Wednesday, April 11, 2018

Algebra 2 Problems of the Day

Algebra 2 is not my usual subject, but I do get asked about the problems occasionally. So I've decided to run a couple of Regents problems daily for a while. If there's a positive reaction (or at least, a lack of negative reaction), I may continue it.

More Algebra 2 problems.

January 2018
3. For the system shown below, what is the value of z?


y = -2x + 14
3x - 4z = 2
3x - y = 16

(1) 5
(2) 2
(3) 6
(4) 4

Answer: (4) 4
Substitute -2x + 14 for y in the 3rd equation
3x - (-2x + 14) = 16
3x + 2x - 14 = 16
5x = 30
x = 6
Substitute 6 for x in the 2nd equation
3(6) - 4z = 2
18 - 4z = 2
-4z = -16
z = 4



4. The hours of daylight, y, in Utica in days, x, from January 1, 2013 can be modeled by the equation y = 3.06 sin(0.017x - 1.40) + 12.23. How many hours of daylight, to the nearest tenth, does this model predict for February 14, 2013?
(1) 9.4
(2) 10.4
(3) 12.1
(4) 12.2

Answer: (2) 10.4
February 1 is 31 days after January 1. February 14 is 13 days after February 1. So 31 + 13 = 44.
3.06 sin(0.017(44) - 1.40) + 12.23 = 10.3733...
Make sure the calculator is in radians mode, not degree mode (which would give you 12.1952 ... sneaky!)


EDIT: fixed missing decimal point, which was a typo that didn't affect the answer.



Comments and questions welcome.

at

2 comments:

  1. AnonymousSaturday, May 18, 2019 4:21:00 PM

    Problem 4 with an explanation is not available anywhere (not even the January 2018 JMAP). Thank you so much for helping me understand this problem!

    - A very grateful sophomore at a performing arts high school in New York City

    ReplyDelete
  2. (x, why?)Saturday, May 18, 2019 5:06:00 PM

    You're welcome. I'm surprised the answer wasn't there, but then, I can see that it's "just" a simple plug-in problem if once you realize that it's the 44th day of the year. And you're calculator is in the correct Mode.

    Also, thank you for bringing my attention to the post -- I just noticed a typo. I left out a decimal point. The answer is still correct. It was just a typo, but it was entered correctly in the calculator.

    ReplyDelete