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Name _______________________________________ Date __________________ Class __________________
S.ID.1*
Select all correct answers.
SELECTED RESPONSE
Select the correct answer.
3. The data below are the distances (in
megaparsecs) from Earth of several
nebulae outside the Milky Way galaxy.
Which of the following values are
necessary to make a box plot of the
data? (All computed values have been
rounded to three decimal places.)
1. The data sets below show the numbers of
cookies purchased by students at a bake
sale. Which of the data sets is
represented by the dot plot?
0.032 0.214 0.263 0.450 0.500
0.800 0.900 1.000 1.100 1.400
1.700 2.000
0.032 megaparsec
2 2 4 4 1 1 5 1 3 2 1
0.357 megaparsec
2 4 4 2 3 3 2 1 1 3 5 1
2 2 1
0.377 megaparsec
1 2 1 1 2 1 2 2 3 4 5 1
3 4 4
0.850 megaparsec
3 2 2 3 1 3 1 4 4 5 1 1
1 2 2
1.250 megaparsecs
0.863 megaparsec
1.350 megaparsecs
2.000 megaparsecs
2. The data below are the percent change in
population of 20 states between 1950
and 1960. Which of the following set of
intervals should be used to make a
histogram of the data?
CONSTRUCTED RESPONSE
4. The data below are the number of beds
in a sample of 15 nursing homes in
New Mexico in 1988.
3.7 5.3 6.8 7 8.1 10.2 13.3 13.7
14.7 15.5 18.3 21.8 21.9 21.9
24.1 25.5 31.1 31.5 39.4 39.9
44 59 59 60 62 65 80 80 90
96 100 110 116 120 135
5.0% to 9.9%, 10.0% to 19.9%,
20.0% to 29.9%, and 30.0% to 34.9%
a. Find the minimum and maximum of
the data.
0.0% to 9.9%, 10.0% to 19.9%,
20.0% to 29.9%, and 30.0% to 39.9%
________________________________________
b. Find the first, second, and
third quartiles.
0.0% to 9.9%, 10.0% to 14.9%,
15.0% to 19.9%, 20.0% to 24.9%,
25.0% to 29.9%, and 30.0% to 39.9%
________________________________________
0.0% to 9.9%, 10.0% to 29.9%,
and 30% to 39.9%
c. Make a box plot of the data.
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Algebra 1
103
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
5. The data below are the average annual
starting salaries (in thousands of dollars)
of 20 randomly selected college
graduates. Make a dot plot of the data
values.
8. The following data values are the
percents of the vote that the Democratic
candidate won in 20 randomly selected
states in the 1984 presidential election.
37.5
42.3
30.1
47.5
42 37 40 37 45 39 43 47 36
34 40 43 42 40 37 44 36 46
39 35
33.9 43.1 48.1 27.9 48.7
39.0 20.9 45.6 26.4 28.7
35.5 38.2 47.7 41.8 44.0
48.6
a. Order the data.
________________________________________
________________________________________
6. For the following data, create a dot plot
and a box plot.
________________________________________
________________________________________
1 7 4 15 10 3 17 6 14 14 3
6 9 7 11
b. Choose reasonable intervals and
make a frequency table.
Percent Interval
Frequency
7. Billy incorrectly made a box plot for the
following data. His work is shown below.
Identify and correct his errors.
c. Create a histogram of the data.
The following data are the amounts of
potassium, in grams, per serving in
randomly selected breakfast cereals.
25 25 30 30 35 35 40 45 50
55 60 60 60 70 85 90 95 95
105
Billy’s box plot:
________________________________________
________________________________________
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Algebra 1
104
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
S.ID.2*
3. What is the best measure of spread to
use to compare the two data sets?
SELECTED RESPONSE
Select the correct answer.
Income of ten recent graduates from
college A (in thousands of dollars
per year):
1. What is the best measure of center to use
to compare the two data sets?
Grams of sugar per serving in cereal
brand A:
0 35 38 39 45 47 50 51 52 52
Income of ten recent graduates
from college B (in thousands of
dollars per year):
29 35 36 37 38 39 41 42
46 400
Grams of sugar per serving in cereal
brand B:
Median
Either the mean or the median
Interquartile range
Either the standard deviation or the
interquartile range
Median
Select all correct answers.
Either the mean or the median
4. Set A below is skewed left, set B is
roughly symmetric, and set C is skewed
right. Choose the values below that
should be used to compare the
spread of the data sets.
Interquartile range
Either the standard deviation or the
interquartile range
2. What is the best measure of center to use
to compare the two data sets?
Set A
23
42
43
48
55
56
57
59
Data Set A:
Data Set B:
Set B
35
38
42
45
49
52
57
61
Set C
40
42
44
45
45
47
49
70
5.0
8.5
8.8
13.5
14.0
Median
14.5
Either the mean or the median
46.9
Interquartile range
47.8
Either the standard deviation or the
interquartile range
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Algebra 1
104
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
6. The heights, in inches, of randomly
selected members of a choral company
are given according to their voice part.
CONSTRUCTED RESPONSE
5. The annual salaries (in thousands of
dollars) of 15 randomly selected
employees at two small companies are
given. Indicate the shape of the data
distributions. Then, compare the center
and spread of the data and justify your
method of doing so.
Soprano
(in.)
60
62
62
64
65
65
66
66
67
68
Company 1:
22 36 37 37 37 39 39 42 42
45 45 46 46 150 200
Company 2:
21 37 38 38 38 39 42 45 45
46 46 47 48 62 250
Alto
(in.)
60
61
62
63
64
65
66
69
70
72
Tenor
(in.)
64
66
66
67
68
70
72
73
74
76
Bass
(in.)
66
68
68
69
70
70
71
72
73
75
________________________________________
a. Which two voice parts typically have
the tallest singers? Explain why you
chose the statistic you used to
compare the data sets.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
b. Which two voice parts typically have
singers that vary the most in height?
Explain why you chose the statistic
you used to compare the data sets.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
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Algebra 1
108
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
S.ID.3*
SELECTED RESPONSE
Select the correct answer.
Select all correct answers.
2. The data set below shows 15 students’
scores on a test. Describe the shape of
the data distribution if the student who
scored 100 is not included in the data set.
1. If the extreme values are removed from
this data set, which of the following
statistics change by more than 1?
