansion of 4 5 6 ? 7 8 9 4 6 1 3 1 3 4 6 1 3 1 3 2 3 1 3 1 2 A. 2 5 8 B. 2 5 8 C. 4 5 6 7 9 7 9 4 6 7 9 7 9 4 6 8 9 7 9 7 8 2 3 1 3 1 2 4 6 1 3 1 3 D. 4 5 6 E. 2 5 8 8 9 7 9 7 8 7 9 7 9 4 6 28. Which of the following best represents the graph of f(x) below? A. f x x 4 x 2 3x 1 B. f x x3 x 2 4x 1 C. f x x 5 x 2 1 D. f x x 4 3x 3 x 2 1 E. f x x3 x 2 4x 1 3 4 29. Which of the following represents A 1 if A ? 2 1 1 3 4 1 1 4 1 1 4 1 3 2 1 3 2 A. 2 1 B. 2 3 C. 5 2 3 D. 5 4 1 E. 5 5 5 4 1 30. Which of the following represents the solution x2 5x 3 0 5 13 5 13 A. B. C. 5 13 D. 5 13 E. 5 2 2 3 31. Which of the following is equivalent to ? 2i 3 2 1 6 3 3 3 A. B. i C. i D. 3i E. 3i 5 5 5 5 5 2 2 32. If the real zeros of f x x 2 9x 8 are a and b, and if a > b, find the value of 3a – 2b. A. 19 B. –19 C. 13 D. –13 E. 40 33. Given 3 is a zero of f x x3 3x 2 x 3 , which of the following represents the SUM of the other two zeros? A. –2 B. 2 C. 0 D. 1 E. –1 5x 34. Which of the following best represents the domain of g x ? 5x A. , 0 , 0, B. , 5 C. , 5 D. 5, E. 5, 1 35. Which of the following are vertical asymptotes of f x x 2 x 5 I. x = -2 II. x = 5 III. y = 0 A. I only B. II only C. III only D. I and II only E. I, II and III x2 36. Which of the following is not in the domain of f x 2 x 3x 2 I. 0 II. 1 III. 2 A. I only B. II only C. III only D. II and III only E. I, II and III 37. The graph below best represents what type of function? A. reciprocal B. cubic C. quartic D. trigonometric E. exponential 38. Which of the following expressions simplifies to –1? x4 7x x2 x 6 I. II. III. 4x x7 6 x x2 A. I only B. II only C. III only D. I and II only E. II and III only 39. When graphed, which of the following will contain a „vertical asymptote‟ as part of the graph? x2 5x 6 x2 x4 I. f x 2 II. g x III. h x x x6 4 x2 4x A. I only B. II only C. III only D. I and II only E. I, II and III 2x 2 40. Which of the following represents a vertical asymptote of f x ? x 5x 4 2 I. x = -1 II. x = -4 III. x = 0 A. I only B. II only C. III only D. I and II only E. i, II and III x2 1 41. Which of the following values is not in the domain of g x 2x 2 A. 1 B. 2 C. –1 D. 0 E. domain is , 42. Which of the following best represents the graph of y 31 x ? A. B. C. D. 43. If the solutions to x2 5x 6 0 are a and b, which of the following represents the value of a + b? A. –6 B. –5 C. 0 D. 5 E. 6 44. Which of the following is a solution to x2 4x 1 0 ? A. 2 3 B. 4 2 3 C. 2 i 3 D. 4 2i 3 E. 1 3 45. Which of the following best represents the graph of f x x 1 4 ? 2 A. B. C. D. E. 46. Which of the following represents the remainder when x4 2x3 4x2 5 is divided by x + 3? A. 94 B. –2 C. –14 D. 4 E. 28 47. A polynomial function of degree four has zeros of i and 1 i . Which of the following is also a zero of the function? 1 A. 1 i B. C. 1 i D. 1 E. 0 i 48. Which of the following represents a quadratic function whose vertex is (-1, 2) and passes through (0, 4)? A. f x 2 x 1 2 B. f x 4 x 1 2 C. f x x 4 2 2 2 D. f x x 1 2 E. f x 2 x 1 2 2 2 49. How many real solutions are there to 5x2 7x 16 0? A. 0 B. 1 C. 2 D. 3 E. 4 50. Given the graph of the function below, which of the following is a zero of the function? I. -2 II. 0 III. 2 A. I only B. II only C. III only D. I and III only E. I, II, III 51. When rewritten in a + bi form, 16 2i 3 4i 2 A. 19i B. 13 2i C. 13 2i D. 17 2i E. 15 2i 52. Factor x3 y3 A. x y x2 xy y2 B. x y x2 xy y2 C. x y x2 2xy y2 D. x y x2 2xy y2 E. x y x2 xy y2 53. The graph