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Algebra 1 Final Exam REVIEW Second Semester 2012 Name ________________ This will be a 25 point assignment. 15 points for completion and the last 10 points will be randomly selected questions graded for accuracy. ALL WORK THIS PACKET AND FINAL ANSWERS ON ANSWER SHEET. YOU WILL TURN IN THIS PACKET + THE ANSWER SHEET. Useful Formulas: x b b 4ac x 2a 2 z= Study each system of equations. If the system has only one solution, name the solution. If the system has NO solutions, write NO SOLUTION. If the system has INFINTELY many solutions, write INFINITE SOLUTIONS. 2 lines 1. ONE ( ) 2. ONE ( ) NO SOLUTIONS INFINITE SOLUTIONS 3. ONE ( ) NO SOLUTIONS INFINITE SOLUTIONS NO SOLUTIONS INFINITE SOLUTIONS 4. Use the graphing method to determine the solution of the system of linear equations. 2 y=− x+1 3 y= 2 x−3 3 5. Use the elimination method to determine the solution of this system of equations. 5x + 3y = 26 −2x + 3y = −2 6. Describe the steps you have to take to solve the given system of equations using elimination. Finish the problem and find the solution! 2x + 5y = 17 x − 3y = −8 7. Describe the steps you have to take to solve the given system of equations using elimination. Finish the problem and find the solution! 3x + 4y = −1 2x + 7y = −5 8. One number is 8 more than another number. The sum of the numbers is 6. What are the numbers? (hint: set up a system of equations to help yourself solve) 9. In the expression x-9, what is the exponent? what is the leading coefficient? 10. Simpify 54 • 515. Write the answer as a power to a power. 11. Simplify (34)8. Write your answer as a power to a power. 12. Simplify (−2x5y3)6 13. Evaluate (a • a3)2 when a = 2. 14. Simplify: exponents. x−12 • x5 • x−3 Your answer should not contain negative 15. Rewrite (7x−2y)(-6xy−3) without negative exponents. 16. Simplify: x8 Your answer should not contain negative exponents. x2 17. Simplify (5x)2 • (2x)0 18. Simplify (3xy)4(−2x)2 19. 2x Simplify 3 3 4 3x y 6 xy • 5 x 7 2 xy 6 20. Simplify 21. Rewrite 9.4 x 105 in decimal form. 22. Rewrite 0.00000000257 in scientific notation. 2 23. Evaluate the product (8.3 x 108) • (6.1 x 10-3) and express the answer in scientific notation. 24. Evaluate 1.5 x 10 6.5 x 10 4 9 hint: please let your calculator help you!!!! 25. Find the sum: (7x2 + 3x - 5) + ( -4x + 5x2 + 8y3) 26. Find the difference: (3x2 + 8x + 1) - (−x2 − 8x + 6) 27. A rectangle has a length of 4x - 1 and a width of x + 7. Which expression would represent the perimeter? (draw a picture to help yourself) 28. Simplify: (4x2 + 7x − 6) − (3x2 + 9x − 8) + ( -7x2 + 5) 29. Simplify: 6x(2x2 - 4) 30. Simplify: (2x - 5)(x + 7) 31. Simplify: (x + 10)(x − 10) 32. Find the product of (x + 2)(3x2 − 5x + 6) 33. The length of a rectangle is (3x + 5). The width is (x − 2). Find the area. Match each trinomial with its factor. You will not use all choices. _____34. x 8x 15 _____35. x 2 8x 15 _____36. x 2x 15 F. (x 5)(x 3) G. (x 5)(x 3) H. (x 5)(x 3) J. (x 5)(x 3) 2 2 Match each trinomial with its factor. You will not use all choices. _____37. x 4x 4 _____38. x 4 _____39. x2 4 A. Prime B. (x 2)(x 2) C. (x 2)(x 2) D. (x – 2)2 2 2 Match each trinomial with its factor. You will not use all choices. 2 _____40. 9x − 4 _____41. 9x2 + 12x + 4 _____42. F. Prime G. (3x – 2)2 H. (3x 2)(3x 2) J. (3x 2)(3x 2) 2 9x + 4 43. Factor the following trinomials, which one is a perfect square trinomial? A) x2 + 6x - 16 B) x2 + 8x + 16 44. Factor the following trinomials, which one is a perfect square trinomial? A) 4x2 + 12x + 9 45. Simplify: (4x - 3)2 B) 49x2 + 28x + 4 46. Find the mean, median, and mode for this data set. Round to the nearest hundredth if necessary. 12, 15, 12, 17, 18, 17, 20, 14, 12 mean ______ 47. median ______ 8 What is What is What is What is What is the the the the the 14 16 12 mode ______ std. deviation _____ 23 27 median of the data represented above?_____ smallest value in the data set?_____ first quartile of the data set?_____ third quartile of the data set?_____ mean? ________ Simplify each expression. 48. 51. 49 ______ 100 ______ 49. 52. 16 ______ 121 ______ 81 50. 25 ______ 53. 7 ______ 64 Solve each equation. Exact answers only, no decimal answers. 54. x2 = 225 55. 57. Simplify 24 58. Simplify 7 25 59. Simplify −7 20 60. Simplify 61. Simplify: 62. Simplify: 5 • 7 2 512a b 3 6 48x y 8 -4x2 = 44 56. 2(x + 2)2 = 10 63. Write the following equations in standard form: A) 2x + 5 = x2 B) x2 + 5 = 2x C) 7 + x2 = 5x 64. Name the solutions of the equation (x - 5)(x + 6) = 0 65. Name the solutions of the equation x2 - 6x + 9 = 0. 66. Identify b in the following equation x2 − 3 = -5x 67. Given a = 2; b = −3; c = −5, find b2 − 4ac 68. Name the zeros of the function shown in the graph. _____ Give the factors of these zeros: _______________ 69. Find the solutions to: 2x2 – 7 = x (leave answers in exact form, no decimals) 70. What is the discriminant for the following equation: -x2 – 5x - 10 = 0 71. For the same equation: -x2 – 5x - 10 = 0 How many solutions will you get? A) two real solutions B) one real solution C) no real solutions 72. What does it mean to have a z-score of -5? 73. Scientists conducted an aerial survey of a seal sanctuary and recorded the number x of seals they observed during each survey. The numbers of seals were normally distributed with a mean of 82 seals and a standard deviation of 12.1 seals. Find the z-score for a sample of 95 seals. 74. Completely factor: 75. Completely factor: 2x2 + 10x + 12 3x2 − 75 76. Make a box and whiskers plot for this data set. 20, 12, 8, 24, 15, 17, 11, 8, 32 77. Solve this equation using the quadratic formula!! x2 + 6x = 40 Provide both the exact answers and the decimal answers. 78. a) Your PSAT score was a 450 on the writing portion. The national mean was 550 and the national standard deviation was 42. Show how you would find the z-score for your PSAT score. b) According to your z-score are you average? Above average? Below average? c) What PSAT score (to the nearest whole number) would be associated with a z-score of 3 ? 79. Simplify: 4 x 512 x y 3 10 13 80. Solve : (be sure to provide all solutions) 81. Solve: (be sure to provide all solutions) 82. Solve and graph your solutions for the following situation: 83. Solve and graph your solutions for the following situation: