Monday, June 22, 2015

New York State Algebra I (Common Core) Regents, June 2015 Parts 3 and 4

Here is Part 3 of the Algebra 1 Common Core Regents exam. Here are the links to Part 1 and Part 2.

Part 3

33. Albert says that the two systems of equations shown below have the same solutions.

8x + 9y = 48
12x + 5y = 21
8x + 9y = 48
-8.5y = -51

Determine and state whether you agree with Albert. Justify your answer.

Solve the second system first. If -8.5y = -51, then divide and get y = 6. Then 8x + 9(6) = 48.

8x + 54 = 48
8x = -6
x = -0.75

Substitute these numbers into the first system: 12(-0.75) + 5(6) = 21 ?

-9 + 30 = 21 (?)
21 = 21 (check)

Albert was correct.
Don't forget to say that Albert was correct even though there is NO CREDIT for saying he is correct without the justification.

34. The equation to determine the weekly earnings of an employee at the Hamburger Shack is given by w(x), where x is the number of hours worked.

Determine the difference in salary, in dollars, for an employee who works 52 hours versus one who works 38 hours.
Determine the number of hours an employee must work in order to earn $445. Explain how you arrived at this answer.

This is how overtime generally works in the real world.
The 38 hour employee earned $380. (38 * 10)
The 52 hour employee earned $400 + 12 * 15 = $580. The difference is $200.

In order to earn $445, they need to work 40 hours, earning $400, and then another $45, which at $15/hour is three more hours, for a total of 43 hours.

35. An online electronics store must sell at least $2500 worth of printers and computers per day. Each printer costs $50 and each computer costs $500. The store can ship a maximum of 15 items per day. On the set of axes below, graph a system of inequalities that models these constraints.

Determine a combination of printers and computers that would allow the electronics store to meet all the constraints. Explain how you obtained you answer.

First, the inequalities you need to graph are:

p + c < 15
50p + 500c > 2500

The graph looks like this:

Possible combinations that would work would be, for example, 0 printers and 5 computers, or 10 printers and 4 computers.

36. An application developer released a new app to be downloaded. The table below gives the number of downloads for the first four weeks after the launch of the app.

Write an exponential equation that models these data.
Use this model to predict how many download the developer would expect in the 26th week if this trend continues. Round your answer to the nearest download.
Exponential regression, which can be done in the calculator.
Since I don't have one handy, I can see that it increases by 60, 90, 135 ... which increasing by half, so an equation could be
y = 120(1.5)^(w-1)

Using that formula, on the 26th week, there would be 3030140 downloads (rounded).

Using that formula, on the 52nd week, there would be 1.15 X 10^11 downloads, which is not a reasonable number because it is more than the number of people on the planet to begin with, all of whom, by this point, would have already downloaded it.

I'm curious if anyone is going to explain that apps die out after a few months and wouldn't keep growing.

Part 4

This question is worth 6 credits.

37. A football player attempts to kick a football over a goal post. The path of the football can be modeled by the function h(x) = -1/225 x2 + 2/3 x, where x is the horizontal distance from the kick, and h(x) is the height of the football above the ground, when both are measured in feet.

On the set of axes below, graph the function y = h(x) over the interval 0 < x < 150.

Determine the vertex of y = h(x). Interpret the meaning of this vertex in the context of the problem.

The goal post is 10 feet high and 45 yards away from the kick. Will the ball be high enough to pass over the goal post? Justify your answer.

The graph looks like the one below. Put the equation in your calculator and check the Table of Values. Note that your graphing calculator defaults to showing from -10 to +10, not 1 to 150, so you won't see it unless you change the display settings. Also, be careful about entering the equation. I entered "255" instead of "225" the first time and you can see the erasures. I didn't realize my mistake until I noticed that 75 wasn't the vertex, which I reasoned it should be.

The vertex of y=h(x) is (75, 25), which means that at 75 feet away from the kicker, the ball will reach a maximum height of 25 feet and start descending.

At 45 yards, or 135 feet, the ball will be 9 feet of the ground (135, 9), so it will not pass over the goal post, which is 10 feet high.

That's it for this test. Finally complete. Except for some illustrations, which will be added when they are available.

21 comments:

Anonymous said...

By any chance will integrated geometry from Friday be up today??

Karrina said...

Lol i'm dying for you to grade Geometry forget algebra

(x, why?) said...

I'm grading Geometry today, so I have the test.
I can scan in my answers for the open-ended later today (or this evening). I don't know how long it will take me to type up the multiple-choice questions.

Anonymous said...

Thank you so much for posting these! You probably don't know, but I was wondering of you knew of anyone who posts answers to science regents?

Anonymous said...

For 36 I said that the app wouldn't have the same popularity in a year. Do you think I'll receive credit?

Anonymous said...

WHen will you be posting the answers to the algebra 2 trig regents?

Anonymous said...

When will the geometry multiple choice be up?

carlito said...

Hah, I used the exponential regression function on the TI 83 and it gave me: 80(1.5)^x. It checked out.

Anonymous said...

Can u scan the geometry answers tonight

Anonymous said...

Is a 92 a good grade for this regent

Anonymous said...

Hi.. Do you know the password for the "protected" document pdf file on nysedregents test has The regents exams protected. Also, if not , do u know when they will no longer be protected ?? By the way, this is for GEOMETRY. Also, will u be posting the answers for the geometry regents examination ??

Anonymous said...

For number 36, I said no because the number would be so large that it would be meaningless. Will I receive credit?

(x, why?) said...

I'm sure whoever is grading it will accept that answer.

Anonymous said...

aw i got a 92 by stupid mistakes, couldve gotten that 100%!

Anonymous said...

Me too! It was the highest grade in my school lol

Anonymous said...

for number 35, if you graphed the second inequality with the slope of -1/10 as a positive slope, how many credits would you get off?

and if my combination of numbers would be 4 printers and 8 computers, would that work?
and if i didnt explain how i obtained my answer, how many credits would i get off?

Anonymous said...

by 35 is a combination of 11 printers and 4 computers correct? because 11+4 is less then or equal to 15 an if you put it in the equation you get 2550 which is greater then or equal to 2500

Anonymous said...

For Part IV, how many points would you het out of six if you got the graph and the vertex right? I got the part asking about whether the ball will go over the post wrong though, so is that 4/6 in total?

(x, why?) said...

1. Yes, 11+4 will work. I gave two examples. Anything from the Shaded area or on the lines will work. Sorry, I should have been clearer that those were examples, not the only answers.

2. Graphing the line with the wrong slope (e.g., +1/10 instead of -1/10) is a graphing error with a loss of one point. Generally speaking one graphing or calculating errors is -1, 2 or more is -2. A conceptual error (graphing lines instead of inequalities, graphing broken lines instead of solid lines, graphing a parabola somehow) loses half credit for the problem.

(x, why?) said...

Re Part IV: I didn't grade this exam, so I didn't see the rubric. If you have the graph and the vertex question right, I can't see you getting less than 4 out of 6. I don't know if the last part was worth 1 point or 2.

If you did any work for it, but got a wrong answer, you might've gotten partial credit, depending upon the error.

So probably 4 or 5 out of 6.

◆アササテシ♪★ said...

I got 100 :) Just found out today from an email I received from my teacher!