Digital SAT · Math · Complete guide
How to Use Desmos on the Digital SAT
Nova here. The Digital SAT has the Desmos graphing calculator built right in, and used well it can win you points and cut careless mistakes. This is the full guide: why graphing beats algebra, 15 techniques you can click through, and the moments to close the calculator and use your head.
Why graphing beats algebra
Solving by algebra alone is like running a race in the wrong shoes. You can finish, but you are working harder and slipping more than you need to.
The algebra way
- One flipped sign while you rearrange or substitute, and the answer is wrong.
- Rewriting into y = mx + b or completing the square burns minutes you need later.
- It is all in your head, so the mental load piles up and tires you out for Module 2.
The Desmos way
- The answer is a click. Desmos auto-marks the points that matter (crossings, roots, vertex, intercepts) with grey dots; click a grey dot for its exact coordinates.
- You see the answer, so a wrong one looks wrong. "No solution" and tangency become obvious.
- It takes the equation in any form, so there is nothing to rearrange first.
The 15-second rule: The rule of thumb: if the by-hand path would take more than about 15 seconds, graph it. If you can factor it or do the arithmetic in your head faster, do that. The calculator is for the questions where it actually saves time.
What you'll learn
- Turn "solve for x" into "find where two graphs cross", so you skip the algebra.
- Read a parabola's roots, vertex, and intercepts by clicking, not by factoring or completing the square.
- Fit a line or curve to data, and pull the mean, median, or standard deviation from a list in one step.
- Test an unknown constant with a slider, and know the moments to close the calculator and use your head instead.
Start here
- What Desmos Is and Where It Lives on the SATThe free calculator built into the digital SAT, and how to open it.
- Desmos Basics: The InterfaceType an equation, read the graph, and the four buttons that matter.
- Your First Graph in DesmosType an equation, watch it draw, click the answer.
- Typing Math in DesmosExponents, fractions, and roots without getting stuck.
The 15 techniques, easiest to hardest
Grouped by how hard they are to use in Desmos. Each card is labeled with the SAT topic it covers, plus the cue in the question that should make you reach for it. Every technique is its own lesson: the algebra-vs-Desmos contrast, a step-by-step walkthrough, and a real SAT question to try.
Start here
Type an expression, then read or click a point.- 1Solve Any Equation by GraphingAlgebraTurn "solve for x" into "find where two graphs cross".SolvesSolve for xLinear equationsNonlinear equationsExponential equationsWhere two graphs crossWhen you see: The question says "solve for x", or asks which value makes an equation true.
- 2Graph a System of Two Linear EquationsAlgebraTwo lines, one meeting point. Find it without touching algebra.SolvesSystems of equationsPoint of intersectionBreak-even pointsWhen you see: Two linear equations, and you need the point where they meet.
- 3Read a Line's Slope and Intercepts from Its GraphAlgebraSlope, x-intercept, y-intercept: three answers, one graph.SolvesSlopeInterceptsEquation of a lineWhen you see: You need a line's slope, x-intercept, or y-intercept.
- 4Read a Parabola's Vertex, Roots, and InterceptsAdvanced MathEvery "find the max, min, or zero" question turns into pointing at a graph.SolvesParabola vertexMax or minRoots and zerosWhen you see: A parabola question asks for the vertex, the maximum or minimum, or the zeros.
- 14Model Exponential Growth and DecayGraph y = a·b^x and read the starting value, the trend, and any future value.SolvesExponential growthExponential decayGrowth and decay modelsValue at a timeWhen you see: An exponential model like y = a·b^x, and you need the start value, the trend, or a value at a time.
- 15Solve Trig Equations in Degree ModeFlip Desmos to degrees, graph the trig equation, and click the crossing.SolvesTrig equationsDegree modeSine and cosine valuesAnglesWhen you see: A trig equation or value in degrees (sine, cosine, or tangent).
- 5Find a Circle's Center and Radius from Its EquationGeometrySkip completing the square. Graph it and measure.SolvesCircle centerCircle radiusCircle equationsWhen you see: A circle's equation, and you need its center or radius.
