Posts filed under: new SAT

Most people spend the majority of their test prep time attempting to master content. This is a good thing! Without content knowledge, you’re in trouble. However, if you want to set yourself up for success, you should also be devoting some time to learning the rules of the game—you can’t develop effective strategy until you know the rules! One of the most important rules of any game is how the scoring works.

Below is a summary of the math scoring tables from the 8 official practice tests, which are a pretty good representative sample. You can see the highest, lowest, and “probable” (average over the 8 tests, rounded to the nearest 10) scaled score each raw score receives on the Official 8.

There are a few good use cases for this. First, you may know that you need to hit a certain score in order to qualify for something (a scholarship, a summer studies program, etc.). Knowing how many you need to get right to get there can help you strategize about which topics to focus on and which to ignore.

I expect people will also use this to speculate about how they might have done after tests (e.g., “I’m pretty sure I only got 5 wrong and I answered everything else—what might my score be?”).

Now that the Daily PWN email list has been going for a while and I’ve got some good data on the questions, I thought I’d compile a list of the ones people are missing most frequently. If you’re looking for a quick skill sharpening on some tough problems, why not give these a try?

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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.

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.

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

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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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.

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:

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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