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Name: ______________________ Class: _________________ Date: _________ Algebra Intro - Quarter 2 Benchmark Review Short Answer Solve the equation. Then check your solution. 1. −6z + 13 = −11z − 7 2. 6 + 17z = 13z + 18 3. 4 5 2 k – 5 = –7 + 5 k 4. − 45 w + 1 4 = 1 5 1 + 3w 5. 15(−42x + 40) = 15(−8x + 244) 6. 4 – 35 (3a + 4) = 7 7. 1 2 d (15 + 7d) = − 4 Solve the proportion. If necessary, round to the nearest hundredth. 8. 6 7 9. 104 b = p 42 = 13 10 Graph the points given below. 10. {(3, 1), (2, –5), (2, 4), (3, 3)} Express the ordered pairs below as a graph and a table. 11. {(4, 0), (3, 2), (3, 0), (–3, –2), (4, –1)} 1 ID: A Name: ______________________ ID: A 12. The table below shows the yearly sales of a CD player in a particular store. Year Sales 1 55 2 100 3 145 4 490 5 235 6 280 Find an equation for the table above. 13. The table below shows the number of copies a copier can make related to the number of minutes the machine has been running. Time (min) Number of Copies 2 15 4 30 6 45 8 60 10 75 Find the number of copies the copier can make in 20 minutes. 14. Jordan is 3 years less than twice the age of his cousin. If their ages total 48, how old is Jordan? 15. Joji earns 3 times as much as Masao. If Joji and Masao earn $4500.00 together, how much money does Masao earn? 16. One line segment is 5 cm more than 4 times the length of another. The difference in their lengths is 35 cm. How long are they? Write an algebraic expression for each verbal expression. 17. the product of 5 and twice a number 18. the sum of one-third of a number and 27 19. 42 decreased by twice some number Write a verbal expression for each algebraic expression. 20. 4n 3 + 6. 21. 7 + t = 11 2 Name: ______________________ ID: A Evaluate each problem below. 22. 1 • 4 • 9 • 1 3 2 23. 6 • 8 + 29 + 7 + 3 • 7 24. 2 3 [(15 – 7) ÷ 2]. 3 2 25. 5•2 −4•3 . 1+3 26. 6 + 3 (4 ) . 7−1 2 2 27. 2 6 + (3 + 4) − (21 ÷ 3 + 4 • 2) 4 3 14 − 3 • 1 + 2 − (5 − 1) • 2 . Substitute and Evaluate 28. 3w + (8 – v)t if w = 4, v = 5 and t = 2. 29. w2 + n(v2 – t) if w = 4, n = 8, v = 5, and t = 2. 30. 3nw − w 2 + t 3 if w = 4, n = 8, v = 5, and t = 2. Name the set or sets to which each number below belongs. 31. 21 3 32. − 49 33. 36 4 34. 0 3 Name: ______________________ ID: A 35. -0.33333.... Simplify completely 36. 3x2 y(2x2 y – 5xy2 + 8y3 x2 ) 37. 5hk2 (2h 2 k – hk3 + 4h 2 k2 ) 38. (11m 2 – 2m n + 8n 2 ) + (8m 2 + 4m n – 2n 2 ) 39. (x2 + 5y) – (2x2 + 6y) 40. 5n 2 (n – 6) – 2n(3n 2 + n – 6) + 7(n 2 – 3). 41. (7u 2 v – 3uv + 4uv2 ) – (4uv – 3u 2 v – 2uv2 ) 42. (8w2 + 4w – 2) + (2w2 – w + 6) 43. 15w – 6w + 14w2 44. 7(2y + 1) + 3y 45. 3x + 4(5x + 2) 46. 3 + 6(5a + 4an) + 9na Solve 47. 1 = y − 5 9 9 48. 14 = − s 5 49. –8x = –56 50. − 7 y = −6 9 4 Name: ______________________ ID: A 51. 1 = x − 2 5 5 52. 31 = − n 6 53. − 5 w = −9 8 54. –6n = 16 55. −13 = − n 4 56. w + (–8) = –21 Use the table that shows 2006 airmail letter rates to Greenland. Weight (oz) 5.0 6.0 7.0 8.0 Rate ($) 4.20 5.05 5.90 6.75 57. Write the data as a set of ordered pairs. 58. Draw a graph that shows the relationship between the weight of a letter sent airmail and the total cost. Use the graph. 59. State the location of each point above as an ordered pair. 5 Name: ______________________ ID: A Use the graph. 60. What Quadrant is the point (-3, 3) located in? 61. Katherine is 6 inches taller than Emily. If Katherine is 68 inches tall, write and use an equation to find Emily’s height. 62. A potted tree weighs 21 pounds. The pot weighs 3 pounds. If w represents the weight of the tree without the pot, write an equation to find the weight of the tree without the pot. 63. David had $350. After shopping, he was left with $235. If c represents the amount he spent, write an equation to represent this situation. Then use the equation to find the amount of money David spent. 64. Jack’s school is 20 miles from his house. He has already traveled 13 miles. If d represents the distance he still needs to travel to reach his school, write an equation to represent this situation. Then use this equation to find the distance Jack still needs to travel to reach his destination. 65. A candle is 4 inches tall and burns at the rate of 0.6 inch per hour. If the height of the candle after x hours is 1.5 inches, write an equation to represent the situation. Then use this equation to find the expected number of hours in which the candle melted to 1.5 inches. 66. In a random sample of 2000 bolts, 350 were found to be defective. If there are 5500 bolts, how many bolts are expected to be defective? Write and solve an equation to find the answer. 67. In a random sample of 400 customers at a fast food restaurant, it was determined that 124 customers ordered a salad. If the restaurant typically has 1200 customers in a day, how many of these customers will probably order a salad? 6 ID: A Algebra Intro - Quarter 2 Benchmark Review Answer Section SHORT ANSWER 1. –4 2. 3 3. −5 4. 683 5. 6. 7. 8. 9. –6 –3 –2 36 80 10. 1 ID: A 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. x y 4 0 3 2 3 0 −3 −2 4 −1 y = 45x + 10 150 31 $1125.00 10 cm and 45 cm 5(2x) 1 n + 27 3 42 –2n 4 times n cubed plus 6 Seven plus a number is equal to eleven. 6 105 32 1 7 35 11 18 200 88 natural numbers, whole numbers, integers, and rational numbers integers and rational numbers 2 ID: A 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. natural numbers, whole numbers, integers, and rational numbers Rational numbers, integers, whole numbers Rational Numbers 6x4 y2 – 15x3 y3 + 24x4 y4 10h 3 k3 – 5h 2 k5 + 20h 3 k4 19m 2 + 2m n + 6n 2 –x2 – y –n 3 – 25n 2 + 12n – 21 10u 2 v – 7uv + 6uv2 10w2 + 3w + 4 2 55. 56. 57. 9w + 14w 17y + 7 23x + 8 3 + 30a + 33an 2 3 –70 7 5 7 7 3 5 –186 2 14 5 2 −2 3 52 –13 (5.0, 4.20), (6.0, 5.05), 7.0, 5.90), (8.0, 6.75) 58. 59. 60. 61. 62. 63. (-3, -1), (-3, 2), (0, 1), (4, 3) Quadrant II 6 + y = 68; 62 inches 3 + w = 21 $350 − c = $235; $115 47. 48. 49. 50. 51. 52. 53. 54. 3 ID: A 64. 13 + d = 20; 7 miles 65. 1.5 = −0.6x + 4; about 4.17 hour 66. 2000 d = 5500; about 963 bolts 350 67. 372 4