<p>Algebra I Final Review 2011</p><p>Multiple Choice Identify the letter of the choice that best completes the statement or answers the question.</p><p>Match the function rule with the graph of the function.</p><p>____ 1. a. y c. y 5 5</p><p>4 4</p><p>3 3</p><p>2 2</p><p>1 1</p><p>–5 –4 –3 –2 –1 1 2 3 4 5 x –5 –4 –3 –2 –1 1 2 3 4 5 x –1 –1</p><p>–2 –2</p><p>–3 –3</p><p>–4 –4</p><p>–5 –5</p><p> b. y d. y 5 5</p><p>4 4</p><p>3 3</p><p>2 2</p><p>1 1</p><p>–5 –4 –3 –2 –1 1 2 3 4 5 x –5 –4 –3 –2 –1 1 2 3 4 5 x –1 –1</p><p>–2 –2</p><p>–3 –3</p><p>–4 –4</p><p>–5 –5</p><p>____ 2. Which of the quadratic functions has the narrowest graph? a. b. c. d.</p><p>____ 3. Is rational or irrational? a. rational b. irrational ____ 4. For which discriminant is the graph possible? y 6 4 2</p><p>–4 –2 2 4 x –2 –4 –6 –8 –10</p><p> a. b. c.</p><p>Short Answer</p><p>5. Write the polynomial in standard form. 4g – g3 + 3g2 – 2</p><p>6. Label by degree and number of terms. 6x3 – 9x + 3</p><p>Simplify the difference.</p><p>7. (4w2 – 4w – 8) – (2w2 + 3w – 6)</p><p>8. Simplify the sum. (4u3 + 4u2 + 2) + (6u3 – 2u + 8)</p><p>Simplify the product.</p><p>9. 8x2(4x2 + 4y6)</p><p>10. 7a3(5a6 – 2b3)</p><p>Factor the polynomial.</p><p>11. 40w11 + 16w6</p><p>12. Find the GCF of the terms of the polynomial. 8x6 + 32x3 13. The Johnsons want to cover their backyard with new grass. Their backyard is rectangular, with a length of 3x – 5 feet and a width of 4x – 10 feet. However, their rectangular swimming pool, along with its surrounding patio, has dimensions of x + 8 by x – 2 feet. What is the area of the region of the yard that they want to cover with new grass?</p><p>Simplify.</p><p>14.</p><p>15.</p><p>16. (2n2 + 4n + 4)(4n – 5)</p><p>17. (2k + 3)(2k2 – 4k – 3)</p><p>Find the square.</p><p>18.</p><p>Find the product.</p><p>19. (4p – 6)(4p + 6)</p><p>Complete.</p><p>20. z2 + 9z – 90 = (z – 6)(z + )</p><p>Factor the expression.</p><p>21. d2 + 10d + 9</p><p>22. 6x2 + 5x + 1</p><p>23.</p><p>24. 25. r2 – 49</p><p>26. 49b2 – 36</p><p>27. Identify the vertex of the graph. Tell whether it is a minimum or maximum. y 4</p><p>3</p><p>2</p><p>1</p><p>–4 –3 –2 –1 1 2 3 4 x –1</p><p>–2</p><p>–3</p><p>–4</p><p>28. Graph f (x)  2x 2  4x 1. Label the axis of symmetry and vertex.</p><p>29. 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 . 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? 30. Simplify .</p><p>Solve</p><p>31. 7 + 6 = 13</p><p>32.</p><p>33.</p><p>34.</p><p>35.</p><p>36.</p><p>37.</p><p>38.</p><p>39. Find the number of real number solutions for the equation.</p><p>40.</p><p>41.</p><p>42.</p><p>Simplify the radical expression.</p><p>43.</p><p>44.</p><p>45.</p><p>46.</p><p>47.</p><p>Simplify the radical expression by rationalizing the denominator.</p><p>48.</p><p>49. Simplify the expression.</p><p>50.</p><p>51.</p><p>52. (6 – 11)(6 + 11)</p><p>53.</p><p>54.</p><p>55.</p><p>56.</p><p>57.</p><p>58.</p><p>59.</p><p>60. 61.</p><p>62.</p><p>63.</p><p>64.</p><p>65.</p><p>66.</p><p>67.</p><p>68.</p><p>Solve the equation. Check your solution.</p><p>69.</p><p>70.</p><p>71. Solve the equation. Identify any extraneous solutions.</p><p>72.</p><p>73.</p><p>74. Evaluate for x = –3 and y = 2.</p><p>Write the number in scientific notation.</p><p>75. 8,670,000,000</p><p>76. 0.0805</p><p>Write the number in standard notation.