Saturday, June 20, 2015

New York State Algebra I (Common Core) Regents, June 2015 Part 2

I'll be working all weekend (yes, even on Fathers Day) grading exams, so getting these answers up will take some time. I'll edit the answers when I have time to make illustrations.

Part 2

25. Graph the function y = |x - 3| on the set of axes below.

Explain how the graph of y = |x - 3| has changed from the related graph y = |x|.

This absolute value graph is V-shaped, with a slope of -1 on the left side and 1 on the right side. It's vertex is at (3, 0).
The change from y = |x| is that the graph has shifted three units to the right.

26. Alex is selling tickets to a school play. an adult ticket costs $6.50 and a student ticket costs $4.00. Alex sells x adult tickets and 12 student tickets. Write a function f(x), to represent how much money Alex collected from selling tickets.

f(x) = 6.50x + 4.00(12) or
f(x) = 6.50x + 48.00

27. John and Sarah are each saving money for a car. The total amount of money John will save is given by the function F(x) = 60 + 5x. The total amount of money Sarah will save is given by the function g(x) = x2 + 46. After how many weeks, x, will they have the same amount of money? Explain how you arrived at your answer.

One way: Enter y1 = 60 + 5x and y2 = x2 + 46 into your graphing calculator and look at the Table of Values. Copy the Table of Values onto your paper (and explain that this is what you did).

WeekJohnSarah
165 47
270 50
375 55
480 62
585 71
690 82
795 95
8100 110
In seven weeks the amounts will be the same.

Second way: Solve the following quadratic equation: x2 + 46 = 60 + 5x

x2 + 46 - 60 - 5x = 0
x2 - 5x - 14 = 0
(x - 7)(x + 2) = 0
x = 7 or x = -2
Throw out -2 as irrelevant. In seven weeks the amounts will be the same.

28. If the difference (3x2 - 2x + 5) - (x2 +3x - 2) is multiplied by 1/2X2, what is the result, written in standard form.

The subtraction gives you 2x2 - 5x + 7. Times 1/2x2 gives x4 - 2.5x3 + 3.5x2.

29. Dylan invested $600 in a savings account at 1.6% annual interest rate. He made no deposits or withdrawals on the account for 2 years. The interest was compounded annually. Find, to the nearest cent, the balance in the account after 2 years.

Because it is only 2 years, you have your choice of using the compound interest formula (exponential growth) or using the simple interest formula, adding the interest and using the simple interest formula a second time on the new amount (the principal). The second method takes longer, but is good if you forgot the first formula.

The formula given in the reference table is overly complex -- it's like that because you'll need that one in the future. On the other hand, the example in question 17 in Part 1 is a better example to use.

(600)(1.016)2= 619.3536 = $619.35
Or (600)(1.016) = 609.60 and (609.60)(1.016) = 619.3536 = $619.35

30. Determine the smallest integer that makes -3x + 7 - 5x < 15 true.

-8x + 7 < 15
-8x < 8
x > -1
The smallest integer that makes this statement true is 0 (because it has to be greater than -1).

31. The residual plots from two different sets of bivariate data afe graphed below.

Explain, using evidence from graph A and graph B, which graph indicates that the model for the data is a good fit.

FOR MORE INFORMATION ABOUT RESIDUALS, CHECK OUT MY PREVIOUS POST ABOUT THE QUESTION FROM THE AUGUST 2014 REGENTS EXAM.

Basically, Graph A is a better model because the residuals are scattered about and there is no pattern to them. Graph B is not a good fit because the residuals form a pattern, which is sort of a curve. This can happen, for example, when a linear model (linear regression) is used but a quadratic regression would be better. (You don't need the last sentence -- only the part about why A is good and B is bad.)

32. A landscaper is creating a rectangular flower bed such that the width is half of the length. The area of the flower bed is 34 square feet. Write and solve an equation to determine the width of the flower bed, to the nearest tenth of a foot.

A = L * W = 34. L = 2W
(2W)(W) = 34
2W2 = 34
W2 = 17
W = SQRT(17) = 4.123105626 = 4.1 feet.

That's it for Part II. Hopefully, I'll have Part III up Sunday or Monday.
Happy Fathers Day to all your Fathers (and to you, too, if you are a Father).

15 comments:

Anonymous said...

For number 31 on the part two algebra one common core exam, i did everything else correctly on the test except this, so close to a hundred, but for this question, i wrote that graph B would be a better fit because it closely resembles a parabolic curve and can be closely modeled by a quadratic equation. Why isnt this correct, if there indeed is a pattern, couldn't it be modeled to then have a better correlation coefficient. Anyway, how many points will i get for this response. Thanks!

(x, why?) said...

Check the link in the post for the explanation. Remember that residuals are not the scatter plot, they are differences from the line of best fit. That line should roughly go through the middle, so points would be scattered equally on both sides, not mostly on one side.

Anonymous said...

OOOOOOOHHHHHHHHH I got it, thanks. By the way, will i recieve at least one credit for my response or no? Thanks Again! :D

(x, why?) said...

I have not seen the rubric, but generally if the answer is Yes/No or A/B, or something where there's a 50/50 guess, just guessing the right answer without the correct justification isn't worth anything.

Matt Southard said...

Will you being posting another part? & when are the grades given back to our teachers ?

Anonymous said...

Matt Southard, our teachers should be recieving our grades by the 26th, or next week :)

(x, why?) said...

I hope to post more, but I have been putting in overtime grading Regents exams (17 hours at that, so far) and people are asking about all FOUR math exams that were given this week.

I've only seen two of them, and I don't post Algebra 2 because I haven't taught it, so my explanations might be a little off for some of the material. Generally, I only post the Alg 2 questions that I think my freshmen could handle.

Anonymous said...

For question 32, if i put the number 4.123105626 feet as the answer for my width will i still recieve full credit even though i didn't round to 4.1 feet?

Anonymous said...

A quick note about number 28: I factored out an X^2 from my final answer and lost a point :( Remember to never factor you answer if it states to leave in in standard form!

Anonymous said...

Although you got 4.123105626 feet, which is technically the correct answer, the directions clearly stated to round to the nearest tenth. Because it was stated in the directions, you would lose one point.

Anonymous said...

when is part 3 being posted?? i really need it!

Anonymous said...

Thank you, Mr. Burke for doing all of this work. NYS has not yet released the exam to the public on its site, http://www.nysedregents.org/algebraone/. I appreciate the time that you have spent doing this. I hope that you get some well-deserved rest next week.

Anonymous said...

thank you for doing this for our understanding

Anonymous said...

Thank you for every thing

Anonymous said...

thanks!! number 27 really helped. especially with the graph