- 6Check if Two Expressions Are EquivalentAdvanced MathGraph both, and if they land on the exact same curve, they are equal.SolvesEquivalent expressionsSimplifyingFactoring checks
Data moves
Build a list or table, then let a formula do the work.- 7Find Mean, Median, or Standard Deviation from a ListDataDump the numbers in, let a formula do the sorting.SolvesMeanMedianStandard deviationRangeWhen you see: A list of numbers, and you need the mean, median, or standard deviation.
- 8Build a Table to Test Several x-values at OnceAdvanced MathStop plugging in one number at a time. Evaluate the whole list in one shot.SolvesFunction tablesTest many x-valuesCompare outputsWhen you see: You need to test several x-values against the same function at once.
- 9Fit a Line or Curve to Data (Regression)DataFeed Desmos the data points, let it hand you the equation.SolvesLine of best fitCurve of best fitPredict from dataWhen you see: A table of data points, and you need the line or curve that fits them.
- 10Find a Residual from a Line of Best FitDataHow far a real point misses the model, and which direction the miss goes.SolvesResidualsActual vs predictedWhen you see: A line of best fit, and you need a residual (how far a real point misses the model).
Interactive
Drag a slider or test a region.- 11Graph a System of Inequalities to Test a PointAlgebraShaded regions overlap exactly where every inequality agrees.SolvesSystems of inequalitiesTest a pointFeasible regionsWhen you see: A system of inequalities, and you need to check whether a point satisfies all of them.
- 12Use a Slider to Test an Unknown ConstantAlgebraDrag a value around until the graph does what the question describes.SolvesUnknown constantFind the value that fitsWhen you see: An unknown constant, and you need the value that makes the graph behave a certain way.
- 13Find a Constant for the Number of SolutionsAdvanced MathDrag the constant until the graph shows one crossing, or two, or none.SolvesNumber of solutionsOne, two, or no solutionsTangencyLine and parabola
Interface settings to know
Switch to Degree mode for trig
Desmos defaults to radians. For any trig question, click the wrench icon and choose Degrees, or every sine, cosine, and tangent value comes out wrong.
Convert decimals to fractions
Desmos shows decimals like 1.333. SAT choices are usually fractions. Click the round fraction-converter button next to a value to turn 1.333 into 4/3.
Use subscripts for tables
When building a table for a regression, name the columns x_1 and y_1 so the regression binds to the right data.
Turn on Projector Mode for clearer graphs
Desmos draws thin lines by default, which makes a crossing or intercept hard to pin down. Open the wrench icon (Graph Settings, top right) and turn on Projector Mode for thicker lines and larger labels, so the points you click are easier to hit exactly.
Use Zoom Fit to frame your data
After you type data into a table, the points can land off the default screen. Click the small magnifying-glass icon next to the table to Zoom Fit, and Desmos snaps the view to frame every point at once.
Widen the axis bounds when the graph looks empty
Desmos opens on a small window from -10 to 10 on both axes. If a crossing, vertex, or data point sits outside that box, the graph can look empty even when an answer exists. Open the wrench icon and widen the x and y bounds until the point you need comes into view.
Reset the view with the House icon
If you pan around and lose the graph, click the House icon on the right toolbar to snap the view back to the origin. It is the fastest way to get un-lost without retyping anything.
When NOT to use Desmos
- Abstract-constant questions. When a question asks for the value of a constant that makes a system have no solution or infinitely many, sliders estimate and mislead. Set slopes or coefficients equal algebraically.
- Questions that factor in seconds. If you can factor or plug in faster than you can type and click, do that.
- Desmos-proof abstract questions. Some newer items are written so the graph tells you nothing. Recognize them and reason symbolically.
- Symbolic rewriting. Desmos solves and graphs numerically, so it cannot factor, expand, or simplify an expression for you. When a question asks you to rewrite or factor an expression, do that step by hand.
Put these Desmos moves to work
SAT Prep Quest drills run these calculator techniques on real SAT questions and adapt to the ones you miss, so the moves become automatic before test day.
Practice freeSAT is a registered trademark of the College Board, which was not involved in producing, and does not endorse, this product. Score estimates are Learner Labs projections, not official College Board scores.