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MAT0022 DEVELOPMENTAL ALGEBRA Name:___________________________ PRACTICE FINAL Simplify each expression. Solve each equation for the specified variable. 1. 9 3 42 • 2 10 14. Solve for p: 6p − 5q = 3 2. 24 2(3 9)2 32 15. Solve for y: 3x + 4y = 7 3. Solve each inequality. 9 16 8 16. 4x + 6 3(3x 5) 4. 17 16 24 17. 24 − 5x > −3x + 18 Evaluate the expressions for the given values of x and y. 5. 5xy x2; x = 4 and y = 2 6. x2 − 2xy + 3y2; x = −2 and y = −1 Translate and solve. 18. Eight times the difference of some number and 5 is 32. Find the number. 19. Twelve subtracted from three times a number is 6 more than the number. Find the number. Simplify each expression. 7. 3x – 2(5x + 5) + 4 20 The product of five and a number is the same as the number increased by 44. Find the number. 8. −2(5y + 3) – 9y – 13 Solve each problem. 9. 5x – 3 − 4(x – 5) 21. The perimeter of a rectangle is 28 feet. Find the length of the rectangle if the length is 4 feet less than two times the width. Solve each equation. 10. 8 2(a 1) 9 a 11. 7(2 x 3) 6 x 1 7 x 12. 13. 1 3 y 2 y 1 3 4 3 x 2 1 3x 7 ©Palm Beach State College 22. The number of women attending a conference was three less than twice the number of men. If 51 people attended the workshop, how many were women? Simplify each expression. 23. (2r 3 s 2t )(5st 6 ) 24. ( x3 y5 z 0 )( x4 y 2 ) Page 1 of 4 Developmental Algebra – Practice Final Simplify each expression. Factor each expression completely. 25. (a 7b2c0 )3 38. 5x2y3 − 15x3y + 10xy2 39. 16 x4 y 2 8x3 y 2 4 x2 y 2 26. ( x3 y 2 z )5 40. 25x2 − 16y2 2 6 3 27. 28. x y z x11 yz 4 41. 64a4 − 9b2 x6 y 5 x 2 y3 Factor each expression completely. 2 42. 9y − 3x + 3y − xy Write the number in scientific notation. 29. 0.0000415 43. ax − a + bx − b Write the number in standard form. 44. 4x2 − 11x + 6 30. 6.102 × 106 45. 5x2 13x 6 Add the polynomials. Solve each equation. 31. (2x2 − 3x − 5) + (−8x2 + 5x − 2) 46. 3y2 − 4y − 15 = 0 Subtract the polynomials. 2 2 32. (x + 2x − 5) − (6x − 4x − 1) 47. 4a2 9a 5 0 2 Multiply the polynomials. 48. x + 7x − 60 = 0 33. 6x3 (3x2 − 5) 49. x2 − 2x − 48 = 0 34. −4x2y (5x3y2 − 2x2y + 3x) Simplify each expression. 35. (3x − 2)(4x + 1) 50. 2 x2 7 x 4 x 2 16 51. x2 4x 3 x2 1 36. (4x − 5y)2 37. (2x − 7)(2x + 7) ©Palm Beach State College Page 2 of 4 Developmental Algebra – Practice Final Simplify each expression. Assume the variable represents a non-negative number. Graph each linear equation. 59. y = −4x − 5 52. 60a6 53. 144 x7 y 4 6 5 4 3 2 1 -6 -5 -4 -3 -2 -1 Simplify each expression. 54. 3 2 3 21 55. 3 2 75 27 y x 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 60. 2x + y = 4 6 5 4 3 2 1 56. 4 5 6 45 80 Find the x-intercept for the given line. -6 -5 -4 -3 -2 -1 57. 2x + 5y = 15 Find the y-intercept for the given line. -1 -2 -3 -4 -5 -6 y x 1 2 3 4 5 6 58. x + 3y = 2 ©Palm Beach State College Page 3 of 4 Developmental Algebra – Practice Final ANSWER KEY 1. 25 27. 53. 12 x3 y 2 x y5 x9 z x8 y8 2. −57 3. −1 4. 23 5. 24 29. 4.15 × 10−5 56. 10 5 6. 3 30. 6,102,000 15 57. , 0 2 28. 54. 6 3 7 55. 12 3 2 7. 7x 6 31. −6x + 2x − 7 8. 19y 19 32. −5x2 + 6x − 4 9. x + 17 10. a 1 4 11. x 3 36 12. y 5 7 13. x 6 5q 3 14. p 6 7 3x 15. y 4 5 33. 18x − 30x 5 3 4 2 2 37. 4x2 − 49 2 2 38. 5xy(xy − 3x + 2y) 40. (5x − 4y)(5x + 4y) 45. (x − 3)(5x + 2) 5 46. y , y 3 3 43. (x − 1)(a + b) 5 47. a , a 1 4 49. x = −6, x = 8 y7 24. x b6 25. a 21 50. 2x 1 x4 51. x3 x 1 y10 x15 z 5 ©Palm Beach State College 60. 6 5 4 3 2 1 -6 -5 -4 -3 -2 -1-1 -2 -3 -4 -5 -6 y x 1 2 3 4 5 6 48. x = −12, x = 5 10 23. 3 5 r st 26. x 1 2 3 4 5 6 41. (8a2 + 3b)(8a2 − 3b) 18. 8(x 5) = 32; x = 9 22. 33 women y -6 -5 -4 -3 -2 -1-1 -2 -3 -4 -5 -6 39. 4x2y2(4x2 − 2x + 1) 44. (x − 2)(4x − 3) 21. 8 ft 6 5 4 3 2 1 36. 16x2 − 40xy + 25y2 17. x < 3 20. 5x = x + 44; x = 11 59. 35. 12x − 5x − 2 42. (3 + y)(3y − x) 19. 3x 12 = x + 6; x = 9 3 34. −20x y + 8x y − 12x y 16. x 21 5 2 58. 0, 3 3 52. 2a3 15 Page 4 of 4 Developmental Algebra – Practice Final