Simultaneous Equations on the SAT

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Simultaneous Equations on the SAT

Today we are going to talk about simultaneous equations on the SAT. Traditionally, students take what I call the isolate and dominate approach to simultaneous equations. That is, instead of seeing how the equations relate to each other in an attempt to find the right answer, students figure out what one of the values equals, plugs that new equation into the prompt, solves for x or y and then re-plugs in that number. That is a lot of work! That Isolate and dominate approach absolutely works on the SAT, in algebra 2, and on your simultaneous equation problems. But there HAS to be a better way. This is the SAT, after all. The SAT Blue Book talks a lot of smack about this not being a logic test and you not needing test preparation. “Just paying attention to your teachers will be enough,” they say. As if all high school curricula are the same. As if all high school teachers are equally adequate and no students receive private tutoring for high school subjects. Richard Koch wrote a great book called The 80/20 Principle. In it, he says that you should never play a game where you do not create the rules. Unfortunately, you have to take the SAT to get into a great university. Because you cannot create the rules, you need to do everything in your power to tip the game in your favor. That’s why using what we learn in high school, isolate and dominate simultaneous equations is not really going to work on this test. Instead, we need to think of a smarter way. In todays...
Rations and Proportions on the SAT

Rations and Proportions on the SAT

Thank you so much for checking out this ratio and proportion lesson. I want to make today’s post short and sweet. So short, and sweet, that I’ll just jump straight to the video. Ratios and Proportions Ratios and Proportions are deceptively easy. They just LOOK really hard on the test. If this video cleared up some of your misunderstandings, please let me know in the comments below. I really enjoyed making this lesson. I look forward to hearing from you...
Functions and Weird Symbols on the SAT

Functions and Weird Symbols on the SAT

Hi! I’m really glad you are here. I’m super into coffee at the moment, so I will try to make this as quick as possible so I can go jump on a bed or punch a shark. (Note: It is my lifelong dream to punch a shark in the snout.) When I was in high school, functions were so totally easy. I mean, you get something funky like: f(x) = 2x + 2 and then you are asked for f(4) or something. When I was younger, all I knew to do was replace the x in the first statement with a 4, and viola! Functions on the SAT are pretty much just like my experience in high school. But, because the ETS gets paid to make you hate yourself, it has to make those f(u)unctions as complicated as possible. But how can you make a function complicated if it kind of is only plug-and-play? Beating Functions In math and in my other passion, computer science (or comp-sci for my magically nerdy brothers and sisters), a function is a “correspondence that associates each input with exactly one output.” What-the-huh? It means that if you put in one value, 4, you’ll get back only one value, 10. In the math we are rockin’ on the SAT, these relate to coordinate geometry. The f(x) refers to the x in our (x,y). While the = 4x + 3 refers to the y in our (x,y). So the idea is to plug in some numbers for your x, figure out what you get for your y, put in on those coordinate plane, recognize your...
Mean, Median, Mode

Mean, Median, Mode

SAT questions come in all kinds of wonderfully complicated shapes and sizes. Some problems require you to simply solve for x, find an area of a circle, or factor a couple of numbers and master those rules of divisibility. Today, I want to review another concept that tends to creep up on the SAT often: Mean, median, and mode Mean, median, and mode are basic concepts that you should have learned in grade school. But, the very fact that you learned how to find the mean so long ago means that in order to properly test your SAT ability, the test writers have to create complicated question-types. While teaching my students, taking this test, and reviewing the official guide, I have discovered a limited number of ways the SAT can test average. Those ways are: Hidden variable Change in value Adding new information Partial average Incomplete sum Beat the Mean As you can see, there are a lot of ways the test writers attempt to confound you. In today’s video lesson, I walk through what mean, median, and mode really mean and then give you a unique strategy that I use in my private classes! After the break I talk about a pretty important SAT strategy and my progressive learning system. An Updated Progressive Learning System I talk a lot about testing strategy on this website. There is a very obvious reason for that: without a strategy, techniques, and pacing skills, your knowledge won’t be enough. This free blog series is intended to give you all the knowledge you need to do really well on the SAT. Really well....
Finding X and Inequalities on the SAT

Finding X and Inequalities on the SAT

Solving for X is pretty much an SAT establishment. If you cannot quickly and without error find X, your chances at a killer SAT score are totally not awesome. Just imagine getting the following fairly simple question: 3x – 7 = 2 If you do not know that x = 3, then you are in the right place. If you are thinking to yourself, “Goodness, Craig, why are you wasting my time with that!”, good for you! Remember, these introductory SAT posts are ‘SAT Math Basics‘. We are rocking through the basics before we hit up some advanced math. The purpose of these posts is not to be an exhaustive SAT manual. That would be counter-productive. This guide is here to be an evergreen lesson for all future SAT students. And that works! Inequalities and Find X Solving for X is not the only tricky beast I’m breaking down in this video. I also show you how the very simple process of solving for x can be used to do more complicated problems involved inequalities. Imagine have the following question: 46 < (2x + 3) < 12 After you watch the video, you’ll learn that the process for rocking this question in the same process (more or less) that you used to totally dominate the previous question. This is all true because the SAT is not going to kill you, it’s not going to stress you out, and it’s not going to dominate your ability to go to an awesome school. What are you waiting for? Go solve for x and rock your inequalities: The Final Word SAT Math...
Divisibility and Percent Change on the SAT

Divisibility and Percent Change on the SAT

In my last post I talked about some of the very basic SAT math concepts. Today, I want to do the same thing, but make the topic a bit more complicated. Today, we are going to break through the rules of divisibility, percents, fractions, and percent change. Students who cannot quickly convert decimals into fractions waste precious time on simple things like long division and calculation. The SAT is a timed test. You will need to be as effective and efficient as possible throughout the entire experience. If you don’t understand, there are books and tutors that you can use. It is with that understanding that we move to our lessons. The Rules of Divisibility The SAT test writes assume you know what makes a number divisible by another number. Briefly, a number is divisible by another number if you are able to divide it and get an integer. And integer is a whole number (ie. 1, 2, 10, 50). So, if you divide 50 by 2, you will get 25. That means that 50 is divisible by 2, because when you divide 50 by 2, you get an integer. Understanding the rules of divisibility naturally requires you to understand remainder. You’ll absolutely get the remainder problems correct after watching this lesson. In this video I break down how you can quickly and easily find the rules of divisibility: In case you want a quick cheat sheet, I actually put together a PDF magical cheat sheet. Cool, huh?¬†Download Now Fractions, Percents, and Percent Change on the SAT The SAT assumes you have knowledge of fractions and fraction conversion. And...