June 2016 Integrated Algebra Regents, Part II

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 II

All questions in this section were open-ended and worth 2 points.

31. Jim calculated the area of a triangle to be 51.75 cm². The actual area of the triangle is 53.24 cm². Find the relative error in Jim's calculation of the area to the nearest thousandth.

Relative error is defined as the difference between the two amounts divided by the actual amount. Write the answer as a decimal. Do NOT convert to a percent.

53.24 - 51.75 = 1.49.
1.49 / 53.24 = 0.028 to the nearest thousandth. (Not rounding correctly will cost you one of the two points.)

See image below:

32. A 12-foot ladder is placed against a wall. The ladder makes an angle of 73^o with the floor. Determine, to the nearest tenth of a foot, how high up the wall the ladder will reach.

You are given the hypotenuse and you are looking for the side opposite the given angle. That means that you need to use sine, which is opposite / hypotenuse.

sin 73 = x / 12
So 12 * sin 73 = x. You can put this in your calculator, which must be in degree mode.

x = 11.5, to the nearest tenth. Again, correct rounding is important.

Using the wrong trig function will cost you half credit (one point). Two mistakes mean 0 credits.

See image below:

33. On the sets of axes below, draw the graph of the function y = 3^x. Include the interval -2 < x < 2.

You can make a table of values or just plot points to show your work: (2, 9), (1, 3), (0, 1), (-1, 1/3), (-2, 1/9). The last two would be approximate to graph. This is to be expected. You might want to label them, but the rubric didn't say it was required.

Draw the curve through the points.

See image below:

How did you do?

Any questions?

---

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.