How to Hack the Hard Math Section of the Digital SAT

Are you taking the digital SAT soon and wondering how you can hack the hard math section? In this blog, I’m going to show you some tips that can help you finish the test faster, help you get that 800 that I know you want, or something close to it.

I’m going to share with you some of the tips that have helped me get perfect scores and that have helped my students get perfect scores. If you want more practice for the digital SAT, I have also created an online video-based and online practice-set-based course for the digital SAT. It includes three original practice tests right now. We’re going to be adding a fourth this month, and we hope to add more tests and more material in the future as well.

Desmos Sliders

My first hack: Desmos Sliders. If you do not know how to use a slider in Desmos, you are totally missing out here. If you want an x-y equation with a third additional variable, that’s when you know it’s slider time. So, on Desmos, type in the equation, and “add slider” should pop up, allowing you to add a slider for the additional variable. One tip on sliders: if you ever realize you’re not getting where you need to go, you can change the range. So, if I don’t want -10 to 10, I can change this to 10 to 12. I can also change the step to 0.5, and then it’ll step up every 0.5. Now, you can add the second equation, and you can kind of see what’s going on in the problem. Then, you can use the slider to change the value of the third variable to find the solution to the problem. In the example problem in the video, the solution has to be below -6 or above 2, and only one of the answer choices fits those boundaries. Using that slider made this much easier to solve, so make sure to keep those in mind when doing these problems.

TI-84 Programs

Next hack: TI-84 programs. Even though Desmos is amazing and I started doing a lot more stuff in Desmos than I used to do in the TI-84, I will say there are a few TI-84 programs that can come in handy for the digital SAT. One of my favorites—which I don’t use on every test because there is not always a long division problem on every test—is a program that does synthetic division, which is helpful if there is a polynomial long division problem on the test.

If you look at the answer choices for the problem in the video, you can see how all of the answer choices have a remainder, which is a clue that this is a synthetic or a long division problem. So, if you don’t want to do that yourself, you can make your calculator do it for you. How? Well, there are a couple of programs that you can get online. I do not have any affiliation with these people; I’m just passing on the good news and the good words. One of them is Ryan’s blog, which has a synthetic division program. You just type in the powers and the coefficients, and it spits out an answer. On the problem in the video, if you use the same code, you would get a remainder of -2, which would tell you that the answer is D, just off the remainder alone.

Another way that you can do this is with the polynomial remainder theorem. If you know that, you can actually just plug 3 in to get -2 as well. So, that’s another way that you can do this. It works here because all I need is the remainder, but if I needed more than the remainder, the polynomial division program would speed up the process a little bit and give it to me in the most lazy way possible.

Ryan’s program: http://ryanng27.com/2021/12/ti-84-plus-ce-synthetic-division-program.html

Code for polynomial division: http://tibasicdev.wikidot.com/polynomial-division

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Ratio Shortcut

Third hack: ratio shortcut. If you don’t know the shortcut, you should. The basic idea is that if I have a single dimension of something and that’s in some ratio to another dimension of a similar something, we can go between ratios.

So, if you have two cubes, let’s say that a side of the smaller one is x and a side of the larger one is 2x. If I want the ratio of the volume of these two cubes, all I need to do is take that ratio of 1:2 and cube it. And that gives me 1:8 as the volume ratio. I could also get the surface area ratio by taking the single dimension ratio and squaring it, because surface area is an area and area is always square units. So, it’s going to be a 1:4 ratio for surface area.

So, here we have a problem. If a pond has a surface area of 16 square fathoms, how many square feet is the surface area of the pond if 1 fathom is equal to 6 feet? Since I need this in square feet, I need to convert the units. But I can’t just convert by multiplying by six, because this is one fathom in a single dimension to six feet, not fathom squared to feet squared. So, what I have to do is take this one fathom to six feet and square the whole thing to get square feet to square fathoms. So, this is 1 fathom squared over 36 feet squared. Now, I’m going to flip this upside down because I want the 36 on top, and I’m just using dimensional analysis here. The fathom squared cancel, and I’m just going to multiply 16 times 36, which I can do on the calculator. The answer is 576, and that’s how we solve that ratio shortcut.

If you want more awesome, hard problems like this to practice for your SAT, be sure to check out our digital SAT online self-paced course. We also have private tutoring, and right now we have a live class coming up with me for the month of April that’s in preparation for the May SAT. So, if you’re taking the May SAT and you want to do a live class with me, make sure you sign up at supertutortv.com.

We hope this was helpful!


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