Get the Math and Points: June 2016 CC Algebra I Regents #2

June 2016 Alg I 2
This question is categorization and is easy to figure out with some close reading:
A fifth degree expression has a highest power of 5 so that takes out answers (2) and (3) leaving (1) and (4).
A leading coefficient of 7 is exactly what it sounds like — does answer choice (1) or (4) have a first term that starts with a 7?
A constant of 6 is 6 without any algebra or variables so find that to confirm your answer!:)

June 2016 CC Alg I Regents #1

June 2016 Alg I 1

We can either recognize the factoring as DOTS Difference of Two Squares and see that the 16 would be 4 x 4 (not 8 x 8).  Then by checking the signs of the remaining answers (3) and (4) we would see that answer (4) would give us a trinomial and not the binomial given.

Another way to do this would be to use the TI-84:
Here is answer (1) compared to the original expression, um, not  a match!

June 2016 CC Alg I 1AJune 2016 CC Alg  1A tableJune 2016 CC Alg I 1A graph

Below is answer (2) compared to the original expression.  Also not a match!!
June 2016 CC Alg I 1BJune 2016 CC Alg I 1B tableJune 2016 CC Algebra I 1B graph

And now to check answer (3) and from the table voila!!  also we only see one graph which means the Y= are the same:)
June 2016 CC Alg I 1cJune 2016 CC Alg I 1C TableJune 2016 CC Alg I 1c graph

 

 

 

June 2016 Brain Teaser Solution

Q: The following equations are incorrect.  Fix them using these rules.
No other numbers can be written.
No inequality symbols can be used like a “greater than” sign, a “less than” sign or “not equal to” sign.1 1 1 =6
2 2 2 =6
3 3 3 =6
4 4 4 =6
5 5 5 =6
6 6 6 =6
7 7 7 =6
8 8 8 =6
9 9 9 =6
0 0 0 =6There can be multiple answers for one equation.

Hint: you can use ! and square roots
A:
(1+1+1)! = 3! = 3 x 2 x 1 = 6
2 + 2 + 2 = 6
3 x 3 – 3 = 6
4 + 4/sqrt(4) = 6
5 + 5/5 = 6
6 + 6 – 6 = 6
7 – 7/7 = 6
8 – sqrt(sqrt(8 + 8) = 2
9/sqrt(9)  + sqrt(9) = 6
(0! + 0! +0!)! = 6
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