Welcome

• 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. Patterns and Recursions2. Linear Models and Systems3. Statistics4. Functions and Functions Transformation5. 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 PolicyHomework (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, 2015Objectives: 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 . 22 13 15x x

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.

1n nU U 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 SequenceA 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.

1 n nU U r

August 28, 2015Objectives:1. Write a recursive formula from a table and a

graph.

Warm-Up: Factor the following:3 2a. 6 15 12x x x 2b. 8 15x x

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 1 2 3 4 ……… 125 12.5 20 ………

nU

n 1 2 3 4 ……… 102.2 7.7 26.95 ………

nU

August 31, 2015Objectives:1. Explore geometric sequences that model

growth and decay.

Warm-UpFactor.

2a. 5 6x x 3 2b. 3 15 18x x x

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, 2015Objectives:1. Investigate sequences the approach a limit in

the long run.2. Identify what a shifted geometric sequence

is.Warm-Up.Factor. 3 22 14 24x x 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, 2015Objectives:• Identify a “Shifted Geometric sequence”.• Find the long run value ( Limit) of a shifted

geometric sequence using a graph, calculator and algebra.

Warm Up:

2a. 8 26 15x x 2b. 3 7 2x x

Real World - Problem

September 4th, 2015Objective: Explore and describe using academic language how to find the long run value of a shifted geometric sequence.Warm - Up

September 8, 2015Objectives:1. Identify different characteristics of different

types of recursive formulas.2. Describe the rate of change of arithmetic

and geometric sequences.Warm-UpFind the slope of the line containing each pair of points. a. (3, -4), and (7,2) b. (5, 3) and (2, 5)

September 10, 2015Objectives: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

220 0.45x x 210 13 3x x

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 30-day-old caterpillar has eaten 151,677 leaves in its brief lifetime, how many will it eat the next day?

September 14, 2015Objectives:1. Define and apply the formula for Partial Sum

of a Geometric Series.

_______________________________________Warm-Up.Factor.

1 1 1(1 ) or =

1 1

n n

n n

u r a a rS S

r r

210 26 12x x

September 15, 2015Objectives: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.

1 1 1(1 ) or =

1 1

n n

n n

u r a a rS S

r r

• 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?

3. How long must you work at this job before your total earning exceeds $ 1 million?

1 1 1(1 ) or =

1 1

n n

n n

u r a a rS S

r r

• 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.