10
40
41
41
42
42
43
43
43
44
45
45
45
46
65
70
75
77
72
75
77
73
75
78
74
75
80
74
76
100
The data distribution is skewed right.
The data distribution is symmetric.
The data distribution is skewed left.
It is impossible to determine the
shape of the data distribution.
Mean
Standard deviation
3. The ages of ten employees at a small
company are shown below.
Median
Interquartile range
30, 32, 35, 35, 38, 38, 38, 40, 40, 45
Range
If the data set were expanded to include
a new employee who is 20 years old, how
would the mean of the data set change?
The mean decreases by 2 years.
The mean decreases by about
1.6 years.
The mean increases by about
1.6 years.
The mean does not change.
Select the correct answer for each lettered part.
4. The table shows the batting averages of 12 professional baseball players last season. If the
value 0.360 is removed from the data set, how do each of the following statistics change?
0.360
0.305
0.285
0.325
0.296
0.279
0.325
0.296
0.279
0.319
0.291
0.277
a. Mean
Decreases
No change
Increases
b. Median
Decreases
No change
Increases
c. Standard deviation
Decreases
No change
Increases
d. Interquartile range
Decreases
No change
Increases
e. Range
Decreases
No change
Increases
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Algebra 1
108
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
CONSTRUCTED RESPONSE
5. The values of several homes sold by a realtor are listed below.
$150,000
$175,000
$175,000
$200,000
$200,000
$200,000
$225,000
$250,000
$250,000
$400,000
a. Create a line plot for the data, where the points represent the values in thousands of
dollars. Describe the shape of the data.
b. What value(s) in the data set are outliers? Explain.
________________________________________________________________________________________
________________________________________________________________________________________
c. If the outlier(s) from part b are removed, how do the median and interquartile range
change? How does the shape of the data change?
________________________________________________________________________________________
________________________________________________________________________________________
6. The table shows Amanda’s scores on her last 15 quizzes.
70
77
83
72
78
84
75
80
87
76
80
90
76
82
90
Suppose on her next quiz, Amanda scores a 96.
a. How does the shape of the data distribution change if 96 is included?
________________________________________________________________________________________
________________________________________________________________________________________
b. How does the mean of the data set change if 96 is included? the median?
________________________________________________________________________________________
________________________________________________________________________________________
________________________________________________________________________________________
c. How does the standard deviation change if 96 is included? the interquartile range?
Round your answers to the nearest tenth.
________________________________________________________________________________________
________________________________________________________________________________________
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Algebra 1
104
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
S.ID.4*
For items that ask you to use the standard
normal distribution, refer to the standard
normal table on the next page.
Use the following information to match
each interval of weights with the
approximate percent of the data values
that fall within that interval.
SELECTED RESPONSE
A data set consisting of the weights of 50 jars
of honey has a mean weight of 435 grams
with a standard deviation of 2.5 grams. The
data distribution is approximately normal.
Select the correct answer.
1. The scores for the mathematics portion of
a standardized test are normally
distributed with a mean of 514 points and
a standard deviation of 117 points. What
is the probability that a randomly selected
student has a score of 610 points or less
on the test? Use the standard normal
distribution to estimate the probability.
29.4%
79.4%
20.6%
68%
____ 4. 432.5 g to 435 g
____ 5. 427.5 g to 442.5 g
____ 6. 432.5 g to 437.5 g
____ 7. 430 g to 440 g
____ 8. Greater than 440 g
____ 9. Less than 435 g
2. If the mean of a data set is 20, the
standard deviation is 1.5, and the
distribution of the data values is
approximately normal, about 95% of the
data values fall in what interval centered
on the mean?
18.5 to 21.5
15.5 to 24.5
17 to 23
14 to 26
A
B
C
D
E
F
G
H
2.5%
16%
34%
50%
68%
84%
95%
99.7%
CONSTRUCTED RESPONSE
10. The IQ scores of the students at a school
are normally distributed with a mean of
100 points and a standard deviation of
15 points. Use the standard normal
distribution to estimate each percent.
a. The percent of students with an IQ
score below 80 points
Select all correct answers.
3. Which of the following data sets are NOT
likely to be normally distributed?
________________________________________
b. The percent of students with an IQ
score below 127 points
The day of the month on which
randomly selected students
were born
________________________________________
The final exam scores of all students
taking the same class and given
the same final exam in a large
school district
11. The wing lengths of houseflies are
normally distributed with a mean of
45.5 mm and a standard deviation of
3.92 mm. Use the standard normal
distribution to estimate each percent.
The number of wheels on the next
100 vehicles that pass by a point
along a highway
a. The percent of houseflies with wing
lengths over 35 millimeters
The heights of tenth-grade male
students at a large high school
________________________________________
b. The percent of houseflies with wing
lengths over 50 millimeters
The IQs of the students at a large
high school
________________________________________
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Algebra 1
109
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
12. The grapefruits harvested at a large
orchard have a mean mass of 482 grams
with a standard deviation of 31 grams.
Assuming that the masses of these
grapefruits are approximately normally
distributed, Jess uses the 68-95-99.7 rule
to estimate the percent of grapefruits that
have masses between 451 grams and
544 grams. Jess incorrectly reasons that
since 451 grams is 2 standard deviations
below the mean and 544 is 2 standard
deviations above the mean, 95% of the
grapefruits have masses between
451 grams and 544 grams. Identify his
error and determine the correct estimate.
b. What percent of the male students at
Bart’s school are less than 64 inches
tall? Explain. (Hint: Use the
68-95-99.7 rule.)
________________________________________
________________________________________
14. The scores on a recent district-wide math
test are normally distributed with a mean
of 82 points and a standard deviation of
5 points. Use the standard normal
distribution to answer each question.
a. What percent of students scored
between 70 and 75 on the test?
Show your work.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
b. What percent of students scored at
least 90 on the test? Show your
work.
________________________________________
13. The heights of the male students at Bart’s
school are normally distributed with a
mean of 68 inches and a standard
deviation of 2 inches.
________________________________________
________________________________________
a. What percent of the male students
at Bart’s school are more than
68 inches tall? Explain.
c. What percent of students scored at
most 65 on the test? Show your
work.
