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Posts filed under: new SAT

How’d you feel about the December SAT?

If you took the December SAT, how about filling out this quick survey? These surveys are an informal way to assess how hard the tests were compared to the released practice tests. Once you’ve answered the questions, you’ll be able to see how hard everyone else thought the test was.

If you’re looking to stoke/assuage your fears about how the scoring table will turn out, you might find this useful. It’s a great way to see, at a glance, whether your impression of how hard the section were compared to your peers’ impressions.

 
This form is no longer accepting responses, but you can view the results here.

Proving Grounds #9

Here’s another Proving Grounds installment! The aim of the following five-question quiz is to work your graphing calculator muscles, so my recommendation is that you try to solve them by graphing even if your first inclination would be to solve them another way. My solutions for this drill will be entirely calculator-based; spend enough time…

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Did you take the November SAT? How’d you feel about it?

If you took the November SAT, why not fill out this quick survey as an informal way to assess how hard it was compared to the released practice tests? Once you’ve answered the questions, you’ll be able to see how hard everyone else thought the test was. Those of you looking for something to stoke/assuage your fears about how the scoring table will turn out might find this useful; it’s a great way to see, at a glance, whether your impression of how hard reading, math, and writing were compared to the released practice tests matches everyone else’s.

This survey is no longer accepting responses. You can see the results here.

Did you take the October SAT? How’d you feel about it?

If you took the October SAT, why not fill out this quick survey as an informal way to assess how hard it was compared to the released practice tests? Once you’ve answered the questions, you’ll be able to see how hard everyone else thought the test was.

This survey is over, but if you’re curious, the results are below.


october_2016_sat_difficulty_-_google_forms_1

Proving Grounds #8

It’s been a while since we did one of these! The following five-question quiz (all about a histogram, by special request) will be available to everyone for one week, and then it will only be available to registered Math Guide Owners. (If you don’t have a Math Guide, now is a pretty good time to…

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Math Skills for the New SAT: Completing the Square

The new SAT requires you to know a number of special equation forms—to know which one you need to use in a given situation, and to know how to get into that form if it’s not the one you’re given by using algebraic manipulation. Some equation forms (vertex form of a parabola and the standard circle equation immediately spring to mind) contain binomial squares, e.g. (x+1)^2, as essential ingredients. To get a non-standard equation into these forms, you’ll often have to complete the square. I know, I know, you’ve done this a million times in school. Still, I often find students haven’t done this in a long time and need a little bit of a refresher. So here we are.

First, the equations in question.

Vertex form of a parabola: y=a(x-h)^2+k, where the vertex of the parabola is at (h,k).

Standard circle equation: (x-h)^2+(y-k)^2=r^2, where a circle with radius r has its center at (h,k).

Say you’re given a parabola that’s not in vertex form and you need to put it in vertex form. How do you do that?

No calculator; grid-in

y=x^2-8x+6

The parabola formed when the equation above is graphed in the xy-plane has its vertex at (a,b). What is the value of a-b ?

Completing the square isn’t the only way to solve this question, but I’d argue it’s the fastest. All we need to do to go from the given form to the vertex form is figure out which binomial square the x^2-8x part of the equation is the beginning of. With practice, this becomes second nature and you probably won’t need the rule, but the rule is that x^2+b is the beginning of \left(x+\dfrac{b}{2}\right)^2.* In this case, that means that x^2-8x is the beginning of (x-4)^2.

Now, what do you get when you FOIL out (x-4)^2? You get x^2-8x+16. That’s not what we have above—we have x^2-8x+6 instead. Luckily, we can do anything we want to the right side of the equation provided that we keep the equation balanced by doing the same thing to the left, so we can just add 10 to both sides!

y=x^2-8x+6

y+10=x^2-8x+6+10

y+10=x^2-8x+16

From there, we’re almost done. Now we can convert the right side to the binomial square we wanted, and then get y by itself again to land in vertex form.

y+10=(x-4)^2

y=(x-4)^2-10

So, there you have it: the parabola in question has a vertex of (4,-10). Since the question said the vertex was at (a,b), we know that a=4, b=-10, and a-b=4-(-10)=14. So, 14 is the answer.

