Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Fundamental theorem of algebra wikipedia , lookup
System of linear equations wikipedia , lookup
System of polynomial equations wikipedia , lookup
Signal-flow graph wikipedia , lookup
Quadratic equation wikipedia , lookup
Quartic function wikipedia , lookup
Elementary algebra wikipedia , lookup
History of algebra wikipedia , lookup
Due Dates: Algebra I First Semester Exam Review Questions Name _________________ Show work on a separate sheet of paper if you cannot fit it onto the review sheet. 1. Find the value of 16 + 12x – x3 when x = 2 2. Evaluate: 3. Evaluate: 12 + 48 6 4. Evaluate: 5 (42 + 7). 5. Evaluate: ––16 6. Find the value of 4y2 2 + 16 when y = 3. 7. Simplify the expression 11x – 2y + 5y – 3x 8. Simplify: 11y + 3(7 – y) 9. Simplify –4(2x + 3) + 5x 10. Simplify 2(3x – 4) – 2(x – 4) 11. Is x = 5 a solution of the equation 2x – 5 = 9 + x? Yes or No? 12. Which equation does NOT have a solution of w = 5? A. 3w – 4 = 11 C. 12 + 2w = 22 B. 10w – 22 = 38 D. 17 = 22 – w 13. Is (–1, 9) a solution to the equation 3y – 3x = 30? Yes or No? – (–6) – (–9) + –4 Circle each set of numbers the given number is included in. (Look at notes from ring of reals) 14. –3 Whole Real Rational Integer Natural Irrational 15. 1 2 Whole Real Rational Integer Natural Irrational 16. 0 Whole Real Rational Integer Natural Irrational 17. 13 Whole Real Rational Integer Natural Irrational Solve each equation for questions 18 – 29 x 19 4 18. –6 = 3 + x 19. 20. 3x – 5 – 2x = 3 21. 22. 3(x – 7) = x – 4 + 2x 23. 4(3 – x) + 5x = –3(x + 8) 24. 5x – 2(x + 4) = 4 (5 – x) 25. 2(r – 5) + 3 = 5(r + 4) – 19 26. 3(y + 2) + 7 = 4(y – 1) + 4 27. 2(x + 4) + 3x = 5(x + 1) + 3 2 x 4 12 3 28. x2 3 10 6 30. A = 1 bh 2 29. (proportion … cross multiply) 2x 5 x 9 3 Solve for h. 31. Solve the equation 2L + 2W = P for L 32. Rewrite in function form: 2x + 4y = 20 (this means solve for y) 33. Write an inequality to model the real life situation describe below (DO NOT SOLVE!): The product of $35 and the number of club members (M) is less than 650. Write an equation and solve for questions 34 & 35. 34. Three less than twice a number is seventeen. 35. The sum of five and three times a number is 20. For questions 36 & 37, write let statements, an equation and solve. Write answer in a sentence. 36. The smaller of two numbers is 14 less than the larger and their sum is 64. Find the smaller number. 37. The sum of three consecutive even integers is 66. What is the larger integer? 36a) y varies directly to x. Write an equation that relates x & y when x = 4 and y = 12. b) y varies inversely with x. Write an equation that relates x & y when x = 4 and y = 12. 37. The graph of a direct variation ALWAYS passes through the ________________? Which property of real numbers is demonstrated in each problem below? 38. 3(x + 2) = 3x + 6 39. a + b + c = b + a + c 40. a + (b + c) = (a + b) + c? 41. Evaluate the following using the function f(x) = 10x – 2. a. f(3) = b. f(-2) = c. f(0) = Given f(x) = 5x – 2 complete the following: ____________ 42. Find f(3) ___________ 43. Find x if f(x) = 18 44. A. What is the missing value for the function shown in the chart? B. Write an equation to describe the function. Input 3 5 Output –2 0 7 9 ? 4 45. Which does NOT represent a function? A. (1, 4) , (6, 5) , (4, 2) , (5, 0) C. (1, 4) , (6, 3) , (3, 2) , (7, 1) B. (1, 2) , (3, 5) , (4, 2) , (5, 0) D. (1, 2) , (3, 5) , (1, 6) , (4, 7) 46. Is this a function? Yes or No? Input 7 5 Output –2 1 4 7 2 3 47. Is this graph a function? Write either < , >, or = that would correctly compare the given numbers. 48. – 3 ______ – 4 49. 3 ______ 4 50. 2 ______ 2 Solve and graph each inequality. (remember to switch the inequality when you DPE or MPR by a negative) 51. x <4 52. 3x – 6 > 3 0 53. –2x + 4 < 16 0 54. 2x + 7 > –2x – 1 0 0 55. –3x + 6 < 4x – 8 56. –22 < 4x – 10 0 0 Using the graph to the right answer questions 57-61. 57. Graph point A with coordinates (–4, –3). 58. What quadrant does point B lie in? 59. Name the ordered pair for point C. 60. Name the ordered pair for point D. 61. What is the location of points C AND D? (Two answers) C D B 62. Find the slope given the points (5, 4) and (3, 4). 63. Find the slope of the line that passes through the points (6, –3) and (4, 6)? 64. Find the slope of the line passing through the points (7, –6) and (7, 4). 65. Find the slope of the line that passes through the points (6, –3) and (9, 4)? 66. What is the slope AND y-intercept of the graph of 3x + 2y = 14? (Two answers) 67. What is the slope of any line parallel to the line y 68. What is the equation of line A? A 69. What is the slope of line A? 70. What is the equation of line B? 71. What is the slope of line B? 72. What is the slope of line D? 73. What is the x-intercept of line D? 74. What is the y-intercept of line D? 75. Use a t-chart (table) to graph the equation y = –3x + 3 x y 5 x6 3 B D 76. Use x & y intercepts to graph the equation y – 2x = 4 77. Use slope-intercept form to graph the equation 3x – 4y = 8 78. Rewrite in standard form: y = –5x + 6 79. Rewrite y = 2 x – 3 into standard form. 5 80. Write an equation in slope intercept form of a line with slope of 2 and has a y-intercept of –6. 81. Write an equation in standard form of the line with m = –3 and b = 7. (since you have the y intercept and slope, start with slope intercept equation first, then rewrite in standard form) 82. Write an equation in slope intercept form for line D drawn below. D (find the y intercept and count slope) A What is the equation of line A written in: 83. slope intercept form: 84. rewrite into standard form: There will be a matching section on the exam for vocabulary. These are the words that need to be studied. absolute value base difference domain exponent greater than less than natural numbers origin parallel lines perpendicular lines point slope form product quotient range rational number slope formula slope intercept form standard form sum variable whole numbers The semester one Algebra I Exam topics: Chapter 1: All Lessons Chapter 2 : Lessons 2.1 - 2.6 Chapter 3: All Lessons (Skip 3.7) Chapter 4: All Lessons Chapter 5: Lessons 5.1, 5.2, 5.4 Chapter 6: Lessons 6.1 - 6.3 Chapter 12: Lesson 12.1