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(0017(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!)



Comments and questions welcome.

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