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ALGEBRA TAKE HOME 3
**SHOW ALL WORK**
1) What is the common difference in the sequence
1)
2)
,
,
,
?
3)
4)
2) What is a formula for the nth term of sequence B shown below?
1)
3)
2)
4)
3) What is the common ratio of the geometric sequence
1)
2) 2
3)
?
4)
4) What is the formula for the nth term of the sequence
1)
3)
2)
4)
?
5) The diagrams below represent the first three terms of a sequence.
Assuming the pattern continues, which formula determines
1)
3)
2)
4)
6) What is the fifteenth term of the sequence
1)
2) 81,920
3)
4) 327,680
, the number of shaded squares in the nth term?
?
7) The third term in an arithmetic sequence is 10 and the fifth term is 26. If the first term is
equation for the nth term of this sequence?
1)
3)
2)
, which is an
4)
8) If a sequence is defined recursively by
1) 1
2) 5
9) If
and
for
, then
is equal to
3)
4) 17
and
1)
2)21
, then
3) 11
4) 43
10) A sunflower is 3 inches tall at week 0 and grows 2 inches each week. Which function(s) shown below can be
used to determine the height,
, of the sunflower in n weeks?
I.
II.
III.
1) I and II
2) III, only
3)II, only
4) I and III
11) A cell phone company charges $60.00 a month for up to 1 gigabyte of data. The cost of additional data is
$0.05 per megabyte. If d represents the number of additional megabytes used and c represents the total charges
at the end of the month, which linear equation can be used to determine a user's monthly bill?
1)
3)
2)
4)
12) Which graph shows a line where each value of y is three more than half of x?
1)
2)
3)
4)
13) A satellite television company charges a one-time installation fee and a monthly service charge. The total cost
is modeled by the function
. Which statement represents the meaning of each part of the function?
1)y is the total cost, x is the number of months of service, $90 is the installation fee, and $40 is the service
charge per month.
2)y is the total cost, x is the number of months of service, $40 is the installation fee, and $90 is the service
charge per month.
3)x is the total cost, y is the number of months of service, $40 is the installation fee, and $90 is the service
charge per month.
4)x is the total cost, y is the number of months of service, $90 is the installation fee, and $40 is the service
charge per month.
14) A company that manufactures radios first pays a start-up cost, and then spends a certain amount of money to
manufacture each radio. If the cost of manufacturing r radios is given by the function
, then the
value 5.25 best represents
1) the start-up cost
2) the profit earned from the sale of one radio
3) the amount spent to manufacture each radio
4) the average number of radios manufactured
15) Which situation could be modeled by using a linear function?
1) a bank account balance that grows at a rate of 5% per year, compounded annually
2) a population of bacteria that doubles every 4.5 hours
3) the cost of cell phone service that charges a base amount plus 20 cents per minute
4) the concentration of medicine in a person’s body that decays by a factor of one-third every hour
16) A population that initially has 20 birds approximately doubles every 10 years. Which graph represents this
population growth?
1)
2)
3)
4)
17) Some banks charge a fee on savings accounts that are left inactive for an extended period of time. The
equation
represents the value, y, of one account that was left inactive for a period of x years.
What is the y-intercept of this equation and what does it represent?
1) 0.98, the percent of money in the account initially
2) 0.98, the percent of money in the account after x years
3) 5000, the amount of money in the account initially
4) 5000, the amount of money in the account after x years
18) Is the equation
a model of exponential growth or exponential decay, and what is the rate
(percent) of change per time period?
1) exponential growth and 12%
3) exponential growth and 88%
2) exponential decay and 12%
4) exponential decay and 88%
19) Mr. Smith invested $2,500 in a savings account that earns 3% interest compounded annually. He made no
additional deposits or withdrawals. Which expression can be used to determine the number of dollars in this
account at the end of 4 years?
1)
3)
2)
4)
20) Krystal was given $3000 when she turned 2 years old. Her parents invested it at a 2% interest rate
compounded annually. No deposits or withdrawals were made. Which expression can be used to determine how
much money Krystal had in the account when she turned 18?
1)
3)
2)
4)
21) Kathy plans to purchase a car that depreciates (loses value) at a rate of 14% per year. The initial cost of the
car is $21,000. Which equation represents the value, v, of the car after 3 years?
1)
3)
2)
4)
22) The current student population of the Brentwood Student Center is 2,000. The enrollment at the center
increases at a rate of 4% each year. To the nearest whole number, what will the student population be closest to
in 3 years'?
1) 2,240
2) 5,488
3) 2,250
4) 6,240
23) Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates (loses value) at a rate of 5%.
What will its approximate value be at the end of the fourth year?
1) $33,250.00
2) $28,507.72
24) The value in dollars,
3) $30,008.13
4) $27,082.33
, of a certain car after x years is represented by the equation
. To
the nearest dollar, how much more is the car worth after 2 years than after 3 years?
1) 2589
2) 15,901
3)6510
4)18,490
25) Sam’s grades on eleven chemistry tests were 90, 85, 76, 63, 94, 89, 81, 76, 78, 69, and 97. Which statement is
true about the measures of central tendency?
1) mean > mode
3) mean < median
2) mode > median
4) median = mean
26) Kelsey scored the following points in her first six basketball games: 22, 14, 19, 22, 8, and 17. What is the
relationship between the measures of central tendency of these data?
1) mode > median > mean
2) mean > median > mode
3) median > mode > mean
4) mode > mean > median
27) What is the mode of the data shown in the following table?
1) 12
2) 13
3) 12.5
4) 51.5
28) Which correctly compares the mean and median of the set of data shown
in the accompanying table?
1) The mean and median are equal.
2) The mean exceeds the median by 2.
3) The median exceeds the mean by 2.
4) The mean exceeds the median by 2.5.
29) What is the range for the following data?
1) 50
2) 58
3) 11
52, 32, 61, 82, 63
4) 61
30) The table below shows five numbers and their frequency of occurrence.
The interquartile range for these data is
1) 7
2) 7 to 12
3) 5
4) 6 to 13
31) What is the best approximation of the population standard deviation of the measures
1) 1
2) 2
3) 5
4) 10
32) Mayken collected data about the size of the honors classes in her school building.
This set of data is shown in the accompanying table.
Which statement about the range of this sample is true?
?
1) range = mean
2) range < mean
3) range > mean
4) range < standard deviation
33) Christopher looked at his quiz scores shown below for the first and second semester of his Algebra class.
Semester 1: 78, 91, 88, 83, 94
Semester 2: 91, 96, 80, 77, 88, 85, 92
Which statement about Christopher's performance is correct?
1) The interquartile range for semester 1 is greater than the interquartile range for semester 2.
2) The median score for semester 1 is greater than the median score for semester 2.
3) The mean score for semester 2 is greater than the mean score for semester 1.
4) The third quartile for semester 2 is greater than the third quartile for semester 1.
34) Isaiah collects data from two different companies, each with four employees. The results of the study, based
on each worker’s age and salary, are listed in the tables below.
Which statement is true about these data?
1) The median salaries in both companies are greater than $37,000.
2) The mean salary in company 1 is greater than the mean salary in company 2.
3) The salary range in company 2 is greater than the salary range in company 1.
4) The mean age of workers at company 1 is greater than the mean age of workers at company 2.
35) Tanner and Robbie discovered that the means of their grades for the first semester in Mrs. Merrell’s
mathematics class are identical. They also noticed that the standard deviation of Tanner's scores is 20.7, while
the standard deviation of Robbie's scores is 2.7. Which statement must be true?
1) In general, Robbie's grades are lower than Tanner's grades.
2) Robbie's grades are more consistent than Tanner's grades.
3) Robbie had more failing grades during the semester than Tanner had.
4) The median for Robbie's grades is lower than the median for Tanner's grades.
36) The test scores for 10 students in Ms. Sampson’s homeroom were 61, 67, 81, 83, 87, 88, 89, 90, 98, and 100.
Which frequency table is accurate for this set of data?
1)
3)
2)
4)
37) A movie theater recorded the number of tickets sold daily for a popular
movie during the month of June. The box plot shown
represents the data for the number of tickets sold, in hundreds.
Which conclusion can be made using this plot?
1)
2)
3)
4)
The second quartile is 600.
The mean of the attendance is 400.
The range of the attendance is 300 to 600.
Twenty-five percent of the attendance is between 300 and 400.
38) The given box plot represents the results of tests
scores in a math class.
What do the scores 65, 85, and 100 represent?
1)
, median,
2)
, , maximum
3) median, , maximum
4) minimum, median, maximum
39) The box plot below represents the math test scores of 20 students.
What percentage of the test scores are less than 72?
1) 25
2) 50
3) 75
4) 100
40) The box plot below represents a set of grades in a college statistics class.
Which interval contains exactly 50% of the grades?
1) 63-88
3) 63-95
2) 75-81
4) 75-88
41) The accompanying box plots can be used to compare
the annual incomes of three professions. Based on the box-and-whisker
plots, which statement is true?
1) The median income for nuclear engineers is greater
than the income of all musicians.
2) All nuclear engineers earn more than all police officers.
3) The median income for police officers and musicians is the same.
4) A musician will eventually earn more than a police officer.
42) Corinne is planning a beach vacation in July and is analyzing the daily
high temperatures for her potential destination. She would like to choose
a destination with a high median temperature and a small interquartile
range. She constructed box plots shown in the given diagram.
Which destination has a median temperature above 80 degrees
and the smallest interquartile range?
1) Ocean Beach
2) Serene Shores
3) Whispering Palms
4) Pelican Beach
43) For 10 days, Romero kept a record of the number of hours he spent listening to music.
The information is shown in the given table.
Which scatter plot shows Romero’s data graphically?
1)
2)
3)
4)
44) Which scatter plot shows the relationship between x and y if x represents a student score on a test and y
represents the number of incorrect answers a student received on the same test?
1)
2)
3)
45) What is the correlation coefficient of the linear fit of the
data shown, to the nearest hundredth?
4)
1) 1.00
2)
3) 0.93
4)
46) Which value of r represents data with a strong positive linear correlation between two variables?
1)0.89
2) 0.34
3) 1.04
4) 0.01
47) What could be the approximate value of the correlation coefficient
for the accompanying scatter plot?
1)
2)
3)
4) 0.90
48) The relationship of a woman’s shoe size and length of a woman’s foot,
in inches, is given in the accompanying table.
The linear correlation coefficient for this relationship is
1) 1
2)
3) 0.5
4) 0
49) Which calculator output shows the strongest linear relationship between x and y?
1)
2)
3)
50) The table below shows the number of grams of carbohydrates, x,
and the number of Calories, y, of six different foods.
Which equation best represents the line of best fit for this set of data?
1)
3)
2)
4)
4)