1. Ohio Graduation Test 2007 – Math Data Analysis and Probability: Benchmark A 26, 43; Benchmark B 1; Benchmark C 5; Benchmark D 22, 31; Benchmark E 34; Benchmark G 34; Benchmark H 17; Benchmark J 23, 39; Benchmark K 20264315223134 17233920 Patterns, Functions, and Algebra: Benchmark A 2, 18; Benchmark C 44; Benchmark E 7; Benchmark F 24; Benchmark H 38; Benchmark J 30218447243830 Number, Number Sense and Operations: Benchmark A 19, 28; Benchmark D 3; Benchmark E 35; Benchmark F 40; Benchmark G 8, 32; Benchmark H 3; Benchmark I 28192833540832 328 Measurement: Benchmark B 41; Benchmark C 27; Benchmark D 21, 36; Benchmark F 4, 94127213649 Geometry and Spatial Sense: Benchmark A 10, 33; Benchmark B 29; Benchmark C 25; Benchmark E 6, 10; Benchmark F 37, 42103329256103742 Process Standard: Benchmark A 38; Benchmark B 4, 22, 28; Benchmark E 10; Benchmark G 3438422281034 Not slated for Public Release as of 7/1/08: Questions: 11-16 To print a PDF of the OGT Test, go to www.ode.state.oh.us

2. 1.Rubin used an altimeter to measure and record his height above sea level at different times during his hike in the mountains. Which type of data display could Rubin use to show how his height above sea level changed with time? 1.Line graph 2.circle graph 3.stem-and-leaf plot 4.box-and-whisker plot index

3. 2. The first four rows of a number array are show below. Row 10 Row2030 Row405060 Row 70 80 90 100 What number will be at the far right end of row 7? 1.150 2.210 3.280 4.360 index

4. 3. The figure shows four points on a number line. Which point most accurately represents 150 1.A 2.B 3.C 4.D index

5. 4. Helga earns $6.30 per hour working part-time at the grocery store. She records her starting and ending times each day on her time card. Scoring Guidelines Write the answer on separate paper. Helga’s Time Card DateInOut Monday 7/25 10:30 a.m.2:00 p.m. Tuesday 7/26 12:45 p.m.3:30 p.m. Wednesday 7/27 Thursday 7/28 12:00 p.m.4:45 p.m. Friday 7/29 11:15 a.m.3:45 p.m. In your Answer Document, determine Helga’s total wages for the week. Show your work or provide an explanation for your answer. Respond completely. (2 points) index

6. 5. The noon temperatures are recorded for 7 consecutive days in Cleveland, Ohio. The sum of the 7 temperatures is positive. Which statement about these 7 temperatures must be true? 1.The mean of the temperatures is positive. 2.The mode of the temperatures is positive. 3.The median of the temperatures is positive. 4.The minimum of the temperatures is positive. index

7. 6. The net creates a pyramid. 1.A 2.B 3.C 4.D index

8. 7. Jamie is buying peanuts and walnuts. He wants to spend exactly $30. The graph below shows all possible ways that he can split the $30 between the peanuts and the walnuts. What does the point N on the graph represent? 1.Spending all $30 on walnuts 2.spending all $30 on peanuts 3.spending $20 on peanuts and $10 on walnuts 4.spending half of the $30 on peanuts and half of the $30 on walnuts index

9. 8. Tina plays on the Lakewood High softball team. During her first season, she went to bat 27 times and got 6 hits. If she continues to hit at about the same rate, how many total hits will she have if she bats 40 times? 1.4 2.9 3.15 4.19 index

10. 9. Erica took two days to drive 1,020 miles. On the first day, she drove 10 hours at an average speed of 62 miles per hour. On the second day, her average speed was 57 miles per hour. Approximately how long did she drive on the second day ? 1.7.0 hours 2.8.6 hours 3.10.9 hours 4.17.0 hours index

11. 10. The diagram below shows two of the faces of a prism. Ellen is constructing this triangular prism out of cardboard. Ellen plans to draw a shape (a net of the prism) on a piece of cardboard that she can cut out and fold to make the prism. In your Answer Document, sketch a net of the prism that Ellen could use. Place the dimensions on the net. Respond completely. (2 points) Scoring Guidelines Write the answer on separate paper. index

12. 17. Casey has one afternoon to run errands involving buying a sweater, mailing a package and buying groceries. There are 3 clothing stores, 2 post offices and 4 grocery stores within a 10-mile radius. How many combinations of 1 clothing store, 1 post office and 1 grocery store are available within a 10-mile radius? 1.3 2.9 3.19 4.24 index

13. 18. Nancy decided to breed gerbils to sell to a pet store. She started with 2 gerbils and determined that they should quadruple in number every 4 months. Nancy sold all of the gerbils to the pet store at the end of 1 year. How many gerbils did Nancy sell to the pet store? 1.24 gerbils 2.66 gerbils 3.128 gerbils 4.512 gerbils index

14. 19. Jupiter’s diameter is 88,640 miles. How is this measurement expressed in scientific notation? 1.8.864 × 10 3 miles 2.0.864 × 10 4 miles 3.8.864 × 10 4 miles 4.88.64 × 10 4 miles index

15. 20. Luca randomly chose a marble from a bag, recorded the color and replaced the marble before choosing again. The table shows the number of times each color of marbles was chosen. According to the data in the table, what is the experimental probability of picking a green marble? 1. 17 / 100 2. 1 / 4 3. 17 / 83 4. 17 / 25 index

16. 21. Marcia’s house is approximately ten miles east of the airport. A jet is flying directly over her house after taking off from the airport and flying approximately twelve miles, as shown in the diagram below. Approximately how many miles high is the jet when it flies over Marcia’s house? 1.2.0 miles 2.6.6 miles 3.12.0 miles 4.15.6 miles index

17. 22. The Ohio Big Tree Program lists the largest living specimen of each kind of tree found in the state. Three measurements are needed to assign a score to each tree: Circumference (1 inch = 1 point) Height (1 foot = 1 point) Average crown spread (1 foot = ¼ point) The score is found by adding the number of points for each measurement. Four trees and their measurements are given below. Scoring GuidelinesWrite the answer on separate paper. index In your Answer Document, calculate the scores for each of the four trees in the table. Arrange the trees in order based on their scores. Show work or provide an explanation to support your answer. Write a formula for computing the score assigned by the Ohio Big Tree Program. Respond completely. (4 points)

18. 23. Each week, Ms. Haroma has each of the 25 students in her class write his or her own name on a piece of paper. All the pieces of paper are put in a jar and 1 student’s name is drawn from the jar. If Jamie’s name was drawn last week, what is the probability that it will be drawn again this week? 1.½ 2. 1 / 25 3. 1 / 50 4. 16 / 25 index

19. 24. Marcy and Troy disagreed about the answer to a problem. Marcy said that the equation they were working on had more than one solution. If Marcy is correct, on which of these equations could they have been working? 1.2x+ 4 = 3x + 4 2.2x + 4 = 3x + 5 3.2x + 4 = 2(x + 2) 4.2x + 4 = 2(x + 3) index

20. 25. In which figure is the measure of 1 NOT equal to 60? ABCDABCD 1.A 2.B 3.C 4.D index

21. 26. An inspector at a nail factory checks a sample of nails to measure their deviation from the standard length. Positive deviation means a nail is too long, and negative deviation means it is too short. Based on the inspector’s chart above, what is true of the nails produced at this factory? 1.The nails produced all have the standard length. 2.The nails are much more likely to be too long than too short. 3.The nails are much more likely to be too short than too long. 4.The nails are about as likely to be too long as they are to be too short. index

22. 27. In the diagram below, line segment AT is a diameter of the circle with center O. What is the area of the shaded part of the circle? 1.18.3 cm 2 2.42.3 cm 2 3.145.6 cm 2 4.194.1 cm 2 index

23. 28. Light travels at a speed of 1.86 × 105 miles per second. A light-year is defined to be the distance that light travels in one year. In your Answer Document, determine the number of miles in one light-year. Write your answer in correct scientific notation. Show all of your work or provide an explanation for your answer. Respond completely. (2 points) Scoring Guidelines Write the answer on separate paper. index

24. 29. Points E, F, G, and H are midpoints of the sides of quadrilateral ABCD. If AC = 12 and BD = 8, what is the perimeter of quadrilateral EFGH? 1.96 2.40 3.20 4.4 index

25. 30. A construction company buys $38,400 worth of new equipment, the value of which decreases linearly so that its value after 8 years is $2,200. By what amount is the value of the equipment decreasing per year? 1.$ 275 2.$4,525 3.$4,800 4.$5,075 index

26. 31. To test the effect of a new medication on reaction time, two groups of 5 adults were asked to step on a pedal as soon as they saw a flashing light on a video screen. One group received the medication, and the other group did not receive the medication. The reaction times, in fractions of a second, are shown for each of the two groups. Group receiving medication: 0.55, 0.65, 0.60, 0.50, 0.70 Group not receiving medication: 0.20, 0.30, 0.25, 0.20, 0.30 How much longer is the mean reaction time of the group receiving the medication than the group not receiving the medication? 1.0.35 seconds 2.0.40 seconds 3.0.50 seconds 4.1.75 seconds index

27. 32. Six hundred sixty students cast their votes for Junior Class President at Hillmark High School. The results are shown in the graph below. If one-third of those who voted for Zach were girls, how many girls voted for Zach? 1.220 2.165 3.110 4.55 index

28. 33. The figure shows a three- dimensional object when viewed from above. Which of these objects could the sketch represent? 1.Pentagonal pyramid 2.rectangular prism 3.square pyramid 4.triangular prism index

29. 34. The local newspaper publishes a list of the five most popular radio stations. Lisa’s favorite station is not on the list. At school, she asks two of her friends what their favorite station is, and they both choose Lisa’s favorite station. Based on this, Lisa decides her favorite station should have been on the list. In your Answer Document, explain why Lisa’s conclusion is not valid by giving two reasons why her sample is biased. Respond completely. (2 points) Scoring Guidelines Write the answer on separate paper. index

30. 35. Which of the following shows 0.125, −2.1, -1/2, and 1.2 × 10 2 ordered from least to greatest? 1.1.2 × 10 2, 0.125, -1/2, −2.1 2.0.125, -1/2, −2.1, 1.2 × 10 2 3.−2.1, -1/2, 0.125, 1.2 × 10 2 4.1.2 × 10 2, -1/2, 0.125, −2.1 index

31. 36. Janice had a 5-inch high by 3-inch wide photo enlarged to a 3.5-foot tall poster. What should be the approximate width of the poster? 1.1.5 feet 2.2.1 feet 3.4.5 feet 4.5.8 feet index

32. 37. The quadrilateral below is to be translated 6 units to the right and 3 units down. Which ordered pair is not the coordinates for a vertex of the translated image? 1.(3, –4) 2.(3, –1) 3.(3, 2) 4.(1, –1) index

33. 38. Mr. Richards needs to price items that must be sold within 90 days, and he has two options. In Option A, Mr. Richards prices items at $225 and gives $1.00 off the price for every day that the item does not sell. For Option B, he prices items at $250 and gives $2.00 off for every day the item does not sell. In your Answer Document, write an equation for each option that relates the price of the item to the number of days that the item has not sold. Use the equations to find the day on which the two options yield the same price. Respond completely. (2 points) Scoring Guidelines Write the answer on separate paper. index

34. 39. Rob has 3 red, 4 white, 2 blue, and 5 green T-shirts in his drawer. He picks a red shirt on Monday without looking. He notices a stain and puts the shirt in the wash. Without looking, Rob then picks another shirt from his drawer. What is the probability he will pick a red shirt on his second try? 1.A 2.B 3.C 4.D index

