The SAT sometimes approaches math a bit differently than we’re used to in math class. One of these differences in approach is in the way some SAT math problems ask us to...

# How to Use Desmos on the Digital SAT

If you’ve spent any time preparing for the digital SAT, you’ve noticed that there is a calculator right in the interface for the math sections. It’s tempting to use, especially if you don’t fully trust your mental math skills or you’re not completely comfortable with harder algebra and coordinate geometry questions. But should you use it? And if so, when? While calculators can sometimes be useful on the SAT and can sometimes shave a few seconds off a problem, they can also lead test takers astray. Rounding the values for 𝝅 or √2 may lead to incorrect responses, and typing numbers and operations too quickly can hide key concepts and result in careless mistakes. For tests like the SAT, where there’s no partial credit and you can’t show your work, the calculator can be both a blessing and a curse.

### What is Desmos

Many SAT test takers may have had some exposure to the free online graphing calculator Desmos, and the digital SAT includes it in the testing environment. Desmos is an extremely powerful tool, and there is absolutely no shame in using it to help you get through a tough problem if you need it. The trick is learning the kinds of questions that lend themselves well to the calculator, and to make sure that you practice using it ahead of time so that you don’t get stuck trying to fiddle around with the technology rather than focusing on the content of each individual problem.

However you choose to use a calculator on the Digital SAT remember this cardinal rule: Desmos (or any other calculator) is NOT meant to take the place of **learning the math**. You’ll use it most effectively if you know the concepts well and can identify how a calculator might be able to save you time. In fact, when you study, you should make it a point to try problems without a calculator first, to develop your ability to identify concepts and strategies.

### When to Use DESMOS

- You’re not fully confident with your “mental math” skills (remember the SAT isn’t heavy on computation, but sometimes you just want to be sure of your arithmetic).
- You’re working on a graphing/coordinate geometry problem that has clearly identifiable characteristics on the graph (e.g. points of intersection, x or y intercepts).
- You’re a bit stuck on one of the SAT’s famous (and feared) “constant problems”.
- You’re comfortable entering in tabular data quickly (e.g. function tables) but less confident with the algebra.

### When Not to Use Desmos

- You know how to solve the problem conceptually and within a reasonable amount of time.
- You want the calculator to “solve the problem for you” without thinking about what the question is asking.
- You haven’t read the problem carefully.
- You’re dealing with very large numbers that are out of range of a standard calculator.
- You’re dealing with irrational numbers (yes, Desmos and many graphing calculators can often handle these, but questions featuring these values are usually best handled conceptually).

### Answering an Official Practice Question with Desmos

Let’s try an example from College Board:

You can absolutely use algebra to solve this equation. We’re not going to work that through fully here, but since the question is given in vertex form, the x-coordinate of the vertex is easy to find (4), then you can solve for the roots and find the value of t that way.

If you’re not as comfortable with that method, here’s how you can do it in Desmos:

Simply type in the equation and look for critical points on the graph (you may need to zoom in and out to make sure the graph shows the entire parabola).

### Attacking Harder Digital SAT Math Questions with Desmos

Let’s look at a more challenging practice question, also from College Board, that includes a constant:

As with any question, read carefully, determine what the concepts are, and think about how you might solve it algebraically. For this problem, the clue is that the line and the parabola intersect at a single point. So, you can solve these two equations simultaneously and use the discriminant (b^{2 }- 4ac) from the quadratic equation to find your answer:

y=2.25 and y=-4x^{2 }+ bx, so -4x^{2 }+ bx - 2.25 = 0

b^{2}-4(-4*-2.25)=0 (when the discriminant is zero, there is a single solution)

b^{2}= 36

b=6

If you’re comfortable with this method, great! But if not, Desmos might give you a leg up.

Let’s see how to use it:

First, plug in the equations (one on each line, and make sure each equation has an x and a y (the y can be written in function notation – f(x) as well)

OK, the first equation, the line, shows up without issue. But where’s the parabola?

The problem is that the constant “b” hasn’t been given a value yet, so Desmos doesn’t know how to draw the graph. Click on the blue “b” under “add slider”. This will allow you to choose the value of b.

Ah–there’s the parabola! But it’s clearly not touching the line, so we need to move the slider until the two graphs touch at a single point (you may need to zoom in to see it clearly). You’ll find that both 6 and -6 will work, since 6 or -6 will both give you 36 when squared. But the problem only asks for the positive value of b, so you'll manually input the correct answer of 6!

In some cases, you may need to adjust the endpoints of the slider too to make sure you have enough room to move it around. Try experimenting with this well ahead of the test so you can learn your way around Desmos.

### Final Thoughts on Using Desmos on the Digital SAT

Desmos is an extremely powerful tool, and you’ll only be using a tiny fraction of its functionality on the test, if you use it at all. But it can definitely be helpful, so why not spend some time learning how you can make it work for you? Remember you don’t have to use it, but it’ll be there just in case.

If you have additional questions about the Digital SAT, subscribe to this blog where we'll continue to share tips for the test or schedule a free Digital SAT tutoring consultation to learn how one of our MyGuru experts can help you understand how you personally should best address Desmos and all other aspects of the test!