June 2017: Common Core Algebra Regents, Part 2

The following are the questions and answers (and commentary) for part of the New York State Algebra Regents exam. If you have any questions or comments (or corrections), please add them in the Comments section.

My apologies for typos, particularly if they are in the questions, because then the answers are subject to change.

Answers to Part III can be found here.

June 2017, Algebra I (Common Core), Part II

25. Express in simplest form: (3x² + 4x - 8) - (-2x² + 4x + 2)

5x² - 10.
Show something on the paper to indicate where you got this: line them up vertically; distribute the "-1" and combine like terms. Something, so you'll be sure to get both points. (Frankly, this is the kind of question that you should be able to do without showing any work. It can all be done in your head.)

26. Graph the function f(x) = -x² - 6x on the set of axes below.
State the coordinates of the vertex of the graph.

See the graph below. The vertex is at (-3, 9). You need to state the point and have a correct graph to get both points.

27. State whether 7 - SQRT(2) is rational or irrational. Explain your answer.

It is irrational because 7 is rational and SQRT(2) is irrational and the sum or difference of a rational and an irrational number is always irrational.

28. The value, v(t), of a car depreciates according to the function v(t) = P(.85)^t, where P is the purchase price of the car and t is the time, in years, since the car was purchased. State the percent that value of the car decreases by each year. Justify your answer.

The car's value decreases by 15% each year because 1.00 - .85 = .15, which is 15%.

29. A survey of 100 students was taken. It was found that 60 students watched sports, and 34 of these students did not like pop music. Of the students who did not watch sports, 70% liked pop music. Complete the two-way frequency table.

	Watch Sports	Don't Watch Sports	Total
Like Pop
Don't Like Pop
Total

Answer: see table below
Because 60 of 100 watched sports, then 40 did not, so the bottom row is 60, 40, 100.
Of 60, 34 did not like pop, so 26 did. First column is 26, 34, 60.
TWIST -- they used percentages in the next portion of the question.
Of the 40, 70% liked pop music. (.70)(40) = 28, and 40 - 28 = 12.
The second column is 28, 12, 40.
Add the totals for each row. Last column is 54, 46, 100.

	Watch Sports	Don't Watch Sports	Total
Like Pop	26	28	54
Don't Like Pop	34	12	46
Total	60	40	100

30. Graph the inequality y + 4 < -2(x - 4) on the set of axes below.

See graph below.

If you recognize point-slope form then you know that the slope of the boundary (broken) line is -2 and (4, -4) is a point on that broken line.

If you didn't recognize that, you could subtract 4 from each side and put

y = -2(x - 4) - 4
into your graphing calculator, and get the table of values.

Or use the Distributive property and created your own table from the following:

y < -2(x - 4) - 4
y < -2x + 8 - 4
y < -2x + 4

31. If f(x) = x² and g(x) = x, determine the value(s) of x that satisfy the equation f(x) = g(x).

Substitute x² = x
Subtract x² - x = 0
Factor x(x - 1) = 0
Find the zeroes: x = 0 or x - 1 = 0, so x = 0 or x = 1.

32. Describe the effect that each transformation below has on the function f(x) = |x|, where a > 0.
g(x) = |x - a|
h(x) = |x| - a

g(x) will shift f(x) a units to the right.
h(x) will shift f(x) a units down.
Both graphs will have the same shape.

End of Part II

How did you do?
Comments, questions, corrections and concerns are all welcome.
Typos happen.