________________________________________
________________________________________
________________________________________
________________________________________
Standard Normal Table
z
3
2
1
0
0
1
2
3
.0
.0013
.0228
.1587
.5000
.5000
.8413
.9772
.9987
.1
.0010
.0179
.1357
.4602
.5398
.8643
.9821
.9990
.2
.0007
.0139
.1151
.4207
.5793
.8849
.9861
.9993
.3
.0005
.0107
.0968
.3821
.6179
.9032
.9893
.9995
.4
.0003
.0082
.0808
.3446
.6554
.9192
.9918
.9997
.5
.0002
.0062
.0668
.3085
.6915
.9332
.9938
.9998
.6
.0002
.0047
.0548
.2743
.7257
.9452
.9953
.9998
.7
.0001
.0035
.0446
.2420
.7580
.9554
.9965
.9999
.8
.9
.0001 .0000
.0026 .0019
.0359 .0287
.2119 .1841
.7881 .8159
.9641 .9713
.9974 .9981
.9999 1.000
(Note: In the table, “.0000” means slightly more than 0 and “1.000” means slightly
less than 1.)
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Algebra 1
110
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
S.ID.5*
SELECTED RESPONSE
Select the correct answer.
1. Carly surveyed some of her fellow students to determine whether they are more afraid of
spiders or snakes, are equally afraid of both, or are afraid of neither. She organized the
data into the two-way relative frequency table below. What is the joint relative frequency of
the students surveyed who are boys and are equally afraid of both snakes and spiders?
Boys
Girls
Total
Spiders
0.23
0.21
0.43
Snakes
0.17
0.19
0.36
Both
0.06
0.09
0.15
Neither
0.04
0.02
0.06
Total
0.49
0.51
1
(Note: Rounding may cause the totals to be off by 0.01.)
0.06
0.09
0.15
0.40
Select all correct answers.
2. Which of the following statements are supported by the survey data in the two-way
frequency table?
Males
Females
Total
Right-handed
82
79
161
Left-handed
23
16
39
Total
105
95
200
The joint relative frequency that a person surveyed is female and left-handed is about
0.168, or 16.8%.
The conditional relative frequency that a person surveyed is female, given that the
person is right-handed, is about 0.4907, or 49.07%.
The joint relative frequency that a person surveyed is male and is right-handed is about
0.41, or 41%.
The conditional relative frequency that a person surveyed is right-handed, given that
the person is male, is about 0.5093, or 50.93%.
The marginal relative frequency that a person surveyed is left-handed is about 0.195,
or 19.5%.
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Algebra 1
103
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
Match each situation with the correct value.
A magazine conducts a survey of a high school graduating class to ask whether the students
plan to attend a four-year college, attend a two-year college, enter the military, or get a job.
Match the situation with its value, based on the two-way frequency table, rounded to two
decimal places as necessary.
Women Men
Total
Four-Year College
63
75
138
Two-Year College
12
18
30
Military
8
10
18
Job
15
10
25
Total
98
113
211
____ 3. The joint relative frequency of students surveyed who are men and
plan to attend a four-year college
____ 4. The marginal relative frequency of students surveyed who plan to
enter the military
____ 5. The conditional relative frequency that a student plans to get a job,
given that the student is a woman
A
B
C
D
E
F
0.06
0.07
0.09
0.15
0.36
0.65
____ 6. The conditional relative frequency that a student is a woman, given
that the student plans to attend a two-year college
CONSTRUCTED RESPONSE
7. The manager of a factory tested 50 items produced during each of the three work shifts.
The data are summarized in the two-way frequency table below.
Not defective
Defective
Total
1st shift 2nd shift 3rd shift
48
49
41
2
1
9
50
50
50
Total
138
12
150
a. What is the conditional relative frequency that a tested item is defective, given that it
was produced during the first shift? during the second shift? during the third shift?
________________________________________________________________________________________
________________________________________________________________________________________
________________________________________________________________________________________
b. Does one shift seem more likely to produce a defective product than the other two
shifts? Explain using the results from part a.
________________________________________________________________________________________
________________________________________________________________________________________
________________________________________________________________________________________
________________________________________________________________________________________
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Algebra 1
103
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
S.ID.6a*
SELECTED RESPONSE
Select all correct answers.
Select the correct answer.
3. Emile collects data about the amount of
oil A, in gallons, used to heat his house
per month for 5 months and the average
monthly temperature t, in degrees
Fahrenheit, for those months. The scatter
plot shows the data. The function
A(t)  1.4t  96 best fits these data.
Use A(t) to determine which of the
following statements are true.
1. The data for the distance d, in miles,
remaining for a train to travel to its
destination t hours after it departs a
station are shown in the scatter plot.
Which of the following functions best fits
the data?
d(t)  50t  300
d(t)  50t
Emile would use about 82 gallons of
oil to heat his house for a month with
average temperature 10 F.
d(t)  50t  300
d(t)  50t
Emile would use about 85 gallons of
oil to heat his house for a month with
average temperature 15 F.
2. Darnell is tracking the number of
touchdowns t and the number of points p
his favorite football team scores each
game this season. He made a scatter plot
to display the data. Which of the following
functions for the relationship between the
number of points scored per game and
the number of touchdowns scored per
game could be the line of best fit passing
through the points (1, 10), (3, 24), and
(5, 38) on the scatter plot?
Emile would use 0 gallons of oil to
heat his house for a month with
average temperature 70 F.
Emile would use about 5 gallons of
oil to heat his house for a month with
average temperature 55 F.
Emile would use 96 gallons of oil to
heat his house for a month with
average temperature 0 F.
p(t)  7
p(t)  7t  3
p(t)  7t  3
p(t)  7t  3
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Algebra 1
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Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
c. Use the linear function from part b to
predict the height of the hot air
balloon when it started to descend.
Explain.
CONSTRUCTED RESPONSE
4. The data for the height h, in meters, a hot
air balloon is above the ground in terms
of time t, in minutes, after it starts
descending are shown in the table.
Time, t
Height, h
(minutes)
(meters)
10
1100
15
900
20
800
25
700
30
500
________________________________________
________________________________________
d. Use the linear function from part b to
predict how long, to the nearest
minute, it takes for the hot air balloon
to descend to the ground. Explain.
________________________________________
a. Construct a scatter plot of the data
and use the data points at t  10 and
t  30 to draw a line of best fit.
________________________________________
5. A company moved to a new office
building 8 years ago. The relationship
between the number of workers w and
the time t, in years, after the company
moved is shown in the scatter plot.
b. Use the results from part a to write a
linear function that represents the
line of best fit. Show your work.
