Ohio Graduation Test 2006

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 F 2 Benchmark H 31,
39 Benchmark J 5, 14 Geometry 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 3 Number
Sense Benchmark A 26 Benchmark B 38 Benchmark
D 23 Benchmark G 4, 8 Benchmark H 33 Benchmark
I 43 Patterns, 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
2
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?

• A. 11 days
• B. 16 days
• C. 18 days
• D. 20 days

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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?

• 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.

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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?

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

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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)
Write the answer on separate paper.
Scoring Guidelines
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6
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 Teresas next spin will allow
her to move her piece onto the board?

1. ¹/16
2. ¼
3. ½
4. ¾

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6. Which graph represents a linear function?

1. Picture Choice 1
2. Picture Choice 2
3. Picture Choice 3
4. Picture Choice 4

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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?

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

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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?

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

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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?

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

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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)
Write the answer on separate paper.
Scoring Guidelines
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11. The figure shows the net for a
three-dimensional object. When folded, which
object will this net produce?

1. Picture Choice 1
2. Picture Choice 2
3. Picture Choice 3
4. Picture Choice 4

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12. Jennifer is designing a quilt. The pattern
for one part is shown in the rectangle. Triangles
ADC and EBF are similar. ABBC. What is the
length of EF?

• A. 5 in.
• B. 6 in.
• C. 10 in.
• D. 12 in.

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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?

• A. 1,200 cm3
• B. 11,000 cm3
• C. 24,000 cm3
• D. 36,000 cm3

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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?

1. 1/10
2. 3/10
3. 7/10
4. 4/5

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15. The first five rows of a number array are
shown.What is the sum of the numbers in row
8?

• A. 175
• B. 224
• C. 231
• D. 260

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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)
Write the answer on separate paper.
Scoring Guidelines
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23. The figure shows four points on the number
line. Which point represents v27?

1. R
2. S
3. T
4. V

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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 Sarahs pay and the hours
she works?

• A. y 4x
• B. y 6.5x
• C. y 4x 10
• D. y 6.5x 10

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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?

• A. ?2 and ?3
• B. ?2 and ?5
• C. ?3 and ?5
• D. ?4 and ?5

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26. The power output of a nuclear reactor is 2.4
107 watts. Which number expresses the same
value in standard notation?

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

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22
27. The scatterplot below indicates the number of
sit-ups and push-ups completed by each student in
Mr. Jenkins physical education class. If Mary
did 35 push-ups, approximately how many sit-ups
did she complete?

• A. 30
• B. 35
• C. 45
• D. 50

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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)
Write the answer on separate paper.
Scoring Guidelines
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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?

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

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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?

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

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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?

• A. 2
• B. 4
• C. 6
• D. 12

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32. Which equation is equivalent to
x2 100x 2,400 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

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33. Which number is not a perfect square?

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

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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)
Write the answer on separate paper.
Scoring Guidelines
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35. A video game company reports the sales of
video games for the first 11 months. The
companys 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?

• A. 4.8
• B. 5.0
• C. 5.2
• D. 5.4

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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

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

• A. 37
• B. 45
• C. 53
• D. 74

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

• 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.

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34
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?

• A. 125
• B. 126
• C. 625
• D. 626

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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)
Write the answer on separate paper.
Scoring Guidelines
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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?

1. Picture Choice 1
2. Picture Choice 2
3. Picture Choice 3
4. Picture Choice 4

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42. The diagram below gives the lengths of all
but one side of pentagon ABCDE. What is the
perimeter of pentagon ABCDE?

• A. 39 cm
• B. 42 cm
• C. 43 cm
• D. 44 cm

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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?

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

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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?

• 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.

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Question 4 Scoring Guidelines
Points 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.
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Q. 4 Scoring Continued
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Question 4 Scoring Continued
Points 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.
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Question 10 Scoring Guidelines
Points 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
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Q. 10 Scoring Continued
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Question 10 Scoring Continued
Points 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 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.
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44
Question 22 Scoring Guidelines
Points 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.
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Question 28 Scoring Guidelines
Points 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
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Q. 28 Scoring Continued
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Question 28 Scoring Continued
Points 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.
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Question 34 Scoring Guidelines
Points 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) (52) (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.
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Question 40 Scoring Guidelines
Points 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
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Q. 40 Scoring Continued
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Question 40 Scoring Continued
Points Description
4 Cont. Sample Response Continued OR Student 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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Q. 40 Scoring Continued
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Question 40 Scoring Continued
Points 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.
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Q. 40 Scoring Continued
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Question 40 Scoring Continued
Points 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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