below best represents what type of function? A. square root B. cubic C. quartic D. logarithmic E. exponential 4x 5 2 54. =? A. 16x 25 2 B. 16x2 40x 25 C. 16x2 20x 25 D. 8x 10 E. 16x 25 x 2 3x 1 55. Which of the following represents the remainder of ? x 1 A. -2 B. -1 C. 0 D. 1 E. 2 Advanced Algebra Honors – Semester Review Name ________________________________ Part II – Calculator Required (28 questions – 40 minutes) 56. Which of the following best represents an even function? A. f x x 2 4 B. f x 2x 4x 6 C. f x x 4 D. f x 5x 1 E. f x 2x 4 2 2 2 2 3 57. Which of the following best represents a solution to 0.3x 0.7 500 x 347.72 ? A. x = 147.72 B. x = 2.28 C. x = –5.7 D. x = –2.28 E. x = 5.7 x y z 5 58. Which of the following represents the solution to 3x 2y z 2 ? 2x y 3z 10 A. (1, -1, 3) B. (2, -5, -2) C. (-1, 7, 13) D. (3, -9, -7) E. (17, 1, 38) 59. Bobby and his dad were blowing up balloons for a party. Bobby blew up 2 balloons for every 3 that his dad blew up. If they blew up a total of 80 balloons, how many did his dad blow up? A. 30 B. 32 C. 48 D. 50 E. 80 3 6 1 1 0 5 60. Given A and B 1 2 7 , find 3A – 2B. 0 5 2 7 2 7 18 13 7 18 2 11 18 7 7 18 13 18 A. B. C. D. E. 9 2 11 8 0 11 8 2 19 20 2 9 20 13 20 1 2 4 0 3 5 61. 3 1 6 1 6 2 ? 0 2 1 4 1 0 1 5 9 141 73 128 A. 4 7 8 1 B. 91 C. 47 33 73 D. –84 E. does not exist 91 4 3 1 101 38 62 6x 4y 26 62. If the solution to is (a, b), what is the value of a + b? 7x 5y 11 A. 5 B. -5 C. 3.5 D. 4 E. 24.2 63. Which of the following represents a function in terms of x? I. 3y 2x 9 17 II. 2x2 x 4y III. y 2 2x 3 A. I only B. II only C. III only D. I and II only E. I and III only 64. Which of the following best represents the slopes of normal (perpendicular) lines? 1 A. y = 0 B. x = 0 C. undefined D. m1 E. 0 m2 2 65. Which of the following best represents 2x3 in simplified form? A. 4x5 B. 2x6 C. 4x5 D. 4x6 E. 2x5 66. Which of the following represents the equation of a vertical line? 1 A. y = 0 B. x = 0 C. undefined D. m1 E. 0 m2 x2 4 67. Which of the following best represents the range of f x 4 x 3 A. , 6.47 , 6.47, B. , C. , 2.47 , 2.47, D. , 2.47 , 6.47, E. , 0.76 , 5.24, 68. Which of the following is an odd function? A. y 2x2 3x B. y 3x 3 x C. y 2 x3 x5 D. y 4 E. y 3x 7 Questions 69-71 use the graph below: 2 3 1 69. The graph of 1 has a slope described best by which of the following? Circle the letter of your choice. A. zero B. undefined C. positive D. negative E. none of these 70. The graph of 2 has a slope described best by which of the following? Circle the letter of your choice. A. zero B. undefined C. positive D. negative E. none of these 71. The graph of 3 has a slope described best by which of the following? Circle the letter of your choice. A. zero B. undefined C. positive D. negative E. none of these 72. If f x x 2x , evaluate f 3t 2 A. 3t 2 6t B. 3x2 6x C. 9t 2 3t D. 9x2 3x E. 9t 2 6t 73. Which of the following best estimates 3x 4x3 when x = 2.2? A. –35.9 B. –36.0 C. –674.8 D. –2.2 E. –35.8 74. Three lines are represented below by two points which lie on each line. Which lines are parallel? I. (6, 3) and (4, 2) II. (-3, 9) and (1, 7) III. (0, 4) and (2, 0) A. I and II B. I and III C. II and III D. none are parallel E. all are parallel 75. The cost of renting a car to drive to Florida for Spring break is $55 per day plus $0.13 per mile driven. If the round trip is 1632 miles, how much does it cost (before tax) to rent a car for a ten day long Spring break? A. $1687.13 B. $212.16 C. $55.13 D. $267.16 E. $762.16 1 2 3 76. Which of the following is a third column expansion of 4 5 6 ? 