OGT Math Half-Length Practice Test

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OGT Math Half-Length Practice Test
Data Analysis and Probability Benchmark A 2
Benchmark C 6 Benchmark G 16 Benchmark J
19 Geometry and Spatial Sense Benchmark A 13
Benchmark F 10 Measurement Benchmark B 17
Benchmark E 4 Number Sense Benchmark A 8
Benchmark B 11 Benchmark E 5 Benchmark F
15 Patterns, Functions and Algebra Benchmark A
1 Benchmark C 9 Benchmark D 12 Benchmark E 7
Benchmark F 3, 14 Benchmark H 18 Mathematics
Processes Benchmark A 10 Benchmark B 5
Benchmark D 6
To print a PDF of the OGT Practice Test, go to
www.ode.state.oh.us
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1. The table below contains the results of
abiology experiment. Assuming the pattern shown
in the table continues, what is the value of b?

1. 108
2. 130
3. 162
4. 243

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2. The box-and-whisker plot below describes the
weights of a sample of 100 chickens. What
statement can be made about the data, using the
graph alone?

1. The range of the weights is 3 lb.
2. The median weight is less than 2 lb.
3. Twenty-five percent of the chickens weigh less
   than 1 lb.
4. Fifty percent of the chickens weigh more than 2
   lb.

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3. Which equation is equivalent to 3(2x 5)
4(x 3)?

1. 2x 27
2. 2x 27
3. 10x 27
4. 10x 3

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4. Darius and his father are constructing a set
ofbunk beds as shown in the diagram below. What
is the measure of angle X?

1. 540
2. 390
3. 150
4. 120

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5. Three different opinion polls show different
results for the proportion of voters expected to
vote for Candidate A in an election for
mayor. Poll 1 Nine of every 20 voters are
expected to vote for Candidate A. Poll 2 The
percentage of voters expected to vote for
Candidate A is 52. Poll 3 There are 130,000
people expected to vote, and of these, 55,000
are expected to vote for Candidate A.In your
Answer, determine which of these polls shows the
greatest favorable result for Candidate A. Show
your work or provide an explanation for your
answer. (2 points)
Write the answer on separate paper.
Scoring Guidelines
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6. A set of data contains 10 negative numbersand
4 positive numbers. Which one of thesestatements
must be true?

1. The mean is a negative number.
2. The median is a negative number.
3. The mode is a negative number.
4. The range is a negative number.

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7. Travis went on a long trip. The graph below
represents the relationship between distance and
time. During what interval was Travis average
rate of travel the fastest?

1. 0 to 6
2. 6 to 8
3. 8 to 11
4. 11 to 16

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8. Which expression represents 270,000 written in
scientific notation?

1. 270 103
2. 27 104
3. 2.7 105
4. 0.27 106

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9. The table below shows values for x and y.
Which of these equations represents the
relationship between x and y?

1. y x-1
2. y x19
3. y x2 -1
4. y 2x2 -5

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10. Triangle DEF has vertices with coordinates
D(2, 1), E(1, 5) and F(2, 3). Draw and label
triangle DEF on the grid provided. Draw the
triangle D'E'F' by translating each vertex of
triangle DEF three units to the right and two
units down. Appropriately label triangle
D'E'F'. Draw the triangle D''E''F'' by
translating each vertex of triangle D'E'F' two
units to the left and seven units up.
Appropriately label triangle D''E''F''. Describe
the movements necessary to performa single
translation of each vertex from triangle DEF to
triangle D''E''F''. (4 points)
Write the answer on separate paper.
Scoring Guidelines
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11. Which number is irrational?

1. -2
2. 8
3. 3
4. 22/8

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12. Julie does not want to spend more than
300on ice skating. Her skates will cost 42,
her lessons will cost a total of 56, and the
practice time will cost 7.50 per hour. Which
inequality should Julie use to determine the
maximum number of hours, h, she can practice
without spending more than 300?

1. 567.50hlt300
2. 427.50hlt300
3. 7.50h - 42 - 56 300
4. 42 56 7.50h 300

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13. Daniel cut the corner off a cube as shown in
the diagram below. Points A, B and C are the
midpoints of the edges of the cube. What type of
three-dimensional figure has been cut off?

1. Cone
2. Cube
3. triangular prism
4. triangular pyramid

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14. Pippi calculates her total earnings for the
month with the equationE 15m 5b,where E is
the total number of dollars she earns, m is the
number of lawns she mows, and b is the number of
hours she baby-sits. If Pippi mows 6 lawns, how
many hours must she baby-sit to earn a total of
200?

1. 20
2. 22
3. 40
4. 45

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15. The population density of a state, in people
per square mile, is found by dividing the
population of the state by its area in square
miles. Florida has an area of 53,936 square
miles. In 1998, Florida had a population of
14,915,980 and a population density of 276.5
people per square mile.Describe the conditions
under which a different state could have a
smaller population than Florida but have a
greater population density. (2 points)
Write the answer on separate paper.
Scoring Guidelines
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16. George wants to conduct a survey todetermine
the types of music that the studentswant at a
school dance.Which sample population should
Georgesurvey to represent the entire student
body?

1. survey the teachers
2. survey the captain from each sports team
3. randomly survey two people from each homeroom
   class
4. randomly survey 50 people from the freshman class

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17. Gene has a cylinder with radius 4 inches
andheight 2 inches. He cut the cylinder in
halfalong the length of the diameter, as shown
in the diagram below. What is the area of the
shaded cross-section?

