NAME DATE PER. FALL FINAL EXAM REVIEW ALGEBRA 1 Solve = 6 3v = -3(c + 5)

Transcription

1 FINAL EXAM REVIEW, p. 1 NAME DATE PER. FALL FINAL EXAM REVIEW ALGEBRA 1 Solve = 6 3v = -3(c + 5) (x 3) = x + 2(x - 5) = 4(x + 8) 5. r x 1 2x 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:

2 FINAL EXAM REVIEW, p If the perimeter of the rectangle below is 42, find the value of x. (4x + 3) Equation: (x 2) Solve d > t 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.

3 FINAL EXAM REVIEW, p 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 D = R = D = R = 19. D = R =

4 FINAL EXAM REVIEW, p 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 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.

5 FINAL EXAM REVIEW, p Write an equation to represent the table of values. x y 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 =

6 Identify the slope and y-intercept, then sketch the graph of each equation x + 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 = x = 4 m = y-intercept = m = y-intercept =

7 FINAL EXAM REVIEW, p 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 = 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?

8 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 x-intercept of 6 and y-intercept of has a y-intercept of -12 and a rate of change of parallel to y = 3 5 x + 2 and goes through (-6, -3) 41. perpendicular to y = 6x + 1 and goes through (12, -5)

9 FINAL EXAM REVIEW, p 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 < 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)

10 FINAL EXAM REVIEW, p Graph x + y > 3-4x + y < x y 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 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.

11 FINAL EXAM REVIEW, p Draw the solutions for the system below, and identify the solution region. y < 3x + 5 y > 2x 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 = What is the solution in the system of equations from problem #59?

12 FINAL EXAM REVIEW, p Which inequality represents the graph shown below? A. 5x + y 4 B. x + 5y 20 C. x + 5y 20 D. 5x + y Draw the graph to represent the solution set of 6x + 3y 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 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 a.) What is the range of the function for this situation? b.) What is the rate of change for the function?

13 FINAL EXAM REVIEW, p 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 = r C. r = 75 4w D. r = w

14 FINAL EXAM REVIEW, p 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 = 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)

15 FINAL EXAM REVIEW, p The table represents some points on the graph of a linear function. x y 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

16 FINAL EXAM REVIEW, p The function y = (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 Which equation models the graph of line l?