Transcript OGT Math 2007

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 20
Patterns, Functions, and Algebra:
Benchmark A 2, 18; Benchmark C 44;
Benchmark E 7; Benchmark F 24; Benchmark H 38; Benchmark J 30
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 28
Measurement:
Benchmark B 41; Benchmark C 27; Benchmark D 21, 36;
Benchmark F 4, 9
Geometry and Spatial Sense: Benchmark A 10, 33; Benchmark B 29;
Benchmark C 25; Benchmark E 6, 10; Benchmark F 37, 42
Process Standard: Benchmark A 38; Benchmark B 4, 22, 28; Benchmark E 10;
Benchmark G 34
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
1.
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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.
2.
3.
4.
Line graph
circle graph
stem-and-leaf plot
box-and-whisker plot
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2. The first four rows of a number array are
show below.
Row
Row
Row
Row
70
40
80
20
50
90
10
30
60
100
What number will be at the far right end of row 7?
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36
0
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28
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0
0
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21
150
210
280
360
15
1.
2.
3.
4.
3. The figure shows four points on a number line.
Which point most accurately represents 150
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1.
2.
3.
4.
A
B
C
D
A
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B
C
D
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.
Helga’s Time Card
Date
In
Out
Monday
7/25
10:30 a.m.
2:00 p.m.
Tuesday
7/26
12:45 p.m.
3:30 p.m.
Thursday
7/28
12:00 p.m.
4:45 p.m.
Friday
7/29
11:15 a.m.
3:45 p.m.
Wednesday
7/27
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)
Write the answer on separate paper.
Scoring Guidelines
index
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.
2.
3.
4.
The mean of the
temperatures is positive.
The mode of the
temperatures is positive.
The median of the
temperatures is positive.
The minimum of the
temperatures is positive.
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The mean of the t...
The mode of the t...
The median of the...
The minimum of th...
6. The net creates a pyramid.
1.
2.
3.
4.
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A
B
C
D
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A
B
C
D
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?
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1.
2.
3.
4.
Spending all $30 on walnuts
spending all $30 on peanuts
spending $20 on peanuts
and $10 on walnuts
spending half of the $30 on
peanuts and half of the $30
on walnuts
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Spending a...
spending a...
spending $...
spending h...
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?
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1.
2.
3.
4.
4
9
15
19
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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
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2. 8.6 hours
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3. 10.9 hours
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4. 17.0 hours
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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)
Write the answer on separate paper.
Scoring Guidelines
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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?
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24
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0%
19
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9
3
9
19
24
3
1.
2.
3.
4.
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.
2.
3.
4.
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24 gerbils
66 gerbils
128 gerbils
512 gerbils
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24 gerbils
66 gerbils
128 gerbils
512 gerbils
19. Jupiter’s diameter is 88,640 miles.
How is this measurement expressed in
scientific notation?
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1.
2.
3.
4.
8.864 × 103 miles
0.864 × 104 miles
8.864 × 104 miles
88.64 × 104 miles
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8.864 × 103 miles
0.864 × 104 miles
8.864 × 104 miles
88.64 × 104 miles
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.
2.
3.
4.
17/
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100
1/
4
17/
83
17/
25
17/100
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1/4
17/83
17/25
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?
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1. 2.0 miles
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2. 6.6 miles
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3. 12.0 miles
4. 15.6 miles
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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.
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)
Write the answer on separate paper.
Scoring Guidelines
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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?
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1. ½
2. 1/25
3. 1/50
4. 16/25
½
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1/25
1/50
16/25
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?
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1.
2.
3.
4.
2x+ 4 = 3x + 4
2x + 4 = 3x + 5
2x + 4 = 2(x + 2)
2x + 4 = 2(x + 3)
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2x+ 4 = 3x + 4
2x + 4 = 3x + 5
2x + 4 = 2(x + 2)
2x + 4 = 2(x + 3)
25. In which figure is the measure of
1 NOT equal to 60?
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1.
2.
3.
4.
A
B
A
B
C
D
C
D
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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.
2.
3.
4.
The nails produced all have the
standard length.
