Cracking the Digital SAT® Math Section with Desmos: A Student's Guide
Since March 2024, the Desmos calculator has been integrated directly into the SAT's test-taking software for every student taking the Digital SAT. This built-in, online graphing calculator allows students to perform complex calculations, graph equations, analyze functions, and visualize mathematical concepts directly within the test interface. Using it is fast, brain-dead, and accurate. On a test where the score is all that matters, we LOVE that. While Desmos can’t be used for every type of problem on the SAT, it will solve a lot of them. This article will show what types of SAT Math problems you can use the Desmos SAT calculator to solve, and I’d encourage you to try these methods, even if you know how to solve the problem traditionally.
Desmos on the Digital SAT®: An Overview
The transition to the Digital SAT® (DSAT) introduces Desmos®, a built-in graphing calculator that replaces the need for a handheld device. Desmos is integrated into the Digital SAT® platform. Students, therefore, don’t need to bring a separate calculator.
Mastering Desmos: Key to SAT® Success
The Desmos® calculator is a game-changer, but only if students know how to use it efficiently. Practicing beforehand ensures confidence and speed on test day. Teachers play a key role in helping students become comfortable with Desmos® before the SAT®. Help students recognize when to use Desmos® vs. other methods. Horizon Education integrates Desmos® into our SAT® prep platform, allowing students to practice using the same tools they’ll encounter on test day.
Solving Systems of Equations
Desmos is powerful for solving systems of equations. The answer will be the point where these two graphs intersect. The point should be automatically highlighted by Desmos. Scroll out on your graph if you don’t see anything right away. You should see vertical lines.
A Word of Caution with Linear Systems
I want to particularly highlight that first one, since Desmos is usually so powerful for solving systems of equations. This problem looks like the other systems of equations problems where we definitely want to use Desmos, but it is not. You can tell this is a linear system of equations because the x in both equations is only to the power of 1 (x1). If you see this, you need to solve for the slopes of these equations and set them equal to each other because these equations are parallel lines. Do NOT use Demos with constant slider for this.
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Finding Intersections of Shaded Areas
In the graph, find the lowest point where the two shaded areas overlap.
Regression Analysis
In line 1, type table. In the x1 column, type your x-values from your points. Click the dropdown which says Linear Equation and select from the menu the type of equation you are trying to model. Here that would be Exponential Regression.
Identifying Key Points on a Graph
If you hover over your line, Desmos will highlight the y-intercept (and x-intercept(s)) automatically. If you hover over your line, Desmos will highlight the maximum (or minimum) point automatically.
Transformations of Functions
In line 2, type h(5 - 2x). This will give you a transformed graph of the original function. The value of g(x) is 0 at its x-intercepts, which will be marked automatically. Desmos will handle all the standard transformations. Try typing 7h(x), -g(h + 7), and h(2x) - 8.
Utilizing Answer Choices
Your answer choices are x-values.
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Calculating the Mean
In line 1, type mean( ). Put your list of numbers in the parentheses, separated by commas. Mean (13, 15, 25, 26, 29, 29, 34, 37). Generally, I advise that you avoid using Desmos for these if you can solve them traditionally, but Desmos will work in a pinch.
Problems Where Desmos Might Not Be the Best Choice
You can use Desmos to solve these, but it is very slow since you cannot copy and paste the equations. In line 1, type table. Type a bunch of random x-values (numbers) in the first column.
Dealing with Discriminant Problems
You can do this problem with Desmos, but it is finicky. In general, if it is free response and you know how to do it by using the discriminant, I would do that. In line 2, type g(x) = x^2 + 8x + a. For constants, I typically stick to a and b in Desmos. You should see an option pop up to add a slider for a. Slide the slider back and forth until you can get the lines to only meet at one point. If you need to extend the range of the slider (default is -10 to 10), you can click on the numbers at the end of the range to type your own custom values.
Non-Intersection Problems
This problem is almost, but not quite, a classic intersection problem. It is effectively asking what values of d make g(x) = 3x^2 − 24x + d and h(x) = 0 not intersect. Like the previous problem type, I would generally use the discriminant rule instead if it is a free response question, but it can be done in Desmos. Start typing in values for c until you get the two lines to intersect at 1 point. Beyond that value for a they will not intersect, so that will be your answer.
Challenge: Here is a harder version of variation 1.
Note: If you are worried about the “infinitely many” case, click the icon near the line number to hide on of the function.
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