Algebra 1 FINAL EXAM REVIEW Spring Semester Material …

1 Algebra 1 FINAL REVIEW Packet Name: _____. Per.: _____ Date: _____. Algebra 1. FINAL EXAM REVIEW . Spring Semester Material (by chapter). Your Algebra 1 FINAL will be on _____ at _____. You will need to bring your textbook and number 2 pencils with you to the FINAL exam. The FINAL exam will cover the entire year. Re- REVIEW the Material from the fall Semester as well. Do not lose this packet. Replacement packets will cost $$$. 1. Algebra 1 FINAL REVIEW Packet What You Must Memorize For FINAL b b2 4ac 1) Quadratic Formula: x= 2a 2) Standard Form: ax2 + bx + c = 0. 3) Perfect Squares from 0 to 169: 0 , 1 , 4 , 16 , 4) Discriminant: b2 - 4ac 5) Complete the Square: x2 5x + ___.

2 2. 5 25. 2 4. 6) Direct Variation: y=kx 7) Inverse Variation: 8) Vertex: 9) Pythagorean Theorem: a2 + b2 = c2. 10) X and Y Intercepts: To find y-intercept, set x's equal to zero. To find, x-intercepts, set y equal to zero and solve for x. 2. Algebra 1 FINAL REVIEW Packet ** show your work wherever applicable for full credit **. Chapter 5. Match each of the following polynomials with its special term name. 1. 4x2 + 27x 8 _____ a) trinomial 2. 5x3y10 _____ b) binomial 3. 3x + 5x3 _____ c) monomial Add or subtract the following polynomials. 4. (8t2 10t + 2) + (8t + 13) _____. 5. (x2 + 5x 1) (7x2 + 2) _____.

3 6. (x4 + 7x3 + 7) (2x4 4x3 + 1) _____. 7. (3n3 + n2 n 4) + (5n3 4n2 + 11) _____. Write in decimal form (standard notation). 8. 8 104 10. 9 10-3. 9. 105 11. 10-6. Write in scientific notation. 12. 400,000 14. 13. 5412 15. 3. Algebra 1 FINAL REVIEW Packet Simplify the following. Leave all answers with positive exponents. 16. x2 x7 22. (2w2x4)3. 17. (a4)12 28x 2. 23. y 9. x14. 18. (3b)3 24. x6. 8. x . 25.. 19. 9770. y . 1. 20. 7d4 d6. 5 3 26.. df 5 f 5. 21. 6x8y 8 3t4 v3. 27. 21t2 v6. Multiply or Divide. Express your answers in scientific notation. 28. ( 102)( 10 7) 102. 29. 105. 4. Algebra 1 FINAL REVIEW Packet Multiply.

4 30. 3x(4x 9) _____. 31. 4x2(x + 6) _____. 32. 2x2(15x3 10) _____. Multiply the following. Use your choice of methods, but show your work!! 33. (x + 9)(x 6) 36. (x 6)(x 8). 34. (x + 3)(4x + 5) 37. (7x + 3)(7x 2). 35. (3x 1)(8x + 1) 38. (3x3 2x2 + 6)(x + 5). 5. Algebra 1 FINAL REVIEW Packet Chapter 6. Factor out the largest possible monomial. 39. 5x2 15 40. 8a + 10b 16 41. 3c4 6c2 15c Factor completely (remember they are not always ready to go ). 42. x2 + 9x + 14 43. y2 15y + 54 44. t2 + 8t + 15. 45. m2 + 23m 24 46. x2 x 12 47. x2 + xy 42y2. Factor the following differences of squares completely. 48. x2 121 49.

5 100a2 144 50. 5m2 20. 6. Algebra 1 FINAL REVIEW Packet Factor the following perfect square trinomials completely. 51. x2 + 18x + 81 52. 25m2 + 30m + 9 53. 4y3 16y2 + 16y Factor completely (remember they are not always ready to go ). 54. 3y2 20y + 12 55. 2x2 13x 45 56. 18n3 + 33n2 6n Solve for the given variable. 57. (a 5)(a + 2) = 0 58. x(x 3) = 0 59. y2 + 23y 24 = 0. 7. Algebra 1 FINAL REVIEW Packet Chapter 10. Multiply or Divide. 2 3 3 7. 60. 61.. 3 16 4 8. 5x x 5x x 62. 63.. 2 15 2 15. Add or Subtract. 3 7 1 5. 64. + 65.. 4 4 3 7. 66. (5x 7) (8x 12) (12x + 4) (4x + 3). 67.. 5 5. Simplify Completely. 12x4y6 3x + 9.

