FINAL EXAM REVIEW, p. 1 NAME DATE PER. FALL FINAL EXAM REVIEW ALGEBRA 1 Solve. 1. 24 = 6 3v 2. 12 = -3(c + 5) 3. 5 2(x 3) = 63 4. 7x + 2(x - 5) = 4(x + 8) 5. r 1 10 3 2 6. x 1 2x 2 5 4 Write an equation, and then solve. 7. Ben joined The Fitness Place for an initial membership fee of $55 and $32 per month. If he paid a total of $279, how many months was Ben a member? Equation: 8. A decorator charges $40 for an initial consultation, then $80 per hour. Another decorator just charges $90 per hour. How long is a job for which the two decorators charge the same price? Equation:
FINAL EXAM REVIEW, p. 2 9. If the perimeter of the rectangle below is 42, find the value of x. (4x + 3) Equation: (x 2) Solve. 10. 9 3d > -9 11. 3t 6 > 6(t + 1) Write an inequality, and then solve. 12. Tammy earns money by mowing lawns for her neighbors. She currently has $75 and plans to mow lawns until she has at least $200 in savings. If she earns $20 for every lawn she mows, how many more lawns does she have to mow to reach her goal? Inequality: Answer the following. 13. Create a table that represents a function. 14. Create a table that does NOT represent a function.
FINAL EXAM REVIEW, p. 3 15. Find the range for f(x) = -3x² + 4 for the domain D= {1, -2, -3} 16. If f(x) = 2 3x find f(-3). Identify the domain and range of each graph. 17. 18. D = R = D = R = 19. D = R =
FINAL EXAM REVIEW, p. 4 20. The table below shows the relationship between total tuition costs, T, and the number of semester hours taken at Blinn College. semester hours taken, h total tuition cost, T 1 553 2 581 3 609 4 637 a) Find the function that would represent this relationship. = b) What is the rate of change for the function? c) What is the value of T(16)? 21. Suppose the total cost, C, of renting a car is $25 per day, d, plus an initial fee of $100. a) Write a function that best describes this relationship if d represents the number of days the car is rented. b) Write a description for the rate of change c) What would be the total cost of renting a car for 9 days? d) Find the number of days you could rent a car for $275.
FINAL EXAM REVIEW, p. 5 22. Write an equation to represent the table of values. x y 2-1 4-3 6-5 8-7 23. Determine the slope of the line shown. m = 24. Find the slope of the line through the points (3, 7) and (-1, -4). m = Identify the slope and y-intercept, then sketch the graph of each equation. 25. y = 5 3 x 4 m = y-intercept =
Identify the slope and y-intercept, then sketch the graph of each equation. 26. 4x + 2y = 10 FINAL EXAM REVIEW, p. 6 Slope intercept form : m = y-intercept = 27. 3x y = 5 Slope intercept form : m = y-intercept = 28. y = -5 29. x = 4 m = y-intercept = m = y-intercept =
FINAL EXAM REVIEW, p. 7 30. What is the equation of the line shown in the graph? Equation: 31. Find the rate of change and y-intercept of the line with the equation 5x 2y = 6. 32. If (x, -6) is a solution to the equation 3x + 2y = 18, what is the value of x? 33. If the point (5, y) is a solution to the equation 2x 4y = 30, what is the value of y? 34. Using the graph shown answer the following. a) What is the zero? b) What is the y-intercept?
FINAL EXAM REVIEW, p. 8 Using the given information, write the equation of each line. has a slope of -4 and goes through the point (-6, 2) 35. Point slope form: Slope Intercept form: 36. passes through (2, 7) and (-4, 4) 37. x-intercept of 2 and y-intercept of 3 38. x-intercept of 6 and y-intercept of -4 39. has a y-intercept of -12 and a rate of change of -6 40. parallel to y = 3 5 x + 2 and goes through (-6, -3) 41. perpendicular to y = 6x + 1 and goes through (12, -5)
FINAL EXAM REVIEW, p. 9 42. 43. a horizontal line that passes through the point (9, -6) a line with an undefined slope that passes through the point (-6, 3) 44. Parallel to the x-axis that passes through (2,3) 45. Perpendicular to the x-axis that passes through (5,7) 46. Parallel to the y-axis and passes through the point (-4, 6) 47. Perpendicular to the y-axis and passes through the point (2, 3) 48. Graph 6x + 2y < -14 49. In #48, which of the following coordinates represents a solution to the inequality? A. (1, 10) C. (-2, 1) B. (-4, 2) D. (-1, -4)
FINAL EXAM REVIEW, p. 10 50. Graph x + y > 3-4x + y < 4 51. x 1 2 3 y 3 5 7 a) Find the function that could be used to represent the table above. b) What is the value of y when x is 5? 52. Does the table shown represent a direct variation? If so, write its equation. x y 3 9 6 18 9 27 53. If y varies directly as x, and y is 72 when x is 30, find the equation that represents this situation. 54. What is the linear parent function? Identify the slope and y-intercept. Equation: m: b: 55. Draw the graph that represents the equation 5x - 3y = 15.
