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1
Algebra 1: Supplemental Unit
Name: _____________________
Homework Assignment Sheet UPDATED ASSIGNMENT SHEET
All homework is listed by date assigned and is due the following class period.
Date
In-Class
32
F
5/30
Arithmetic Sequences
33
M
6/2
34
T
6/3
35
W
6/4
Geometric Sequences
36
Th
6/5
More Sequences
More Sequences
More Sequences
More Sequences
37
F
6/6
38
M
6/9
Review
Homework
HW32
HW30 Worksheet
Pg. 576: 5-7, 11-14
Pg. 578: 5-11, 44-47, 56-59
HW33
HW33 Worksheet
Pg. 576: 9, 10
Pg. 578: 15-20, 25-28, 40-43, 48-50
HW34
HW34 Worksheet
Pg. 580: 5-8, 11-13, 32-36, 42-48
HW35
HW35 Worksheet
Pg. 580: 1-4, 14-16, 29-30, 58, 59, 61, 62, 69, 72
HW36
HW36 Worksheet
Pg. 582: (see below)
Solve by square roots: 34, 36
Solve by factoring: 48, 52
Solve by quadratic formula: 42, 45
Solve by completing the square: 39, 41
HW37
HW37 Worksheet
Pg. 582:
Solve by square roots: 33, 37
Solve by factoring: 50, 56
Solve by quadratic formula: 53, 55
Solve by completing the square: 46
Print Final Exam Review Packet by Tues 6/10
HW38
HW38 Worksheet
Pg. 568: 15-23 all (Show all work as you solve for
the variable, then state any ‘unusual’ answers such
as “no solution” or “identity.”)
Print Final Exam Review Packet by Tomorrow!
2
Warm Up Day 32
Write a sentence to describe the pattern in each problem. Then find the next two terms in the list.
1.) 16, 21, 26, 31,...
2.) 28, 20, 12, 4,...
Pattern Description:
Pattern Description:
Next Two Terms:
Next Two Terms:
3.) 6, 18, 54, ...
4.) 4, -8, 16, -32,...
Pattern Description:
Pattern Description:
Next Two Terms:
Next Two Terms:
Notes 32
2.) Create a table of values to display the data for the number of dots over time. Be sure to label the
columns.
3.) Assuming that the sequence continues in the same way, how many dots are there at 5 minutes?
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4.) Graph the data for the first 3 minutes on the graph below.
This is considered a ____________ function because its graph is a ________.
5.) Let’s write an equation to describe this function.
Let f(x) = total number of dots and x = number of minutes
Total number of dots = (starting number of dots) + (increase in dots per minute)(# of minutes)
6.) Use the equation above to answer the following questions:
a) How many dots are there at 10 minutes?
b) How many dots are there at 20 minutes?
c) How many dots are there at 100 minutes?
d) How many dots are there at t minutes?
7.) Write your equation in slope-intercept form.
a) What is the slope of the line?
b) What is the meaning of the slope? Include units in your answer.
c) What is the y- intercept of the line?
d) What is the meaning of the y-intercept? Include units in your answer.
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Key Vocabulary from Today
Arithmetic Sequence: Lists of numbers that have a _____________ added to get the next term in the
list.
Example of an arithmetic sequence:
this sequence is arithmetic because _____________________________________________
Example of a non- arithmetic sequence:
this sequence is not arithmetic because __________________________________________
f(1) = value of the 1st term in the sequence
f(2) = value of the 2nd term in the sequence
.
.
f(n-1) = value of the term before the nth term in the sequence
f(n) = value of the nth term in the sequence
Common Difference: the positive or negative _____________ that is __________to a term get the next
term in the sequence.
d = common difference
Recursive Formula: A recursive formula is used to describe a term in terms of the number that came
before it in the sequence. This formula can be used if you know the value of the previous term in the
sequence.
(The next term) = (The term before it) + d
f ( n)  f ( n  1)  d
f (n) = value of the term you are looking for (nth term)
f (n  1) = value of the previous term
d = common difference
Explicit Formula: An explicit formula is used if you don’t know the previous term’s value and/or you
want to find a term far out in the sequence (ex: you want to find the value of the 450th term).
f ( x )  mx  b
m = common difference (d)
b = value of the 0th term
Arithmetic sequences create _________________ and the slope of the explicit formula
________________________ of the sequence.
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Extra Practice:
Find the common difference of each arithmetic sequence. Graph each sequence. Write a recursive and
explicit formula for each sequence.
1.) 2, 5, 8, 11, …
Term Number
1
2
3
4
Term Value
Common Difference:____________________
Recursive Formula:___________________
Explicit Formula:_____________________
2.) 24, 20, 16, 12, …
Term Number
1
2
3
4
Term Value
Common Difference:____________________
Recursive Formula:___________________
Explicit Formula:_____________________
3.) 18, 12, 6, 0, …
Term Number
1
2
3
4
Term Value
Common Difference:____________________
Recursive Formula:___________________
Explicit Formula:_____________________
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Warm Up Day 33
Use the figure below to answer each question that follows it.
1.) Draw Figure 0.
2.) Draw Figure 4
3.) Describe the pattern that represents the growth of the figures.
4.) Complete the table of values below and graph the data.
Figure
0
1
2
3
4
# of Squares
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Notes 33
Previously, we explored arithmetic sequences. They are lists of numbers that have a ___________
______________ between each sucessive term. This means that you will ______ this number to the
value of a given term to find the value of the next term.
Example: List the first six terms of an arithmetic sequence whose first term is -5 and whose common
difference is 3:
Today, we will explore geometric sequences. They are lists of numbers that have a __________
___________ between each successive term. This means that you will ______ this number to the value
of a given term to find the value of the next term.
Example: List the first four terms of a geometric sequence whose first term is -1 and whose common
ratio is 3:
Vocabulary for Today
Geometric Sequences – Lists of numbers that have a common number multiplied to get the next term in
the list.
Common Ratio – the amount multiplied each time (integer or fraction) to get the value of the next term
in the sequence.
Recursive Formula— A recursive formula is used to describe a term in terms of the number that came
before it in the sequence. This formula can be used if you know the value of the previous term in the
sequence.
(The next term) = (The term before it)(r)
f ( n)  f ( n  1)  r
f (n) = value of the term you are looking for (nth term)
f (n  1) = value of the previous term
r = common difference
Explicit Formula – An explicit formula is used if you don’t know the previous term’s value and/or you
want to find a term far out in the sequence (ex: you want to find the value of the 450th term).
f ( x)  a  b x
a = value of the 0th term
b = common ratio
When graphed, geometric sequences create ________________________________ and that the
growth/decay rate (b) of the explicit formula is the ________________ of the sequence.
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1.) Describe and label the pattern of change you see in the above sequence of figures.
2.) Assuming the sequence continues in the same way, how many dots are there at 5 minutes?
3.) Create a table of values to display the data for the number of dots over time. Be sure to label the
columns.
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4.) Graph the data for the first 5 minutes on the graph below.
A recursive formula is a formula that uses the previous term, f(n-1), to find the next term f(n) in the
sequence.
(The next term) = (The term before it)(r)
f ( n)  f ( n  1)  r
f (n) = value of the term you are looking for (nth term)
f (n  1) = value of the previous term
r = common difference
5.) Write a recursive formula to describe how many dots there will be after t minutes. Leave your answer
in terms of f(t-1) and f(t).
An explicit formula is a formula that can be used to find any term value in the sequence.
f ( x)  a  b x
a = value of the 0th term
b = common ratio
6.) Write an explicit formula to describe how many dots there will be after t minutes. Leave your answer
in terms of f(t) and t.
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Extra Practice:
Find the common ratio of each geometric sequence. Graph each sequence. Write a recursive and explicit
formula for each sequence.
1.) 2, 4, 8, 16, …
Term Number
1
2
3
4
Term Value
Common Ratio:____________________
Recursive Formula:___________________
Explicit Formula:_____________________
2.) 24, 12, 6, 3, …
Term Number
1
2
3
4
Term Value
Common Ratio:____________________
Recursive Formula:___________________
Explicit Formula:_____________________
3.) 1, 4, 16, 64,…
Term Number
1
2
3
4
Term Value
Common Ratio:____________________
Recursive Formula:___________________
Explicit Formula:_____________________
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Warm Up Day 34
Mary starts with $2 in her bank account. Each day her money triples (gets multiplied by 3)
1.) Create a table of values for how much money she will have for the first 5 days.
Day #
Money
0
$2
1
2
3
4
5
2.) Graph this data.
3.) Does this situation describe a linear or exponential function?
Why?
4.) Does this situation model an arithmetic or geometric sequence?
Why?
5.) Write a recursive formula to describe the amount of money Mary has in her account after t days.
Leave your answer in terms of f(t-1) and f(t).
6.) Write an explicit formula to describe the amount of money Mary has in her account after t days.
Leave your answer in terms of f(t) and t.
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Notes 34
1.) Describe the pattern you see.
2.) Does this situation model an arithmetic or geometric sequence?
Why?
3.) How many push-ups will Scott do on day 10?
4.) Complete the table below with the number of push-ups Scott will do on the first five days. Then graph
the data on the graph below.
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5.) What is the recursive model for the number of push-ups Scott will complete on any given day? Leave
your answer in terms of f(t-1) and f(t) where t is the number of days that he does push-ups.
5.) What is the explicit model for the number of push-ups Scott will complete on any given day? Leave
your answer in terms of f(t) and t, where t is the number of days that he does push-ups.
6.) Ally is also including push-ups in her workout and says she does more push-ups than Scott because
she does fifteen push-ups every day. Is she correct? Explain. (If you are stuck, you can complete the chart
below to explore their push-up routines.)
Day #
Ally
Scott
Who does more
push-ups?
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Warm Up 35
1.) Determine if each sequence is arithmetic or geometric. Write a complete sentence explaining how you
made this decision for each sequence. The first sentence is modeled for you.
1 1
(A) 8, 2, , ,...
2 8
This sequence is ________________ because the common _____________ is _____________.
(B) 12, 9, 6, 3,...
2.) Identify the common difference or common ratio. Then find the 5th and 6th terms in each sequence.
(A) 18, 22, 26, 30
Common difference/ratio: ____
5th term: ____
6th term: ____
5th term: ____
6th term: ____
(B) 2, 6,  18, 54
Common difference/ratio: ____
3.) Aubrey has $16 in her piggy bank. Each time she refuses to take a nap, she loses 25 cents from her
piggy bank. Assuming that she doesn’t earn any money in the meantime, how much money does Aubrey
have in her piggy bank if she refuses to take 5 naps?
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Notes 35
1.)
How many people will receive the email on day 3?
How many people will receive the email on day 4?
2.) Will this situation be modeled by an arithmetic sequence or a geometric sequence?
Why?
What would you expect this graph to look like?
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3.) Complete the table and graph below. Be sure to label your axes.
Day #
# of People
0
0
1
8
2
80
3
4
5
6
7
5.) Write a recursive formula to describe the amount of people who receive the email on day t. Leave
your answer in terms of f(t-1) and f(t).
6.) Write an explicit formula to describe the amount of people who receive the email on day t. Leave your
answer in terms of f(t) and t.
7.) How many people, in total, have received the email in the first four days?
How many people, in total, have received the email in the first week?
8.) If Bill gives away a Super Bowl of ice cream worth $4.95 to every person that receives the email
during the first week, how much potential income will he have lost in that week?
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Warm Up 36
1. {8, 5, 2, -1…}
term number, n
term value, f(n)
common
difference:
Explicit rule:
What is value of
the 10th term in
the sequence?
slope =
2.) For the function, f ( x)  4 x  6 , answer the following questions.
(A) What is the value of f (2) ?
(B) What is the value of x when f ( x)  18 ?
(C) What is the meaning of f(0) on the graph of the function of f(x)?
y intercept=
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Notes 36
1.) When the candy machine is full, how many individual candies does it hold?
2.) For each quarter paid, the machine releases 7 candies. Use this to answer the following:
a) How many candies are released with 2 quarters?
b) How many candies are released with 4 quarters?
c) How many candies are released with 5 quarters?
d) Look for a pattern above. How many candies are released when n quarters are inserted in the machine?
3.) Represent the number of candies left in the machine after n quarters have been inserted in the
machine. Let f(n) represent the number of candies left in the machine.
(Candies left in the machine) = (Initial number of candies) – (candies released)
4.) Assuming that each customer spends only one quarter on candy, about how many customers will buy
candy before the machine is empty? Use the formula you wrote in #3 above. (Hint: If n represents the
number of quarters and f(n) represents the number of candies left in the machine, which value do you
know and which value are you solving for?)
5.) Assume that each customer spends only one quarter on candy. Use this to answer the following:
a) How much money is in the machine after 5 customers buy candy?
b) How much money is in the machine after 10 customers buy candy?
c) How much money is in the machine after 30 customers buy candy?
d) How much money is in the machine after n customers buy candy?
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6.) To avoid theft, the store owners don’t want to let too much money to collect in the machine, so they
take all the money out when they think the machine has about $25 in it. The tricky part is that the store
owners can’t tell how much money is actually in the machine without opening it up, so they choose when
to remove the money by judging how many candies are left in the machine. About how full should the
machine look when they take the money out? How do you know? Assume that each customer spends
only one quarter.
a) How many customers need to buy candy for the machine to have $25 in it?
b) How many candies did these customers release from the machine?
c) Determine how full the machine will be at this point.
% full = (# of candies left)/(starting # of candies)
20
Warm Up Day 37
Determine if each sequence is arithmetic or geometric. Find the common difference or common ratio.
Then write a recursive and an explicit formula for each sequence.
1.) 3, 6, 12, 24,...
2.) 5, 8, 11, 14...
Circle One: Arithmetic or Geometric
Circle One: Arithmetic or Geometric
Common Difference or Ratio: ______________
Common Difference or Ratio: ______________
Recursive Formula: ____________________
Recursive Formula: ____________________
Explicit Formula: ____________________
Explicit Formula: ____________________
3.) 19,  25,  31,  37,...
4.) 32, 8, 2,
1
,...
2
Circle One: Arithmetic or Geometric
Circle One: Arithmetic or Geometric
Common Difference or Ratio: ______________
Common Difference or Ratio: ______________
Recursive Formula: ____________________
Recursive Formula: ____________________
Explicit Formula: ____________________
Explicit Formula: ____________________
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Notes 37
1.) Complete a chart showing how many candies Augustus will earn each day for the first five days.
Label your columns with units.
2.) Is this an arithmetic sequence or geometric sequence?
Why?
3.) Write a recursive formula that shows the number of candies that Augustus earns on day t with his
father’s plan. Leave your answer in terms of f(t-1) and f(t).
4.) Write an explicit formula that shows the number of candies that Augustus earns on day t with his
father’s plan. Leave your answer in terms of f(t) and t.
5.) Use the explicit formula to find how many candies Augustus will have on day 30 in this plan.
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6.) Complete a chart showing how many candies Augustus will earn each day for the first five days on
this plan. Label your columns with units.
7.) Is this an arithmetic sequence or geometric sequence?
Why?
8.) Write a recursive formula that shows the number of candies that Augustus earns on day t with his
father’s plan. Leave your answer in terms of f(t-1) and f(t).
9.) Write an explicit formula that shows the number of candies that Augustus earns on day t with his
father’s plan. Leave your answer in terms of f(t) and t.
10.) Use the explicit formula to predict the number of candies that Augustus would earn on the 30th day
with his plan.
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11.) Complete a chart showing how many candies Augustus will give away each day and how many he
will have leftover for the first five days on this plan.
day
# given away
# left over
12.) Use the chart above to find the common ratio between each successive term.
13.) Write an explicit formula to describe the amount of candy that would be left in the pile after t days.
Leave your answer in terms of f(t) and t.
14.) How many pieces of candy will be left on day 8?
15.) After how many days would the candy be gone?
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Warm Up Day 38
Determine if each sequence is arithmetic or geometric. Find the common difference or ratio. Then graph
the sequence and determine if each sequence is linear or exponential.
1.)
Term Number
0
1
2
3
Term Value
3
6
12
24
Circle One: Arithmetic or Geometric
Common Difference/Ratio: _____________
Circle One: Linear Graph or Exponential Graph
2.)
Term Number
0
1
2
3
4
Term Value
20
16
12
8
4
Circle One: Arithmetic or Geometric
Common Difference/Ratio: _____________
Circle One: Linear Graph or Exponential Graph
3.)
Term Number
0
1
2
3
4
Term Value
16
12.5
9
5.5
2
Circle One: Arithmetic or Geometric
Common Difference/Ratio: _____________
Circle One: Linear Graph or Exponential Graph
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Notes 38
Would the graph of this data be linear or exponential? Explain how you reached this conclusion.
Would the graph of this data be linear or exponential? Explain how you reached this conclusion.
26
Would the graph of this data be linear or exponential? Explain how you reached this conclusion.
Would the graph of this data be linear or exponential? Explain how you reached this conclusion.
Would the graph of this data be linear or exponential? Explain how you reached this conclusion.
27
Would the graph of this data be linear or exponential? Explain how you reached this conclusion.
Would the graph of this data be linear or exponential? Explain how you reached this conclusion.
Would the graph of this data be linear or exponential? Explain how you reached this conclusion.
28
Would the graph of this data be linear or exponential? Explain how you reached this conclusion.