Algebra 2 CP. June 2015 Final Exam REVIEW. Exam Date: Time: Room:

Transcription

1 June 2015 Final Exam REVIEW Student s Name: Teacher s Name: Exam Date: Time: Room: The Algebra 2 exam will consist of approximately 55 multiple choice questions, each worth the same number of points. The exam will cover the following sections from the textbook. Chapter 6: Chapter 7: Chapter 8: Note: School policy mandates a penalty for cheating on an exam to be a grade of zero for that exam. The term cheating includes intent to cheat. Calculators may be checked for the inclusion of extraneous material. No papers should be placed in the calculators. The programs may be checked and erased. Any information there may be considered intent to cheat. Before the exam, clear your calculator of any formulas, notes, or any such items, which could be perceived as useful, or providing an unfair advantage. The best solution is to RESET and clear the calculator memory. There may be spot checks regarding programs and memory. In addition, NO CELL PHONES are permitted in the testing area. Any other electronic devices may be perceived as intent to cheat. Keep all such devices out of the testing area. Mr. Matheus, Mrs. Buonomo-Gramata, Mrs. Dengel, Mr. Dominguez, Ms. Keeble, Mr. Ladolcetta, Ms. Prigge, Mr. Memory & Mr. Wasserman

2 1. Find an equation in factored form with integral coefficients with solutions and 2. Find an equation in factored form with integral coefficients with solutions and 3. Use synthetic substitution to evaluate when. a. c. d. 4. Divide: using long division 5. Divide: by using synthetic division 6. Divide: using long division 7. Divide: by using synthetic division 8. Solve by using your graphing calculator. Round your answer to the nearest thousandths. 9. Solve: 10. Solve: 11. Solve: 12. Solve: 13. Simplify: 14. Convert to radical form. For questions simplify the following expressions. Write your answer with positive exponents Is equal to? Justify your answer. 20. Solve: 21. Solve: 22. Solve: 23. Solve:. How many of the solutions are extraneous? 2

3 24. Let and. Find ( ). a. c. d. 25. Let and. Find the following and identify their domains: a. c. 26. Let and. Find the following and identify their domains: a. 27. Let and. Find 28. Let and. Find. 29. Let. Find ( ) a. c. d. 30. Let. Find and state its domain and range. Is a function? 31. Let and. Find and its domain. 3

4 32. Find the inverse of. Graph both the function and inverse, and identify each domain and range. 33. Find the inverse of the function. Then find ( ). 34. Identify the domain and range of the function 35. The projected worth (in millions of dollars) of a large company is modeled by the equation. The variable represents the number of years since What is the projected annual percent of growth, and what should the company be worth in 2007? 36. A company had a total debt of $320,000 in Between 1980 and 1987 it was able to reduce its debt 15% each year. Write an exponential model for the situation. Approximate the company s debt in 1987 to the nearest $ Find the value of $1000 deposited for 10 years in an account paying 6% annual interest compounded monthly. 38. Find the domain, range, and horizontal asymptote for the function 39. If $5500 is deposited in an account at the bank and earns 9% annual interest, compounded continuously, what is the amount in the account, rounded to the nearest dollar, after 6 years? 40. Write an exponential function of the form whose graph passes through the given points and. Round all values to the nearest hundredth. 41. Iodine-131 is used to find leaks in water pipes. It has a half-life of 8.14 days. Write the exponential decay function for a 200-mg sample. Find the amount of iodine-131 remaining after 72 days. 4

5 For questions 42 and 43, and represent integers. Determine whether the statement is sometimes, always, or never true. 42. A root of the equation is and are roots of the equation. 44. Solve the following equation completely: 45. Given the equation, find the domain and range as well as the horizontal asymptote. 46. Evaluate: 47. Rewrite the following exponential equation as a log equation: 48. Rewrite as a single log: 49. Expand: 50. Expand: 51. Evaluate:. Round to the nearest hundredth. 52. Solve:. Round to the nearest hundredth. 53. Solve:. Round to the nearest hundredth. 54. An initial investment of $400,000 is made into an account with 3% interest compounded continuously. How long will it take for the investment to be valued at $450,000? 55. Solve:. Round your answer to the nearest 1/100 th. 56. Simplify the rational expression. State any restrictions on the variable. 57. Simplify the rational expression. State any restrictions on the variable. 58. Which model would best fit the data in the table? a. Linear Quadratic c. Cubic d. Absolute Value x f(x)

6 59. For which quadratic equation is -3 the constant term? a. ( ) c. ( )( ) d. 60. Factor the expression a. c. d. 61. Find the factored form of the polynomial Factor the expression. 63. Factor. a. c. d. a. c. d. a. c. d. 64. Simplify: a. c. d. 65. Write an example of a quartic trinomial function written in standard form that has a quadratic term with a coefficient of 3. 6

7 66. Solve 67. Given and, find the linear term of. 68. Use synthetic division to determine whether is a factor of 69. When a polynomial is divided by a binomial, and the remainder is zero, what conclusion(s) can be made? 70. Use a calculator to find solutions to 71. Solve 72. List all possible rational solutions to 73. Rewrite in standard form. Classify the polynomial by degree and the number of terms. 74. Find the relative maximum, relative minimum, and zeros of the function 75. Identify the cubic model that fits the following list of points: 76. Find the zeros of the function and state the multiplicity of multiple zeros 77. For determine the zeros. State the multiplicity of any multiple zeros. For the function in each graph, identify the zeroes and each zero s multiplicity

8 80. Graph the function ( ). 8

9 Answer Key c. D: (D) a. D: x -4 D: x -4, 4 D: (D) D: [ ), R: Not a function 31., No x = x = 5 (x = 0 is extraneous) 24. (C) 25. a. D: 33. ( ) 34. [ ) [ ) 35. ; D: 9

10 The binomial is a factor of ; Never 43. Never cubic polynomial with 4 terms 74.,, A 60. C 61. B 62. C 63. B 64. A Yes 76., and with a multiplicity of and, both with a multiplicity of 2 78., -3 has multiplicity of and, both with a multiplicity of