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NYS Algebra 2 Regents June 2011 – bad inverse question

June 21, 2011 pm30 9:55 pm

32. If f(x) = x^2 - 6 find f^{-1}(x).

What do you think?  Horrible?  It was a two point question, and an answer of f^{-1}(x) = \sqrt{x+6} earned 1 point. What answer were they looking for?

I have no confidence in New York State’s ability to create a good test of mathematics, at any level.

52 Comments leave one →
  1. doug permalink
    June 21, 2011 pm30 10:13 pm 10:13 pm

    The first thing I thought was, “Hey, that doesn’t even have an inverse (unless you restrict the domain)!” (Yes, I think in parentheses sometimes.)

    The second thing I thought was, “I wonder what jd2718 will make of this?”

    I do remember the 2-point answer in the scoring guide including plus-or-minus. Making this a two point question suggests that whoever wrote (and approved) that question cared more about students following a specific procedure (“Swap x and y, then solve for y”) than students understanding the math (Why not just make it a cubic instead of a quadratic?).

    (By the way, whatever you typed as the 1 point answer shows up as “Formula does not parse” in red text with yellow highlighting. )

    • June 21, 2011 pm30 10:28 pm 10:28 pm

      I forget the “t” in “sqrt” – thanks for the alert.

      Even better, this is from a listserve:

      I called the state today about question #32. I told the woman that by definition, for a function to be invertible it must be 1-1. Her response was that every function has an inverse, it just that every inverse is not necessarily a function. She said that the inverse could just be a relation. I told her that she was wrong and then quoted her a definition that says that a function is invertible if and only if it for every input there is exactly one corresponding output value. I then said that it was only invertible only if we restrict the domain to all value greater than or equal to zero, or all values less than or equal to zero. It the domain is restricted in this way, the student shouldn’t write positive or negative. She said that they can receive full credit if they only stated the positive solution, given that they explained that they restricted the domain to make it 1-1. I asked her why did I have to expect so much from the kids when a bunch of adults who made the!
      exam, didn’t make that distinction? She told me that i wasn’t going to win the argument.

      • June 22, 2011 am30 9:37 am 9:37 am

        Who the heck is proof reading these tests. I called the state and am awaiting their return call. It is the opinion of our department that #19 is also invalid, as there is no correct choice since none of the choices is a function. It is impossible to understand how we, as mathematicians, beat definitions into the kids’ heads and the state seems to think that they can redefine established terms. As a matter of fact, as a trick question on some of our local tests we intentionally ask for the inverse of a non 1-1 function to see if the kids recognize that the the question has no answer.

        • yelnats permalink
          June 22, 2011 pm30 11:06 pm 11:06 pm

          The test makers are owned by the same guys who assigned AAA ratings to subprime mortgage backed securities.

  2. June 21, 2011 pm30 10:21 pm 10:21 pm

    The question is an embarrassment. The solution is a demonstration of profound mathematical ignorance by the exam writers and reviewers.

    Several of the multiple choice questions were bad, as well, but this was the worst.

    • June 21, 2011 pm30 10:29 pm 10:29 pm

      I’ll post 16 later. It’s the one with two correct answers. Apparently the State caught THAT mistake after printing but before mailing them out.

  3. June 21, 2011 pm30 10:29 pm 10:29 pm

    My second least favorite was the “which graph is not a function” (the one with the step functions and 1/x and tan(x)) – because I know we’re supposed to assume those were the graphs of 1/x and tan(x) – but the way they drew them made them look like they had vertical regions – why would a kid assume a particular function? It really looked like three of them were not functions, and you only had the graphs to go by.

    • June 21, 2011 pm30 10:30 pm 10:30 pm

      As I solved the exam (out loud, with kids sitting with me) I said “I bet they mean these to line up…”

      I have no confidence in NY State’s ability to write a good mathematics exam, on any level.

      • June 21, 2011 pm30 11:21 pm 11:21 pm

        Meanwhile, we had the students put their answers on Scantron sheets, not knowing about the mistake on #16. We had to leave that question off the answer sheet and check each scantron manually.

