Desmos on the SAT: 10 moves, and when to skip it

The 10 moves

1. Graph both sides of an equation. To solve 3(x − 2) = x + 8, type y = 3(x − 2) and y = x + 8 and click where they cross. The x-value is the solution. Or move everything to one side and read the x-intercepts.
2. Solve a system by clicking the intersection. Type both equations as they're given. The point where they cross is (x, y). Lines on top of each other mean infinitely many solutions; parallel lines mean none.
3. Click for the vertex, zeros and intercepts. Click a parabola and Desmos marks its vertex, x-intercepts and y-intercept as gray points. Click one to read its coordinates.
4. Use a slider for an unknown constant. Type the equation with the letter in it, like y = kx + 3, and accept "add slider." Drag k until the graph does what the question asks: touches once, overlaps, or never meets.
5. Fit a model with regression. Put the points in a table (x₁, y₁), then type y_1 ~ m x_1 + b for a line or y_1 ~ a b^{x_1} for an exponential. Desmos reports m and b, or a and b.
6. Find matching coefficients with the tilde. For "which values make these expressions equivalent," write the identity with ~ instead of =, use x₁ for x, and give x₁ a list of test values with at least as many values as unknowns, like x_1 = [1, 2, 3].
7. Get statistics from a list. Type L = [3, 7, 7, 10, 13], then mean(L), median(L) or stdev(L). Use square brackets: curly braces mean something else in Desmos.
8. Shade inequalities. Type each inequality and Desmos shades it, solid for ≤ and ≥, dashed for < and >. The overlap is the solution set. Check a point you're unsure of by typing it in.
9. Graph a circle as given. Desmos graphs x^2 + y^2 − 6x + 4y − 3 = 0 directly. Click the top and bottom points: the center is halfway between them and the radius is half the distance.
10. Test the answer choices. When the setup is hard but the choices are numbers or graphs, type each choice in and see which one works. It's slower than solving directly, so save it for when you're stuck.

Mistakes that cost points

• Not zooming out. An intersection can be off the screen. Zoom out before deciding there's no solution.
• Missing parentheses. 2/3x and 2/(3x) are different graphs. Type the parentheses the question implies.
• Degrees vs. radians. For any trig question, check the angle mode in settings first.
• Copying a rounded decimal. Desmos shows rounded values but keeps more digits. If the question wants an exact answer, use the fraction toggle or work it out by hand.
• Forgetting the subscripts or the test list in regression. Without them it quietly does nothing.

When to skip Desmos

Desmos isn't always faster. A good rule: if you can do it by hand in about 15 seconds, do it by hand. By hand usually wins on:

• Translating word problems into equations. Desmos can't set up the problem for you.
• Geometry and trig facts: similar triangles, special right triangles, angle relationships, area and volume.
• Reading graphs, tables and study designs in Problem-Solving and Data Analysis.
• "Which must be true" and structure questions, where the point is to see the algebra.

The skill isn't "always use Desmos." It's knowing in a few seconds which route is faster for the question in front of you.

How to practice

• Practice with the calculator you'll use. Graphite's built-in calculator works next to every question, and our lessons teach the Desmos moves above, each with the by-hand route too.
• Learn one move at a time. Do five questions with one move until it's automatic, then mix it in.
• Time both routes. On questions you could do either way, try both and notice which was faster. That's how you build the 15-second judgment.