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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
Algebra I
Representations of Functions
While on vacation, Jorge and Jackie traveled to Bryce Canyon National Park in Utah. They were impressed by the differing elevations at the viewpoints along the road. The graph describes the elevations for several viewpoints in terms of the time since they entered the park.
1. The graph represents a function E(t). Describe why the graph represents a function. Identify the domain and range of the function.
2. Is this discrete or continuous data? Explain.
3. What is the y-intercept? Interpret the meaning of the y-intercept in the context of the problem.
4. Identify a relative maximum of the function represented by the graph.
5. What is the absolute maximum of the function represented by the graph? What does it represent?
6. Identify a relative minimum of the function represented by the graph.
7. What is the absolute minimum of the function represented by the graph? What does it represent?
While at Bryce Canyon National Park, Jorge and Jackie hiked at an average speed of about 2 miles per hour.
8. Complete the table below to show the distance hiked by a person whose constant speed is 2 miles per hour.
9. Write a function f(x) to describe the data in the table. What are the reasonable domain and range?
10. Create a graph of the function.
11. How long will it take this person to hike 5 miles? Justify your answer.
12. On the same coordinate grid that you used in Item 10, create a graph of another function by translating the graph 5 units up.
13. Write a function to describe the graph you created in Item 12. Explain how you determined your answer.
Algebra II
Algebra II
Quadratic Graphs, Equations, and Applications
Analyze the graph of the quadratic function below.
The standard form of a quadratic function is
f(x)=ax2+bx+c. What possible values can a and c have for the given quadratic function? Explain your reasoning.
The vertex form of a quadratic function is f(x)=ax-h2+k. What possible values can a, h, and k have for the given quadratic function? Explain your reasoning.
The factored form of a quadratic function is f(x)=ax-r1x-r2. What possible values can a, r1, and r2 have? Explain your reasoning.
Write a quadratic function for the parabola that passes through the point (2, -3) with roots (-6, 0) and (4, 0).
Algebraic Reasoning
Algebraic Reasoning
Explain Domain and Range using the definition
Explain Domain and Range using different terms (words)
Explain Domain and Range on a graph
Solve for the Domain and Range on the following graphs you researched last week:
Linear function - positive slope
Linear function - negative slope
Absolute Value function
Quadratic Function
Cubic Function
Square Root Function
Exponential Function
Reciprocal Function
Geometry
Geometry
Angles, Parallel Lines, and Perpendicular Lines
The first hill of the Steel Dragon 2000 roller coaster in Nagashima, Japan, drops riders from a height of 318 ft. A portion of this first hill has been transposed onto a coordinate plane and is shown to the right.
1. The structure of the supports for the hill consists of steel beams that run parallel and perpendicular to one another. The endpoints of the beam shown by BC are (0, 150) and (120, 0). The endpoints of the beam shown by AD are (0, 125) and (100, 0).
Verify and explain why the two beams are parallel.
If ∠DAB = 125°, what is the measure of ∠CBA? Justify your reasoning.
2. Determine the equations of the lines containing the beams from Item 1, and explain how the equations of the lines can help you determine that the beams are parallel.
3. A third support beam is perpendicular to the beam shown by BC. If marked on the coordinate plane, the line containing this beam would pass through the point (60, 75). What is the equation of the line containing this third beam? Explain how you determined your answer.
The diagram below shows a section of the steel support structure of a roller coaster. Use the diagram for Items 4–6.
4. Given JK || PL , m∠JKL = (10x + 5)° and ∠PLK = (12x − 1)°, what is the measure, in degrees, of ∠JKL and ∠PLK? Explain how you determined your answer.
5. Explain how an engineer could determine whether PN || LM by measuring two angles in the diagram.
6. Write a two-column proof.
Given: JK || PL, ∠1 ≅ ∠2
Prove: ∠3 ≅ ∠4
Math Models
Math Models
The formula for the interest on money invested with simple interest is I=Prt. Explain what each variable in the equation represents.
Simple Interest
What is the total interest on a principal investment of $10,000 at 3.5% simple interest in 5 years? In 10 years?
The formula for the current balance of an investment with compound interest is A=P1+rnnt . Explain what each variable in the equation represents.
Compound Interest
$10,000 is deposited in an account with a 3.5% annual interest rate. Determine the balance in the account in 5 years if the interest is compounded annually. What is the total interest earned?
$10,000 is deposited in an account with a 3.5% annual interest rate. Determine the balance in the account in 5 years if the interest is compounded quarterly. What is the total interest earned?
$10,000 is deposited in an account with a 3.5% annual interest rate. Determine the balance in the account in 5 years if the interest is compounded monthly. What is the total interest earned?
Compare the results for compound interest to the results for simple interest. Which investment - simple or compound - resulted in a greater return? Why?
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