June 2019 Algebra I Regents Parts 3 & 4

The following are some of the multiple questions from the June 2019 New York State Common Core Algebra I Regents exam.

June 2019 Algebra I, Part III

Each correct answer is worth up to 4 credits. Partial credit can be given. Work must be shown or explained.

33. A school plans to have a fundraiser before basketball games selling shirts with their school logo. The school contacted two companies to find out how much it would cost to have the shirts made. Company A charges a $50 set-up fee and $5 per shirt. Company B charges a $25 set-up fee and $6 per shirt.

Write an equation for Company A that could be used to determine the total cost, A, when x shirts are ordered. Write a second equation for Company B that could be used to determine the total cost, B, when x shirts are ordered.

Determine algebraically and state the minimum number of shirts that must be ordered for it to be cheaper to use Company A.

Answer:
Write equations from each verbal expression.
A = 5x + 50
B = 6x + 25
To find when A is less than B, start with A < B and then substitute and solve.

A < B
5x + 50 < 6x + 25
-x < -25
x > 25

The number of shirts must be more than 25, so the minimum number of shirts is 26.

34. Graph y = f(x) and y = g(x) on the set of axes below.

f(x) = 2x² - 8x + 3
g(x) = -2x + 3
Determine and state all values of x for which f(x) = g(x).

Answer:
A parabola and a line will intersect at either one or two points. If it's two, you have to make sure you have them both on your graph.
Label which line is which, even if it's "obvious".
Label the points of intersection.
Answer the question, supplying only the values of x (not f(x) or g(x)).

Check the graph:

The values of x for which f(x) = g(x) are 0 and 3.
Do NOT write (0, 3), which looks like a point on the graph, or an interval. Neither would be a correct answer.

35. The table below shows the number of hours ten students spent studying for a test and their scores.

Write the linear regression equation for this datq set. Round all values to the nearest hundredth.

State the correlation coefficient of this line, to the nearest hundredth.

Explain what the correlation coefficient suggests in the context of the problem.

Answer:
Enter the data into two lists, L₁ and L₂.
Make sure DiagnosticOn has been set. (If you don't know, just do select it from the Menu.)
Press STAT to get to the statistics menu and arrow over to CALC. Choose option 4, LinReg(ax+b).
You will get a = 7.79, b = 34.27 and r = .98, rounded to the nearest hundredth.

The linear regression is y = 7.79x + 34.27

The correlation coefficient is r = 0.98

In the context of this problem, the correlation coefficient suggest a strong positive correlation between the number of hours spent studying and test scores.
(It's not enough to just say that it's a strong positive correlation.)

36. A system of inequalities is graphed on the set of axes below.

State the system of inequalities represented by the graph.

State what region A represents.

Answer:
Working backward, you need to find the slope and y-intercept of each of the lines.
Note that the line with the negative slope is broken, so it is not equal. Also, note that both lines are shaded below, so you need to use less than, or less than or equal to.

The broken line has a slope of -3 and a y-intercept of 3, so
y < -3x + 3
The solid line has a slop of 2 and a y-intercept of -2, so
y < 2x - 2

Region A represents the solution to the system of inequalities.

The entire gray region represents the values of y that are less than -2x - 2 only.

August 2018 Algebra I, Part IV

A correct answer is worth up to 6 credits. Partial credit can be given. Work must be shown or explained.

37. When visiting friends in a state that has no sales tax, two families went to a fast-food restaurant for lunch. The Browns bought 4 cheeseburgers and 3 medium fries for $16.53. The Greens bought 5 cheeseburgers and 4 medium fries for $21.11.

Using c for the cost of a cheeseburger and f for the cost of medium fries, write a system of equations that models this situation.

The Greens said that since their bill was $21.11, each cheeseburger must cost $2.49 and each order of medium fries must cost $2.87 each. Are they correct? Justify your answer.

Using your equations, algebraically determine both the cost of one cheeseburger and the cost of one order of medium fries.

Answer:
Browns: 4c + 3f = 16.53
Greens: 5c + 4f = 21.11

Check by putting it into each equation. Stop if one if incorrect.
4(2.49) + 3(2.87) = 16.53?
18.57 =/= 16.53
The Greens are incorrect.

Notice that they ask you to find c and to find f. They don't ask you to find (c + f), which would have be trivial -- just subtract the two equations.

Now that I wrote that, I want to try something that I normally wouldn't do. It's a little extra work, but it uses smaller numbers and I like smaller numbers.

5c + 4f = 21.11
4c + 3f = 16.53
c + f = 4.58
(3)(c + f) = (4.58)(3)
3c + 3f = 13.74

4c + 3f = 16.53
3c + 3f = 13.74
c = 2.79
2.79 + f = 4.58
f = 1.79

By subtracting, I found the cost of 1c + 1f, which I could then multiply by three to solve the system of equations. Normally, I wouldn't do it that way, but it was something I noticed -- Number Sense to the rescue! And that saved me from doing it the following way, by finding Least Common Multiples:

4c + 3f = 16.53
5c + 4f = 21.11
(4)(4c + 3f = 16.53)
(3)(5c + 4f = 21.11)
16c + 12f = 66.12
15c + 12f = 63.33
c = 2.79

4(2.79) + 3f = 16.53
3f = 5.37
f = 1.79

End of Exam

How did you do?

Questions, comments and corrections welcome.