January 2016 New York Algebra I (Common Core) Part 2

Below are the questions with answers and explanations for Part 2 of the Algebra I (Common Core) Regents exam for January 2016. The multiple-choice questions appeared in a previous post. The rest of the questions will appear in a later post.

As always, in order to get this thread up quickly, the images have been omitted. They will be added at a later date.

Each question in Part 2 is worth 2 credits, for a total of 16 credits. Partial credit will be given. Basically, you can have one computational, conceptual, graphing or rounding error, but as long as you have a consistent answer, you can still get a point. Two different mistakes, and there is no credit for the answer.

January 2016 Algebra 1 (Common Core) Regents, Part 2

25. The function, t(x) is shown in the table below. (image omitted)
Determine whether t(x) is linear or exponential. Explain your answer.

The function t(x) is linear because the slope is consistent. Take any pair of points and you will find the slope is -2.5/2 or -1.25. Use a couple of pairs of points as examples to prove your point.

If you're curious, the function is t(x) = -1.25x + 6.25, but that isn't necessary for the question. In fact, that answer isn't any good unless you had the work to back it up.

26. Marcel claims that the graph below represents a function. (image omitted)
State whether Marcel is correct. Justify your answer.

Marcel is incorrect. It is not a function because when the graph does not pass the vertical line test. The line x = 2 goes through two points on the graph. Both are closed circles.

27. Solve the equation for y.

(y - 3)² = 4y - 12

Square the binomial: y² - 6y + 9 = 4y - 12
Move everything to the left: y² - 10y + 21 = 0
Factor: (y - 7)(y - 3) = 0
solve y = 7 or y = 3.

You could have also completed the square or used the quadratic formula after putting it in standard form. If you made one computational error, but continued until the end and gave an answer, you would've gotten one point.

28. The graph below shows the variation in the average temperature of Earth's surface from 1950-2000, according to one source. (image omitted)
During which years did the temperature variation change the most per until time? Explain how you determined your answer.

The largest change was between 1960 and 1965 when the slope of the graph was -.15/5. It is the steepest part of the graph. The increase from 1975 to 2000 is a constant .1/5.

Be careful with the fractions and decimals. I just typed them incorrectly, but I caught the mistake before I posted them. (Had the decimal point in the wrong position.)

29. The cost of belonging to a gym can be modeled by C(m) = 50m + 79.50, where C(m) is the total cost for m months of membership.

State the meaning of the slope and y-intercept of this function with respect to the costs associated with the gym membership.

It costs $79.50 to joint the gym. That is a one-time fee that you pay even if you go for zero months. $50 is the monthly fee, which is paid for the number of months, m.

Note that this was just a definition question with nothing to work out. Common Core is doing a lot of that.

30. A statistics class surveryed some students during one lunch period to obtain opinions about television programming preferences. The results of the survey are summarized in the table below. (image omitted)
Based on the sample, predict how many of the schools 351 males would prefer comedy. Justify your answer.

70 out of (70 + 35) males preferred comedy. That is 70/105 or 2/3.

Multiply (2/3)(351) = 234 males.

31. Given that a > b, solve for x in terms of a and b.

b(x - 3) > ax + 7b

Follow the steps:

bx - 3b > ax + 7b
bx > ax + 10b
bx - ax > 10b
x(b - a) > 10b
x < 10b/(b - a)
Because a > b, that makes (b - a) a negative number, and when you divide by a negative number, the inequality symbol has to flip around.
(Also, since a > b, (b - a) cannot equal zero, so it is okay to divide by it.)

32. Jacob and Jessica are studying the spread of dandelions. Jacob discovers that the growth over t weeks can be defined by the funtion f(t) = (8)*2^t. Jessica finds that the growth function over t weeks is g(t) = 2^t+3.

Calculate the number of dandelions that Jacob and Jessica will each have after 5 weeks.

Based on the growth from both function, explain the relationship between f(t) and g(t).

f(t) = 8(2)⁵ = 8(32) = 256.
g(t) = 2⁵⁺³ = 2⁸ = 256.

Based on the growth, the two functions are the same.
This is because g(t) = 2^t+3 = 2^t * 2³ = 2^t * 8 = f(t).

I'll be honest here. I have no clue what they are going for in this last question. Based on only one data point, you can only conclude that the are the same function for that one input. It isn't enough to say the functions are the same. It is easy to prove that they are the same (as I showed above) but that isn't what they asked.

End of Part 2
How did you do?