Desmos for the digital SAT

Level 1: The moves everyone should know

• Graph an equation — type it exactly as written; Desmos handles y = forms, inequalities, and even unsimplified equations.
• Find intersections — graph both equations and click/tap the intersection point. This solves most systems-of-equations questions instantly.
• Find zeros and intercepts — graph the function and click where it crosses the axes.
• Check an answer — plug your solution back in, or graph both sides of an equation as two curves and look for the intersection.

Level 2: Intermediate

• Solve without isolating y — type the equation in any form (e.g. 3x + 2y = 12); Desmos graphs it anyway.
• Evaluate functions — define f(x) = …, then type f(7) to evaluate.
• Tables — great for "which table represents the function" questions: define the function, add a table, compare.
• Vertex and extrema — graph a quadratic and click the vertex; no vertex-form algebra needed.
• Inequalities and shaded regions — type the inequality directly to see the solution region.

Level 3: Advanced

• Regression — for line/curve-of-best-fit questions, enter data in a table and use y₁ ~ mx₁ + b.
• Sliders for parameters — for "for what value of k…" questions, use a slider and watch when the condition holds (e.g., when two graphs are tangent: exactly one intersection).
• Systems with a parameter — "no solution" means parallel lines: use sliders or match slopes visually.
• Batch-checking choices — graph all four answer choices at once and see which satisfies the condition.

The 15-second Desmos decision

When Desmos is usually faster: systems of equations, quadratic roots/vertex, "how many solutions," intersection points, checking messy algebra, median/mean of a list (use the median() and mean() functions).

When your head is usually faster: simple linear equations, percentage and ratio arithmetic, questions asking for an expression rather than a number, exponent rules, and anything where typing the problem takes longer than solving it.

Common Desmos mistakes

• Typing an expression wrong (misplaced parentheses, forgotten negative) and trusting the pretty graph anyway — re-read your input.
• Reading the wrong intersection when curves cross more than once — check the question's domain.
• Answering with the x-value when the question asks for y (or the sum, or the product).
• Rounding a long decimal when the answer wants an exact fraction — click the value to toggle forms where available.
• Using Desmos as a substitute for understanding — the calculator executes; you still have to set up the math.

Practice tools and lessons