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1 Name: Date: Period: Mrs. K. Williams ID: A Review Assignment: Chapters 1-7 CHAPTER 1- solve each equation x 7 67 x = 2. 6 m m = x x = p p = CHAPTER 2- Determine whether each graph represents a function. Use the vertical line test, if necessary. 1

2 Name: ID: A 8. CHAPTER 3/4 Use the informal method to determine the rate of change for the data in each table. The rate of change is constant for the data in each table. Write the rate as a unit rate. Number of Hours Total Number of Miles Traveled y 6x 90 y = Slope: Graph each equation with your graphing calculator and sketch its graph on the given grid. Determine the slope of the line. 12. y 4x Determine the rate of change for each situation. 9. Clayton wants to purchase tickets for the rides at a carnival. He can choose to purchase tickets individually or he can purchase a ticket package. The package includes 25 tickets for $ What is the cost per ticket if he purchases the package? Rate of Change: 13. y 1 3 x 5 Determine the slope of the line represented by each equation. Solve for y and then identify the slope. 10. y 5(2x 3) y = Slope: 2

3 Name: ID: A CHAPTER 5 Convert the fraction to a decimal by dividing the numerator by the denominator. Use bar notation to write repeating decimals Decimal: 25. CHAPTER Decimal: Write the fraction that represents the repeating decimal. 26. c = Fraction: Fraction: x = 27. A 12-foot ladder is set up 5 feet from the base of a building. How far up the building does the ladder reach? Round your answer to the nearest tenth of a foot. Determine if the square root is a rational or irrational number. Explain your reasoning How far up does the ladder reach?

4 Name: ID: A Determine the distance between ( 3, 1) and (5, 6) by graphing and connecting the points, creating a right triangle, and applying the Pythagorean Theorem. c = 29. x = 30. Use the converse of the Pythagorean Theorem to determine if the triangle is a right triangle. Explain your answer. Distance between ( 3, 1) and (5, 6) = 32. A 15-foot ladder is set up 5 feet from the base of a building. How far up the building does the ladder reach? Round your answer to the nearest tenth of a foot. How far up does the ladder reach? 4

5 Name: ID: A 33. Karen is planting a tree. She wants to use two guy wires to stabilize the tree. If Karen places the guy wires 8 feet up the trunk and 7 feet from the base, how much total wire will she need for both guy wires? 36. x = 37. Use the converse of the Pythagorean Theorem to determine if the triangle is a right triangle. Explain your answer. How much will Karen need for 2 guy wires? Determine whether the given side lengths form a right triangle. 35. c = 5, 8, Determine whether the given side lengths form a right triangle. 16, 30, Use the converse of the Pythagorean Theorem to determine whether the triangle shown is a right triangle. Explain your reasoning. x = Is this a right trianlge? 5

6 Name: ID: A 41. Determine the unknown length. Round your answer to the nearest tenth, if necessary. CHAPTER Use the parallelogram shown in the coordinate plane to answer each question. a = 42. Determine the distance between ( 5, 2) and ( 2, 5) by graphing and connecting the points, creating a right triangle, and applying the Pythagorean Theorem. a. Reflect parallelogram GHIJ over the x-axis. b. What do you notice about the ordered pairs of the original figure and the ordered pairs of its reflection over the x-axis? 44. Triangle ABC is shown on the coordinate grid. Distance between ( 5, 2) and ( 2, 5) = a. Translate ABC 6 units horizontally. Label the image A B C. How are the values in the ordered pairs affected by the translation? 6

7 Name: ID: A 45. Reflect parallelogram QRST over the line x Use the parallelogram shown in the coordinate plane to answer each question. 46. Triangle ABC is shown on the coordinate grid. a. Reflect parallelogram GHIJ over the y-axis. 48. Use the trapezoid shown in the coordinate plane to answer each question. a. Translate ABC 5 units vertically. Label the image A B C. How are the values in the ordered pairs affected by the translation? a. Reflect trapezoid JKLM over the x-axis. b. Ordered Pairs: J (, ) J (, ) K (, ) K (, ) L (, ) L (, ) M (, ) M (, ) 7

8 Name: ID: A 49. Look at the trapezoid shown on the coordinate plane. a. Translate trapezoid ABCD 5 units horizontally. Label the image A B C D How are the values in the ordered pairs affected by the translation? 50. The graph shows a triangle and the line y = 2. a. List the ordered pairs for the vertices of Triangle 1. b. Reflect Triangle 1 over the line y = 2. Label the reflection 2. 8

