/

Posts filed under: main blog

The Daily PWN

Hey guys, just a quick post here to announce a new feature I quietly launched on the site a couple weeks ago; people who have found it seem to like it so far. You can now sign up to receive practice math questions, automatically delivered to your inbox once a day. I’m calling it “The Daily PWN” (creative, right?) and you can expect the questions to be challenging, but not ridiculously so. Each question has a thorough explanation, and a comments section in case you want to discuss it or ask questions.

If that sounds like it’d be helpful for you, all you need to do is sign up using the form below.

Note that you can also sign up for (or unsubscribe from) other automated site updates using the form. Just make sure that the updates you want to receive have checkmarks on them before you submit.

Sign up:

Subscribe to:

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…

This content is for Math Guide owners only.
Log In Buy a Math Guide Verify your Math Guide ownership

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.

Minor updates to the Math Guide

A few weeks ago, I made some minor adjustments to the Math Guide to incorporate the additional official material released by the College Board: tests 5 and 6 (download them here). If you purchase new copies of the Math Guide from the PWN store (or anywhere else) now, your book will have breakdowns of those tests at the back. (If you own a copy that doesn’t have those breakdowns, you can download them in the Math Guide Owners Area—get registered here.)

I also reformatted the official question lists at the end of each chapter—some of them were getting long and it was getting confusing to have multiple page numbers for each question. My new philosophy is that you know whether you have the tests in a book or printed out from your computer, and you know how to find #27 in section 4 of test 3 without me telling you which page it’s on. New official question listings look like this:

All the same information as the old tables in a more compact package.

One result of this is that books printed after these changes went live have slightly different paginations because some of the old end-of-chapter tables took up more than one page. I don’t anticipate this being a real problem for anyone, but if you’d like to download the new table of contents, that’s available for download in the Math Guide Owners Area, too.

Site update: Math Guide Owner verification

Just a quick bit of business here: I’ve automated the Math Guide Owner membership process. You no longer need to email proof of purchase to me to gain access (everybody at once: YAASSSS!!)—all you need to do is go to this page, scroll to the bottom, and verify your book ownership by answering one randomized question about the book’s content (e.g., what’s the fifth word on page X?). From now on, you’ll be able to get your discount code instantly, instead of having to wait for an email response from me.

Note: If you purchased your book from the PWN store, you already have Math Guide Owner privileges through the account from which you made the purchase.

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…

This content is for Math Guide owners only.
Log In Buy a Math Guide Verify your Math Guide ownership

A basic quadratic formula program for your calculator

This is not really SAT specific or even particularly SAT useful, but I made the video above to help you create a basic quadratic formula program for your TI graphing calculator if that’s a thing you’d like to do.

If you’ve programmed things into your calculator before and don’t feel like watching a whole video, you can also just enter the program below. Make sure you’re careful with your quotation marks and parentheses, and always test the program with multiple quadratics to make sure it’s always giving you correct answers before you use it for anything important.

:Disp "AX2+BX+C=0"
:Prompt A
:Prompt B
:Prompt C
:Disp "ROOTS:"
:Disp (-B+√(B2-4AC))/(2A)
:Disp (-B—√(B2-4AC))/(2A)

 

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…

This content is for Math Guide owners only.
Log In Buy a Math Guide Verify your Math Guide ownership

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…

This content is for Math Guide owners only.
Log In Buy a Math Guide Verify your Math Guide ownership

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: