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Page 1: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

Ohio Graduation Test 2006 – MathData Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark F 2; Benchmark H 31, 39; Benchmark J 5, 14Geometry and Spatial Sense: Benchmark B 37; Benchmark C 25; Benchmark D 29; Benchmark E 11; Benchmark G 40 Measurement: Benchmark A 34; Benchmark B 13, 30; Benchmark C 42; Benchmark D 7, 12; Benchmark E 3Number Sense: Benchmark A 26; Benchmark B 38; Benchmark D 23; Benchmark G 4, 8; Benchmark H 33; Benchmark I 43Patterns, Functions and Algebra: Benchmark A 15; Benchmark B 6; Benchmark C 28; Benchmark D 36; Benchmark E 24; Benchmark F 1; Benchmark G 32; Benchmark H 10; Benchmark J 41

Not slated for Public Release as of 7/1/09:Questions: 16 - 21

To print a PDF of the OGT Test, go to

www.ode.state.oh.us

Page 2: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

1. A producer has $2 million budgeted for costs related to filming a movie on location. She estimates

the costs to be: c = $108,000n + $175,000

where c = costs in dollars and n = number of days. What is the greatest number of days she can film on

location and remain within the budget?

0%

0%

0%

0% A. 11 days B. 16 days C. 18 days D. 20 days

index

Page 3: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

2. A scientist is studying the effect of rainfall on the height of a certain

species of sunflower. The scatterplot shows the

results. What conclusion do the data support?

index

0%

0%

0%

0% A. This species of sunflower will not grow over 7 feet high. B. With over 4.0 centimeters of rain per week, this species of

sunflower will grow over 12 feet high. C. If the rainfall is less than 2 centimeters, then this species

of sunflower can still reach its maximum height. D. This species of sunflower grows tallest when there are

between 2.5 and 3 centimeters of rain per week.

Page 4: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

3. Jennifer wants to close off a rectangular area in her lawn so that she can leave her dog outside. She buys enough fencing to close off 252 square feet of lawn. If the length of the enclosure is 21 feet, what

is the width?

0%0%0%0%

A. 12 feet B. 14 feet C. 231 feet D. 273 feet

A. 12 feet B. 14 feet C. 231 feet D. 273 feet

index

Page 5: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

4. Adam was going to buy a new lawn mower from Lawn Care Depot for $169, less a 10% discount. He

saw the same mower on sale at Tractors-R-Us. Their mower originally cost $210 and was on sale for 13 off. In your Answer Document, determine the sale price of the mower at each store. Show your work or provide

an explanation to support your answer. Identify which store would be the most economical

place to purchase the mower. (2 points)

indexScoring Guidelines

Write the answer on separate paper.

Page 6: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

0%

0%

0%

0%

5. Teresa is playing a new board game. She must spin the spinner twice and get the same number both times in order to place her piece on the board. The diagram

below shows the result of her first spin. Each number on the spinner has an equal chance of occurring. What is the probability that Teresa’s next spin will allow her to

move her piece onto the board?

A. ¹/₁₆B. ¼C. ½D. ¾

index

Page 7: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

6. Which graph represents a linear function?

1 2 3 4

0% 0%0%0%

1. 2.

3. 4.

index

Page 8: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

7. Alicia is 5 feet tall. She casts a shadow that measures 6 ½ feet long at the same time that a

sculpture in the park casts a shadow 12 feet long. Which of the following is the approximate height of

the sculpture?

0%0%0%0%

A. 9 feet B. 16 feet C. 27 feet D. 78 feet

A. 9 feet B. 16 feet C. 27 feet D. 78 feet

index

Page 9: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

8. Jerry is planning to buy a stereo system priced at $840 through an installment plan. This plan requires a down payment of $190 and 24 monthly payments

of $32.35. How much more will Jerry pay for the stereo system by using the installment plan rather

than paying cash?0%0%0%0%

A. $ 63.60 B. $ 126.40 C. $ 253.60 D. $ 650.00

A. $ 63.60 B. $ 126.40 C. $ 253.60 D. $ 650.00

index

Page 10: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

9. Which graphical representation would be most useful in comparing the change in average earnings of

male employees versus average earnings of female employees over the course of a 50-year period?

0% 0%0%0%

A. circle graph B. double line graph C. box-and-whisker plot D. back-to-back stem-and-

leaf plot

index

Page 11: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

10. Mrs. Foyle told Yolanda that her test had 38 problems worth a total of 100 points. Each test

problem is worth either 5 points or 2 points. Yolanda wanted to determine how many 2-point and how many 5-point questions are on the test. In your Answer Document, determine how many

questions of each point-value are on the test. Show your work or provide an explanation to support

your answer. (2 points)

indexScoring Guidelines

Write the answer on separate paper.

Page 12: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

11. The figure shows the net for a three-dimensional object.

When folded, which object will this net produce?

0% 0%0%0%

1. 2.

3. 4.

index

Page 13: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

12. Jennifer is designing a quilt. The pattern for one part is

shown in the rectangle. Triangles ADC and EBF are similar. AB=BC.

What is the length of EF?

0%

0%

0%

0% A. 5 in. B. 6 in. C. 10 in. D. 12 in.

index

Page 14: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

13. An aquarium is 60 centimeters long, 20 centimeters wide and 30 centimeters high.

What volume of water, in cubic centimeters, does the aquarium contain if it is 2/3 full?

0%0%0%0%

A. 1,200 cm3 B. 11,000 cm3

C. 24,000 cm3 D. 36,000 cm3

A. 1,200 cm3

B. 11,000 cm3

C. 24,000 cm3

D. 36,000 cm3

index

Page 15: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

14. Jack has a box with 10 unlabeled computer CD-ROMs. He knows that 2 are music CDs, 3 are game CDs, and 5 are picture CDs. Jack randomly selects a

CD from the box. Which value represents the probability that the selected CD is a music or picture

CD? 0%0%0%0%

1/10 3/10 7/10 4/5

A. 1/10B. 3/10C. 7/10D. 4/5

index

Page 16: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

15. The first five rows of a number array are shown.

What is the sum of the numbers in row 8?

0% 0%0%0%

A. 175 B. 224 C. 231 D. 260

index

Page 17: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

22. The following table contains math contest scores of two teams in a high school math contest.

In your Answer Document, calculate the mean and median for each team. Determine which team

scored better in the contest by comparing these measures. (2 points)

indexScoring Guidelines

Write the answer on separate paper.

Page 18: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

23. The figure shows four points on the number line. Which point represents

√27?

0%

0%

0%

0% A. RB. SC. TD. V

index

Page 19: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

24. The graph, as shown, represents the amount of money Sarah can earn at her part-time

job. Which of the following equations best represents the

relationship between Sarah’s pay and the hours she works?

0%0%0%0%

A. y = 4x B. y = 6.5x C. y = 4x + 10 D. y = 6.5x + 10

A. y = 4x B. y = 6.5x C. y = 4x + 10 D. y = 6.5x + 10

index

Page 20: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

25. A worker painted stripes for spaces in a parking lot. The worker first painted a center stripe that marked the front of the parking spaces. Then he painted parallel stripes marking the sides. Which angles will be congruent to angle 1 if all the side stripes are parallel? 0%0%0%0%

A. ∠ 2 and ... B. ∠ 2 and ...

C. ∠ 3 and ... D. ∠ 4 and ...

A. 2 and 3 ∠ ∠B. 2 and 5 ∠ ∠C. 3 and 5 ∠ ∠D. 4 and 5 ∠ ∠

index

Page 21: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

26. The power output of a nuclear reactor is 2.4 × 107 watts. Which number expresses the same value

in standard notation?

0% 0%0%0%

A. 2,400,000 watts B. 9,400,000 watts C. 16,800,000 watts D. 24,000,000 watts

index

Page 22: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

27. The scatterplot below indicates the number of sit-ups

and push-ups completed by each student in Mr. Jenkin’s

physical education class. If Mary did 35 push-ups, approximately

how many sit-ups did she complete?

0%

0%

0%

0% A. 30 B. 35 C. 45 D. 50

index

Page 23: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

28. The maximum heart rate is the highest number of beats per minute recommended for a person while exercising. The rate is dependent upon the age of the person as shown below. The relationship is linear. In your Answer Document, copy and complete the table. Write an equation that can be used to find the maximum heart rate for any age. Show your work or provide an explanation for how you determined your equation. (2 points)

indexScoring Guidelines

Write the answer on separate paper.

Page 24: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

29. Three vertices of a quadrilateral are (–1, –1),

(1, 2) and (5, 2). When used as the last vertex,

which point would make the quadrilateral a

trapezoid?

0%0%0%0%

A. (3, 0) B. (3, –2) C. (–5, 0) D. (7, –1)

A. (3, 0) B. (3, –2) C. (–5, 0) D. (7, –1)

index

Page 25: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

30. Artie constructed a decorative planter using ten 4-inch squares attached to a rectangular base as shown

below. What is the volume of his planter?

0%0%0%0%

A. 160 cub... B. 192 cub... C. 256 cub... D. 384 cub...

A. 160 cubic inches B. 192 cubic inches C. 256 cubic inches D. 384 cubic inches

index

Page 26: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

31. Marty bought 4 new books today. He plans to read 2 of these while on vacation. How

many combinations of 2 books from the group of 4 books could he choose to read?

0% 0%0%0%

A. 2 B. 4 C. 6 D. 12

index

Page 27: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

32. Which equation is equivalent to

0%

0%

0%

0% A. (x – 40)(x – 60) = 0 B. (x – 30)(x – 80) = 0 C. (x + 20)(x – 120) = 0 D. (x + 20)(x + 120) = 0

index

x2 – 100x + 2,400 = 0?

Page 28: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

33. Which number is not a perfect square?

0%0%0%0%

A. 729 B. 1,280 C. 3,600 D. 5,329

A. 729 B. 1,280 C. 3,600 D. 5,329

index

Page 29: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

34. The diagram below shows the dimensions of a wall that needs to be painted. The door represented by the shaded rectangle is not to be painted. In your Answer Document, determine the area, to the nearest square foot, of the wall that is to be painted. Show your work or provide an explanation for your answer. (2 points)

indexScoring Guidelines

Write the answer on separate paper.

Page 30: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

35. A video game company reports the sales of video games for the first 11 months. The company’s

goal is to sell an average of 5 million games per month.

What is the minimum number of video games the company must

sell in the 12th month to meet its goal?

0%0%0%0%

A. 4.8 B. 5.0 C. 5.2 D. 5.4

A. 4.8 B. 5.0 C. 5.2 D. 5.4

index

Page 31: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

36. A local art museum charges admission to groups according to the following rates. Groups of fewer than 50 people are charged a rate of $4.00/person. Groups of 50 people or more are charged a reduced rate of $3.50/person. How much money will a group of 49 people save in admission costs if it can recruit one additional member?

A. $ 0.50 B. $ 21.00 C. $ 175.00 D. $ 196.00

0% 0%0%0%

A. $ 0.50 B. $ 21.00 C. $ 175.00 D. $ 196.00

index

Page 32: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

37. ∆ABC ∼∆DEF. What is the measure of angle D?

0%

0%

0%

0% A. 37° B. 45° C. 53° D. 74°

index

Page 33: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

38. If X is a real number, which statement is false?

0%0%0%0%

A. X may be both ... B. X may be both ...

C. X may be both ... D. X may be both ...

A. X may be both an integer and an even number.

B. X may be both an integer and a rational number.

C. X may be both a rational number and a negative number.

D. X may be both a rational number and an irrational number.

index

Page 34: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

39. A large corporation uses a telephone chain to notify employees of company closings due to bad weather. The plant manager calls 5 people in the first round of the telephone chain. Each of those people calls 5 other people in the second round of the telephone chain. If the pattern continues, how many employees are called in the 4th round of the telephone chain?

0%0%0%0%

A. 125 B. 126 C. 625 D. 626

A. 125 B. 126 C. 625 D. 626

index

Page 35: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

40. Triangle ABC is shown on the graph. In your Answer Document,

show that the segment connecting the midpoints of AB and BC is parallel to AC

and one-half its length. Show your work or provide

an explanation for your answer. (4 points)

indexScoring Guidelines

Write the answer on separate paper.

Page 36: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

41. Jessica participated in a walk-a-thon to raise money for a local charity. She began walking at a rate of 3 miles per hour. The

graph represents her distance walked as a function of time. If Jessica had walked at

an average rate of 2 miles per hour, which of the following accurately

illustrates how this graph would appear, using the same scale?

0% 0%0%0%

1. 2. 3. 4.

index

Page 37: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

42. The diagram below gives the lengths of all but

one side of pentagon ABCDE. What is the

perimeter of pentagon ABCDE?