Let’s practice with a few more, shall we? Try to do the following drill without a calculator. All three questions are grid-ins.

1.
y=x^2-12x+33

The parabola formed when the equation above is graphed in the xy-plane has its vertex at (a,b). What is the value of a+b ?

Question 1 of 3

2. When the equation y^2=(x+3)(-x+5) is graphed in the xy-plane, it forms a circle. What is x-coordinate of the center of the circle?

Question 2 of 3

3. What is the radius of the circle with equation x^2+y^2+6x-10y=2 ?

Question 3 of 3


 

 
 
 
 
 
 
* I’m intentionally limiting this post to scenarios where the leading coefficient in the square being completed is 1. So far, I have not seen an official question of this type where that is not the case.

Proving Grounds #7

I’m back after a hiatus with another Proving Grounds Quiz. Usual Proving Grounds rules apply: this quiz is open to everyone for a week, but then it’s only open to Math Guide owners. Good luck! *Data source: City of Bridgeport Office of Policy and Management. Accessed 2015-06-14 at http://www.bridgeportct.gov/content/89019/96401/default.aspx…

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Rate the difficulty of the June SAT

With so few tests of the new format having been administered, it’s still a bit of an open issue whether the released practice materials do a good job simulating the test’s difficulty and content or not. Therefore, if you took the June SAT today, I’d love it if you’d fill out this quick survey. (Curious how the last few of these surveys came out? See March here and May here.)

This survey is now closed, but you can view its results below.

 

Proving Grounds #6

I’m back with another Proving Grounds quiz. These quizzes are available to everyone for one week, and then they’re only available to Math Guide owners. Want to join the swelling ranks of the PWN Army of Math Guide owners? You can buy the guide directly from me through the PWN store, or grab it on…

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March SAT scores and the new concordance tables

Big day today in SAT land—March SAT scores are finally out for most test-takers, and the College Board has released a score conversion app that allows users to compare old SAT scores to new SAT scores. I messed around with the converter a bit tonight. Interestingly, new SAT scores seem to be higher than old SAT scores. For example, 600 Verbal 600 Math on the new SAT would be only 550 Reading 580 Math 530 Writing on the old SAT. Likewise, 700s on the new SAT would be 660R 670M 650W on the old SAT, and 500s on the new SAT would be 460R 460M 430W on the old SAT.

I’m not sure what I was expecting, but I found these results surprising. That said, I’m just plugging in round values to get a rough sense of what’s going on. I’m curious what those of you who took the old SAT and also have scores from the March (new) SAT are seeing. Are the concordance tables accurate?

(I’ve discovered since the first version of this post, wherein I complained that College Board didn’t just release tables, that they actually did also release tables. My bad! You can find those here if, like me, you’d rather get a view of the whole field at once.)

Did you take the May SAT? How’d you feel about it?

If you took the May SAT today, why not fill out this quick survey as an informal way to assess how hard it was compared to the released practice tests?

Results:

Official Test Math Explanations

As I did for the last iteration of the SAT, I’ve been collecting the explanations I write on my Q&A sites for Official Test questions in a Google Spreadsheet for easy reference. The new test is still new, so I haven’t been asked MOST of the questions yet, but I figure it’s time to get this page out into the world. If you’re working through the official SAT practice tests and you have a sneaking suspicion that the official explanation is unnecessarily complicated, well, then here’s a way to get a second opinion.

PS: Download the Official Tests here.

Proving Grounds #5

Last week was a no-calculator installment of the Proving Grounds—this week it’s all grid-ins! Remember, if you want to access previous Proving Grounds quizzes, or if you want to be able to access this and future ones after they’ve been up for a week, all you have to do is be a Math Guide owner. You…

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Proving Grounds #4

Another Proving Grounds quiz coming your way. This one you should do without your calculator. Remember, Proving Grounds quizzes are available to everyone for one week, and then only available to Math Guide owners. Not a Math Guide owner yet? Got $20? :)…

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Proving Grounds #3

Time for another Proving Grounds installment, folks. Remember, these quizzes are available for one week for everybody, and then they’re for Math Guide owners only. “How can I get to be a Math Guide owner?” you ask?! Well, either you buy one right from me, or you forward me your receipt from some place like…

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