  4. June 21, 2011 pm30 10:48 pm 10:48 pm

    Personally, the “Find the value of x in the equation” questions really irritate me. Since x is a variable, it has no value. What they obviously want, but for some reason don’t say, is the value of x that satisfies the equation. Is that so hard?

    I can’t believe they are going to stand behind this “All functions have inverses” argument.

    • June 21, 2011 pm30 10:52 pm 10:52 pm

      Call in tomorrow. The Math B Circle question, remember that? At first they said no to everyone who called, but eventually they yielded.

      But the arrogance without knowledge is mind-blowing. Not knowing math bothers me, but insisting that they do?

    • June 21, 2011 pm30 11:08 pm 11:08 pm

      For the record, the (dubious) argument that some function inverses are relations is not applicable here as the question asks for f^{-1}(x) , which implies that the inverse is a function as it is expressed in function notation.

      • Bpeled permalink
        June 22, 2011 am30 7:49 am 7:49 am

        Exactly. Which is the same thing for the cos^-1 question (# 19). Inverse cos is a well-defined function with a well defined (and limited!) domain and range! None of the graphs they showed was the graph of inverse cos — not one! Who vets these tests?

  5. June 21, 2011 pm30 10:52 pm 10:52 pm

    Can someone explain to me the importance of my students being able to use angles that are in Degrees Minutes Seconds notation? That question is shitty. And why is Brian using completing the square to solve the quadratic? Why can’t we just solve the quadratic equation like EVERY REASONABLE PERSON WOULD DO IT.

    This exam is getting worse. It pisses me off that my kids bust their ass to learn how to solve law of sines problems, including ambiguous cases, and they don’t test it. It all comes down to a guessing game for the teachers, and that isn’t fair to the students. We just don’t have the time to cover the material effectively.

    • Matt K permalink
      June 23, 2011 pm30 9:32 pm 9:32 pm

      I agree that these tests are guessing games. Where the hell are the trig equations! So NYS, you are telling me now that finding the exact value of sin 75 is important enough to be a 4 point question?! My kids basically started with 84 instead of 88 points because of it. One lousy trig app problem on part 1?! And we all know about #32. They should just admit they are wrong award the kids the 2 points. Can we also just get rid of 64’s on the grade scale? Other grades are skipped. Why kill a kid with a 64 when he/she worked their tail off all year(especially on a test with bogus questions) Can we please go back to goood ol’ Course I, II, and III? Lastly, WHO ARE THESE PEOPLE WHO WRITE THESE TESTS! I mean what are their names? I think we have the right to know who they are and question them, not harrass them of course:)

  6. June 21, 2011 pm30 11:09 pm 11:09 pm

    I wasn’t a fan of question 13 either. We can assess whether kids can tell the difference between combinations and permutations without trying to trick them with extraneous information.

    And as long as we’re talking about questions that sucked, yeah, if I had a dollar for every time I saw DMS notation outside of teaching in NYC, I would be flat broke.

    In 19: Why restrict the range if you’re not going to restrict it into a function?

    25: My room didn’t have a clock, so I went to another room and brought one in.

  7. June 22, 2011 am30 12:07 am 12:07 am

    Wait…you guys are allowed to discuss these questions with your kids? We’re legally bound not to in Indiana with our Algebra I ECA exams…

    • June 22, 2011 am30 12:14 am 12:14 am

      Do you guys grade the state tests that your students take? We do here in NY.

    • Anonymous permalink
      July 24, 2011 pm31 12:51 pm 12:51 pm

      Indiana, the state whose legislature declared the value of pi to be 3, and then tried to collect royalties on the idea to be used for education in Indiana where they surely would have needed it had students done all their calculations using pi=3

  8. Anonymous permalink
    June 22, 2011 pm30 12:25 pm 12:25 pm

    Does anyone else think that we have an argument that y=x^2-6x-27 is a valid “equation” with sum of the roots = 6 and product of the roots = -27? My students were given an acuity problem that had a y = 3x^3 + x^2 –3x – 1 and were asked to find the roots. It mentioned nothing about being set equal to zero. I have a kid with a 64 because of this issue.