0%

0%

0%

0% A. 39 cm B. 42 cm C. 43 cm D. 44 cm

index

Page 38: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

43. The area of Alaska is about 6 × 105 square miles. The area of Rhode Island is about 1.5 × 103 square miles. What is the difference between the area of

Alaska and the area of Rhode Island?

0%0%0%0%

A. 4.5 × 102 squa... B. 4.5 × 105 squa...

C. 5.985 × 105 sq... D. 5985 × 105 squ...

A. 4.5 × 102 square miles B. 4.5 × 105 square miles C. 5.985 × 105 square miles D. 5985 × 105 square miles

index

Page 39: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

44. In 1993, the median age of brides in Ohio was 27.0 years and the median age of grooms was 28.9

years. Based on this information, which of the following statements must be true?

0%0%0%0%

A. Most br... B. The you... C. Half of... D. All the...

A. Most brides were 27 years old. B. The youngest groom was 28.9

years old. C. Half of the grooms were 28.9 years

old or older. D. All the grooms were older than the

brides were.

index

Page 40: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

Question 4 – Scoring GuidelinesPoints Description

2 The focus of the item is to calculate discounts of original prices. The response states that the sale price of the lawnmower at Lawn Care Depot is $152.10 and the sale price at Tractors-R-Us is $140. The student identifies Tractors-R-Us as the most economical place to purchase the mower. Sample Response:Lawn Care $169 × .9 = $152.10 Tractors - R- Us $210 × 23 = $140 The mower costs less at Tractors - R - Us.

index Q. 4 Scoring Continued

Page 41: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

Question 4 – Scoring ContinuedPoints Description

1 The 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 a correct calculation for either store and a conclusion that is consistent with the values given for both stores. • Fail to identify the best buy but provide correct prices for the two stores. • Contain the correct answers ($152.10, $140, Tractors-R-Us) but work is incomplete or missing.

0 The response indicates inadequate understanding of the task. For example, the response may: • State that Tractors-R-Us is more economical but provide no work or explanation. • Include unrelated statements or work.

index

Page 42: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

Question 10 – Scoring GuidelinesPoints Description

2 The focus of the item is to determine the number of 2-point and 5-point questions on the test. The response indicates that there are 30 two-point and 8 five-point questions with supporting work or explanation.Sample Response: Use a system of equations: x + y = 38 2x + 5y = 100 ∴x = 30 2-point questions y = 8 5-point questions OR Use a table to guess-and-check:

Number of 2 – points 35 32 30

Number of 5-points 3 6 8

Total number of points 85 94 100

index Q. 10 Scoring Continued

Page 43: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

Question 10 – Scoring Continued

Points Description1 The 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 the correct answer with missing or incomplete work. • Provide an incorrect answer based on slightly flawed equations. • Provide correct equations or demonstrate a valid process but contain a calculation error in determining the solution.

0 The response indicates inadequate understanding of the task. For example, the response may: • Contain one answer (8 or 30) with no correct work. • Include unrelated statements or work.

index

Page 44: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

Question 22 – Scoring GuidelinesPoints Description

2 The focus of the item is to determine the mean and median for each team and make a comparison of these measures. The response contains the mean and median for each team (Team A – mean 85, median 85; Team B – mean 86, median 87) and compares them to determine that Team B scored higher for both measures.Sample Response: The mean for team B is higher (86 vs. 85) and the median is also higher (87 vs. 85). These two measures of center suggest that team B scored better.

1 The 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 mean for both teams or median for both teams and makes the comparison based on only one measure of center. Contain calculation errors in determining one or two of the measures but make a correct comparison based on the values provided. Contain the four correct measures of center with no comparison to determine that Team B scored better.

0 The response indicates inadequate understanding of the task. For example, the response may: • Contain fewer than four correct measures of center for the two teams with no comparison of the measures. • State that Team B scored better with no support. • Include unrelated statements or work. index

Page 45: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

Question 28 – Scoring GuidelinesPoints Description

2 The focus of the item is to complete a table and to determine an equation that models the data in the table. The response contains a completed table and an equation for the relationship shown in the table.Sample Response: (see table)R decreases by 1 for each additional year in age, so the slope is –1.