Suppose a linear function that fits the
25 95
data is w(t) =
t + . Using that result
3
3
and the point corresponding to t  8,
predict the number of new workers the
company will have two years from now.
Explain.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
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Algebra 1
104
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
S.ID.6b*
SELECTED RESPONSE
Select all correct answers.
1. The table shows the median weight, in pounds, of babies born at a particular hospital for the
first 6 months after they are born. The line y  1.7x  8.1 is fit to the data in the table,
resulting in the residual plot below. Which of the following are true?
Age
(months)
0
1
2
3
4
5
6
Median weight
(pounds)
7.4
9.9
12.3
13.1
15.4
16.9
17.5
The residuals do not appear to follow a pattern.
The residuals are mostly below the x-axis.
The residuals are relatively small compared to the data values.
The residuals are relatively large compared to the data values.
The line is a good fit to the data.
Select the correct answer.
2. The plot shows the residuals when a line is fit to a set of data. Based on the residual plot,
which statement best describes how well the line fits the data?
The line is a good fit because the residuals are all
close to the x-axis and are randomly distributed
about the x-axis.
The line is not a good fit because the residuals
are not all close to the x-axis.
The line is not a good fit because the residuals
are not randomly distributed about the x-axis
The line is not a good fit because the residuals
are not all close to the x-axis and are not
randomly distributed about the x-axis.
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Algebra 1
103
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
CONSTRUCTED RESPONSE
3. The table shows the time, in seconds, of the men’s gold-medal-winning 400 m runner at the
Olympics from 1948 to 1968.
Year
1948 1952 1956 1960 1964 1968
Time (sec) 46.30 46.09 46.85 45.07 45.15 43.86
a. Draw a scatter plot of the data.
b. The line y  0.14x  46.65, where x is the number of years after 1948 and y is the
winning time in seconds, is fit to the data. Draw the line on the scatter plot.
c. Complete the table with the values predicted by the function in part b, and then plot the
residuals on the graph below.
Year Actual
Predicted Residual
time
time (sec)
(sec)
(sec)
1948 46.30
1952 46.09
1956 46.85
1960 45.07
1964 45.15
1968 43.86
d. Use your results from part c to describe the fit of the line.
________________________________________________________________________________________
________________________________________________________________________________________
________________________________________________________________________________________
________________________________________________________________________________________
________________________________________________________________________________________
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Algebra 1
104
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
S.ID.6c*
SELECTED RESPONSE
2. The scatter plot shows the relationship
between the time t, in years after 1900,
and the life expectancy L, in years, at
birth for a certain country. Do the data on
the scatter plot suggest a linear
association? If so, what is a function that
represents the line of best fit?
Select the correct answer.
1. The scatter plot shown suggests the
association between the values of x with
the values of y is linear. What is the
y-intercept, rounded to two decimal
places, of the linear function that
represents the line of best fit?
1.96
Yes; L(t)  39.67t  0.37
11.15
Yes; L(t)  0.24t  74.33
11.41
Yes; L(t)  0.37t  39.67
22.36
No; the data on the scatter plot do
not suggest a linear association.
Select all correct answers.
3. The relationship between the amount of data downloaded d, in megabytes, and the time t,
in seconds, after the download started is shown. The data points on the scatter plot suggest
a linear association. Which of the following statements are true?
The data points on the scatter plot suggest a
negative correlation.
The data points on the scatter plot suggest a
positive correlation.
For every second that passes, about
1 additional megabyte is downloaded.
For every second that passes, about
0.5 additional megabyte is downloaded.
The function that represents the line of best fit
is approximately d(t)  0.51t  1.04.
The function that represents the line of best fit
is approximately d(t)  1.04t  0.51.
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Algebra 1
103
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
CONSTRUCTED RESPONSE
5. A bottled water company is examining the
sales of its product. The executives are
analyzing the number of bottles sold per
year b, in millions, as a function of time t,
in years since 1990. The data are shown
in the table.
4. The table shows the relationship between
the average price for a gallon of milk p, in
dollars, in terms of time t, in years after
1995. When the data is plotted on a
scatter plot, the data suggest a linear
association.
Time, t
Price, p
(years after
(dollars)
1995)
1
2.62
3
2.70
5
2.78
6
2.88
9
3.15
12
3.40
14
3.30
16
3.57
Time, t
(years)
1
3
5
6
8
9
11
14
16
18
a. Find a linear function that represents
the line of best fit. Round the
slope and p-intercept to two
decimal places.
Bottles sold,
b
(millions)
1.6
2.3
3.1
3.5
4.2
4.4
5.1
5.9
6.4
7.1
a.Sketch points on the scatter plot using
the data from the table.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
b. Use the results from part a to
estimate the average price for a
gallon of milk in 2006 to the nearest
cent. Explain.
________________________________________
b. The function b(t)  0.32t  1.47
represents the line of best fit for the
data. About how many more
bottles were sold in 2007 than in
1992? Explain.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
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Algebra 1
118
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
S.ID.7*
2. The linear equation c  6.5n  1500
models cost c, in dollars, to produce
n toys at a toy factory. What is the
c-intercept, and what does it mean in this
context?
SELECTED RESPONSE
Select the correct answer.
1. The linear equation
c  0.1998s  76.4520 models the
number of calories c in a beef hot dog
as a function of the amount of sodium s,
in milligrams, in the hot dog. What is
the slope, and what does it mean in
this context?
The c-intercept is 6.5. The cost
increases by $6.50 for each toy
produced.
The c-intercept is 6.5. The number of
toys produced increases by about 6.5
for each $1 increase in cost.
The slope is 0.1998. The number of
calories is increased by 0.1998 for
each 1 milligram increase in sodium.
The c-intercept is 1500. It costs
$1500 to run the factory if no toys are
produced.
The slope is 0.1998. The amount of
sodium, in milligrams, is increased by
0.1699 for each increase of 1 calorie.
The c-intercept is 1500. The factory
can produce 1500 toys at no cost.
The slope is 76.4520. This is the
number of calories in a beef hot dog
with no sodium.
The slope is 76.4520. This is the
amount of sodium, in milligrams, in a
beef hot dog with no calories.
Select the correct answer for each lettered part.
