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Name_____________________________________Date________________Period_____ Algebra 1 ~ Review for Final Exam ~ FALL 2012 Problems 1-3, solve and graph. 1. 5x − 7(x+ 1) > −9 answer:______ 2. −p + 6p ≤ 4 + 6p answer:______ 3. x x answer:______ 4. Latisha is on page 30 of her book and reads 3 pages every night. Sal is on page 40 of the same book and reads 2 pages every night. How long will it take Latisha to be further in the book than Sal? Write and solve an inequality. Write your answer in a sentence. 5. Jasmine and her sister are saving to buy MP3 players. Jasmine has $50 and plans to save $10 per week. Her sister has $80 and plans to save $7 per week. In how many weeks will Jasmine have more money saved than her sister? Write and solve an inequality. Write your answer in a sentence. 6. A principal is choosing between two fieldtrips. The first costs $600. The second costs $240 plus $40 per student. For what number of students is the first trip less expensive? Write and solve an inequality. Write your answer in a sentence. 7. Give the domain and range of the relation. Tell whether the relation is a function. x 3 3 4 5 y 2 –2 7 9 D:_______________ R:_______________ Function?_______ 8. Give the domain and range of the relation. Tell whether the relation is a function. D:_______________ R:_______________ Function?_______ 9. Express the relationship {(-5, 7), (-1, 4), (3, -2), (4, -6)} as a table, a mapping, and as a graph. x y Problems 10-14, determine a relationship between the x- and y-values. Write an equation in y = mx + b. 10. x y 0 5 1 10 2 15 3 20 1 15 2 12 Equation: ____________________ 11. x y -1 21 0 18 Equation: ____________________ 12. x y 2 14 4 18 6 22 8 26 Equation: ____________________ 13. y-intercept:_______ slope:______ equation: ____________ 14. Write an equation that shows the relationship between x and y in (1, -3 ) and ( 2, -1 ) slope:______ y-intercept:_______ equation: ____________ 15. This table shows the number of people at a festival at certain times during the day. Independent (x):___________ Dependent (y):___________ During which time interval did the number of people increase at the greatest rate?___________ What was the rate of change for that interval?__________ Solve the following equations for the given variables. 16. 48 = 14 + 2(z – 1) 17. A truck company charges $300 plus $15 per hour. Another company charges $120 plus $35 per hour. How long would a job take for the cost to be the same at both companies? Name_____________________________________Date________________Period_____ Part 2 Review for Final 18. 74a + 28 = 72a – 12 19. Write equation to represent “23 less than a number is 8.” Then solve. 20. Write an equation to represent “the quotient of 55 and a number is 5.” 21. Write an equation to represent the relationship “the product of a number and 12 is 60.” Then solve the equation. 22. A fitness company charges $500 plus $30 per hour. Another company charges $320 plus $40 per hour. How many hours would it take for the cost to be the same at both companies? 23. The triangles shown have the same perimeter. What is value of the x? X+8 2X+5 X+2 3X - 2 X+4 X 24. Given the equation 3x+4y=-8, solve for y. 25. Given the function h(x) = ½ x – 3, what is h (12)? 26. Given the function F(x) = 3x + 2, what is F(–4)? 27. Given the function For f(x)= 5x, find f(x) when f(x) = 30. 28. F(x) = 6x – 1, find f(x)= –5 29. Use the graph below to answer the following questions. a. f(3)=______ b. f(-2)=______ 9 8 7 6 5 4 3 2 1 c. f(x)=0 ______ d. f(x)=-7_____ -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6 -7 -8 -9 30. –4+(–3)= _____ 31. 