1. 48 p square inches
2. 24 p square inches
3. 16 square inches
4. 8 square inches

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18. A system of equations is shown below.3x 2y
192x - y 1What is the solution to the
system of equations?

1. x 1, y 1
2. x 3, y 5
3. x 7, y 1
4. x 19, y 1

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19. Carlos and Tiesha empty a bag of 100 colored
candies and count the number of each color, as
shown in the following chart. They return all
the candies to the bag and shake the bag.
Carlos removes 5 candies, 2 of which are blue.
Tiesha then pulls out one candy. What is the
probability that Tiesha pulls out a blue candy?

1. 6.67
2. 13.68
3. 15.00
4. 15.79

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Question 5 Short Answer Scoring Guidelines
Points Student Response
2 The response identifies Poll 2 as the most favorable and shows work used to compare the proportions in each poll through a common measurement.
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 Correctly compare two of the polls. Work for the third is incorrect or missing. OR Determine one of the values incorrectly but correctly use the values to make a comparison based on these values. OR Compare the three polls however, it fails to identify or incorrectly identifies which poll is most favorable for candidate A. OR Identify poll 2 as the correct choice and in the comparison of the three polls fails to use a common measurement.
continued
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Question 5 - continued
Points Student Response
0 The response indicates inadequate or no understanding of the task, and the task does not meet the requirements for one point. For example, the response may Fail to provide evidence of minimal understanding of the concept. OR Only identify poll 2 as the correct solution without supporting work. OR Recopy information provided in the item with no work. OR Show no apparent understanding of the task. OR Be blank or the student writes, I do not know or includes unrelated statements or work.
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Question 10 Short Answer Scoring Guidelines
Points Student Response
4 The focus of this item requires the student to correctly graph triangle DEF and perform the two translations in sequence. Finally, the student will identify the translation moves that would take triangle DEF to the third triangle in the sequence. Labeling is identified within the item and should be included within the response. The response shows triangle DEF and both transformations clearly and correctly drawn, and all triangles DEF, DE F, and DEF?are appropriately labeled. An explanation is provided that correctly describes the transformation from triangle DEF to triangle DEF?by translating each vertex one unit to the right and five units up. The work shown is organized and completely accurate.
3 The response clearly addresses the key aspects of the task however, it includes errors in completing one or two of the components. For example, the response may Show triangle DEF and both transformations correctly graphed and appropriately labeled, but the description of the transformation from DEF to D''E''F''?is missing or incorrect. OR Show triangle DEF graphed correctly and labeled. One transformation is done incorrectly, (example D'E'F' moves to the left, or down) but everything else is correct, based on this error. OR Contain one minor error in any part of the process. For example, triangle DEF is graphed incorrectly however, all other parts of the task are correct based on the incorrect triangle. OR Show triangle DEF and both transformations correctly graphed, but the labels are missing. The description of the transformation from DEF and D"E"F" is correct.
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continued
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Question 10 - continued
Points Student Response
2 The response provides evidence of a partial correct answer and/or solution process. The response may adequately address some of the components of the task, but it contains major gaps or flaws in other components. For example, the response may Show triangle DEF and one of the transformations graphed correctly, but the other transformation is either done incorrectly or is missing. The description given is related only to the one transformation or is missing. OR Show triangle DEF, and both transformations have been graphed correctly, but labels are missing and the description for the single transformation is unclear or missing. OR Show triangle DEF incorrectly graphed. Both transformations are consistent with the original graph, with or without labels. The description is incorrect based on the transformation or is missing. OR Show triangle DEF incorrectly graphed. One of the two transformations has an error, but is consistent with the original graph with or without labels. The description is correct based on the transformation.
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Question 10 - continued
Points Student Response
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 Show triangle DEF correctly graphed, but both transformations are incorrect or missing. OR Describe the movements necessary for a single transformation, but the graphs are omitted or incorrect. OR Show triangle DEF incorrectly graphed, but there is one correct transformation (two congruent triangles that match one of the translations mentioned in the questions).
0 The response indicates inadequate or no understanding of the task, and the task does not meet the requirements for one point. For example, the response may Fail to provide evidence of minimal understanding of the concept. OR Incorrectly plot only the points for triangle DEF. OR Recopy information provided in the item with no work. OR Show no apparent understanding of the task. OR Be blank or the student writes, I do not know or includes unrelated statements or work.
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Question 15 Short Answer Scoring Guidelines
Points Student Response
2 The success of this item hinges on the response communicating an understanding that the area of the state must be smaller than the area of Florida in order for the population density to be higher in the case where the population is lower. The supporting work and/or explanation are clear and complete. One approach is a written description of the ratios. Another approach is to actually pick numerical values that give correct answers to this problem.
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 Identify that the area of the state is smaller than that of Florida however, it states that the population remains the same or is larger than that of Florida. OR Not make a distinction between population and landmass being larger or smaller. The supporting work and/or explanation is not complete or clear.
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Question 15 continued
Points Student Response
0 The response indicates inadequate or no understanding of the task and/or incorrect use of the key elements or information. The response does not meet the criteria required to earn one point. For example, the response may Fail to provide evidence of minimal understanding of the concept. OR Recopy information provided in the item with no work. OR Show no apparent understanding of the task. OR Be blank or the student writes, I do not know or includes unrelated statements or work.
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