Name: Date: Period: Algebra I - Study Guide for Final Multiple Choice Identify the choice that best completes the statement or answers the question. To truly study for this final, EXPLAIN why the answer you chose is the correct answer (or why the others are not correct). 1. Solve 1 6x 30 4x 2 x 7. 3 A) x 6 C) x 4 1 4 B) x 11 D) x 1 Write an inequality for the graph. 2. A) x < 8 B) x 8 C) x > 8 D) x < 8 3. A) m 1 2 B) m 1 2 C) m > 1 2 D) m 1 2 4. Solve 3 2x 5 9. A) x 4 or x 1 C) all real numbers B) x 4 and x 1 D) no solution 5. Which of the following is a linear function? A) y x 2 4 C) y 1 (x 4) 2 B) y x 2 D) y 2 x 3 6. Solve 3n 6 21. A) n 5 and n 5 C) n 9 and n 5 B) n 9 and n 9 D) no solution 1
7. Which equation is represented by the graph? A) y 5 8 x 9 8 B) y 8 5 x 9 5 C) y 5 8 x 9 8 D) y 8 5 x 9 8 8. Which linear function f has the values f(0) 3 and f( 4) 0? A) f(x) 3 4 x 4 B) f(x) 3 4 x 3 C) f(x) 4 3 x 4 D) f(x) 4 3 x 3 9. Solve 6(x 4) x 5(x 2). A) x 17 B) x 7 C) x 7 D) no solution 10. Which inequality is different? A) x is no more than 12. C) x is at most 12. B) x is less than or equal to 12. D) x is no less than 12. 2
11. Which properties of equality justify steps c and f? a. 23 11 4x b. 23 11 ( 4x) c. 23 11 11 ( 4x) 11 d. 23 11 11 11 ( 4x) e. 34 4x f. 34 4 4x 4 g. 8.5 x A) Addition Property of Equality; Subtraction Property of Equality B) Subtraction Property of Equality; Multiplication Property of Equality C) Multiplication Property of Equality; Division Property of Equality D) Addition Property of Equality; Division Property of Equality 12. The map shows Hope Road and the construction site for the new library. Find the equation of a street that passes through the building site and is parallel to Hope Road. A) y = 1 3 x + 4 C) y = 1 3 x 4 B) y = 3x + 4 D) y = 1 3 x + 4 3
13. d < 2 Graph the inequality. A) C) B) D) Graph the function. 14. y x 1 A) C) B) D) 4
15. Which compound inequality is represented by the graph? A) 5 x 2 11 C) 5 x 2 11 B) 10 2x 4 22 D) 10 2x 4 22 The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation. 16. Time (days) Cost ($) 3 75 4 100 5 125 6 150 A) B) C) D) 75 dollars per day; the cost is $75 for each day. 1 25 dollars per day; the cost is $25 for each day. 1 1 dollars per day; the costs $1 for 150 days 150 1 dollars per day; the cost is $25 for each day. 25 17. A line contains the point 0,7 and has the same slope as the line 3x y 4. Which of the following is the equation of the line in slope-intercept form? A) 3x y 7 C) y 7 3x B) y 3x 4 D) y 3x 7 18. If f(x) 3x 12, find the value of x so that f(x) 36. A) 120 B) 16 C) 24 D) 8 5
Graph the function. Compare the graph to the graph of f(x) = x. Describe the domain and range. 19. g(x) x 2 A) C) translation 2 units right and 2 units up domain: all real numbers range: y 2 translation 2 units right domain: all real numbers range: y 0 B) D) translation 2 units left domain: all real numbers range: y 0 translation 2 units left and 2 units down domain: all real numbers range: y 2 Which number is a solution of the inequality? 20. 3x 15 3 A) 6 B) 9 11 C) 5 D) 6 11 6
21. Which inequality is represented by the graph? A) y 2 3 x 1 B) y 2 3 x 1 C) y 2 3 x 1 D) y 2 3 x 1 Write a function rule for the table. 22. x f(x) 2 8 3 12 4 16 5 20 A) f(x) x 4 B) f(x) x 4 C) f(x) 4x D) f(x) 4x 7
Match the equation with its graph. 23. 7x + 7y = 49 A) C) B) D) Short Answer Solve the inequality. Then sketch a graph of your solution. 24. 8 2x 4 4 25. 2w < 18 26. d 2 6 8
Simplify the expression. 27. 3 15 3 2 4 28. 1 ( 12m + 38) 2 29. 3 3 32 12 4 30. 4(20 12) (4 3) 31. Evaluate f x 2x 5 for x = 3. Are the graphs of the lines in the pair parallel? Explain. 32. y = 1 6 x + 8 2x + 12y = 11 Write the equation of a line that is perpendicular to the given line and that passes through the given point. 33. y 2 x 9; ( 6, 5) 3 9
34. What are the coordinates of point A? 35. Evaluate the expression (ab) 2 for a = 4 and b = 3. Find the slope of the line that passes through the pair of points. 36. (1, 7), (10, 1) Find the slope and y-intercept of the line. 37. y = 4 3 x 3 10
Graph the function. 38. y 2x 3 Tell whether the lines for each pair of equations are parallel, perpendicular, or neither. 39. 7x 4y = 4 x 4y = 3 40. Find the slope of the line. 11
Write the slope-intercept form of the equation for the line. 41. 42. Evaluate u + xy, for u = 18, x = 10, and y = 8. 43. Use the slope and y-intercept to graph the equation. y = 4 3 x + 3 Find the x- and y-intercept of the line. 44. 2x + 3y = 18 12
Solve the equation. 45. 2 10 z 3 46. 5p 7 18 43 47. You are driving to visit a friend in another state who lives 440 miles away. You are driving 55 miles per hour and have already driven 275 miles. Write and solve an equation to find how much longer in hours you must drive to reach your destination. Write an equation of a line with the given slope and y-intercept. 48. m = 1, b = 4 Write an equation for the line that is parallel to the given line and that passes through the given point. 49. y = 5x + 3; ( 6, 3) Solve the inequality. 50. a + 8 2(a 12) > 0 13
ID: A Answer Section Algebra I - Study Guide for Final MULTIPLE CHOICE 1. A 2. C 3. A 4. A 5. C 6. C 7. A 8. B 9. B 10. D 11. D 12. A 13. C 14. A 15. B 16. B 17. D 18. D 19. C 20. A 21. C 22. C 23. B SHORT ANSWER 24. 2 x 4 25. w > 9 26. d 8 or d 4 27. 108 28. 6m + 19 29. 867 30. 128 1
ID: A 31. 11 32. Yes, since the slopes are the same and the y-intercepts are different. 33. y 3 2 x 4 34. (1, 1) 35. 144 36. 2 3 37. 38. 4 3 ; 3 39. neither 40. 1 4 41. y = 3x 1 42. 98 43. 44. x-intercept is 9; y-intercept is 6. 45. 16 46. 35 47. 55h 275 440; h 3 2
ID: A 48. y = x + 4 49. y = 5x 27 50. a < 32 3