Ohio Graduation Test 2008 – Math Data Analysis and Probability : Benchmark A 18; Benchmark B 39;...

Ohio Graduation Test 2008 – MathData Analysis and Probability : Benchmark A 18; Benchmark B 39; Benchmark D 15; Benchmark F 6; Benchmark G 3, 22; Benchmark H 8; Benchmark J 43; Benchmark K 12, 32

Geometry and Spatial Sense: Benchmark B 37 ; Benchmark C 42; Benchmark D 13; Benchmark E 4; Benchmark F 34

Measurement: Benchmark B 29, 44; Benchmark C 20, 36; Benchmark D 9; Benchmark F 16, 33

Number Sense: Benchmark A 40; Benchmark D 2; Benchmark E 30; Benchmark F 10; Benchmark G 5, 14; Benchmark I 19

Patterns, Functions and Algebra: Benchmark A 1; Benchmark B 38; Benchmark C 7, 41; Benchmark D 35; Benchmark E 31; Benchmark F 11; Benchmark H 17; Benchmark I 21

Not slated for Public Release as of 7/1/08:Questions: 23-28

To print a PDF of the OGT Test, go to

www.ode.state.oh.us

1. The owner of a sporting goods store is following a pattern to arrange baseballs into 7 rows for a wall

display. The table shows the number of baseballs in the first four rows of this pattern. How many baseballs are in

the seventh row of this pattern?

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1. 172. 153. 104. 4

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2. On the number line point R represents the square root of a number. Which value could be the square of the number represented by point

R?

0%

0%

0%

0% 1. 137

2. 149

3. 165

4. 173

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3. A restaurant manager is planning a survey todetermine which three desserts are most

preferred by his customers. Which sample would best represent the customers at the restaurant?

0%0%0%0%

Survey all childr... Survey all custom...

Survey all of the... Survey every fift...

1. Survey all children who enter the restaurant.

2. Survey all customers over 50 years old for one week.

3. Survey all of the men that come into the restaurant for one week.

4. Survey every fifth customer that enters the restaurant for one week.

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4. The figure shows two views of the same object. Which net will make the

figure shown?

Pic

ture

Cho

ice

1

Pic

ture

Cho

ice

2

Pic

ture

Cho

ice

3

Pic

ture

Cho

ice

4

0% 0%0%0%

1. 2.

3. 4.

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5. Carmella has a coupon that allows her to buy one pair of shorts at the regular price and get a second pair at half the regular price. The shorts cost $25.50 per pair. When Carmella arrives at the store, she finds that the

shorts are on sale for 30% off the regular price. This sale does not allow coupons to be used on the discounted items. Explain whether two pairs of shorts would cost

less by using the coupon or by buying two pairs of shorts at the sale price. Provide mathematical calculations and/or reasoning to support your answer. (2 points)

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Scoring Guidelines

Write the answer on separate paper.

6. The graph shows the total sales per year for the X300 and X400 speakers produced by an audio manufacturing company. The manufacturer plans to discontinue the X300 speaker when the total sales for the X400 speaker are greater than the total sales for the X300 speaker.

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0%

0%

0%

Based on the trend in the graph, what is the earliest year that the sales of the X400 speaker will be greater than the sales of the X300 speaker? 1. 2000

2. 2003

3. 2006

4. 2009

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7. Michael paid $6.00 for a ticket to a football game. Soft drinks at the game cost $0.75.

Michael bought x drinks at the game. Which equation represents the total amount (y) he

spent?

0%0%0%0%

y = (6 + 0... y = 6x + 0... y = 6 – 0.... y = 6 + 0....

1. y = (6 + 0.75)x

2. y = 6x + 0.75

3. y = 6 – 0.75x

4. y = 6 + 0.75x

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8. One style of jacket comes in three sizes: small,medium or large. These jackets have either

buttons or a zipper. The jackets are available infive different colors. How many different

combinations of this jacket are available?

