Desmos on the digital SAT
The entries worth knowing by heart before test day. Everything here works in the Desmos calculator built into Bluebook — no app, no account, nothing to buy.
The five that matter most
If you learn nothing else, learn these. They cover a large share of the calculator-section questions where Desmos beats algebra outright.
| Type this | What it does |
|---|---|
| y=f(x) | Graph anything and read the answer off the picture. Tap the curve to reveal zeros, intercepts and turning points — Desmos labels them for you. |
| y_{1}=… y_{2}=… | Solving an equation? Graph each side separately and tap where they cross. The intersection is the solution. Works when factoring doesn't. |
| x=3 | A vertical line. Pair it with a curve to read a value off the graph instead of substituting by hand. |
| …{x>0} | Restrict a graph to part of the domain. Useful for piecewise questions and "for positive x" wording. |
| y_{1}~ax_{1}+b | Linear regression on a table. Gives you slope and intercept of the line of best fit in one line. |
Typing shortcuts
Desmos rewrites what you type as proper math as you go. These are the keystrokes that get you there fastest.
| Press | You get |
|---|---|
| / | A fraction. Type the numerator, press /, type the denominator, press the right arrow to get out. |
| ^ | An exponent. Right arrow leaves it — the single most common place students get stuck. |
| sqrt | A square root sign. Typing the letters is enough; Desmos converts it. |
| _ | A subscript, for x_1 and y_1 in regressions. |
| pi | π. Same idea — type the word. |
| abs | Absolute value bars. |
Question types worth a graph
| Question | Fastest approach |
|---|---|
| System of equations | Graph both, tap the intersection. Faster than substitution almost every time, and immune to sign errors. |
| Quadratic roots | Graph it and tap the x-intercepts. No factoring, no formula. |
| Vertex or maximum | Graph it and tap the turning point. Desmos labels the coordinates. |
| Circles | Type the equation as given, even in unexpanded form. Desmos draws it and you read the centre and radius off the picture. |
| Line of best fit | Make a table, then y_{1}~ax_{1}+b. Read a and b from the panel. |
| Exponential growth | Graph it and tap the point you need. Beats rearranging logarithms under time pressure. |
| "For what value of x…" | Graph both sides, or graph one side and add y= the target value. Tap the crossing. |
When not to open Desmos
This is the part most guides skip. Reaching for the calculator has a cost — roughly ten to fifteen seconds of typing — and on some questions that's the whole time you had.
- Arithmetic you can do in your head. Just do it in your head.
- Sum or product of roots — −b/a and c/a are faster than graphing, if you remember them.
- Questions asking for an expression rather than a number. Graphs give numbers.
- Anything where you already see the answer. Trust that.
Not sure which situation you're in?
That's the whole point of CalcHack. Photograph a question and it tells you whether Desmos wins — and exactly what to type if it does.
Scan a question free