5 – 8 = _____ 32. Simplify using order of operations . ________ y f(x)=-abs(x-3)+4 x 1 2 3 4 5 6 7 8 9 33. Simplify using order of operations 3 1 62 6 3 5 34. Simplify the following expression: ________ 2 x 2 3 x 4 x x 2 2 2 x 2 6 x 14 2 b. x 5 x 1 a. c. 2 x 12 x 1 2 d. 2 x 2 x 2 2 35. Which expression is equal to : a.) b.) c.) d.) -(3x - 2) + 3(-2 + 4x) 15x - 4 9x - 4 9x - 8 15x + 8 36. Which simplified equation represents the algebra tile model below? 2x 4 x 2 x A. B. C. D. 3x 2 2 x 2 2 x2 2 2x 2 2x2 2x 2 37. Which simplified equation represents the algebra tile model below? x 2 2 x 4 3x 2 A. B. C. D. x2 2 x 2 x x 2 x2 2 x x 3x 4 Solve the following equations, grid your answer below. 38. 3x 27 39. 1 x7 7 40. 2( y 3) 34 Name_____________________________________Date________________Period_____ Part 3 Review for Final 41. 12 x 15 44. 45. 46. 47. 42. 3x 5 7 x 3 43. 5 y 9 2 y 30 48. Is the function a linear function? ________ If so, graph the function. 49. Use intercepts to graph the line described by the equation . 50. Define rate of change. Write down all the different ways that we described rate of change. __________________________________________________________________________________ __________________________________________________________________________________ 51. Find the slope of the line that contains and . 52. Find the slope of the line. m = _________ y 10 8 6 4 (8, 2) 2 –10 –8 m = __________ –6 –4 –2 –2 –4 –6 –8 –10 2 4 6 8 10 (8, –6) x 53. The graph shows a linear relationship. Find the slope. m = __________ y 10 8 6 4 (–7, 3) –10 –8 –6 –4 2 –2 –2 2 4 6 8 10 x –4 (–8, –5) –6 –8 –10 54. Find the slope of the line that contains (–3, –2) and (4, –2) m = __________ 55. Tara creates a budget for her weekly expenses. The graph shows how much money is in the account at different times. Find the slope of the line. Then tell what rate the slope represents. 2750 2500 (4, 2400) Amount ($) 2250 (12, 2000) 2000 m = __________ 1750 The slope represents: 1500 1250 1000 _______________________________ 750 500 ________________________________ 250 2 4 6 8 10 12 14 16 18 20 22 Time (weeks) ________________________________ Name_____________________________________Date________________Period_____ Part 4 Review for Final 56. Graph the line with the slope and y-intercept –3. 2 3 57. Graph the line with a slope of 3 that contains the point (–3, –4). 5 58. Fill in the second step of the solution process and the justification Step 1: 10x - 2 (x - 3) = 22 Step 2: ____________________ Step 3: 8x +6 = 22 A. 10x - 2x - 6 = 22; combine like term B. 10x - 2x + 6 = 22; distributive property C. 8x - (x - 3) =22; subtract 2 from 5x D. 10x - 2x - 6 = 22; distributive property 59. For his cellular phone services, Joseph pays $45 a month, plus $ 0.45 for each minute over the allowed minutes in his plan. Joseph received a bill of $55.35 last month. How many minutes did he use over the allowed minutes? a. b. c. d. 108 23 43 17.25 60. A movie rental store charges a membership fee of $10 and $1.35 per movie for the first month. Kim paid $19.45, how many movies did she rent that month? a. b. c. d. 7 6 14 5 61. A catering company charges a fixed fee of $110 and $6.25 a person attending the party. If an event cost $303.75, how many people attended that event? a. b. c. c. 31 49 17 3 62. Marco and his friend want to go the movies together and have a total of $47. The ticket are sold $7.5 each how many tickets can they buy? a. 0 tickets b. 6 tickets c. 8 tickets d. 10 tickets 63. Solve the inequality and graph the solutions. 64. Solve the inequality Find the x and y intercepts and then graph. Find the slope. 65. 2y – 6x = 12 66. 9x +18y = -36 67. 2y = -12 + 4x