10 15 25 30

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1. 10

2. 15

3. 25

4. 30

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9. ED and AB are both perpendicular to BD. In

triangle ABC, the length of AC is 4 cm and the

length of AB is 2 cm. If the length of EC is 8 cm, what is

the length of ED?

0%

0%

0%

0% 1. 4 cm2. 4 2 cm3. 8 2 cm4. 16 cm

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1. 2.5x 2

2. x3 + 4

3. x – 2

4. x + x

10. When x > 1, which expression has a value less than x?

0%0%0%0%

1 2 3 4

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11. A sports club is planning a cookout. The foodservice charges $1.75 per person plus a flat

fee of $200. The club can only spend $500 forfood service. Determine the maximum number of people the club will be able to serve. Use a table,

graph, equation or inequality to support your answer. (2 points)

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Scoring Guidelines


12. Mirachelle picked a colored cube from a bag of cubes, recorded the color and returned the cube to the bag. She did this 10 times. The table below shows the color of each cube as it was selected. Using the

information from the table, how many times would a yellow cube be

expected in 30 picks?

4 10 12 30

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1. 42. 103. 124. 30

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13. The coordinates of triangle KLM are K: (–2, –5), L: (0, 1) and M: (6, –2). What type of triangle is KLM?

0%

0%

0%

0%1. obtuse isosceles

2. acute scalene

3. right isosceles

4. right scalene

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14. Central Health Center employs 360 individuals. The graph shows the different types of positions at Central Health Center. Approximately 48% of the physicians and dentists employed by Central

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26 28 36 37

Health Center are women. How many of the physicians and dentists are women?

1. 262. 283. 364. 37

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15. Weekly salaries of the employees at a localvideo store are shown in the table below. What is

the mean weekly salary at this video store?

$230.48 $242.00 $322.67 $350.00

0%0%0%0%0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1. $230.48

2. $242.00

3. $322.67

4. $350.00

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16. Before her trip to Canada, Liz exchanged 300 U.S. dollars for Canadian dollars at a rate of 1 U.S. dollar to 1.35 Canadian dollars. When Liz arrived in Canada, the exchange rate was 1 Canadian dollar to 0.76 U.S. dollars. • Determine the amount of money in Canadian dollars that Liz received for her 300 U.S. dollars.• Determine whether Liz would have received more Canadian money for her 300 U.S. dollars if she had waited to exchange her money in Canada.Show your work or provide an explanation for your answers. (2 points)

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Scoring Guidelines


17. Roni and Kelsey bought the same types of flowers from a florist. Roni bought 5 roses and 2 carnations and

was charged $17.85 before tax. Kelsey purchased 1 rose and 6 carnations and was charged $12.25 before

tax. How much did the florist charge for 1 carnationbefore tax?

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0%

0%

0%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

1. $1.12

2. $1.55

3. $2.15

4. $2.80

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18. The graph shows the percent of the total votes cast

for each of the four candidates in Andersonville’s city council election. If 2,542 people voted in this election, about how many votes did

Lango receive? 0%0%0%0%

76 141 458 915

1. 76

2. 141

3. 458

4. 915index

19. Earth has a surface area of 1.97 × 108 square miles. A new planet has a surface area 13

times the surface area of Earth.What is the surface area of the new planet?

1 2 3 4

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10%

20%

30%

40%

50%

60%

70%

80%

90%

100%1. 1.515 × 107 square miles

2. 2.10 × 108 square miles



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20. The city flag for Celina, Ohio, is shown. The flag has a total area of 5,472 square centimeters. In the center of the flag is a circular design. The diameter of this design is 48 centimeters.

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0%

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What is the approximate area of the flag that is NOT covered by the circular design?

1. 1,763 cm2

2. 1,809 cm2

3. 3,663 cm2

4. 5,321 cm2

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21. For his business, Gil has determined that the time it takes to finish a job varies inversely with the number of workers. This can be expressed as:

where T = time, k is a constant, and w = number of workers. Gil’s records show that 18 workers can finish a job in 6 days. How many days will it take 12 workers to do the same job?

