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June 2010 Integrated Algebra Regents Part IV

June 20, 2010 am30 10:10 am

37. Express in simplest form: \frac{x^2 + 9x + 14}{x^2 - 49} \div \frac{3x + 6}{x^2 + x - 56}

\frac{x^2 + 9x + 14}{x^2 - 49} \div \frac{3x + 6}{x^2 + x - 56} start

\frac{x^2 + 9x + 14}{x^2 - 49} \times \frac{x^2 + x - 56}{3x + 6} multiply by the reciprocal

\frac{(x+7)(x+2)}{(x+7)(x-7)} \times \frac{(x+8)(x - 7)}{3(x + 2)} factor each expression

\frac{(x+7)(x+2)(x+8)(x - 7)}{(x+7)(x-7)3(x +  2)} rewrite as one fraction

\frac{(x+8)}{3} reduce

38. See photo.

I would recommend creating a table to show how many students in each interval:

Interval frequency
41 – 50 2
51 – 60 3
61 – 70 5
71 – 80 8
81 – 90 6
91 – 100 6

Number of students? 30. Could have read that from the original cumulative frequency histogram.

Higher than 70? 8+6+6 = 20

Median? That’s the 15th/16th students (from top or bottom, same person). Has to be sitting in the 71 – 80 interval (12 above, 10 below)

Same frequency? 81-90 and 91-100 both have 6.

39. On the set of axes below, solve the following system of equations graphically for all values of x and y.

y = -x^2 - 4x + 12
y = -2x + 4

I’ll describe the graphs, but I don’t know how to show the result.

The second graph is a line, slope is negative 2, passes through (0,4). Toss (1,2) and (2,0) on the graph, use a straightedge to connect them and extend to the edges of the graphing area provided.

The first graph is a downward-opening parabola. I have 4 points to start with:  (0,12) (easy), (-6,0) and (2,0) (solutions) and (-2,16) (vertex). Throw in (-4,12) (from symmetry) and connect the five points. Should look ok.

We’ve got (2,0) as the first intersection. Check it if you like (good idea, even though they didn’t ask you, but we already know it works in both equations).  And it looks like (-4,12) is the second point. We know it works in the parabola. Good idea to check in the line (yup, it’s good).

Circle the intersection points (I would)

Write: “The solutions are x = 2, y = 0 and x = -4, y = 12” or “… are (2,0) and (-4,12)

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55 Comments leave one →
  1. Nick permalink
    June 20, 2010 am30 11:06 am 11:06 am

    For the cummalative frequency graph, what I you got parts b and c wrong?
    Would you lose a -2 or a-1?

    • chris permalink
      June 20, 2010 pm30 3:45 pm 3:45 pm

      lose 2

      • Nick permalink
        June 20, 2010 pm30 7:02 pm 7:02 pm

        Thanks dude, and according to jd’s answers, I have a 77/87=90.. But I’m waiting for the states but thanks so much jd, I realized the stupid stuff I did!

        • Anonymous permalink
          June 20, 2010 pm30 7:43 pm 7:43 pm

          Same here :P
          I had a 99 average in algebra and got a 92 on this exam. I stupidly messed up Part B of the Histogram, the quadrant question, the distance question (probably the worst mistake I’ve ever made on a test), and the dreaded #30.

          I am going to stare down Geometry questions next year until my eyes are burning from it!!!

        • Nick permalink
          June 20, 2010 pm30 11:47 pm 11:47 pm

          Yea dude, I’m a 98 in algebra, so it was the #30, distance, area I forgot to half the actual circle
          (I only halved the radius);#23 and the stupid frequency histogram parts b and c…that’s a total of -10; 4 MC and -2 on part 4.
          STUPID MISTAKES!!

  2. Anonymous permalink
    June 20, 2010 am30 11:38 am 11:38 am

    thank you

  3. Anonymous permalink
    June 20, 2010 am30 11:50 am 11:50 am

    i got like two mult choice wrong and mayb two points off on the rest

  4. June 20, 2010 pm30 12:51 pm 12:51 pm

    If I got two wrong on the mutliple choice and got the rest of the exam correct what would be my score. Would a curve apply (negative or positive)?

    • Anonymous permalink
      June 20, 2010 pm30 2:29 pm 2:29 pm

      Two multiple choice would be four points off, so that’s a 95 this time around.

    • Anonymous permalink
      June 20, 2010 pm30 2:42 pm 2:42 pm

      Raw Score 83. Scaled Score 95.