OR m= (210-205)/(10-15) = -1

210 = –1 (10) + b, so the y-intercept is 220

Sample Equations: R = -A + 220 or R = 220 – A or A = 220 – R or R - 210 = -1(A-10) or R – 210 = -A + 10 or R = -A + 220

a R

10 210

15 205

20 200

25 195

30 190

35 185

40 180

45 175

50 170

index Q. 28 Scoring Continued

Page 46: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

Question 28 – Scoring ContinuedPoints Description

1 The 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 a completed table, but the equation is incorrect or missing.Contain a correct equation, but the table is incorrect, incomplete or missing.Identify the correct slope or y-intercept of the equation, with or without the completed table.

0 The response indicates inadequate understanding of the task. For example, the response may: Contain a partially completed or incorrectly completed table with no

additional work. Include unrelated statements or work.

index

Page 47: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

Question 34 – Scoring GuidelinesPoints Description

2 The focus of the item is to determine the area, to the nearest square foot, of the wall to be painted. The response indicates that the area to be painted is approximately 214 ft2 with supporting work or explanation. Sample Response: (9 × 22) - (7 × 3) + (½ × 6 × 2) + (5×2) + (½ × 11× 2) + (½ × 5 × 4) = 214 ft2

OR (9 × 22) - (7 × 3) + ½ (22 + 5) 2 + (½ × 5 × 4) = 214 ft2

OR A close approximation based on counting squares.

1 The 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 an incorrect area based on a slightly flawed process (e.g., the area of the entire wall but fail to subtract the area of the door.) • Provide a correct process for finding the area to be painted but contain computational errors. • Provide a correct area to be painted with missing or incomplete work/explanation.

0 The response indicates inadequate understanding of the task.

index

Page 48: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

Question 40 – Scoring GuidelinesPoints Description

4 The focus of this item is the use of coordinate geometry to demonstrate relationships within a geometric figure. The response provides a demonstration that the mid-segment is parallel to and one-half the length of side AC by finding the midpoints of AB and BC and comparing the slope and length of the segment formed with the slope and length of AC or by completely stating the theorem.Sample Response:

Mid-pt AB = , = (5, 5) Mid-pt BC = , = (10, 6)

Side AC: slope = = Mid-segment: slope = =

The slopes are equal so they are parallel Mid-segment: length = =

Side: length= = = 2 Mid-segment is equal to ½ AC

index Q. 40 Scoring Continued

Page 49: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

Question 40 – Scoring ContinuedPoints Description

4Cont.

Sample Response: ContinuedORStudent may provide a graphic solution by locating the midpoints and showing that the “rise over run” is the same for both the midpoint segment and the line and demonstrating that length of the midpoint segment is half the length of side AC using the Pythagorean theorem or similar triangles. OR There is a geometric theorem which states a segment joining the midpoints of two sides of a triangle is parallel to and equal to ½ the length of the third side of the triangle.

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Page 50: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

Question 40 – Scoring ContinuedPoints Description

3 The response clearly addresses the key aspects of the task; however, it includes errors in completing one or two components. For example, the response may: • Correctly locate the midpoints and successfully demonstrate one half of the relationship. For the other part, the response demonstrates a correct procedure but contains computational errors or a minor graphing error (e.g., miscopies initial graph, but correctly demonstrates relationship).

2 The 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: • Correctly locate the midpoints and demonstrate an attempt to compare both slope and length but contain computational errors in each. • Correctly locate the midpoint and correctly compare either the slope or the length algebraically or graphically, but the other is attempted with an incorrect procedure or omitted. • Incorrectly locate the midpoints and attempt to compare both values by correctly finding values for both slopes and lengths or making an appropriate graphical comparison for both relationships. index Q. 40 Scoring Continued

Page 51: Ohio Graduation Test 2006 – Math Data Analysis and Probability : Benchmark A 27; Benchmark B 9; Benchmark C 35; Benchmark D 22; Benchmark E 44; Benchmark.

Question 40 – Scoring ContinuedPoints Description

1 The 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: • Correctly find both midpoints algebraically or graphically but contain no other correct work. • Incorrectly determine the midpoints but correctly determine the slope or length of the mid-segment based on those values. • Find the slope and/or length of AC.

0 The response indicates inadequate understanding of the task. For example, the response may: • Include unrelated statements or work.

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