0%0%0%0%

4 9 12 36

1. 42. 93. 124. 36

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22. The transportation department has selected three possible routes for a new section of highway and wants to know which route landowners and residents of the affected areas prefer. The transportation departmentplans to survey the public by posting the three possible routes on the department’s Web site with a request that all visitors to the Web site vote for their preferred route.

Explain why the design of the survey does not provide arepresentative sample of the landowners and residents of the affected area. Give an example of how the design of the survey could be changed to better represent theaffected population. (2 points)

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Scoring Guidelines


29. Madison is filling balloons with helium. Whenfull, the balloons are nearly spherical in shape

with a diameter of 12 inches. What is the approximate volume of each balloon when it is

full?

115

cubic

inch

es

450

cubic

inch

es

680

cubic

inch

es

900

cubic

inch

es

0% 0%0%0%

1. 115 cubic inches

2. 450 cubic inches

3. 680 cubic inches

4. 900 cubic inches

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30. Which sequence of numerals is equivalent to:

2/3 , 10%, 0.8, 6?

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0%

0%

0% 1. 4/6, 1/10, 8/100, 0.06

2. 0.67, 1.0, 8%, 6.00

3. 66 2/3%, 2/20, 4/5, 6.0

4. 2/3, 0.01, 80%, 6%

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31. The graph of the function f(x) is shown below. Which of the following is NOT a zero of f(x)?

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-4 -3 2 6

1. -42. -33. 24. 6

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32. Joel plays tic-tac-toe on his computer. The computer plays first and randomly places an “X” in one of the grid squares as labeled in the diagram. The frequency table shows the computer’s first move for 50 games.Based on these results, what is the experimental probability that the computer will place an “X” in a corner square on the first move of its next game?

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0%

0%

0% 1. 4/9

2. 19/59

3. 9/25

4. 13/25

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33. Federico is paid $8.50 per hour for the first40 hours he works each week. For each hour

Federico works over 40 hours, he is paid for one-and-a-half hours. One week Federico

works 48 hours. How much does Federico earn for working 48 hours in one week?

$340 $408 $442 $612

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1. $340

2. $408

3. $442

4. $612

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34. The vertices of Triangle I are (1, 3), (2, 1)and (5, 0). Triangle I is reflected across thex-axis, resulting in Triangle II. Triangle II isthen rotated 180o about the origin, resulting

in Triangle III. Draw and label Triangles I, II and III on the same coordinate plane. Describe a

single transformation that would map Triangle I directly onto Triangle III. (4 points)

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Scoring Guidelines


35. A band pays for the use of a location for a concert. The band charges $25 per ticket.

If n represents the number of tickets sold and c represents the cost of the location, which

inequality below describes how many tickets need to be sold to make a profit?

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25c < n 25c > n 25n < c 25n > c

1. 25c < n

2. 25c > n

3. 25n < c

4. 25n > c

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36. Tammy is roofing a house. She must buy

enough shingles to cover the shaded rectangular

areas on both sides of the roof, as shown in the

diagram below. What is the area she must cover?

1 2 3 4

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1. 715 ft2

2. 835 ft2

3. 1,430 ft2

4. 6,600 ft2

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37. An airline executive drew a sketch of a logo on a napkin. She gave the logo to a graphic designer so he could make a

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0%

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0%

mathematically similar version with a computer drawing program. The center line of the new logo needs to be 10 centimeters long. Which of these proportions could the graphic designer use to find the value of y?

1. 4.0/3.8 = y/10.0

2. 3.8/y = 6.8/10.0

3. 6.8/4.0 = y/10.0

4. y/6.8 = 10.0/3.8

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38. Which graph represents a linear function?

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Picture Choice 1 Picture Choice 2

Picture Choice 3 Picture Choice 4

1. 2. 3. 4.

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39. In honor of the new millennium, Stephanie buried a time capsule in her front yard. She sketched the location of key landmarks as shown below. She noted that the capsule was buried equidistant from the oak tree and the elm tree. It is also equidistant

(4, G

)

(7, H

)

(8, G

)

(10,

H)

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from the mailbox and the front door. Which pair of coordinates is the closest estimate for the location of the time capsule?