  5. June 20, 2010 pm30 2:56 pm 2:56 pm

    Nice job presenting the test. I hope your students (and the Googling visitors) appreciate the work you put into this.

    I barely had a chance to look over the test, and I didn’t take a copy home with me because the test was still going on when I left, after a day of grading Geometry tests that still aren’t totally graded and double-checked.

    • June 20, 2010 pm30 3:10 pm 3:10 pm

      I appreciate that, thank you. For better or for worse, my voice comes through the explanations… there may be students out there who find it easy to follow.

      I am in a fortunate (Regents grading) position – we finished geometry lightening fast, and are poised to attack this one bright and early tomorrow. I just want to be done, so I can take care of my other (scheduling) responsibilities, which are now looming large.

      I might come back to A2T parts 2/3/4 later in the week, before the conversion is out. I don’t think I have much to say about Geometry, besides the question that punishes students for not using the calculator… and how simple the proof was.

  6. qwert permalink
    June 20, 2010 pm30 6:33 pm 6:33 pm

    if i got a 67 raw score what is that please answer

    • Anonymous permalink
      June 20, 2010 pm30 7:44 pm 7:44 pm

      67 raw score = 84

  7. lj4lyfe6 permalink
    June 20, 2010 pm30 7:34 pm 7:34 pm

    Well, for number 38, the chart frequency thing, for part c and d i put this:
    C-41-80
    D: 41-90 and 41-100
    Since i put liek the ending write but not in ten point intervals, how many points will i lose, 1 or 2? Thanks. BTW i got 4 wrong on multiple choice, and not sure bout this, depends on this part.

  8. ANANNANANANANANANA permalink
    June 20, 2010 pm30 7:35 pm 7:35 pm

    If you get a 75 raw score whats that?
    is there a different scoring key if your a year ahead?
    Im in eigth grade.

    • Anonymous permalink
      June 20, 2010 pm30 7:39 pm 7:39 pm

      The conversion chart remains the same.
      A 75/87 = 88
      Considering you’re in 8th grade, nice work! :)

      • Anonymous permalink
        June 20, 2010 pm30 8:00 pm 8:00 pm

        There’s no different scoring key, though your school might weight the class a little more. Good luck. :o

      • June 22, 2010 pm30 4:24 pm 4:24 pm

        86 here (I’m an 8th grader too, o well) =P
        I just took the Earth Sci today… does anyone have the answers to that? XD

  9. Anonymous permalink
    June 20, 2010 pm30 7:53 pm 7:53 pm

    JD, just wondering, how do you get the HTML for the expressions? What codes did you use to, say, get the rational expression from #37 into the post? Thanks. :)

    • June 20, 2010 pm30 8:49 pm 8:49 pm

      WordPress, the host of this blog, supports LaTeX, a powerful typesetting program.
      I’ll give some examples, formatted, and then I will show the code. Remove the #s to make them work:

      It can do fractions: \frac{3}{x}
      — I typed $#latex \frac{3}{x}$

      It can do exponents: e^t + e^{2x} + e^{\frac{1}{y}}
      — I typed $#latex e^t + e^{2x} + e^{\frac{1}{y}}$

      It can do roots: \sqrt{n}
      — I typed $#latex \sqrt{n}$

      Subscripts: F_n = F_{n-1} + F_{n-2}
      — I typed $#latex F_n = F_{n-1} + F_{n-2}$

      You can use LaTeX in the comments here. And you can google it and find lots more about using it to control formatting (mathematical and otherwise)

  10. ray permalink
    June 20, 2010 pm30 8:25 pm 8:25 pm

    att anonymous asking about the html
    if you put your mouse pointer over the expression he put in the entry, a bubble comes up and says what he wrote for the html expression (at least on mine)

    • Anonymous permalink
      June 20, 2010 pm30 8:48 pm 8:48 pm

      What browser do you use?

    • June 20, 2010 pm30 8:52 pm 8:52 pm

      to make the code the code execute, precede it with Slatex, but type a $, not an S, and end it with a $.

      • Anonymous permalink
        June 20, 2010 pm30 9:05 pm 9:05 pm

        Thanks :)

        THIS IS A TEST.

        $\frac{1}{3} \$

        • Anonymous permalink
          June 20, 2010 pm30 9:05 pm 9:05 pm

          Hmmm, it didn’t work. :| I wonder what I’m doing wrong…

        • June 20, 2010 pm30 9:08 pm 9:08 pm

          You need to start with Slatex, not just S

          (of course converting the S to a dollar sign)

        • June 20, 2010 pm30 9:09 pm 9:09 pm

          And you have a stray \

          The \ introduces “frac”, it does not end it. The syntax is \frac{num}{den}.