    • Anonymous permalink
      June 22, 2011 pm30 5:30 pm 5:30 pm

      I hada problem with this as well…..does anyone know why the state would specifically put that answer as getting only one point?? If the quad is set to y it still has the same roots since roots are x-intercepts and the procedure would be to substitute zero in for y and solve….

  9. Bpeled permalink
    June 22, 2011 pm30 2:15 pm 2:15 pm

    Anyone see the correction? “Because of variations in the use of f^-1 notation throughout New York State” — what??? Yes, there are variations — those which are mathematically correct and those which are NOT. Can ANYONE find a reputable source that backs a definition of f^-1 notation that does not mean “inverse FUNCTION”???

    And nothing about question #19 — message to graders: “nothing to be seen here, carry on, carry on…”

  10. Anonymous permalink
    June 22, 2011 pm30 3:10 pm 3:10 pm

    My kid studied her tail off for this idiotic exam, has a 96 average for the entire year only to come home and say the things that were on the exam were barely taught. Its embarrassing to the teachers, to the kids, and then if they have any desire to further their math education in college, they are SHOCKED how ill prepared they are, even if they take AP calculus. Most of them abandon any careers that involve Math.
    My oldest is a senior graduating with BS in Chem E, she said when she was a freshman in college, her roommate who was from New England area and also had taken AP Calc was much better prepared for higher level math than my daughter was.

  11. Anonymous permalink
    June 22, 2011 pm30 4:25 pm 4:25 pm

    In addition to #32, I felt the rubrics for #30 was unfair. Why can’t y = be an equation as well? Also, # 36 was very tough as a 4 point question. Very difficult to get any partial credit! Also, much more Algebra than Trig. on the test. No trig equations or Law of Sines.

    • Anonymous permalink
      June 22, 2011 pm30 6:07 pm 6:07 pm

      didn’t this question say equivalent equation. y = would be equivalent wouldn’t it??

      • Anonymous permalink
        June 22, 2011 pm30 7:12 pm 7:12 pm

        The rubric explicitly said the a y= equations would only be worth 1 point. I completely disagree.

  12. June 22, 2011 pm30 5:41 pm 5:41 pm

    On the bright side, this might have sent my department over the edge. I think we have a critical mass willing to try to convince our Board of Ed that we should stop wasting our kids’ time administering this exam.

  13. Anonymous permalink
    June 22, 2011 pm30 5:48 pm 5:48 pm

    umm…i just took that, i think its + or – that gets the other point….

  14. Anonymous permalink
    June 22, 2011 pm30 5:50 pm 5:50 pm

    Do you get full points if you put there is no inverse function?

  15. Anonymous permalink
    June 22, 2011 pm30 5:52 pm 5:52 pm

    As a student who took the exam and had a B+ average every quarter, I could honestly say that this test seemed so unfair. There is no doubt in my mind that I failed it. And I have never failed a test in my life. I worked so hard to pass this test. I was tutored weekly and met with my teacher in school on multiple occasions. You would think that the test would be a bit easier since the state isn’t giving out a test in August OR January. Because of this one test, I won’t be able to receive the diploma I have worked so hard to achieve. It would be a different story if I wasn’t a good student, but I am. The test was all algebra. I worked hard to understand Law of Sines and it wasn’t even on it! I’m sorry but I hope the state does something about this because I passed the course with an 88.3 average and now I may have to retake the course just so I can remember everything. Again, I am quite studious, it would be different if I was bad or math or didn’t care, but neither of those things fit my description as a student. Overall I am so disappointed, and I know the math teachers in my school are absolutely furious.

    • Anonymous permalink
      June 27, 2011 pm30 11:16 pm 11:16 pm

      It is a absolute disgrace what the Department of Education of NYS has done to students like you. The curriculum is loaded and complicated, and geared for mastery by only the top 5%. We need to explore why the state would administer a controversial Algebra 2/ Trig exam and discontinue Aug/Jan make-up examinations at the same time? Are they trying to prove a point? Micromanage the system of education or create a class system? I would like to know exactly how many students will not be receiving a regents diploma with advanced distinction because of this exam. Perhaps, giving these students the chance to make up the exam is the only fair solution. I would also like to know the truth about the possibility of the early release of this regent exam. If there is any truth to this matter then the validity of this exam is at stake. To the students who feel or know they have failed this exam, please stay the course and don’t let this get you down. Check out all your options and make the most educated decision as to the way to proceed in your future. Good Luck!