1. (4, G)2. (7, H)3. (8, G)4. (10, H)

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40. Selena was given five different cells to measure. The table below shows Selena’s results. Write all of the measurements in scientific notation. Order the

values from smallest to largest. (2 points)

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Scoring Guidelines


41. The table shows values for a function. Which

equation represents this function?

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0%

0%

0% 1. y= x2

2. y= x2 + 1

3. y= (x – 1)2

4. y= (x+1)2

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42. When a marble hits a wall, it bounces off the wallat the same angle it hits the wall. If a marble hits a wall at a 22 degree angle, what is the measure of the angle

between the two paths of the marble?

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44° 68° 136° 158°

1. 44°

2. 68°

3. 136°

4. 158°

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43. Drake’s school awarded 450 raffle tickets asincentives. The principal will draw one winning

ticket. The winner will receive a CD player. Drakereceived 3 tickets for good attendance, 5 for making the honor roll, and 2 for tutoring other students. What is the probability that one of Drake’s tickets will be selected by

the principal?

1/1

5 1

/45

1/4

41

1/4

50

0% 0%0%0%

1. 1/15

2. 1/45

3. 1/441

4. 1/450

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44. A compound glue comes in a cylindrical tube divided down the middle to separate the glue agent

from the hardening agent as shown. What is the approximate volume of the section of the tube containing the hardening agent?

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71 cm3 141 cm3 424 cm3 565 cm3

1. 71 cm3

2. 141 cm3

3. 424 cm3

4. 565 cm3

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Question 5 – Short Answer Scoring Guidelines

Points Student Response

2

The focus of this item is to compare the final price of two pairs of shorts either using a coupon to get the second pair at half price or using a discount of 30% on both. The response states that the 30% discounted price is the better buy and provides mathematical support for the answer.

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.

0The response indicates inadequate understanding of the task, and the response does not meet the criteria required to earn one point.

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2

The focus of the item is to use a table, graph, equation or inequality to solve a word problem. The response determines the maximum number of people (171 or 171.4) the club will be able to serve at a cookout for less than $500 using one of these techniques.


0The response indicates inadequate understanding of the task and the response does not meet the criteria required to earn one point.


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2

The focus of the item is to use proportions to compare two different rates. The response states that $300 U.S. can be exchanged for $405 Canadian in the U.S. and that she would not have received more if she had waited to exchange money with correct work or explanation of money when exchanged with the first rate and explains that the second rate would give her less money.

1The response provides evidence of a partially correct answer and/or solution process. The response shows understanding of most of the key elements of the task but contains gaps or flaws.



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2

The focus of this item is to evaluate and improve the design for a survey to determine the preferred route for a new highway. The response explains why the survey design is not representative of the residents in the affected area and provides a change to the survey design to make it more representative.




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4

The focus of this item is to show and describe the results of combinations of translations, reflections and rotations. The response contains the correct three triangles labeled I, II and III on the same coordinate grid and contains the correct single transformation that maps Triangle I to Triangle III.

3The response clearly addresses the key aspects of the task; however, it includes minor flaws.

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.

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.



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2The response contains diameters 2, 3 and 5 written correctly in scientific notation. The five diameters are correctly ordered from smallest to largest.

1

The response provides a partial solution. Diameters 2, 3 and 5 may be correctly written in scientific notation. The order may be incorrect or missing.ORThe scientific notation for the three diameters is incorrect or missing, but the five original values are correctly ordered.ORThe response contains errors in scientific notation, but the student’s values obtained are correctly ordered.ORThe response contains a combination of some correct scientific notation and some correct ordering that indicate some understanding of the concepts involved.

0 The response fails to demonstrate minimal understanding of the task.

Ohio Graduation Test 2008 – Math Data Analysis and Probability : Benchmark A 18; Benchmark B 39;...

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Transcript of Ohio Graduation Test 2008 – Math Data Analysis and Probability : Benchmark A 18; Benchmark B 39;...