How to Use Desmos on the SAT: The One Trick That Saves the Most Time

By Dr. Brink, Ph.D., 32 years teaching mathematics

The short answer: the most powerful thing you can do with Desmos on the SAT is turn any equation into a graph. Graph the left side as its own equation, graph the right side as its own equation, and the point where the two graphs cross is the solution. It works on almost every equation the test gives you, and it is faster and more accurate than grinding through the algebra by hand.

The graphing calculator sits on your screen for the entire SAT Math section, and most students barely touch it. That is points left on the table. You do not need to be clever with it. One move covers a huge share of the equation questions on the test, and two more cover most of the rest. Here they are.

1. Graph both sides. Where they cross is the answer.

Any time you see an equation, do not solve it. Split it in two. Type the left side as one equation and the right side as another, and read off the point where they meet.

EXAMPLE
Solve 3x + 7 = 25.

In Desmos, type y = 3x + 7 and y = 25. The two lines cross at x = 6. That is your answer, and it took about ten seconds.

The real value shows up on the ugly ones, where solving by hand is a two-minute grind and an easy place to slip.

EXAMPLE
Solve x² - 4x = 12.

By hand you would move everything over and factor. In Desmos, type y = x^2 - 4x and y = 12. The parabola crosses the line at x = -2 and x = 6. Both solutions, no factoring, no sign errors.

This is the whole idea. You are not solving the equation, you are letting the two graphs find the answer for you.

2. If there is an extra letter, use a slider.

Some SAT questions put a second letter in the equation, an a or a k, and ask you to find its value. When you type an equation with a letter Desmos does not recognize, it offers to add a slider. Add it, then drag it until the graph does what the question is asking for.

EXAMPLE
The line y = kx + 2 passes through the point (4, 14). Find k.

Type y = kx + 2 and add the slider for k. Also type the point (4, 14). Now drag the slider until the line runs straight through the point. It lands on k = 3.

3. Reading how many solutions there are, straight off the picture.

A whole family of SAT questions asks how many real solutions an equation has, or how many times a graph meets a line. Once both sides are graphed, the picture tells you at a glance. The rule:

Graphs that cross have two real solutions. Graphs that just touch have one. Graphs that never meet have none.

EXAMPLE
How many real solutions does x² + 2x + 5 = 0 have?

Graph y = x^2 + 2x + 5 and y = 0 (the x-axis). The parabola sits entirely above the axis and never touches it. No intersection, so no real solutions. You did not calculate a discriminant, you looked.

Compare three quick cases. x² - 4 = 0 crosses the axis twice, at -2 and 2, so two solutions. x² = 0 touches the axis once, at the origin, so one solution. x² + 2x + 5 = 0 never reaches it, so none. Crosses, touches, misses.

One last thing: know when to put it down

Desmos is built for equations and graphs, and that is where it wins. For a quick piece of arithmetic or a geometry question that is really about an angle or a rule, your pencil is often faster than typing it in. Use the calculator where it saves you time, not on everything. The students who gain the most are the ones who know which questions to hand to it.

Want to practice spotting these? Every question you miss on a free practice test here comes with a worked solution, and 24 of them include a Desmos walkthrough.

Take a free practice test

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