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June 2010 Integrated Algebra Exam Part II

June 19, 2010 pm30 7:25 pm

31. Alexis calculates the surface area of a gift box as 600 square inches. The actual surface area of the gift box is 592 square inches. Find the relative error of Alexis’ calculation expressed as a decimal to the nearest thousandth.

Error = \frac{measured - actual}{actual} so in this case \frac{600 - 592}{592} ≈ 0.014

Deduct a point if you used 600 as the divisor, deduct a point if you misrounded (that’s not exactly how teachers figure it, but works out more or less the same)

32. Perform the indicated operation:    -6(a – 7)

State the name of the property used.

-6a + 42
Distributive

Count them as 1 point each.

33. See photo.
Label the angle (I’m calling it B).  sinB = 30/50, so B = sin^{-1}(\frac{30}{50}), or B ≈ 37

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29 Comments leave one →
  1. Anonymous permalink
    June 19, 2010 pm30 7:59 pm 7:59 pm

    #31
    What do you mean by: “(that’s not exactly how teachers figure it, but works out more or less the same)”?

    • June 20, 2010 am30 10:54 am 10:54 am

      The State does not assign point values to the steps in each problem. It’s a clumsy, ham-fisted attempt to introduce some sort of standards-based or holistic grading. Instead, we get rubrics (rubrics? what kind of name is that for a scoring guide? blyecch) that look like this:

      (2) 0.014 and appropriate work is shown
      (1) one computational error is made, but appropriate work is shown
      (1) one conceptual error is made, but appropriate work is shown
      (1) appropriate work is shown, but the error is rounded incorrectly
      (1) the ratio is correctly set up, the values are correctly substituted, but the error is not calculated
      (0) 0.014 and no work is shown
      (0) response is incoherent or unrelated to the question

      And then we sort of guess how each kid’s paper fits. BTW, I haven’t read the key for this question – I don’t know how close what I just typed is to the real thing. But probably pretty close.

      • Anonymous permalink
        June 21, 2010 pm30 2:16 pm 2:16 pm

        do you need to label like .014 IN SQ is the relative error? i forgot to do that, would i get a point off??

        • suffolk teacher permalink
          June 22, 2010 pm30 8:47 pm 8:47 pm

          if you label the relative error of .014 in square inches the state rubric says to take off 1 point

  2. Anony permalink
    June 19, 2010 pm30 8:17 pm 8:17 pm

    PART 3 AND 4 PLEASE!!!! :)

  3. random permalink
    June 19, 2010 pm30 8:20 pm 8:20 pm

    shit, so far i got a 50 raw score, 78 score. im upset. i could’ve done better. i got silly mistakes on the multiple choice. :(

  4. Anonymous permalink
    June 19, 2010 pm30 8:28 pm 8:28 pm

    y u so slow

  5. pbpcbs permalink
    June 19, 2010 pm30 9:01 pm 9:01 pm

    “Relative error” does have an interpretation problem. According to the official NYS document (http://www.emsc.nysed.gov/ciai/mst/math/glossary/glossaryHS.doc), relative error is defined as:

    ——————–
    relative error (A) The ratio of the absolute error in a measurement to the size of the measurement; often written as a percent and called the percent of error; the absolute error is the difference between an approximation and the exact value.
    ——————–

    So, since any measurement is, by definition, an approximation, and applying the definition of relative error to this problem, you ratio abs(600-592) to 600, and you get .013 rounded.

    On the one hand, this interpretation is echoed in Prentice-Hall, p. 170. In PH, they take the maximum measurement error due to rounding and divide it by the measurement to generate what they call percent of error (which, by definition is 100 times relative error).

    On the other hand, the various A.M.3 problems on past IA tests have consistantly used the “accurate” value in the denominator to generate “relative” error with the instructions that using the measured value should be considered a conceptual error.

    On the third hand (who let an economist into this discussion?), Dr. Math has an extensive discussion (http://mathforum.org/library/drmath/view/65797.html) whose bottom line is that both are imprecisely called relative error and it’s potentially very confusing unless you specify what you are looking for (cue U2 music).

    • June 19, 2010 pm30 9:04 pm 9:04 pm

      Funny, I felt uneasy as I typed that up. Thanks for backing up my gut.

      And you still read this stuff? Wow!