  16. Anonymous permalink
    June 22, 2011 pm30 6:05 pm 6:05 pm

    The sum and roots problem said equivalent equation didn’t it so it could be set to y??

    • Kate Nowak permalink
      June 22, 2011 pm30 6:27 pm 6:27 pm

      An example of an equivalent equation would be 0=2x^2-12x-54. Y= anything only earned 1 point. Which I don’t agree with by the definition of “root” but that’s what the scoring guide said.

      • Matt K permalink
        June 23, 2011 pm30 9:39 pm 9:39 pm

        I think the reason why y = was 1 point is because you are allowing y to be anything. If y was say 2, the quadratic would have diff. roots. You might have to check my explaination though. But, yeah, I thought y= was fine at first also.

        • June 24, 2011 pm30 4:43 pm 4:43 pm

          No, I agree with Kate on this one. If you set y=2, then you can solve for values of x, but those are NOT the roots of the polynomial. I’d have to actually take a look at the question to be sure, but from the other problems I’ve seen so far, I would not be surprised if the wording was vague/incorrect, and the grading rubric similarly so.

  17. June 23, 2011 pm30 12:06 pm 12:06 pm

    Wow, so the Regents exam has gotten worse. That’s not much of a surprise.

    I don’t know if this is a good place to ask the question or not, but does anyone here think that maybe the problem is that we test our student’s ability to perform calculations, and don’t assess their ability to solve actual problems?

    I see Mathematics as a creative, inspiring, pattern finding, problem solving, art-form and not something that can be explicitly tested. Knowing how to solve a quadratic equation is not knowing mathematics IMHO. Being able to solve them is important, but of much less importance than knowing where, why, and for what reason we care about them.

    Can I recommend that those of you here who are complaining about this test check out Paul Lockhart’s “A Mathematician’s Lament” when you get a chance this summer?

  18. ASTRAKA permalink
    June 23, 2011 pm30 5:48 pm 5:48 pm

    I have lost faith in the people who write the regents exams. They do not know mathematics well! They do not know how to write mathematics questions. When you point to them their errors they are unable to understand what you are saying. Their incompetence is infuriating.

  19. Matt K permalink
    June 23, 2011 pm30 9:50 pm 9:50 pm

    I’m really glad I found this blog. I was wondering if I was the only one lamenting for my kids and my teaching abilities. This state is really screwing up our kids. We need to encourage our kids’ parents to call Albany. Maybe with enough calls, those morons will finally listen. They sure as hell don’t listen to us.

  20. June 23, 2011 pm30 10:26 pm 10:26 pm

    How much of the problem is the State’s curricular standards, and how much of the problem is the craptitude of the tests assessing those standards?

  21. Amanda permalink
    June 24, 2011 pm30 3:42 pm 3:42 pm

    Presumably the answer they were looking for was +/- sqrt (x+6) ? You would have got both marks if you had put in the +/-?

  22. anonymous permalink
    June 27, 2011 am30 11:39 am 11:39 am

    Did any of you hear a rumor that a Rush-Henrietta teacher got hold of a field copy of this exam, passed it along to a tutor, and that tutor then used it with his/her students.

    • Anonymous permalink
      June 27, 2011 pm30 4:29 pm 4:29 pm

      I did hear that and that the school’s scores will only be P or F…. where is the news on this one?!?!?!?!?

  23. anonymous permalink
    June 27, 2011 pm30 9:15 pm 9:15 pm

    This P or F is not an acceptable remedy to a situation where God knows how many students had access to the problems on this exam. NYSED needs to go much further and come up with a fair solution for all involved instead of burying its head in the sand with this already flawed regents.

