June 2016 Integrated Algebra Regents, Part IV

On June 2, 2016, New York State gave a special Integrated Algebra Regents exam, which only seniors and "super seniors" were eligible to take. Those were the students who entered high school prior to the implementation of Common Core. This test follows the older curriculum.

I am currently scoring exams, and while I cannot talk about that specifically, I do have a copy of the questions. The work you see below is mine, written on photocopies of the pages that they gave me for scoring purposes.

A cleaner, fuller (and possibly more clear) explanation of the problems may come at a future date. However, this is likely the last time that this test will be administered. Then again, they have said that before.

Part IV

All questions in this section were open-ended and worth 4 points. A computational, graphing or rounding error cost 1 point. A conceptual error (e.g., using the wrong formula) cost 2 points.

37. On the set of axes below, solve the following system of equations graphically for all values of x and y. State the coordinates of all solutions.

y = x² - 4x - 5
y + 3x = 1

You can put the first equation in your graphing calculator to get the table of values for the parabola.
To put the linear equation into the calculator, you first had to subtract 3x from both sides of the equation. This gives you y = -3x + 1.

The graph is shown below. The points of intersection are (-2, 7) and (3, -8).

See image below:

38. Express in simplest form: (x² + 5x + 6)/(x² - x - 12) : (x² + x - 6)/(2x - 10)

First, flip over the second fraction and change the problem to a multiplication problem.

I worked out the rest on the test paper. This is too complicated for markup language.
Either answer is acceptable: the factored answer or the multiplied answer.

See image below:

39. The length of a rectangle is (3*SQRT(8) + 2) and the width is (2*SQRT(2) + 3).
Express the perimeter of the rectangle in simplest radical form.
Express the area of the rectangle in simplest radical form.

A few notes, and then I'll leave the work to the image.
Perimeter is 2L + 2W or 2(L + W).
Area is L * W.
SQRT(8) is simplest radical form is SQRT(4*2) = SQRT(4)*SQRT(2) = 2*SQRT(2).
Terms with SQRT(2) in them can be added just as terms with 'x' could.

See image below:

How did you do?

Any questions?

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If anyone in Brooklyn is looking for an Algebra or Geometry Regents Prep tutor, send me a note. I have a couple of weekly spots available between now and June.