Have you ever used Desmos and been amazed by how many problems it can solve on your SAT practice tests? Well, I’m here with an unfortunate wake-up call for you. If you were going to be taking the digital SAT, word on the street is that this test has gotten harder.
On the March SAT, students are reporting that you can’t Desmos nearly as many questions as you thought you could, and if you try, you are going to be in trouble. So, in this blog, I’m going to give you five scenarios in which you should not turn to Desmos first because it might cost you time.
The Answer Choices Are Ugly Fractions
So, the first situation that you want to avoid Desmos is when the answer choices are super ugly fractions. Don’t use Desmos because when you plug in the point, it’s not going to be exact. You’re going to have to plug all of these into your calculator, and it’s going to be time-consuming. It’s probably faster to just do it the straightforward way. In the problem in the video, it is super easy to find the slope. It’s just rise over run, and since it’s downhill, it is negative. We know the intercept is seven, so we can form that equation, and then we just plug in four to get the answer. You’ll get that ugly fraction, and you don’t have to plug so much stuff into your calculator. Time is so important.
The Answer Choices Include Radicals
Number two: Don’t use Desmos when the answer choices include radicals. If you do, you’re going to have to plug a bunch of stuff in, and it’s going to potentially take quite a bit of time. So, don’t do that. Just substitute and solve, and you’ll be okay.
Open-Answer Questions When Another Way is Easier
Next, do not use Desmos when you have open-answer questions if another way is quicker and easier. So, whenever I have an open-answer question, I do not want to do Desmos first because I know it could get me in trouble.
Here’s an example question:
In the given question, for what value of c does the equation have one solution?
15x^2 – 32x + c = y
I want to know what value of c this has one solution for. This equation is kind of ugly; this isn’t going to be a nice, even kind of parabola. And if I plug it into Desmos and add a slider for c, it will tell me that my answer is between 17 and 17.3, but it won’t actually get me to the answer. So, the fastest and easiest way to solve a problem like this that you know is foolproof is to use the discriminant method. So to use the discriminant, the idea is that when we have the quadratic equation, you know that -b ± √(b^2 – 4ac) / 2a is the discriminant. When this discriminant is 0, we have a double root. When the discriminant is positive, we have two real roots, and when the discriminant is negative, we have no real solutions. So, the situation we’re looking for here is for this to be equal to 0. Plugging in the values into the discriminant equation, we get 256/15. I’m never going to be able to pull that exactly from a Desmos graph. It’s too weird, specific, and ugly. But I can figure it out with the discriminant pretty easily. And I think on the SAT, they don’t grade you down if you don’t put your fraction in the lowest terms, so it should still be correct even if you just put that in.
Other Ways are Faster
Number four: Don’t use Desmos when other ways are faster. With the circle equation in the video, there are two faster ways to solve the problem. One way is to look and see that the x-values of the two endpoints are the same. So, the diameter is just the distance between 5 and 13. Therefore, the radius is just 13-5, which is 8, then divided by 2, which is 4. Since we need r squared, the answer is just 16. The other way I can do this is by plugging in x and y and solving for r squared. Solving the equation this way also gets you 16 for the answer. We have two faster ways, so why mess with Desmos? If I did this in Desmos, I’d get a circle, and then I’d be eyeballing the answer.
You Have to Graph Every Single Answer
And finally, the last situation in which I’m going to tell you not to use Desmos is when you have to graph every single answer to use it. So, in the problem in the video, you can see we have an expression, and we want an equivalent expression. To figure this out, I would have to graph all four of the answer choices. So, I’m at least not going to use Desmos first. I might bookmark this; if you don’t know how to solve the problem but you know how to Desmos it, bookmark it, keep moving, and then come back to it. Because I don’t want you to vortex all your time into the abyss of Desmos on a problem where you have to type four different things in. You might not have time to do that on the hard section of the SAT. So bookmark it, move on, and come back.
So there you go, five times when I would not use Desmos on the SAT. Hopefully that will help you guys crush your test, and good luck on your digital SAT!