  24. July 7, 2011 am31 11:31 am 11:31 am

    First of all, the problem wasn’t stated properly. The question could have said find the Inverse Relation given f(x). Once most students and teachers see the f(x) , f^-1(x) notation, right away they think “function” ; however, there is no rule that says that a relation named f has to be a function. Similarly , a relation named f^-1(x) doesn’t have to be an inverse function. The imbeciles at the Board of Regents could have avoided all of the controversy surrounding this problem by picking a relation that is function and whose inverse is also a function. It’s absolutely frightening to think that these idiots are going to rate us as teachers.

    I don’t mind being rated as a math teacher by people who are capable and competent, but from what I have seen , there are Very few people at the administrative level that are either competent or capable!

  25. Jeff permalink
    July 11, 2011 pm31 9:25 pm 9:25 pm

    If your child or students did not pass the Trig Regents in June of 2011, please email Commissioner King with your concerns or send a certified letter to his office that he must sign for. Parents in our school district have been given this information so they may also contact the Commissioner with their concerns. It’s their child that is loosing out on having to retake the class instead of taking Calculus, miss early college admission possiblities and limit scholarship eligibility. This test should be curved after looking at the failure percentage, not to mention that it should not be valid since two schools had access to the test and used many of the questions in a study guide for their students in Victor High School and Rush Henrietta High School in New York (who knows how many school really had access to the test?). Commission King needs to use the local requirement of a score of 55 to determine pass/failure. That would benefit many of the students that failed the regents and are trying to get into colleges that require an advanced regents diploma. Commissioner King needs to rectify this situation and take immediate steps to help NYS students, especially those students were able to successfully complete Trig class throughout the year.
    Email Commission King at : or call his office at 518-474-5099. Send certified letters to Commissioner King, NYS Education Department, Education Building, 84 Washington Avenue, Albany, NY 12234.

  26. anonymous permalink
    July 12, 2011 pm31 8:11 pm 8:11 pm

    NYSED eliminated the scores for the compromised A2T questions that were included in the June regents. This left too few points to calculate a meaningful grade for the Rush-Henrietta/Victor HS students involved, so they were assigned a pass/fail grade. Jane Briggs, a spokeswoman for NYSED, states that dropping scores for questions these students (and very possibly others) knew from copies of the A2T field test “provides a valid assessment of student achievement for the affected students.” WHAT? Does this woman know anything about test development/construction and validity?

  27. SF Math Teacher permalink
    September 11, 2011 am30 1:13 am 1:13 am

    Greetings from San Francisco,

    You are not alone. CA is experiencing the same damned thing. Currently CA is now giving *four* standardized tests per year: the CAHSEE (NY Regents equivalent), the STR Test (No Child Left Behind Test), and this year we have the MAP/CLAs, which are to be given twice per year.

    Here are some unbelievably crazy things about these two of these tests:

    1. The STR Test covers content from 6 marking periods. However, it is given *six weeks* before the end of the year. Thus, we have to cover six marking periods of content in five marking periods in order for our students to do well on the test.

    2. The MAP/CLA tests are based on district-approved textbooks, which have a specific scope and sequence. My department uses the wonderful (and sadly out of print) Jurgenson’s Geometry text in our honors program. The scope and sequence of the Jurgenson’s test doesn’t match that of the dumbed-down district Geometry text. For example, the district text introduces Coordinate Geometry in the first few chapters; the Jurgensons, nearer to the end.

    *Thus, the MAP/CLAs don’t align with the textbook we use in our classes!*

    When we brought this up they asked us to *adapt our instruction* to fit the test, even though, in my humble opinion, Coordinate Geometry shouldn’t be taught until the end of a Geometry course.

    After reading your posts, I am convinced that the people in charge – the administrators, and particularly the math curriculum administrators, *don’t know what they’re doing.* It’s as if they’ve never taught math, or never even set foot in a math classroom.

    In addition, the state is spending millions of dollars on these tests, while laying off teachers!

  28. Anonymous permalink
    December 18, 2011 am31 1:46 am 1:46 am

    You guys need to stop complaing number 32 is not a hard question and the reason is because one you are supposed to know that the function given is NOT A ONE-ONE FUNCTION!!!! so therefore NO INVERSE IS POSSIBLE and you should know that a RADICAL IS POSITIVE OR NEGATIVE! (+-)


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