6 68. 69. 8x7y2 3x 8. Algebra 1 FINAL REVIEW Packet 3a + 9b 6y2 + 3y 70. 71. 12a2 3y2 + 6y 14a2 14b2 b2 10b + 21. 72. 73. 21a 21b b2 11b + 28. Multiply. 5 4x 2x2 5. 74. 75.. 2x 17 x 2x 4x 4x + 4 m2 4 4m2. 76. 77.. 2x + 2 8x 5m m+2. 9. Algebra 1 FINAL REVIEW Packet Divide. 2x 12x 10x3 2x3y 78. 79.. 7 21 5x 6x2. 7 26 4x 6 6x 9. 80. 81.. x+4 x+4 5 25. Add or Subtract. 4x 6x 5x + 3 3x + 7. 82. + 83. +. 7 7 x+3 x+3. 2w2 + w 9 (4x + 2) (7x 6). 84. 3 85.. w3 w (3x + 1) (3x + 1). 10. Algebra 1 FINAL REVIEW Packet 3x2 + 2x 5 2x2 x + 6 1 5. 86. + 87.. 5x + 1 5x + 1 3x x 5m 3 2u v 88. 89. 2 2. m 1 m(m 1) uv3 u v 3a 1 1 x+4.

7 90. + 91. 2. a+2 a x 4 x x 12. 3 3 15 7. 92. + 2 93. 2 . x 2 x + 4x 12 b 9 2b 6. 11. Algebra 1 FINAL REVIEW Packet Chapter 11. 94. Estimate which two integers each square root is between: a) 73 is between ____ and ____ b) 13 is between ____ and ____. 95. Simplify (show work): a) 180 b) 252. c) x2y3 d) 196b5. 96. Simplify to find (show work): 700. a) 81 25 b). 7. c) 3 7 +8 7 d) 5 24 4 6. 5. e) f) 5 (5 + 5 ). 3. 97. Find the missing side length for each triangle (show your steps): a) b). u 13 2 v 12 5. 12. Algebra 1 FINAL REVIEW Packet 98. Solve (show work): a) 4x + 7 = 15 b) x + 5 + 8 = 19. 99. To hang a math poster in his office, Mr.

8 Zito leaned a 10 foot ladder against the wall, placing the bottom of the ladder on the floor 3 feet away from the wall. How high up on the wall was the ladder? (Show work. A labeled picture is also required). Chapter 13. 100. Write the quadratic formula. Solve the following using the QUADRATIC FORMULA. Complete all blanks. 101. 3x2 + 4 = 8x _____ (standard form). a = _____. substitution b = _____. c = _____. solution(s) for x: 13. Algebra 1 FINAL REVIEW Packet 102. 6x + 5 = -2x2. _____ (standard form). a = _____. substitution b = _____. c = _____. solution(s) for x: 103. Write the formula for the discriminant For questions 5 7, the blanks provided are for the following information: a) Substitute values for a, b, & c into the discriminant formula.

9 B) Find the discriminant. c) Tell how many solutions the quadratic has. 104. 3x2 + 4 = 3x a) d = _____ (substitution). b) d = _____ (simplified). c) _____ (# of solutions). 105. 4x + 2 = 3x2 a) d = _____ (substitution). b) d = _____ (simplified). c) _____ (# of solutions). 106. x2 = 8x 16 a) d = _____ (substitution). b) d = _____ (simplified). c) _____ (# of solutions). 14. Algebra 1 FINAL REVIEW Packet 107. Solve each of the following using the zero-product property. SHOW WORK. a) (x + 10)(x + 24) = 0 b) (2x 6)(5x + 2) = 0. c) x(x + 158) = 0 d) 5x(4x 16)(x + 9) = 0. 108. Solve each of the following equations by factoring: SHOW WORK.

10 A) x2 8x + 16 = 0 b) x2 + 4x 21 = 0. 109. Complete the square for the following: a) x2 + 20x _____ b) u2 26u _____. 110. Solve using any method you want show work!! a) x2 49 = 0 b) x2 + 10x = 4. 15. Algebra 1 FINAL REVIEW Packet Chapter 12. Identify the domain and range for each. Tell if the relation is a function. 111. h: {(3, 1), (2, 4), (3, 5), (4, 8)} 112. j: {(2, 7), (3, 6), (4, 5), (5, 4), (6, 3)}. a) domain: _____ a) domain: _____. b) range: _____ b) range: _____. c) function / not a function c) function / not a function 113. k: {(1, 2), (2, 3), (3, 2), (4, 1)} 114. m: {(4, 5), (4, 2), (4, 1), (4, 3), (1, 6)}.