35. 40. Let x be a negative number. Which expression will be positive? 1.4x 2.X 3 3.X 4 4.X -3 index

36. 41. Bart has a cylindrical pitcher with a radius of 6 cm and a height of 12 cm. He pours 1,300 cubic centimeters of lemonade into the pitcher. Approximately how much more lemonade will the pitcher hold? 1.36 cubic centimeters 2.57 cubic centimeters 3.622 cubic centimeters 4.1,357 cubic centimeters index

37. 42. Jake is using a computer program to design parts for a new car. He has outlined one-half of a part on a coordinate grid. Rather than drawing the second half, he plans to have the computer reflect this shape over the y- axis. Which of the following represents the 5 vertices of the reflected shape? 1.(0, 0); (0, 2); (−1, 3); (−2, 3); (−2, 0) 2.(0, 0); (0, 3); (−1, 3); (−2, 2); (−2, 0) 3.(0, 0); (0, −3); (1, −3); (2, −2); (2, 0) 4.(0, 0); (0, −3); (−1, −3); (−2, −2); (−2, 0) index

38. 43. The histogram below displays student scores on Mr. Dell’s English exam. How many students scored below 70 on the exam? 1.4 2.6 3.9 4.13 index

39. 44. Jackie has a job selling cars. Her monthly salary is $2,000 plus a commission of 1% of her total sales up to $100,000 and 1.5% of additional sales above $100,000. Which graph represents this relationship? 1.A 2.B 3.C 4.D index

40. Question 4 Question 4 – Short Answer Scoring Guidelines index PointsStudent Response 2The focus of the item is to determine the hours worked from a time card and calculate the weekly wages. The response determines Helga worked 15.5 hours and earned total wages of $97.65. 1The response provides evidence of a partially correct answer and/or solution process. The response shows understanding of some key elements of the task but contains gaps or flaws. For example, the response may: Identify the correct number of total hours worked, but fails to find the total wages. Determine the total wages based on an incorrect number of hours (e.g., ignoring the fractional parts of hours, rounding off hours, or miscalculating.) However, this number is multiplied by $6.30 to obtain the total wages based on the incorrect number of hours. Contain a detailed explanation of the steps required, but has incorrect or missing totals. Only state Helga’s total wages are $97.65. 0The response indicates inadequate understanding of the task and the response does not meet the criteria required to earn one point. For example, the response may: Include unrelated statements or work.

41. Question 10 Question 10 – Short Answer Scoring Guidelines index PointsStudent Response 2The focus of the item is to sketch a net of a triangular prism with given dimensions. The response shows a sketch of a net with dimensions labeled appropriately. 1The response provides evidence of a partially correct answer and/or solution process. The response shows understanding of some key elements of the task but contains gaps or flaws. For example, the response may:  Contains a correct net but one or more of the dimensions is labeled incorrectly or missing.  Contains a slightly flawed net (e.g., the student may omit the second triangle, or place the rectangles in an order that does not correspond to the order of the sides of the triangle.) 0The response indicates inadequate understanding of the task and the response does not meet the criteria required to earn one point. For example, the response may:  Include unrelated statements or work.

42. Question 22 Question 22 – Extended Response Scoring Guidelines index PointsStudent Response 4The focus of the item is to calculate scores based on tree measurements, order these scores from largest to smallest (or smallest to largest) and determine a general formula to calculate these scores. The response determines and orders the scores, 1) American Basswood – 261; 2) Eastern Hemlock – 291.05; 3) Black Oak – 328.1; and 4) American Beech 370.75 (order may be reversed). The response includes the general formula, Score = c + h + s/4, to determine the score for any tree in the Big Ohio Tree Program. 3The response clearly addresses the key aspects of the task; however, it includes minor flaws. For example, the response may: Contain an error in one or two of the scores for the four trees, the ranking is correct based on the scores provided and the formula is provided. Contain the correct scores for each of the four trees listed in the chart, the ranking is incorrect or missing. The formula is provided. Contain the correct scores for each of the four trees listed in the chart, the ranking is correct. The formula is flawed or missing. Omit the scores for the four trees; however, ranks the four trees correctly and provides a correct formula. continued

