Algebra 2 8-1 Complete Lesson: Inverse Variation

By Matt Richardson
Last updated over 2 years ago
20 Questions
Note from the author:
A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.
1.

Solve It! You have 20 bags of mulch. You plan to spread the mulch from all the bags to make a rectangular layer that is 3-in. thick.


How many square feet can you cover?
If l and w represent the length and width of the rectangle in feet, what equation relates l and w?
Justify your reasoning.

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2.

Problem 1 Got It? Classify each table as representing a direct variation, an inverse variation, or neither. Identify the function model for the direct and inverse variations.
NOTE: Any model that is neither direct variation nor direct variation will not have a function model.

  • Direct variation
  • Inverse variation
  • Neither
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3.

Problem 2 Got It? Suppose x and y vary inversely, and x = 8 when y = -7.
Drag the appropriate item from the left to respond to each question on the right.

  • -56
  • 26
  • -28
  • What is the function that models the inverse variation?
  • What does the graph of this function look like?
  • What is y when x = 2?
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4.

Problem 3 Got It? After a major storm, your math calss volunteers to remove debris from yards. The table shows the time t in minutes that it takes a group of n students to remove the debris from an average-sized yard.

What function models the time needed to clear the debris from an average-sized yard relative to the number of students who do the work?

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5.

Problem 3 Got It? After a major storm, your math calss volunteers to remove debris from yards. The table shows the time t in minutes that it takes a group of n students to remove the debris from an average-sized yard?

How many students should there be to clear debris from an average-sized yard in at most 25 minutes?

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6.

Problem 4 Got It? The number of bags of mulch you need to cover a planting area varies jointly with the area to be mulched a in square feet and the depth of the mulch d in feet. If you need 10 bags to mulch 120 ft2 to a depth of 3 in., how many bags do you need to mulch 200 ft2 to a depth of 4 in.?

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7.

Problem 5 Got It? How much potential energy would a 41-kg diver have standing on a 10-m diving platform?

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8.

Problem 5 Got It? An 80-kg diver stands on a 6-m diving platform. At what height should a 40-kg diver stand to have equal potential energy? Do you need to find the potential energy of either diver to solve this? Explain.

  • 6 m
  • 9 m
  • 10 m
  • 12 m
  • Yes. You must calculate the potential energy of both divers in order to determine at what height of the second diver their PE will be equivalent.
  • No. You don't need to calculate the potential energy of either diver in order to determine at what height of the second diver the PE will be equivalent.
  • At what height should a 40-kg diver stand to have equal potential energy?
  • Do you need to find the potential energy of either diver to solve this?
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9.

Is the relationship between the variables in the table a direct variation, an inverse variation, or neither? What equation models the direct or inverse variation?

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10.

Is the relationship between the variables in the table a direct variation, an inverse variation, or neither? What equation models the direct or inverse variation?

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12.

Writing: Describe how the pairs in the left column are related based on the equation below.

  • p and s
  • p and qrt
  • Vary jointly
  • Vary inversely
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13.

Error Analysis: A student described the relationship between the variables in the equation below as d varies directly with r and inversely with t. Correct the error in relating the variables.

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14.

Review Lesson 7-6: Solve each equation. Match a solution from the left with each equation on the right.

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15.

Review Lesson 6-2: Multiply and simplify. Match a simplified expression from the left with each expression on the right.

16.

Review Lesson 2-7: Match a description from the left with each equation on the right to describe how the equation is a transformation of the parent function y = |x|.

  • Translate left 2 units.
  • Translate right 2 units.
  • Translate up 2 units.
  • Translate down 2 units.
  • Stretch horizontally by a factor of 2.
  • Stretch vertically by a factor of 2.
  • y = |x| + 2
  • y = |x + 2|
  • y = 2|x|
17.

Vocabulary Review: Which expression(s) do NOT contain a constant term?

18.

Use Your Vocabulary: Use the true and false boxes on the left to tag each statement on the right.

  • true
  • false
  • As the radius of a pizza increases, the circumference of the pizza also increases. This relationship represents a direct variation.
  • As the number of miles a car is driven increases, the number of gallons of gas in the car's tank decreases. This relationship represents an inverse variation.
  • As the number of pages in a book increases, the weight of the book increases. This relationship represents an inverse variation.
19.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.

20.

Reflection: Math Success

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