3. The linear equation p  2376t  73,219 estimates the number of college seniors p who
graduated with a bachelor’s degree in psychology t years after 2000. The linear equation
b  2,376t  56,545 models the number of college seniors b who graduated with a
bachelor’s degree in biology t years after 2000. Classify each statement.
a. The number of psychology degrees increases by about
True
False
73,219 each year.
b. The number of biology degrees increases by about 2376
True
False
each year.
c. About 73,000 students graduated with degrees in
True
False
psychology in 2000.
d. About 57 students graduated with degrees in biology in
True
False
2000.
e. In 2000, more students graduated with psychology
True
False
degrees than biology degrees.
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Algebra 1
103
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
6. The table below shows the height h, in
meters, of a tree that is t years old.
CONSTRUCTED RESPONSE
4. The function d(t)  2.05t  1.27 models
the depth of the water d, in centimeters,
of a filling bathtub at time t, in minutes.
What does the slope of the function
represent in the context of the problem?
What does the d-intercept represent in
the context of the problem? Include any
units in your answers.
Age
(in years)
1
2
3
4
5
6
7
8
9
10
________________________________________
________________________________________
________________________________________
Height
(in meters)
0.7
1.3
1.8
2.5
3.1
3.8
4.2
4.9
5.5
6.2
a. Make a scatter plot of the data from
the table.
________________________________________
________________________________________
5. The function c(r)  2r  12.5 represents
the cost c, in dollars, of riding r rides
at a carnival.
a. How much does it cost to get into the
carnival? Explain.
________________________________________
________________________________________
________________________________________
b. Find a line of best fit.
________________________________________
________________________________________
________________________________________
b. How much does each ride
cost? Explain.
________________________________________
________________________________________
c. Identify and interpret the slope of the
line from part b.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
d. Identify and interpret the h-intercept
of the line from part b.
________________________________________
________________________________________
________________________________________
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Algebra 1
120
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
S.ID.8*
3. What is the type and strength of the linear
correlation in the following data, using x
as the dependent variable? Use
technology if necessary.
SELECTED RESPONSE
Select all correct answers.
1. Which of the following correlation
coefficients indicate a strong linear
correlation?
x
1.2
3.2
3.3
4.5
6.1
6.3
7.1
9.6
9
0.872691
0.658799
0.125866
0.568962
0.798264
0.989862
Select the correct answer.
Strong negative correlation
2. What is the correlation coefficient of
linear fit for the following data set? Use
technology to find the correlation
coefficient. Assume x is the
independent variable.
x
1.4
2.3
4.5
5.8
3.2
1.9
8.7
5.5
6.7
y
5.3
6.7
3.3
4.3
5.5
2.1
0.5
0.75
4.1
Weak negative correlation
Weak positive correlation
Strong positive correlation
CONSTRUCTED RESPONSE
y
4.7
5.0
7.4
8.6
6.7
4.2
11.4
8.0
10.4
4. Consider the following scatter plot. Use
technology to find the line of best fit,
using x as the independent variable and y
as the dependent variable. What happens
to y as x increases? Find the correlation
coefficient. How strong a fit is the line?
Explain.
0.982478
0.328699
0.328699
0.982478
________________________________________
________________________________________
________________________________________
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Algebra 1
104
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
5. The table lists the latitude of several cities
in the Northern Hemisphere along with
their average annual temperatures.
City
Bangkok,
Thailand
Cairo,
Egypt
London,
England
Moscow,
Russia
New Delhi,
India
Tokyo,
Japan
Vancouver,
Canada
13.7N
Average
Annual
Temp.
82.6 F
30.1N
71.4 F
51.5N
51.8 F
55.8N
39.4 F
28.6N
77.0 F
35.7N
58.1 F
49.2N
49.6 F
Latitude
________________________________________
________________________________________
________________________________________
________________________________________
6. The table shows the annual expenditures
on entertainment and reading per person over
10 years. Between entertainment and
reading, which is more strongly correlated
with the passage of time? Describe each
correlation as part of
your answer.
a. Use technology to find the correlation
coefficient of a linear fit using latitude
as the independent variable and
average annual temperature as the
dependent variable.
Year
Entertainment
Reading
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
$1863
$1953
$2079
$2060
$2218
$2388
$2376
$2698
$2835
$2693
$146
$141
$139
$127
$130
$126
$117
$118
$116
$110
________________________________________
________________________________________
________________________________________
b. Describe the correlation. Explain how
you arrived at your answer.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
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Algebra 1
122
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
S.ID.9*
SELECTED RESPONSE
Select all correct answers.
Select the correct answer.
2. Jewelers consider weight, cut grade,
color, and clarity when pricing diamonds.
In researching jewelry prices, Yvonne
makes the following statements based on
her observations. Which of the
statements are statements of causation?
1. Susan measures her son Jeremy’s height
at various ages. The results are shown
below. Which of the following is a
statement of causation?
Age (years)
8
9
10
11
12
13
Height (inches)
44
48
52
55
58
62
Heavier diamonds tend to be sold at
higher prices.
A particular diamond costs $264.
Higher clarity drives up the price
of a diamond.
When Jeremy was 13 years old, he
was 62 inches tall.
There appears to be a relationship
between color and price.
There appears to be a relationship
between Jeremy’s age and height.
A darker color decreases a
diamond’s clarity.
As Jeremy’s age increases, his
height also increases.
Diamonds with lower cut grades
seem to sell at lower prices.
Jeremy’s age affects his height.
Select the correct answer for each lettered part.
3. Identify each of the following statements as a statement of correlation, a statement of
causation, or neither.
1. Taller people tend to have bigger hands.
2. Being tall makes your hands bigger.
3. Shorter people tend to have smaller hands.
4. Being short makes your hands smaller.
5. I’m 6’8” and I have bigger hands than anyone else in my family.
a.
b.
c.
d.
e.
Statement 1
Statement 2
Statement 3
Statement 4
Statement 5
Correlation
Correlation
Correlation
Correlation
Correlation
Causation
Causation
Causation
Causation
Causation
Neither
Neither
Neither
Neither
Neither
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Algebra 1
104
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
5. The table below lists the departure delay
times (in minutes) and arrival delay times
(in minutes) for 10 flights. (A negative
delay time means a flight
departed/arrived ahead of schedule.)
