Welcome
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Advanced Algebra 2 Honors, Fall 2015
William Schooleman, Room 320
720-423-6145
william_schooleman@dpsk12.org
Class Website:
http://mrschooleman.wickispaces.com
Unit of Study
1.
2.
3.
4.
5.
Patterns and Recursions
Linear Models and Systems
Statistics
Functions and Functions Transformation
Function Families and Exponential /
Logarithmic Functions
Materials
• Textbook – Discovering Advanced Algebra 2nd
edition.
• Three ring binder(or equivalent) with dividers
for notes, vocabulary, classwork, homework,
• unit-portfolio, and test / quizzes.
• Standard college rule notebook paper.
• Graph paper
• #2 Pencils and erasers
• Scientific Calculator – A class set will be
available but if you wish to purchase your own I
would recommend the Texas Instrument N-Spire
(the color one is really cool).
Grading Policy
Homework (HW) – 15%
Classwork (CW) – 10%
Assessments: Unit Tests, Quizzes – 50%
Portfolio / Concept Organizers/ Projects – 15%
Semester Final – 10%
Tutoring
If you want additional help just ask!
Scheduled math tutoring is available during
lunch every Monday and in the morning on
Thursday from 7:30 to 8:15 in the morning.
If you are unable to meet at these times
then please speak with me directly or
email me to set up an alternative
appointment. After school tutoring is
available in the tutoring center staffed with
one of the Algebra 2 teachers.
You are responsible for your
own education. If you don’t
understand, raise your hand!
Advocate for yourself, I am here
to help you be successful in
mathematics but you have to be
willing to put in the work and the
effort.
August 26, 2015
Objectives:
1. Write recursive definitions and formulas for
patterns and sequences.
2. Learn to recognize and write formulas for
arithmetic and geometric sequences.
Warm-Up:
Factor .
2 x  13x  15
2
Unit 1 Recursive Sequences
Each square in this pattern has side
length 1 unit. Imagine that the pattern
continues. Find the perimeter of Figure
9. Which figure has a perimeter of 76
units?
Arithmetic Sequence:
An arithmetic sequence is a sequence
in which each term is equal to the
previous term plus a constant. The
constant is called the common
difference.
U n  U n 1  d
The geometric pattern below is
created recursively. If you continue
the infinitely, you will create a fractal.
How many red triangles will there be
at the ninth stage?
Geometric Sequence
A geometric sequence is a sequence in
which each term is equal to the
previous term multiplied by a
constant. This constant is called the
common ratio.
U n  U n 1 r
August 28, 2015
Objectives:
1. Write a recursive formula from a table and a
graph.
Warm-Up:
Factor the following:
a. 6 x 3  15 x 2  12 x
b. x  8 x  15
2
Write a recursive formula for the sequence
graphed. Find the 42nd term.
Write a recursive formula and use it to find the
missing table values.
n
Un
n
Un
1
5
1
2.2
2
12.5
2
7.7
3
20
4
3
4
26.95
……… 12
………
……… 10
………
August 31, 2015
Objectives:
1. Explore geometric sequences that model
growth and decay.
Warm-Up
Factor.
a. x  5 x  6
2
b. 3x  15 x  18 x
3
2
Review percent skills:
Write out the expression for the following>
a. What is 95% of 220?
b. What is 85% of 300?
c. What is 105% of 220?
d. What is 115% of 300?
Investigation: (show work on white boards)
TV central is going out of business
in 8 weeks. Each week until it closes,
the company plans to reduce the price
from the previous week by 15%. A
Flat-screen television is currently
priced at $899. You and your partner
write a recursive formula to find the
price of the television after 8 weeks if
it remains unsold.
Investigation: (show work on white boards)
Gloria deposits $2,000 into a bank
account that pays 7% annual interest
compounded annually. This means the
bank pays her 7% of her account
balance as interest at the end of each
year, and she leaves the original
amount and the interest in the
account. When will the original
deposit double in value?
September 1, 2015
Objectives:
1. Investigate sequences the approach a limit in
the long run.
2. Identify what a shifted geometric sequence
is.
Warm-Up.
Factor.
3
2
2 x  14 x  24 x
Investigation:
Carbon dating is used to find the age of ancient
remains of once-living things. Carbon-14 is
found naturally in all living things, and it decays
slowly after death. About 11.45% of it decays in
each 1,000-year period. Let 100 be the
beginning amount of carbon-14. at what point
will less than 5% remain? Write the recursive
formula you and your partner used and graph
the sequence up to 30,000 years in 1,000 year
increments.
Our kidneys continuously filter our blood,
removing impurities. Doctors take this into
account when prescribing the dosage and
frequency of medicine. Suppose a patient is
given 16 mg. of medication and assume that the
patient’s kidneys filter out 25% of the
medication each day.
Write a recursive formula and determine the
long-run value.
September 2, 2015
Objectives:
• Identify a “Shifted Geometric sequence”.
• Find the long run value ( Limit) of a shifted
geometric sequence using a graph, calculator
and algebra.
Warm Up:
a. 8 x  26 x  15
2
b. 3x  7 x  2
2
Real World - Problem
September 4th, 2015
Objective: Explore and describe using academic
language how to find the long run value of a shifted
geometric sequence.
Warm - Up
September 8, 2015
Objectives:
1. Identify different characteristics of different
types of recursive formulas.
2. Describe the rate of change of arithmetic
and geometric sequences.
Warm-Up
Find the slope of the line containing each pair of
points.
a. (3, -4), and (7,2) b. (5, 3) and (2, 5)
September 10, 2015
Objectives:
1. Apply recursive sequences to loan and
investments that are compounded.
2. Interpret financial language in a recursive
sequence.
Warm-up.
a. Solve
b. Factor
x  220  0.45x
10 x  13x  3
2
Discuss the following financial language:
Principal.
Balance.
Loan.
Investment.
Deposit.
Payment.
Interest rate.
Frequency with which interest is compounded.
Assume that each of the sequences below represents a
financial situation. Indicate whether each represents a
loan or an investment, and give the principal and the
deposit or payment amount.
• A.
Find the balance after 5 years if $500 is
deposited into an account with an
annual interest rate of 3.25% ,
compounded monthly.
B.
You take out a loan for $12,500 at
7.5% , compounded monthly, and you
make payments for $350.
How many months will it take you to
pay off the loan?
September 15, 2014
Objectives:
1. Given a situation with a recursive situation
create a mathematical model and explain
your reasoning.
2. Justify mathematically the common
difference needed to achieve a certain Long
Run value ( Limit).
Extention.
Each day, the imaginary caterpillar
eats 25% more leaves each day
than it did the day before. If a 30day-old caterpillar has eaten
151,677 leaves in its brief lifetime,
how many will it eat the next day?
September 14, 2015
Objectives:
1. Define and apply the formula for Partial Sum
of a Geometric Series.
u1 (1  r )
Sn 
1 r
n
a1  a1r
or Sn =
1 r
n
_______________________________________
Warm-Up.
2
Factor.
10 x  26 x  12
September 15, 2015
Objectives:
1. Define and apply the formula for Partial Sum
of a Geometric Series.
2. Identify the difference of the rate of change
between arithmetic and geometric
sequences.
u1 (1  r )
Sn 
1 r
n
a1  a1r
or Sn =
1 r
n
• Suppose you begin a job with an annual
salary of $54,000. Each year, you can expect a
4.2% raise.
1. What is the salary in the tenth year after you
start the job?
2. What is the total amount you earn in ten years?
u1 (1  r n )
Sn 
1 r
a1  a1r n
or Sn =
1 r
3. How long must you work at this job before your
total earning exceeds $ 1 million?
• At the beginning of January, the Bike MegaMart has 500
bicycles in stock. Each month they plan to sell 25% of their
stock. On the last day of each month, they will receive a
shipment of 200 new bikes.
• a. Write a recursive formula for calculating the number
of bikes in stock at the end of n months.
• b. How many bikes will the MegaMart have at the end of
12 months?
• c. Describe what will happen to the number of bikes in
stock over the long run.