      • random permalink
        June 19, 2010 pm30 9:10 pm 9:10 pm

        so is it 0.013 or 0.014?? was approximately 0.014 ok to rite down? o.O

        • Anonymous permalink
          June 19, 2010 pm30 9:55 pm 9:55 pm

          i wrote .014

  6. pbpcbs permalink
    June 19, 2010 pm30 9:16 pm 9:16 pm

    I’ve had a problem with the “relative error” PI for a long time. My engineering training was that relative error ties to precision (measured value in the denominator) and absolute error ties to accuracy (God-given value in the denominator). PH echos this. Since this is the textbook for many of our students, I believe that dividing by 592 and 600 have to both be accepted for full credit, especially in schools where PH is the textbook.

  7. Anonymous permalink
    June 19, 2010 pm30 9:52 pm 9:52 pm

    ‘put up part 3

  8. Anony permalink
    June 19, 2010 pm30 10:07 pm 10:07 pm

    WHERE R THE OTHER PARTS? HURRRY!!!

  9. Anonymous permalink
    June 19, 2010 pm30 11:07 pm 11:07 pm

    is 56 raw score out of 33 good?

  10. qwert permalink
    June 19, 2010 pm30 11:09 pm 11:09 pm

    I did 1.035 9 i times it by a hundred is that ok

  11. Anonymous permalink
    June 19, 2010 pm30 11:15 pm 11:15 pm

    I think it’s time for NYS to phase these exams out again. This has by far been the most controversial Math Regents Administration I have ever witnessed. Why don’t they just do what other states do and have a regular Algebra-Geometry-Trig sequence? The curriculum is imbalanced and the Regents are inaccurate. A regular system like the ones in most other states would be much better.

    I know, “student accountability” needs to be measured. I am NOT saying that they should do away with the Regents. I just think it’s time for some MAJOR reformatting of the curriculum and exams.

    • June 20, 2010 am30 10:57 am 10:57 am

      I disagree that this administration has been controversial.

      I strongly agree that it is time to phase these exams out. They have no value for our students or our schools. They distort our teaching (to bad tests).

      They need to strongly rethink why we test at all. Why do we give each exam? Right now, the only honest answer is because that’s what we’ve done.

      • Anonymous permalink
        June 20, 2010 pm30 1:22 pm 1:22 pm

        When I said controversial, I was referring to the Algebra II/Trig administration. I was talking about the three exams holistically, not just this one.

  12. Anony permalink
    June 20, 2010 am30 12:00 am 12:00 am

    yeah this test was all messed up. no one knows whos right and wrong.

  13. anonymous permalink
    June 20, 2010 am30 11:18 am 11:18 am

    what if you did actual-measured/ measured and still got the answer right
    will you get points off?

    • Anonymous permalink
      June 20, 2010 pm30 1:21 pm 1:21 pm

      To me, that sounds like a point off.

    • Anonymous permalink
      June 21, 2010 pm30 2:15 pm 2:15 pm

      yes you will, you wouldnt if it was mult choice but the whole point of part 2 is to show your work. how would you have gotten the right answer for that anyway unless you cheated??

  14. Anonymous permalink
    June 20, 2010 pm30 4:43 pm 4:43 pm

    what happens if you used Pythagorean theorem to solve #33 & got 40 as an answer? i dont get it, if that problem could be solved using both ways how was there 2 different answers & would my answer be counted as wrong?

    • Nick permalink
      June 20, 2010 pm30 7:08 pm 7:08 pm

      To find an angle measurement using trigonometry, u need to use the ratio to -1.

      i.e:(sin-1;tan-1;cos-1

      • Nick permalink
        June 20, 2010 pm30 7:11 pm 7:11 pm

        Then, u Wouldnt get ANY points because u have an incorrect math statement of using the theorum to find an angle AND u got the answer wrong…so yea but u only lose two points, that’s good

  15. Anonymous permalink
    June 21, 2010 pm30 4:05 pm 4:05 pm

    umm no actually i got the answer right..i understand what i did was wrong now, i didnt get it before but someone explained it to me, so yeah thanks. i didnt realize it asked for the angle, not the missing side, therefore i used p. theorem instead of trig. but, i still solved it correctly so i should still get partial credit but yeah. oh well.

  16. Anonymous permalink
    June 21, 2010 pm30 4:06 pm 4:06 pm

    actually she wasnt completely wrong…she still used pythag. theorem correctly to solve for a missing side, she just got it mixed up with trig. simple mistake. no worries

  17. Elleinad permalink
    January 28, 2013 pm31 9:54 pm 9:54 pm

    oElleinad
    Isn’t the answer to question #31 1.351? I got that answer by using the formula difference over actual number is equal to percent over 100, and then I crossed multiplied and rounded. If I’m wrong, can you please explain to me why your formula is different than the one I learned.

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