CONSTRUCTED RESPONSE
4. The table below shows the approximate
diameters (in miles) and number of
moons for each of the eight planets in our
solar system. Calculate the correlation
coefficient, r, of the data to three decimal
places. What kind of correlation, if any,
exists between diameter and number of
moons? Does a planet’s diameter
influence the number of moons it
has? Explain.
Planet
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Diameter
(miles)
3032
7521
7926
4222
88,846
74,898
31,763
30,778
Departure
Delay Times
(minutes)
10
5
0
0
5
8
10
10
15
20
Moons
0
0
1
2
62
33
27
13
Arrival
Delay Times
(minutes)
7
6
1
1
3
10
7
12
15
23
a. Is there a correlation between
departure delay times and arrival
delay times? Explain.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
b. Are departure delay times
responsible for all arrival delay
times? Explain.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
c. Are arrival delay times
responsible for all departure delay
times? Explain.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
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Algebra 1
104
Common Core Assessment Readiness
S.ID.1* Answers
1. C
7. Billy misidentified the first, second, and
third quartiles.
2. B
The first quartile is 35 grams, the
second quartile is 55 grams, and the
third quartile is 85 grams.
3. A, B, D, F, H
4. a. The minimum data value is 44 beds.
The maximum data value is 135
beds.
b. The second quartile is 80 beds. The
first quartile is 60 beds. The third
quartile is 110 beds.
c.
Rubric
1 point for identifying the mistake;
1 point for each corrected quartile;
2 points for the box plot
8. a. 20.9 26.4 27.9 28.7
35.5 37.5 38.2 39.0
43.1 44.0 45.6 47.5
48.6 48.7
b. Possible answer:
Percent Interval
20.0% to 24.9%
25.0% to 29.9%
30.0% to 34.9%
35.0% to 39.9%
40.0% to 44.9%
45.0% to 49.9%
c.
Rubric
a. 0.5 point for each value
b. 0.5 point for each value
c. 1.5 points for box plot
5. Order the data: 34 35 36 36 37
37 37 39 39 40 40 40 42 42
43 43 44 45 46 47
30.1 33.9
41.8 42.3
47.7 48.1
Frequency
1
3
2
4
4
6
Rubric
2 points
6. Order the data: 1 3 3 4 6 6 7 7
9 10 11 14 14 15 17
The five-number summary for the data
is 1, 4, 7, 14, 17.
Rubric
a. 0.5 point
b. 1.5 points for reasonable intervals;
1 point for accurate table
c. 2 points
Rubric
1 point for the dot plot;
2 points for the box plot
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Algebra 1 Teacher Guide
1
Common Core Assessment Readiness
S.ID.2* Answers
1. B
6. Sample distributions are shown for
reference.
2. A
3. C
4. A, E, F
5. Sample distributions are shown for
reference.
The salary distributions for both
companies are skewed right. Since the
data sets are skewed right, the centers
should be compared using the medians
and the spreads should be compared
using the interquartile range. The median
salary of company 1 is $42,000 and the
median salary of company 2 is $45,000.
The first quartile for company 1 is
$37,000 and the third quartile is $46,000.
The spread of the salaries at company 1
is $46,000  $37,000  $9000. The first
quartile for company 2 is $38,000 and the
third quartile is $47,000. The spread of
the salaries at company 2 is
$47,000  $38,000  $9000. The center
salary at company 2 is higher, while the
spread of the salaries of the two
companies are the same.
a. Each of the data sets is roughly
symmetric, so the mean or median
could be used to compare the centers
of the data sets. The mean will be
used here. The mean height of the
sopranos is 64.5 inches, the mean
height of the altos is 65.2 inches,
the mean height of the tenors is
69.6 inches, and the mean height of
the basses is 70.2 inches. The tenors
and the basses tend to be the tallest
singers, on average.
b. Each of the data sets is roughly
symmetric, so the standard deviation
or interquartile range could be used to
compare the spreads of each data set.
The standard deviation will be used
here. The standard deviation of the
sopranos is about 2.38 inches, the
standard deviation of the altos is about
3.82 inches, the standard deviation of
the tenors is about 3.8 inches, and the
standard deviation of the basses is
about 2.52 inches. So, the heights of
the altos and the tenors tend to vary
the most.
Rubric
0.5 point for the shape of each
distribution;
1 point for using the median and
interquartile range;
0.5 point each for the medians of each
company;
0.5 point each for the interquartile ranges
of each company;
1 point for comparison
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Algebra 1 Teacher Guide
2
Common Core Assessment Readiness
Rubric
a. 1 point for recognizing that the data
are symmetric and using the mean
or median;
0.25 point for each mean or median;
1 point for correct comparison based
on the values found (mean or median)
b. 1 point for recognizing that the data
are symmetric and using the standard
deviation or interquartile range;
0.25 point for each standard deviation
or interquartile range;
1 point for correct comparison based
on the values found (standard
deviation or interquartile range)
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Algebra 1 Teacher Guide
67
Common Core Assessment Readiness
S.ID.3* Answers
1. B, E
6. a. A sample distribution is shown for
reference.
2. B
3. B
4. a.
b.
c.
d.
e.
Decreases
Does not change
Decreases
Does not change
Decreases
When 96 is included in the data set,
the data distribution skews slightly to
the right.
b. Without the score of 96 points, the
1200
mean is
= 80 points. With the
15
score of 96 points included, the
1296
mean is
= 81 points. So, the
16
mean increases by 1 point if 96 is
included in the data set.
Without the score of 96 points, the
median of the data set is 80 points.
With the score of 96 points included,
80 + 80
the median is
= 80 points.
2
So, the median does not change if
96 is included in the data set.
c. Without the score of 96 points, the
standard deviation is about
5.8 points. With the score of
96 points included, the standard
deviation is about 6.9 points.
Therefore, the standard deviation
increases by about 1.1 points if 96 is
included in the data set.
Without the score of 96 points, the
IQR is 84  76  8 points. With the
value of 96 points included, the IQR
87 + 84
is
- 76 = 9.5 points.
2
Therefore, the IQR increases by 1.5
points if 96 is included in the data
set.
5. a.
The data are skewed to the right.
b. $400,000 is an outlier.
The interquartile range is
$250,000  $175,000  $75,000.
$250,000  1.5($75,000) 
$362,500, so any value larger than
$362,500 is considered an outlier.
c. The median is $200,000 for both
data sets, so the median does not
change. The interquartile range
decreases from $250,000 
$175,000  $75,000 to $237,500 
$175,000  $62,500.
The data distribution is now
roughly symmetric.
Rubric
a. 1 point for line plot;
0.5 point for shape
b. 0.5 point for answer;
0.5 point for explanation
c. 0.5 point for each description
Rubric
a. 1 point
b. 1 point for each statistic
c. 1 point for each statistic
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Algebra 1 Teacher Guide
2
Common Core Assessment Readiness
S.ID.4* Answers
1. C
To correct his error, subtract the percent
of the population that falls between
2 standard deviations below the mean
and 1 standard deviation below the
mean.
2. B
3. A, C
4. C
5. H
95 - 68
= 95 - 13.5
2
= 81.5
So, about 81.5% of the grapefruits
have masses between 451 grams and
544 grams.
95 -
6. E
7. G
8. A
9. D
10. a. z80 =
(
80 - 100
20
=» -1.3;
15
15
Rubric
1 point for identifying the error; 2 points
for the correct estimate
)
P z £ z80 » 0.0912 = 9.12%
b. z127 =
(
13. a. Since the heights of the male students
in Bart’s class are normally
distributed, 50% of the students will
be taller than the mean height. So,
50% of the male students in Bart’s
class are more than 68 inches tall.
b. Since 64  68  2(2), the value is
2 standard deviations below the
mean. The 68-95-99.7 rule indicates
that
95% will be within 2 standard
deviations, 4 inches, of the mean
height. Male students less than
64 inches tall are half of the 5% of
male students who are taller than
68  4  72 inches or shorter than
68  4  64 inches. So, 2.5% of the
male students in Bart’s class are less
than 64 inches tall.
127 - 100 27
=
= 1.8;
15
15
)
P z £ z127 » 0.9641= 96.41%
(Note: Answers may vary depending on
the method of finding the area under the
normal curve.)
Rubric
1 point for each part
11. a. z35 =
(
35 - 45.5
10.5
=» -2.7;
3.92
3.92
)
(
)
P z > z35 = 1- P z £ z35 » 0.9963 =
99.63%
50 - 45.5 4.5
b. z50 =
=
» 1.1;
3.92
3.92
(
)
(
)
P z > z50 = 1- P z £ z35 » 0.1255 =
12.55%
(Note: Answers may vary depending on
the method of finding the area under the
normal curve.)
Rubric
a. 1 point for answer;
1 point for explanation
b. 1 point for answer;
1 point for recognizing the given
height is 2 standard deviations from
the mean;
1 point for recognizing that it’s
necessary to divide the 5% by 2
Rubric
1 point for each part
12. His error is that 451 grams represents
only 1 standard deviation below the
mean, not 2 standard deviations below
the mean.
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Algebra 1 Teacher Guide
2
Common Core Assessment Readiness
70 - 82
12
== -2.4 and
5
5
75 - 82
7
=
= - = -1.4;
5
5
14. a. z70 =
z75
(
)
P (z £ z ) - P (z £ z ) =
P z70 £ z £ z75 =
75
70
0.0808 - 0.0082 = 0.0726 = 7.26%
So, 7.26% of the students scored
between 70 and 75 on the test.
90 - 82 8
b. z90 =
= = 1.6;
5
5
(
)
(
)
P z ³ z90 = 1- P z £ z90 =
1- 0.9452 = 0.0548 = 5.48%
So, 5.48% of the students scored at
least 90 on the test.
65 - 82
17
c. z65 =
== -3.4;
5
5
(
)
P z £ z65 = 0.0003 = 0.03%
So, 0.03% of the students scored at
most 65 on the test.
Rubric
a. 1 point for percent; 1 point for work
b. 1 point for percent; 1 point for work
c. 1 point for percent; 1 point for work
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Algebra 1 Teacher Guide
2
Common Core Assessment Readiness
S.ID.5* Answers
1. A
2. B, C, E
36. The relative frequency table is shown for reference.
Four-Year College
Two-Year College
Military
Job
Total
Women
0.30
0.06
0.04
0.07
0.46
Men
0.36
0.09
0.05
0.05
0.54
Total
0.65
0.14
0.09
0.12
1
(Note: Rounding may cause the totals to be off by 0.01.)
3. E
4. C
5. B
6. A
2
= 0.04
50
1
Second shift:
= 0.02
50
9
Third shift:
= 0.18
50
b. The third shift seems more likely to produce a defective product than the other two shifts
because the conditional relative frequency that a tested item is defective, given that it
was produced during the third shift is more than four times greater than the conditional
relative frequency that a tested item is defective for either of the other two shifts.
7. a. First shift:
Rubric
a. 0.5 point for each shift
b. 0.5 point for answer;
1 point for explanation
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Algebra 1 Teacher Guide
2
Common Core Assessment Readiness
S.ID.6a* Answers
d. 47 minutes; since the hot air balloon
is on the ground when h(t)  0,
substitute 0 for h(t) in the linear
function
h(t)  30t  1400 and solve for t.
0 = -30t + 1400
-1400 = -30t
47 » t
1. C
2. B
3. A, C, E
4. a.
Rubric
a. 1 point for scatter plot;
1 point for line of best fit
b. 1 point for answer;
1 point for showing work
c. 1 point for answer;
1 point for explanation
d. 1 point for answer;
1 point for explanation
5.
b. The point that corresponds to t  10
is (10, 1100) and the point that
corresponds to t  30 is (30, 500).
Find the slope of the line that passes
through these two points.
500 - 1100 -600
=
= -30
30 - 10
20
Substitute 30 for m, 10 for t, and
1100 for h(t) in the equation
h(t)  mt  b and solve for b.
1100 = (-30)(10) + b
1100 = -300 + b
1400 = b
The linear function that relates h(t) in
terms of t is h(t)  30t  1400.
c. 1400 meters; since the hot air
balloon started to descend at time t 
0, substitute 0 for t in the linear
function h(t)  30t  1400 and
simplify.
h(0) = -30(0) + 1400
= 0 + 1400
= 1400
The prediction is that the company
will have about 15 more workers.
Two years from now corresponds to t
 10. Substitute 10 for t in the linear
function to predict the number of
workers in
two years.
25
95
t+
3
3
25
95
w(10) =
(10) +
3
3
250 95
=
+
3
3
= 115
According to the scatter plot, the
company currently has 100 workers.
So, the company will have about
115  100  15 more workers in the
next two years.
w(t) =
Rubric
1 point for answer;
1 point for explanation
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Algebra 1 Teacher Guide
2
Common Core Assessment Readiness
S.ID.6b* Answers
1. A, C, E
2. D
3. a.
d. The distribution of the residuals is
random, but mostly above the x-axis.
The line is not a good fit to the data.
Rubric
a. 1 point
b. 1 point
c. 1 point for expected values; 1 point
for plotting residuals
d. 2 points for appropriate conclusion
b.
c.
Year
1948
1952
1956
1960
1964
1968
Actual
time
(sec)
46.30
46.09
46.85
45.07
45.15
43.86
Predicted Residual
time
(sec)
(sec)
46.65
–0.35
46.09
0
45.53
1.32
45.07
0.10
45.15
0.74
43.85
0.01
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Algebra 1 Teacher Guide
2
Common Core Assessment Readiness
S.ID.6c* Answers
1. D
5. a.
2. C
3. B, C, F
4. a. p(t)  0.06t  2.52 (Note: Accept
reasonable estimates if the method
is reasonable.)
b. Since 2006 is 11 years after 1995,
substitute 11 for t in the function
p(t)  0.06t  2.52.
p(11) = 0.06(11) + 2.52
= 3.18
The price for a gallon of milk in 2006
is about $3.18.
Rubric
a. 1 point
b. 1 point for answer;
1 point for explanation
b. Since 2007 is 17 years after 1990,
substitute 17 into the function.
b(17) = 0.32(17) + 1.47
= 6.91
Since 1992 is 2 years after 1990,
substitute 2 into the function.
b(2) = 0.32(2) + 1.47
= 2.11
Subtract the value of the function at
t  2 from the value of the function at
t  17:
6.91  2.11  4.80
The number of bottles sold in 2007 is
about 4,800,000 more than the
number of bottles sold in 1992.
(Note: this answer is based off of the
function from part b. Mathematical
accuracy should be noted.)
Rubric
a. 2 points
b. 1 point for answer;
1 point for explanation
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Algebra 1 Teacher Guide
74
Common Core Assessment Readiness
S.ID.7* Answers
1. A
6. a.
2. C
3. a.
b.
c.
d.
e.
False
True
True
False
True
4. The slope of the function is 2.05 cm per
minute. The depth increases by about
2.05 cm every minute. The d-intercept
is 1.27 cm. The initial depth of the water
in the bathtub is about 1.27 cm.
Rubric
1 point for interpreting the slope with
correct units;
1 point for interpreting the d-intercept
with correct units
b. By linear regression, the function
that represents the line is
h(t)  0.61t  0.06.
c. The slope is 0.61. The height of
the tree increases by about 0.61 m
each year.
d. The h-intercept is 0.06. The height
of the tree when planted was about
0.06 m.
5. a. The cost to get into the carnival is
$12.50, because the c-intercept of
the function is 12.5.
b. Each ride costs $2, because the
slope of the function is 2.
Rubric
a. 1 point for answer;
1 point for explanation
b. 1 point for answer;
1 point for explanation
Rubric
a. 2 points
b. 2 points
c. 1 point
d. 1 point
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Algebra 1 Teacher Guide
2
Common Core Assessment Readiness
S.ID.8* Answers
1. A, E, F
6. The correlation coefficient using the
year as the independent variable and
the annual entertainment expenditure
as the dependent variable is 0.966473.
Since this is positive and close to 1, it
indicates a strong positive correlation
between the passage of time and the
annual entertainment expenditure per
person. The correlation coefficient using
the year as the independent variable
and the annual reading expenditure as
the dependent variable is 0.973326.
Since this is negative and close to 1, it
indicates a strong negative correlation
between the passage of time and the
annual reading expenditure per person.
2. D
3. B
4. y  0.676901x  1.067251
The slope of the best fit line is positive,
so y increases as x increases.
The correlation coefficient is 0.78238.
Since 0.78238 is closer to 1 than to 0.5,
there is a strong positive correlation
between x and y.
Rubric
2 points for the equation;
1 point for stating y increases as x
increases;
1 point for the correlation coefficient;
1 point for stating there is a strong
correlation;
1 point for reasoning
Note that |1 (0.973326)|  0.026674
and |1  0.966473|  0.033527. Since
0.973326 is closer to 1 than
0.966473 is to 1, 0.973326 is a
stronger correlation. So, there is a
stronger correlation between the
passage of time and reading
expenditures per person.
5. a. 0.960853
b. Since 0.960853 is negative and is
closer to 1 than to 0.5, this
correlation is a strong negative
correlation. So, there is a strong
negative correlation between the
latitude of a city and its average
annual temperature.
Rubric
1 point for each correlation coefficient;
0.5 point each for concluding strong for
both correlations;
0.5 point for stating the
time/entertainment correlation is
positive;
0.5 point for stating the time/reading
correlation is negative;
2 points for concluding that the
time/reading correlation is stronger
Rubric
a. 1 point
b. 1 point for answer;
0.5 point for saying why the
correlation is negative;
0.5 point for saying why the
correlation is strong
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Algebra 1 Teacher Guide
2
Common Core Assessment Readiness
S.ID.9* Answers
1. D
5. a. Yes; flights that departed later
tended to arrive later. This shows a
positive correlation.
b. No; it makes sense a flight that
departs late would arrive late, but
there are other causes for arrival
delay times, such as weather and
traffic (other flights waiting to take off
or land) at the destination.
c. No; since arrival occurs after
departure, any delay in arrival cannot
affect the departure time.
2. C, E
3. a.
b.
c.
d.
e.
Correlation
Causation
Correlation
Causation
Neither
4. r  0.952; there is a strong positive
correlation between planet diameter
and number of moons. It is possible that
a planet’s diameter influences the
number of moons the planet has, but it
is not definite. Larger planets are likely
to
have a stronger gravitational pull for
attracting moons, but there are other
lurking variables.
Rubric:
a. 1 point for answer; 1 point for
explanation
b. 1 point for answer; 1 point for
explanation
c. 1 point for answer; 1 point for
explanation
Rubric:
1 point for correct value of r;
1 point for identifying the strong positive
correlation;
1 point for claiming a planet’s diameter
may influence the number of moons;
1 point for explanation
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Algebra 1 Teacher Guide
2
Common Core Assessment Readiness