  11. Anonymous permalink
    June 20, 2010 pm30 9:07 pm 9:07 pm

    Oh I see!

    $#latex \frac{1}{3}$

    • Anonymous permalink
      June 20, 2010 pm30 9:07 pm 9:07 pm

      Well, no…

      • Anonymous permalink
        June 20, 2010 pm30 9:08 pm 9:08 pm

        $#latex \frac{3}{x}$

    • June 20, 2010 pm30 9:09 pm 9:09 pm

      Almost there, just delete the # (and do not leave a space)

      • Anonymous permalink
        June 20, 2010 pm30 9:32 pm 9:32 pm

        $latex\frac{1}{3}$

  12. Anony permalink
    June 20, 2010 pm30 9:29 pm 9:29 pm

    that is soo uncool how our teacher never taught how to graph or anything like that on the calculator. all we learned on the cal was trig things sine and cos and tan thats all.

  13. qwert permalink
    June 20, 2010 pm30 9:38 pm 9:38 pm

    Thank you all for anwering questions and thanks jd for putting all these stuff up now i have a clue of what i might get ( i didn’t do so well :(

  14. lj4lyfe6 permalink
    June 20, 2010 pm30 10:18 pm 10:18 pm

    For question 38, for part c and d, if you put 41-80 for c and 41-90, 41-100 for d, will they take off two points or one, only thing is i didn’t make it a ten point interval

  15. lj4lyfe6 permalink
    June 20, 2010 pm30 10:19 pm 10:19 pm

    For question 38, for part c and d, if you put 41-80 for c and 41-90, 41-100 for d, will they take off two points or one, only thing is i didn’t make it a ten point interval?

  16. ray permalink
    June 21, 2010 am30 11:48 am 11:48 am

    \frac{(x+8)}{3}

  17. ray permalink
    June 21, 2010 am30 11:53 am 11:53 am

    $latex\frac{(x+8)}{3}$

  18. madi permalink
    June 21, 2010 pm30 7:41 pm 7:41 pm

    I am an 8th grader who just took the Algebra Regents. I had a 100 average all year, and then only got a 93 on the Regents. I am flipping out!!!!!! I feel better that others missed the Part 2 Histogram question. Thanks for showing how to do it. I am so mad I got that wrong!

    • Samantha permalink
      June 21, 2010 pm30 8:04 pm 8:04 pm

      what would my grade be if i only got part c and d wrng on the histogramm?

      • Anonymous permalink
        June 21, 2010 pm30 10:24 pm 10:24 pm

        2 pts out of a possible 4

  19. Anonymous permalink
    June 21, 2010 pm30 10:28 pm 10:28 pm

    Just testing my Slatex.

    \frac{2}{3}

    • June 21, 2010 pm30 10:32 pm 10:32 pm

      I fixed it by adding a space after the x in “latex”

  20. i have no friends permalink
    June 21, 2010 pm30 10:38 pm 10:38 pm

    wow you would delete my comment

  21. Anonymous permalink
    June 21, 2010 pm30 10:40 pm 10:40 pm

    \{x^2 + x - 56}{4x + 12}

  22. Anonymous permalink
    June 21, 2010 pm30 10:41 pm 10:41 pm

    \frac{x^2 + x - 56}{4x + 16}

    • Anonymous permalink
      June 21, 2010 pm30 10:42 pm 10:42 pm

      Yay! :)

  23. Anonymous permalink
    June 21, 2010 pm30 10:47 pm 10:47 pm

    \sqrt{9x^2}

    • Anonymous permalink
      June 21, 2010 pm30 10:47 pm 10:47 pm

      I think I got it now. Thanks so much JD! :)

  24. walter permalink
    June 22, 2010 am30 11:39 am 11:39 am

    $latex\sqrt{9x^2}$

  25. walter permalink
    June 22, 2010 am30 11:41 am 11:41 am

    F_n = F_{n-1} + F_{n-2}

  26. Anonymous permalink
    June 22, 2010 pm30 3:20 pm 3:20 pm

    \frac{Y_{2} - Y_{1}}{X_{2} - X_{1}}

  27. Anonymous permalink
    June 23, 2010 pm30 7:54 pm 7:54 pm

    Does anyone know when jmap.org is going to post the exam? I want to see the rating guide. I’m curious about how the short answers were graded. Thanks! :)

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