With the SAT’s transition to a digital test, they’ve also transitioned to a digital calculator. Students are now given access to a version of Desmos, the most popular online graphing calculator, inside the Bluebook testing app for the entirety of the math section. While students are still permitted to bring their own scientific or graphing calculator, Desmos is meaningfully faster and more powerful. For most students, mastering Desmos will significantly improve their performance and consistency on the digital SAT’s math section.
Every function shall be graphed
Anytime a student doesn’t know what to do with a function—and oftentimes even when they do—it’s a good idea to graph the function on Desmos. Just as with strategies like using the answers and generating examples, graphing functions lets students see concrete representations of functions, which can make all the difference.
Once a function is graphed on Desmos, the calculator will put gray points on any mins, maxes, x-intercepts, and y-intercepts. When students hover over these points, they can see the exact coordinates, and when they click on them, the coordinates will persist even when students mouse away.
Using graphs to solve equations
Desmos is especially useful for finding intersections between lines. While some questions will directly ask for the point where lines intersect—for instance, by asking for the solution to a system of equations—students can actually use Desmos to solve any single-variable equation.
To solve equations by graphing, students should type the left and right side of the equation in separate lines. So, to solve, say, 3x + 5 = 17, they would graph y = 3x + 5 as one equation, and then click or hit enter to move to the next line and put y = 17 as a second equation. Desmos will put a gray point at the intersection between these two functions, and the x-value of that point will be the solution.
This is also useful for word problems that give students an x-value and ask for a y-value and vice versa. If a student is asked to evaluate y = 5x – 2 for x = 4, for example, the answer will simply be the y-value of the intersection between those two lines.
How to practice outside of Bluebook
For students who are using secondary materials to practice outside of Bluebook, the SAT’s version of Desmos is also available here: https://www.desmos.com/testing/cb-digital-sat/graphing. The differences between this version of Desmos and the default web version are minimal, so students who are already used to using Desmos in class shouldn’t worry. The SAT version is intended as an offline calculator, so it disables features like account management, importing images, and saving and sharing graphs. Otherwise, the SAT version of Desmos is fully functional.
What if you can’t see your function?
If a student can’t see a function that they’ve graphed or a key point is off-screen, there are several options. A student can click the minus sign in the upper-right to zoom out, they can click and drag to move the window, or they can click on the wrench and manually input a domain and range. If it looks like the function isn’t showing up at all and they’ve checked for typos, the student should make sure that a colored circle is showing immediately to the left of the equation—if an empty ring is showing, they can click on the ring to turn the designated graph back on.
Doing calculations
While most of the screen space on Desmos is dedicated to a graph, it also functions as a scientific calculator. Students can choose between typing and clicking on the keyboard icon in the bottom left to pull up a scientific calculator interface. As students put in or change numbers, the output will show in the same line, which can allow students to quickly try multiple answer choices for questions where they’re using the answers.
Two common sticking points for students are fractions and exponents. To get an exponent, students should either click on the button showing a to the power of b, or type shift-6 on their keyboard. And to exit an exponent (or a parenthesis, denominator, or radical), students can click the right arrow on either the on-screen keyboard or their physical keyboard. To get fractions, students can simply use the division sign. When they’re done, students can click the fraction symbol immediately to the left of their computation to turn their answer from a decimal into a fraction.
Different students have their own preferences when it comes to calculators, but in my experience, students make the fewest computation mistakes when they write expressions by hand, and then type the entire expression into the calculator once there’s only arithmetic left. That way, students grapple with the problem-solving aspect of questions directly and avoid wasting time doing multiple individual calculations.