9 Review Assignment: Chapters 1-7 Answer Section 1. ANS: 12x Add 7 and Subtract 7. 12x 60 12x Multiply by 12 and divide by x 5 REF: ANS: 6 6 m 18 6 Add 6 and subtract m Ê 12 m ˆ Ë Á 12 12( 12) Divide by 12 and multiply by 12. m 144 REF: ANS: 5.4x Add13andsubtract x x Multiply by 5.4 and divide by x 20 REF: ANS: p Add 22.8 and subtract p p Multiply by 2 and divide by 2. 2 p 10.8 REF: ANS: The scatter plot is not a function. A vertical line can be drawn through (3, 2) and (3, 6). REF: 2.3 1

10 6. ANS: The graph is not a function. A vertical line will cross two y-values for most x-values. REF: ANS: The graph is a function. No vertical line will cross two y-values for any x-value. REF: ANS: Sample answer: Number of hours Number of miles Rate of change 195miles 3hours REF: ANS: Unit rate Package $ tickets $0.75 1ticket 65 miles 1hour The unit rate is $0.75 1ticket. REF: ANS: y 5(2x 3) y 10x 15 slope 10 REF: 3.4 2

11 11. ANS: 10y 6x 90 10y 6x 90 y 6 10 x 9 y 3 5 x 9 slope 3 5 REF: ANS: slope 4 REF: ANS: slope 1 3 REF: 3.4 3

12 14. ANS: REF: ANS: REF: ANS: REF: ANS: 7 9 REF: ANS: Irrational; REF: ANS: Irrational; REF: ANS: Irrational; REF: ANS: Irrational; REF: ANS: Irrational; REF: ANS: Irrational; REF: ANS: Irrational; 20 is a square root that is not a perfect square, so it has no repeating patterns of digits. 61 is a square root that is not a perfect square, so it has no repeating patterns of digits. 101 is a square root that is not a perfect square, so it has no repeating patterns of digits. 24 is a square root that is not a perfect square, so it has no repeating patterns of digits. 62 is a square root that is not a perfect square, so it has no repeating patterns of digits. 63 is a square root that is not a perfect square, so it has no repeating patterns of digits. 47 is a square root that is not a perfect square, so it has no repeating patterns of digits. REF: 5.3 4

13 25. ANS: c 2 c REF: ANS: 6 2 x x REF: ANS: 5 2 x x x The ladder reaches 10.9 feet up the side of the building. REF: ANS: c 2 c REF: ANS: 6 2 x x REF: ANS: No. This is not a right triangle The sum of the squares of the lengths of the two shorter sides is not equal to the square of the length of the longest side, so this is not a right triangle. REF: 6.2 5

14 31. ANS: a 2 b 2 c c c 2 c c 113 c 10.6 The distance between ( 3, 1) and (5, 6) is approximately 10.6 units. REF: ANS: 5 2 x x x The ladder reaches 14.1 feet up the side of the building. REF: ANS: x x 2 x Karen will need about 21.3 feet of wire. REF: ANS: c 2 c REF: 6.1 6

15 35. ANS: 4 2 x x REF: ANS: 10 2 x x REF: ANS: Yes. This is a right triangle The sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse, so this is a right triangle. REF: ANS: No. This is not a right triangle because 89 is not equal to 289. REF: ANS: Yes. This is a right triangle. REF: ANS: No. This is not a right triangle The sum of the squares of the lengths of the two shorter sides is not equal to the square of the length of the longest side, so this is not a right triangle. REF: 6.2 7

16 41. ANS: a a a a a 256 a 16 The unknown leg length is 16 units. REF: ANS: a 2 b 2 c c c 2 c 2 58 c 58 c 7.6 The distance between ( 5, 2) and ( 2, 5) is approximately 7.6 units. REF: 6.4 8

17 43. ANS: a. See the coordinate plane. b. The x-values are the same and the y-values are opposites. REF: ANS: a. The y-values did not change, but the x-values in the ordered pairs of A B C are 6 more than the x-values in the ordered pairs of ABC. REF: 7.1 9

18 45. ANS: REF: ANS: a. The y-values did not change, but the x-values in the ordered pairs of A B C are 3 more than the x-values in the ordered pairs of ABC. REF:

19 47. ANS: a. See the coordinate plane. REF: ANS: a. See the coordinate plane. b. The y-values are opposites and the x-values are the same. REF:

20 49. ANS: a. The y-values did not change, but the x-values in the ordered pairs of trapezoid A B C D are 5 less than the x-values in the ordered pairs of trapezoid ABCD. REF: ANS: a. (2, 5), (7, 9), (8, 5) b. See figure. REF:

The Real Number System and Pythagorean Theorem Unit 9 Part C

The Real Number System and Pythagorean Theorem Unit 9 Part C Standards: 8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion;