Math

Week of April 20

Academic learning at home resources have been created to provide opportunities for students to engage in meaningful learning experience during the school closure. Below you will find a list of activities that your child can complete both independently and with your support.

Learning Logs are to be completed each day when work is done. These logs will be turned in at the end of the week to your teacher. Your teacher will be in contact with you this week. If you have any questions, please contact your teacher.

Algebra I

Linear Functions and Equations

Pedro is planning to add a text messaging feature to his cell phone plan. He has gathered information about the two different plans offered by his wireless phone company.

Plan A: $4.00 per month plus 4 cents for each message

Plan B: 5 cents per message

Use the mathematics you have learned in Algebra I to provide Pedro with the following information for each plan.
- Plan A
  - a table of data
  - a graph of the data
  - the linear function that fits this plan
  - the domain and range of the function
- Plan B
  - a table of data
  - a graph of the data
  - the linear function that fits this plan
  - the domain and range of the function
If Pedro sends 360 messages on average each month, which plan would you recommend that he choose? Support your recommendation using mathematical evidence.
If Pedro knows that his average usage is going to increase to 500 text messages per month, should he change to a different plan? Explain and justify your reasoning.
Explain whether either of the plans represents a direct variation.
Pedro’s friend Chenetta is considering another text messaging plan that advertises the following: “A one-time joining fee of $3.00 and $0.08 per message.”
- Write an explicit formula for the text messaging plan.
- Chenetta knows that she sends and receives about 1800 text messages per month. Use an example and other mathematical evidence to let Chenetta know if you think this plan would be a good deal for her.

Algebra II

Rational Functions

Consider the function f(x) =4/x.
- Complete the table.
- Use the table to graph the function.
- Analyze the function and the corresponding table and graph. Describe the domain, range, and end behavior of the function. Determine all of the asymptotes of the function. Explain your reasoning.
Consider the function h(x) = 5/x .
- Complete the table.
- Use the table to graph the function.

Rational Function Table #1

Rational Function Graph #1

Rational Function Table #2

Algebraic Reasoning

Think of your future career

Select a math calculation from your future career that can be graphed by a linear representation. (ex. Police officer - speeding tickets given; Real Estate Agent - commission on sale of homes)
Write a formula representing the linear relationship
Draw a graph on paper or desmos to represent the relationship
Write a paragraph explaining the real-world relationship, the formula and graph. Be sure to explain the slope and the y-intercept.

Geometry

Transformations

City planner Regina Kane is designing a new plaza for the city. Her plan is organized on a coordinate plane, as shown and described below and to the right.

Hexagonal fountain: centered at (0, 0), two sides of length 2 units
Short rectangular benches: centered at (0, 10) and (0, −10), length 4 units
Long rectangular benches: centered at (10, 0) and (−10, 0), length 8 units
Triangular statue T: vertices at (5, 10), (7, 10), (7, 7)
Flagpoles (shown as dots): at (−2, 10) and (2, −10), next to short benches

1. Why could a single translation map one of the long rectangular benches onto the other long rectangular bench, but not map one short rectangular bench and flagpole onto the other short rectangular bench and flagpole?

2. Describe a rigid motion or composition of rigid motions that maps the rectangular bench at (0, 10) and the adjacent flagpole onto the other short rectangular bench and flagpole.

3. Regina wants to know if it is possible for a composition of rigid motions to map one of the short rectangular benches onto a long rectangular bench. Write a short explanation that you could send to Regina in an email.

4. One of Regina’s assistants glances at the plan and comments that the hexagonal shape has the greatest number of lines of symmetry of all the shapes in the plan. Is the assistant correct? Explain.

5. A landscape architect recommends installing a triangular statue with vertices at (10, −10), (10, −8), and (7, −10).

Is the triangle congruent to triangle T ? Justify your answer.
Propose a series of rigid motions that justifies your answer to part a.

6. Another landscape architect recommends installing a triangular statue with vertices at (−5, 10), (−5, 8), and (−7, 8).

Is the triangle congruent to triangle T ? Justify your answer.
Propose a series of rigid motions that justifies your answer to part a.

Math Models

You are the beneficiary of a trust fund established by your grandparents 21 years ago, when you were born. The original amount of the fund was $15,000. If the money earned interest at the rate of 6% compounded annually, what is the current amount in the fund? How much would be in the fund if it had been invested at 6% compounded monthly?
The parents of a child just received a large inheritance and want to put a portion of the money into a college fund. They estimate that they will need $75,000 in 12 years. If they invest the money at 7% annual interest compounded quarterly, how much should they deposit into the fund?
Your car is for sale. You have received two offers:
- Offer 1: The first buyer offers you $6000. He wants to pay you $2000 now, $2000 in six months, and $2000 in one year.
- Offer 2: The second buyer offers to pay $5600 in cash now.
- What is the present value of offer 1? Assume you can earn 10% interest compounded monthly on your money.
- Which offer is a better deal? Explain.
An advertisement in the local newspaper claims that the APY on a CD that paid 4.5% interest compounded quarterly was 4.58%. Is this claim accurate? Explain.

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