</p><p>77.</p><p>78.</p><p>Simplify the expression. Write the answer using scientific notation.</p><p>79.</p><p>Find the common ratio of the sequence.</p><p>80. 2, –10, 50, –250, . . .</p><p>81. –164, –82, –41, –20.5, . . .</p><p>Find the first, fourth, and eighth terms of the sequence.</p><p>82. Evaluate the function rule for the given value.</p><p>83. for x = –3</p><p>84. Suppose a population of 250 crickets doubles in size every 6 months. How many crickets will there be after 2 years?</p><p>85. Identify the initial amount a and the growth factor b in the exponential function.</p><p>Find the balance in the account.</p><p>86. $2,400 principal earning 2%, compounded annually, after 7 years</p><p>87. What is the solution of the system of equations? y = 3x + 7 y = x – 9</p><p>88. The length of a rectangle is 2 cm more than four times the width. If the perimeter of the rectangle is 84 cm, what are its dimensions?</p><p>Solve the system of equations using substitution.</p><p>89. y = 2x + 3 y = 3x + 1</p><p>90. y = 2x – 10 y = 4x – 8 Solve the system using elimination.</p><p>91. 3x + 3y = –9 3x – 3y = 21</p><p>92. x + 2y = –6 3x + 8y = –20</p><p>93. –10x – 3y = –18 –7x – 8y = 11</p><p>94. By what number should you multiply the first equation to solve using elimination? –3x – 2y = 2 –9x + 3y = 24</p><p>Graph the inequality.</p><p>95. 96.</p><p>97.</p><p>Write the linear inequality shown in the graph. y</p><p>4</p><p>2</p><p>98. –4 –2 O 2 4 x</p><p>–2</p><p>–4</p><p>Solve the system of linear inequalities by graphing.</p><p>99.</p><p>Write a system of inequalities for the graph. 100. y 10</p><p>8</p><p>6</p><p>4</p><p>2 O –10 –8 –6 –4 –2 2 4 6 8 10 x –2</p><p>–4</p><p>–6</p><p>–8</p><p>–10 Algebra I Final Review Answer Section</p><p>MULTIPLE CHOICE</p><p>1. D 2. C 3. B 4. C</p><p>SHORT ANSWER</p><p>5. –g3 + 3g2 + 4g – 2 6. cubic trinomial 7. 2w2 – 7w – 2 8. 10u3 + 4u2 – 2u + 10 9. 32x4 + 32x2y6 10. 35a9 – 14a3b3 11. 8w6(5w5 + 2) 12. 8x3 13. 11x2 – 56x + 66 ft2 14. 15. 16. 8n3 + 6n2 – 4n – 20 17. 4k3 – 2k2 – 18k – 9 18. 19. 16p2 – 36 20. 15 21. (d + 9)(d + 1) 22. (3x + 1)(2x + 1) 23. 2(5x – 2)(2x + 3) 24. 25. (r – 7)(r + 7) 26. (7b + 6)(7b – 6) 27. (0, –1); maximum 28. Axis of symmetry: x = 1 Vertex: (1, -7) 29. 1.13 s; 29.25 ft 12 30. 7 31. 32. x = –1 or x = 1 33. z = –3 or z = 9 34. z = 1 or z = –2 35. c = 0 or c = 4</p><p>36.</p><p>37. 9, 14 38. 1.82, –0.22 39. 0.85, –0.85 40. 2 41. 2 42. 0 43. 44. 12 45.</p><p>46.</p><p>47. 4 5</p><p>48.</p><p>49.</p><p>50. 51. 52. 25 53. 54. 55. 1 56.</p><p>57.</p><p>58.</p><p>59. 60. 61. 62.</p><p>63.</p><p>64. 65.</p><p>66.</p><p>67.</p><p>68.</p><p>69. 144 70. 116 71. 5 72. 5 is a solution to the original equation. The value –8 is an extraneous solution. 73. 0 and 7 are solutions of the original equation. 1 74. 20 4 75. 76. 77. 90,000 78. 0.0907 79. 6.3  1017 80. –5 81. 82. –2; –16; –256 5 83. 9 84. 4,000 crickets 85. 680, 4.3 86. $2,756.85 87. (–8, –17) 88. length = 34 cm; width = 8 cm 89. (2, 7) 90. (–1, –12) 91. (2, –5) 92. (–4, –1) 93. (3, –4) 94. 3 y</p><p>4</p><p>2</p><p>95. –4 –2 O 2 4 x</p><p>–2</p><p>–4</p><p> y</p><p>4</p><p>2</p><p>96. –4 –2 O 2 4 x</p><p>–2</p><p>–4 y</p><p>4</p><p>2</p><p>97. –4 –2 O 2 4 x</p><p>–2</p><p>–4</p><p>98. y</p><p>4</p><p>2</p><p>99. –4 –2 O 2 4 x</p><p>–2</p><p>–4</p><p>100.</p>