FINAL EXAM REVIEW, p. 11 56. Draw the solutions for the system below, and identify the solution region. y < 3x + 5 y > 2x - 8 57. At schlotskys, the cost for a cinnamon roll and a soft drink is $3. The cost for 3 cinnamon rolls and 2 soft drinks is $8. Write a set of equations and determine the cost of a cinnamon roll and a soft drink. Equation 1: Equation 2: Solution: 58. If the graph of f(x)= 2x + 4 is changed to g(x), where the slope is multiplied by -1 and the y-intercept is changed to -8, describe the changes on the graph. 59. Describe the relationship between the graphs of the equations below. y = 1 5 x + 4 and 3x + 4y = 16 60. What is the solution in the system of equations from problem #59?
FINAL EXAM REVIEW, p. 12 61. Which inequality represents the graph shown below? A. 5x + y 4 B. x + 5y 20 C. x + 5y 20 D. 5x + y 4 62. Draw the graph to represent the solution set of 6x + 3y 12 63. Mark works at Kroger, and gets paid $6 an hour for moving pallets around in the stock room. His paycheck also includes a $30 fee per paycheck for his specialization of the machinery. The function can to describe the scenario is f(x) = 6x + 30. He must work more than 15 hours to get the extra $30, but cannot work over 20 hours. Which of the following describes the range of the function? F. { 30, 31, 32, 33, 34, 35} G. { 6, 12, 18, 24, 30, 36} H. { 15, 16, 17, 18, 19, 20} J. { 120, 126, 132, 138, 144, 150} 64. A librarian is moving sets of boxes, and each box can hold 15 pounds of books. she can put up to 8 boxes on the dolly, which already weighs 10 pounds. The dollys weight can be represented by the function f(x) = 15x + 10. a.) What is the range of the function for this situation? b.) What is the rate of change for the function?
FINAL EXAM REVIEW, p. 13 65. The Aggie bus 54 travels two different routes: the george bush route and the wellborn route. The routes are different lengths. On Monday, the bus travels the george bush route 10 times and the wellborn route 7 times for a total of 95 miles. On Tuesday the bus travels the george bush route 7 times and the wellborn route 4 times for a total of 62 miles. Equation 1: Equation 2: What is the length of each route in miles? George Bush Route: Wellborn Route: 66. A teacher ordered pizzas for a meeting after school. She can order cheese pizzas for $10, and pepperoni for $12. She cannot spend more than $115. Write an inequality to represent the combinations of c cheese pizzas and p pepperoni pizzas. 67. Identify the slope of the graph to the right. 68. David works in an ornament shop where he gets paid $75 for the week, but gets charged $4 for every ornament he breaks. Which function best describes his weekly pay (w) in relationship to the amount of ornaments (r) he breaks? A. w = 75 4r B. w = 75 + 4r C. r = 75 4w D. r = 75 + 4w
FINAL EXAM REVIEW, p. 14 69. 70. Which of the following equations has a slope of -4 and goes throught the point (-3, 6)? A. y - 3 = -4(x + 6) B. y + 3 = -4(x - 6) C. y - 6 = -4(x + 3) D. y + 6 = -4(x - 3) 71. What is the equation of the line that has a slope of -3 and passes through the point (4, 6)? A. -3x + y = -14 B. -3x + y = -6 C. 3x + y = 18 D. 3x + y = 22 72. Which equation describes the line with a slope of 3 and a y-intercept of 4? A. y - 0 = 3(x - 4) B. y + 0 = 4(x + 3) C. y + 3 = 3(x - 4) D. y - 3 = 4(x + 3)
FINAL EXAM REVIEW, p. 15 73. 74. The table represents some points on the graph of a linear function. x y 1 4 2 11 3 18 4 25 A. y - 3 = 7(x - 18) B. y + 3 = 7(x + 18) C. y + 3 = 7(x - 18) D. y - 3 = 7(x + 18) 75. Rewrite the following equation in standard form. y = 1 6 x + 8
FINAL EXAM REVIEW, p. 16 76. The function y = 20 + 3(x - 2) can be used to determine the cost of having chick fil a deliver sandwiches to an event. What is the rate of change of the cost in dollars with respect to the number of changes? A. $20 per sandwich B. $3 per sandwich C. $2 per sandwich D. $10 per sandwich 77. The graph of the linear function g is shown. What is the zero of g? 78. What is the value of x in the solution to the system of equations? y = -2x + 2 y = x - 4 A. -2 B. 1 C. 2 D. 3 79. Which equation models the graph of line l?