SAT Math
How to use Desmos on the SAT: equations, tables, and checks
Use the SAT version of Desmos to solve equations, inspect intersections, evaluate functions, and check models without relying on screenshots.
Use Desmos when you can express the question as an equation, intersection, or numerical evaluation. Read the coordinate the question requests and check any domain restrictions before answering.
Practice with the calculator used on the test
Bluebook includes Desmos graphing and scientific calculator options during Math. You can switch between them. College Board also allows approved handheld calculators under its current calculator policy.
Use the College Board version of Desmos for practice, and open it inside Bluebook test preview before test day. The testing version may differ from the ordinary website, so build your routine with the version you will actually use.
I would start with equations and intersections. They give clear outputs you can check by substitution. Trying to learn every menu at once makes it harder to remember the few moves that answer your practice questions.
Solve an equation by graphing both sides
To solve , enter and . Their intersections have x-coordinates and 6. Those are solutions because the two sides have equal values there.
An alternative is to enter and find its x-intercepts. This works because moving everything to one side turns the equation into an expression equal to zero.
Read x when the question asks for an input. Read y when it asks for a function value. For the first graph, the intersection's y-coordinate is 6 at both points; that doesn't mean the equation has only the solution 6.
Systems of Linear Equations · Easy
How many solutions does the given system of equations have?
Choose an answer.
Keep the requested quantity visible
For the system and , the intersection is . If the question asks for x, enter 3. If it asks for , enter 10.
Graphing the system has completed the equation solving, but it hasn't necessarily completed the question. Write the requested expression on scratch paper before entering equations. Substitute the coordinates afterward.
You can check quickly: and . If only one equation works, inspect what you typed. A missing minus sign or parenthesis creates a valid graph of the wrong expression.
Use function definitions and tables for repeated inputs
Enter . Then entering gives 4. Entering gives 19. Using the named function avoids typing the full expression repeatedly.
A table is useful when the question supplies several input values. Put the inputs in the x-column and evaluate the function at those inputs, or compare supplied outputs to a candidate rule. For a linear rule, the rate of change must agree after accounting for the input intervals.
If a problem asks you to fit a stated linear model to a data table, a regression can estimate its parameters. But an estimate from data is not proof that a parameter must have exactly that value. Exact identities and questions about all possible inputs need algebraic reasoning.
Change the window before deciding there is no solution
An intersection may sit outside the default graph window. If meets , the point is . A view centered near zero can hide it.
Adjust the axes to include the relevant region and inspect more than one part of a curve when multiple intersections are possible. For a quadratic, checking only the right-hand branch can miss a negative root.
A zoomed screenshot is not an exact measurement. If the coordinate display is rounded and the answers are exact fractions, use the algebra or compare the proposed fractions by substitution. For , the exact solution is , even if a display shows a decimal approximation.
Know when a graph needs an algebra check
If a question asks for which parameter values a quadratic has exactly one real solution, a slider can suggest a candidate. It can't prove that candidate is the only value or that a near-tangent curve truly touches. Use the discriminant or another exact relationship.
For , one real solution requires , so or . A slider inspection that stops at 6 misses the second value.
For radical equations, check candidates in the original; for rational expressions, check excluded denominator values. Practice these choices in the Math bank: do one question algebraically, one with Desmos, and compare the work. Keep the method that you can execute accurately within the available time.
Try it yourself
Choose an answer.
Sources
Luke Finigan is a student developer and the creator of 1600.now, a free Digital SAT practice platform. About Luke.