43. Question 22Question 22 – continued index PointsStudent Response 2The response provides evidence of a partially correct answer and/or solution process. The response may adequately address some of the components of the task but contain gaps or flaws in other components. For example, the response may: Contain the correct numerical scores for at least two of the four trees listed in the chart, and the ranking is correct based on the four scores provided. The formula is flawed or missing. Contain the correct scores for each of the four trees. The ranking and formula are incorrect or missing. Contain the correct formula and at least two correct scores, the ranking is incorrect or missing. Contain an incorrect formula but the scores and ranking are correct based on the formula provided. continued

44. Question 22Question 22 – continued index PointsStudent Response 1The response omits significant aspects of the task. There is evidence of minimal understanding of the concepts involved in the task and/or solution process; however, the response includes significant errors in most of the components of the task. For example, the response may: Provide only the formula. The scores for the trees are missing and no ranking is provided. Contain the correct numerical score for at least two of the four trees. The ranking and formula are incorrect or missing. Ignore the s/4 in calculations and formula; however, the ranking is correct for the values given. Contain a correct ranking with missing scores and the formula is missing. 0The response indicates inadequate understanding of the task and the response does not meet the criteria required to earn one point. For example, the response may: Contain the values added without considering the s/4, and no ranking or formula is provided. Contain an incorrect ranking with only incorrect scores or missing scores. Include unrelated statements or work.

45. Question 28 Question 28 – Short Answer Scoring Guidelines index PointsStudent Response 2The focus of the item is to determine the number of miles in one light-year and write this number in scientific notation. The response contains the value of ≈ 5.86 x 10 12 with supporting work. 1The response provides evidence of a partially correct answer and/or solution process. The response shows understanding of some key elements of the task but contains gaps or flaws. For example, the response may: Contain the correct value written in scientific notation with incomplete or missing work. Contain the correct value, but it is not written in correct scientific notation. Supporting work is incomplete or missing. Provide a correct process for determining the number of miles in one light- year but contains computation errors. Provide evidence of a partially correct process; (e.g., the conversion process includes the number of minutes in a year, but not the number of seconds.) The value found is written in correct scientific notation. 0The response indicates inadequate understanding of the task and the response does not meet the criteria required to earn one point. For example, the response may: Include unrelated statements or work.

46. Question 34 Question 34 – Short Answer Scoring Guidelines index PointsStudent Response 2The focus of this item is the identification of sources of bias in the sample used for a survey. The response provides two distinct reasons why Lisa’s sample may be biased. 1The response provides evidence of a partially correct answer and/or solution process. The response shows understanding of some key elements of the task but contains gaps or flaws. For example, the response may: Provide one valid reason why the sample is biased. 0The response indicates inadequate understanding of the task, and the response does not meet the criteria required to earn one point. For example, the response may: Include unrelated statements or work.

47. Question 38 Question 38 – Short Answer Scoring Guidelines index PointsStudent Response 2The focus of the item is to write a system of linear equations to model a problem situation. The response includes two correct equations, and a solution. (Day 25 or 26 acceptable with the appropriate equations.) 1The response provides evidence of a partially correct answer and/or solution process. The response shows understanding of some key elements of the task but contains gaps or flaws. For example, the response may: Contain two correct equations but an incorrect solution. Contain a correct solution with supporting work (e.g. table) with flawed or missing equations. Provide an incorrect solution based on slightly flawed equations. 0The response indicates inadequate understanding of the task, and the response does not meet the criteria required to earn one point. For example, the response may: Contain one correct equation with no additional work. Include unrelated statements or work.