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Common Core Algebra I, medium, Regents, test prep

Get the Math and Get the Points Jan 2016 CC Alg I #17

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From the January 2016 Common Core Algebra I RegentsJan 2016 Alg I 17

Notice we are looking for the x value — similar to #1 on this very same Regents!!
https://mathconfidence.com/2016/05/02/get-the-math-and-get-the-points-notice-x/

Input both equations into Y=…absolute value is found either under Math, Number or in the catalog which can be found by doing 2nd zero
For answer choice (1), when x = -2 both Y1 and Y2 are the same :)
For answer choice (2), when x = 2, Y1 = 4 while Y2 = 2
For answer choice (3), when x = 3, Y1 = 4.5 while Y2 = 3
For answer choice (4), when x = -6, here’s another snapshot with the table arrowed up to more negative numbers:
Jan 2016 Alg I 17d
when x = -6, Y1 = 0 while Y2 = 6.

 

Common Core Algebra I, easy, Regents, test prep

Get the Math and Get the Points Jan 2016 CC Alg I #16

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From the January 2016 Common Core Algebra I Regents

Jan 2016 A1 16

This is 2 points easily earned with a TI-84 while learning about the different types of
functions through comparing and contrasting.  We need to check the xy table of each function and see if it matches the given table.

Below is answer (1) not a match.  By the way, check out the change in y — linear!!

Below is answer (2) also not a match.  Check out the change in y — linear!!

 

Onto answer choice (3) see below, um also not a match

And last but certainly not least, answer choice (4) see below: 2 points!!!!!

There are many extensions to this question!!

Linear vs exponential vs cubic in an equation and in a table
Use the TI-84 and also look at the equations to categorize the types of functions.

Two are linear as they look like y = mx + b and will graph in a line.
One of the functions is a power function and one is exponential.

Looking at rate of change of the xy table

Substituting in values of x into each equation to see if they make the equation true
The easiest x value to substitute is usually 0 so try it here and see if the y or f(x) value = 1 as shown in the table

Common Core Algebra I, medium, Regents, test prep

Get the Math and Get the Points Jan 2016 CC Algebra I Regents #14

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From the January 2016 Common Core Algebra I Regents

Jan 2016 Alg I 14

http://www.regentsprep.org/regents/math/algtrig/ate12/completesqlesson.htm

We can use the method of completing the square — see the link above
So far we have x^2 – 8x so we take 1/2 of -8 and square that to complete
(x –  4) (x – 4 ) giving x^2 – 8x + 16

trying answer (1) gives x^2 – 8x + 16 = 9  if we subtract 9 from each side we get:
x^2 – 8x + 7 = 0  close but no cigar

trying answer (2) gives x^2 – 8x + 16 = 23  if we subtract 23 from each side we get:
x^2 – 8x – 7 = 0  matches exactly!!!

OR

we can expand each answer and set it equal to zero to see which one matches the original whether on paper or on the TI-84
On the TI-84, set Y1 = x^2 – 8x – 7 and then set each answer choice to 0 and put into Y2 one by one
Try answer (1) by setting Y2 = (x – 4)^2 – 9, does it match Y1?
Try answer (2) by setting Y2 = (x – 4)^2 – 23, does it match Y1?  :)

 

 

Common Core Algebra I, medium, Regents, test prep

Get the Math and Get the Points CC Alg I Regents #13

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From the January 2016 Common Core Algebra I Regents:Jan 2016 Alg I 13

This is really a rate of change or slope question: (change in y) / (change in x)

For answer choice (1), it took 73 years to go up 5 cents not a lot of increase per year
For answer choice (2), 14-6 = 8 cents over 14 years (1985-1971)
For answer choice (3), 24 – 14 = 10 cents over 21 years (2006 – 1985)
For answer choice (4), 35 – 24 = 11 cents over only 6 years (2012 – 2006)

(We can see that the price change has been increasing by more cents as time goes on)
So which time interval had the most change per year?  Please see below

Jan 2016 Alg I 13