7 8 9 2 3 1 3 1 2 2 3 1 3 1 2 A. 7 8 9 B. 7 8 9 5 6 4 6 4 5 5 6 4 6 4 5 4 5 1 2 1 2 4 5 1 2 1 2 C. 3 6 9 D. 3 6 9 7 8 7 8 4 5 7 8 7 8 4 5 4 5 1 2 1 2 E. 6 9 7 8 7 8 4 5 77. Which of the following best represents the point-slope form of the equation of a line? A. y 3 2 x 1 B. y 0 C. x 2 D. y 2x 1 E. 3x + 2y = 7 x 4 3x2 2x 5 78. Which of the following is the remainder of ? x2 1 A. 2x 5 B. 2x 5 C. x2 1 D. 2x 7 E. 2x 3 Questions 79-84 use the table below: x 0 1 2 3 4 f(x) 1 3 4 2 0 g(x) 4 2 0 3 1 g 1 f 0 79. ? g 1 A. 0.5 B. –1 C. –0.5 D. 1 E. not possible 80. f g 2 =? A. 1 B. 0 C. 4 D. 2 E. not possible 81. f g 3 ? A. 0 B. 1 C. 2 D. 3 E. 4 82. g f 4 ? A. 0 B. 1 C. 2 D. 3 E. 4 83. f 2 f 3 ? A. 6 B. 5 C. 8 D. 11 E. not possible g 84. 4 ? f 1 A. 1 B. 0 C. 4 D. E. not possible 4 85. Which of the following best represents the slope of a horizontal line? 1 A. y = 0 B. x = 0 C. undefined D. m1 E. 0 m2 86. Which of the following is an even function? A. y2 x2 B. y x 4 4x C. y x3 x D. x 2y 3 E. y x 4 x2 2 1 87. Which of the following best represents A 2 if A ? 1 3 4 1 1 3 1 3 1 3 5 1 3 5 A. B. 1 2 C. D. E. 1 9 7 1 2 5 8 49 5 8 3x 2 88. Which of the following best represents the domain of g x ? 2 3x 3 2 2 3 A. , B. 0, C. , D. , E. , 2 3 3 2 89. Where is the relative maximum of f x x 3x ? 2 A. 0 B. 3 C. 2.25 D. 1.5 E. there is no max 90. Which of the following best represents the inverse of f x 3x 2 x2 x 1 x2 A. f 1 x B. f 1 x 2 C. f 1 x D. f 1 x E. does not exist 3 3 3x 2 3 Questions 91-92 using the following information: A 4-H Club member raises only geese (x) and pigs (y). The goal is to maximize profit She wants to raise no more than 16 animals total There can be no more than 10 geese. She spends $15 to raise a goose and $45 to raise a pig, and has $540 available for this project. Each goose produces a profit of $6 and each pig a profit of $20. 91. Which of the following represents the objective function to be maximized? A. z 10x y B. z = x + y C. z = 15x + 45y D. z = 6x + 20y E. z = x – y 92. Determine the constraint inequalities. x y 16 x y 16 x y 16 y 10 x 10 x 10 x y 16 x y 16 A. y 10 B. 15x 45y 540 C. x 10 D. 15x 45y 540 E. 15x 45y 540 15x 45y 540 x 0 15x 45y 540 x 0 x 0 y 0 y 0 y 0 93. Exactly 40000 tickets have been sold for the Super Bowl so far. Some tickets were sold for $200 and some were sold for $100. If the total receipts thus far are $6,100,000, how many tickets have been sold for $200? A. 0 B. 30500 C. 21000 D. 200 E. 19000 94. Which of the following represents the range of f x 2 x 1 3 ? 2 A. , B. 1 , C. , 1 D. 3, E. , 3 95. Where is the relative minimum of f x x 5x 2x 3 ? 3 2 A. –15.06 B. 0.21 C. 3.12 D. –2.79 E. –3.00 96. Lucky‟s stamp collection consists of $0.37 and $0.39 stamps. If she has a total of 40 stamps worth $15.10, how many $0.37 stamps does Lucky have? A. 25 B. 39 C. 37 D. 15 E. 13 97. Which of the following best represents f 3.9 if f x 7x 1 ? 1 10 A. –0.414 B. –28.3 C. –0.353 D. –1 E. 39 98. What is the minimum value of f x 2x 3x 4 2 A. 0.75 B. 4 C. 2.875 D. 2 E. 3 99. Which of the following represents the equation of a line normal to 3x 4y 5 which passes through (-1, -3)? 3 3 3 A. y 3 x 1 B. y 3 4 x 1 C. y 3 x 1 D. y 3 4 x 1 E. y 3 x 1 4 3 4 3 4 100. Which of the following is a zero of the function f x x3 3x 2 4x 12 ? I. 2 II. 3 III. –2 A. I only B. II only C. III only D. I and II only E. I and III only