The nails are much more likely
to be too long than too short.
The nails are much more likely
to be too short than too long.
The nails are about as likely to
be too long as they are to be
too short.
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The nails produce...
The nails are muc...
The nails are muc...
The nails are abo...
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?
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1.
2.
3.
4.
18.3 cm2
42.3 cm2
145.6 cm2
194.1 cm2
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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)
Write the answer on separate paper.
Scoring Guidelines
index
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?
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1.
2.
3.
4.
96
40
20
4
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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
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2. $4,525
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3. $4,800
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4. $5,075
0%
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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?
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1.
2.
3.
4.
0.35 seconds
0.40 seconds
0.50 seconds
1.75 seconds
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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?
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1.
2.
3.
4.
220
165
110
55
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220
165
110
55
33. The figure shows a threedimensional object when viewed from
above. Which of these objects could
the sketch represent?
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1.
2.
3.
4.
Pentagonal pyramid
rectangular prism
square pyramid
triangular prism
Pentagonal...
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rectangula...
square pyr...
triangular...
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)
Write the answer on separate paper.
Scoring Guidelines
index
35. Which of the following shows 0.125, −2.1, -1/2, and
1.2 × 102 ordered from least to greatest?
1. 1.2 × 102, 0.125, -1/2, −2.1
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2. 0.125, -1/2, −2.1, 1.2 × 102
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3. −2.1, -1/2, 0.125, 1.2 × 102
0%
4. 1.2 × 102, -1/2, 0.125, −2.1
0%
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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.
2.
3.
4.
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1.5 feet
2.1 feet
4.5 feet
5.8 feet
1.5 feet
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2.1 feet
4.5 feet
5.8 feet
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?
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1.
2.
3.
4.
(3, –4)
(3, –1)
(3, 2)
(1, –1)
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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)
Write the answer on separate paper.
Scoring Guidelines
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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?
A
B
C
D
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0%
D
0%
C
0%
B
0%
A
1.
2.
3.
4.
40. Let x be a negative number. Which
expression will be positive?
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1.
2.
3.
4.
4x
X3
X4
X-3
4x
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X3
X4
X-3
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
0%
2. 57 cubic centimeters
0%
3. 622 cubic centimeters
0%
4. 1,357 cubic centimeters
0%
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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 yaxis. Which of the following represents
the 5 vertices of the reflected shape?
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1.
2.
3.
4.
(0, 0); (0, 2); (−1, 3); (−2, 3); (−2, 0)
(0, 0); (0, 3); (−1, 3); (−2, 2); (−2, 0)
(0, 0); (0, −3); (1, −3); (2, −2); (2, 0)
(0, 0); (0, −3); (−1, −3); (−2, −2); (−2, 0)
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(0, 0); (0, 2); (...
(0, 0); (0, 3); (...
(0, 0); (0, −3); ...
(0, 0); (0, −3); ...
43. The histogram below displays student scores on Mr.
Dell’s English exam. How many students scored below
70 on the exam?
0%
0%
0%
0%
1.
2.
3.
4.
4
6
9
13
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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?
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0%
0%
0%
1.
2.
3.
4.
A
B
C
D
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Question 4 – Short Answer Scoring Guidelines
Points
Student Response
2
The 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.
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 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.
0
The 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.
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Question 10 – Short Answer Scoring Guidelines
Points
Student Response
2
The 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.
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:
 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.)
0
The 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.
index
Question 22 – Extended Response Scoring Guidelines
Points
Student Response
4
The 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.
3
The 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.
index
continued
Question 22 – continued
Points
Student Response
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:
• 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
index
Question 22 – 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:
• 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.
0
The 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.
index
Question 28 – Short Answer Scoring Guidelines
Points
Student Response
2
The 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 1012
with supporting work.
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 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 lightyear 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.
0
The 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.
index
Question 34 – Short Answer Scoring Guidelines
Points
Student Response
2
The 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.
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 one valid reason why the sample is biased.
0
The 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.
index
Question 38 – Short Answer Scoring Guidelines
Points
Student Response
2
The 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.)
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 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.
0
The 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.
index