Algebra 2 Problems of the Day (open ended)

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August 2017, Part II

All Questions in Part II are worth 2 credits. Work need be shown (or explained or justified) for full credit. Correct numerical answers with no work receive one credit.


27. Verify the following Pythagorean identity for all values of x and y: (x² + y²)² = (x² − y²)²2 + (2xy)²

Answer:

(x² + y²)² = (x² − y²)²2 + (2xy)²
x⁴ + 2x²y² + y⁴ = x⁴ - 2x²y² + y⁴ + 4x²y²
x⁴ + 2x²y² + y⁴ = x⁴ + 2x²y² + y⁴
(check mark!)

As long as you showed the left side and right side to be equal, you should be fine.
You could have only done the right side, leaving the left side as (x² + y²)², and as a final step, reduce the right side to (x² + y²)² as well.

28. Mrs. Jones had hundreds of jelly beans in a bag that contained equal numbers of six different flavors. Her student randomly selected four jelly beans and they were all black licorice. Her student complained and said "What are the odds I got all of that kind?" Mrs. Jones replied, "simulate rolling a die 250 times and tell me if four black licorice jelly beans is unusual." Explain how this simulation could be used to solve the problem.

Answer:
A die has six sides, each of which is just as likely to occur. Each of the six sides could represent a color of a jelly bean in the bag. If, for example, 1, represents "black licorice", you could use the simulation to see how many times that this number would be rolled 4 times in a row after 250 simulations.

Make sure that you explain the simulation for full credit.



Comments and questions welcome.

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