Guide
How to Use Desmos on the SAT
Bluebook, the app the SAT is taken in, has a Desmos graphing calculator built in. Used well, it turns a large slice of SAT Math into typing the question and reading the answer. This guide collects what the Learn Desmos course teaches across its 27 chapters, from the first keystroke to the choice between graphing and regression.
Last updated: September 5, 2026
The calculator you get on test day, and where to practice with it
You sit the SAT in Bluebook, and College Board says Bluebook has to be installed before test day. Its calculator policy page describes an embedded Desmos calculator with two options, graphing or scientific, and says you can toggle between them. The same page says you may bring your own approved handheld instead, that calculators with computer algebra system (CAS) functionality are no longer allowed anywhere in the SAT Suite, and that no calculator at all is permitted during Reading and Writing. Everything below is about the graphing option.
Practice with the calculator you will see on test day. The course's first chapter starts by searching for SAT Desmos on Google and opening the first result: the Desmos graphing calculator built into the testing app, with a green bar across the top. The course treats it as the same calculator the calculator button opens inside Bluebook. College Board's practice page also points to a test preview and full-length practice tests inside the Bluebook app.
The SAT version and regular Desmos differ in one place: the plus menu in the top left. The SAT version only really offers Table (Inference is for AP Statistics, so ignore it); regular Desmos adds a note, a folder and an image. Everything else works the same, so either one is fine for practice.
No copy and paste in Bluebook
Ctrl+C and Ctrl+V are disabled inside Bluebook. Retype what you would have copied, or duplicate the row: edit list, duplicate, done.
Leave the on-screen keypad closed; everything on it is faster from a real keyboard. Undo and redo are Ctrl+Z and Ctrl+Shift+Z (Cmd on a Mac). Trig functions use radians by default; to switch to degrees, open the graph settings with the wrench and pick Degrees, before you type any trig expression.
How Desmos reads what you type
Desmos has no solve button. It reads what you type as math, so the way you type decides what you get. These are the conventions from Section 1 of the course.
| What you want | What to type | Notes |
|---|---|---|
| Add, subtract | , | The minus is the hyphen next to the zero. The result shows at the right edge of the row. |
| Multiply | | Shift+8, shown as a dot. Never type the letter x for times; Desmos reads it as the variable x. |
| Divide | | Only the 3 goes on top, so this is 6.5. To divide the whole sum, highlight first, then press the slash: now it is 4. |
| Exponent | | The caret is Shift+6. Type the parentheses first so everything stays in the exponent: is 8, but is 4. |
| Roots | , , nthroot | For an nth root, type the degree first, then press the right arrow to move under the root. |
| Pi and percent | , % | Typing p then i turns the letters into the symbol. The percent sign is Shift+5. |
| Absolute value | | The vertical bar is Shift+backslash. |
| Inequalities | , | Less than is Shift+comma, greater than is Shift+period. Press equals right after the sign and Desmos joins them into ≤ or ≥. |
Subscripts. A letter followed by a number becomes a subscript: type and Desmos writes x₁. That matters because x₁ is a constant, not the graph's x, which is what makes regression possible. It is also the name of a table's first column.
The tilde. ~ is the regression symbol: hold Shift and press the backtick key (top left, under Escape), or find the squiggle under ABC on the keypad. asks Desmos to find the x₁ that makes both sides equal, and it reports x₁ = 3.
Lists. Square brackets make a list: . , with three dots, gives every integer from 1 to 10. Brackets are required whenever a list is used outside a function; on its own is an error.
Restrictions. Curly brackets (Shift plus the square bracket keys) set a condition. draws the line only to the right of 3. A condition can also restrict a constant: has two answers, 3 and −3, and forces the positive one. Conditions chain: .
Function notation. Type and Desmos graphs it like , but now the rule has a name: on the next line gives 11, and works from the inside out. Desmos cannot evaluate until you have told it what q(x) is.
Variables and constants. Lowercase x and y are the variables, the two axes. Every other letter, including uppercase X, is a constant. Define one with the letter first: ; defines nothing. Never use e, which Desmos reserves for Euler's number, and never define the same letter twice.
Picking your own values
When a question lets you choose a value, never pick 0 or 1, and never give two constants the same value. Multiplying by 1 or adding 0 hides mistakes, and equal constants make different answer choices look identical. and are safer picks.
Tables. Typing table on an empty line creates one. Enter moves down a column and Tab moves across. Every row becomes a point, and the columns are named and .
Graphing questions: read the answer off the picture
Section 2 of the course, Graphing, covers the question types you solve by typing an equation and looking at the picture; the curriculum estimates these at 25.24% of SAT Math question types. Two rules first: put in front of anything you want graphed, and only lowercase x graphs. One short worked example per pattern follows.
The function is defined by . What is the -intercept of its graph?
- Type
, pressing the right arrow after the exponent so the −5x is not dragged up into the power. The question writes the rule as f(x), but what you want here is the picture, so putin front. - Click the curve so Desmos marks its points of interest with gray dots. Click the dot on the y-axis and read the label, (0, 2). The small arrow beside the label exports the point into the expression list.
- If the question asked for y when x = 2 instead, type
on a second line and click where the vertical line meets the curve: (2, 4).
Answer: The y-intercept is 2. Regression would work too ( gives 4 for the second version), but retyping the whole expression is slower than clicking a point the graph already shows.
The graphs of y = 2x + 2 and y = 5x − 4 intersect at one point. What are its coordinates?
- Type
on one line andon the next. - Click one line, then click the gray dot where it crosses the other. The label reads (2, 6).
Answer: (2, 6). A solution of a system is an intersection, so this is also how you count solutions.
Which of the following points is a solution to the system y ≤ 2x + 3 and y > −x − 1? (A) (−4, 0) (B) (0, 4) (C) (2, −4) (D) (1, 2)
- Type
: press = right after < and Desmos joins them into ≤, drawn as a solid line because points on the line count. - Type
on the next line. It is strict, so the boundary is dashed and points on it do not count. - Type each choice on its own line:
,,,. The solution is the region shaded twice. If a point sits close to a boundary, zoom in before you decide.
Answer: Only (1, 2) lands in the double-shaded region, so the answer is D. There is no regression method for inequalities: a tilde needs two equal sides, and an inequality describes a whole region.
is the equation of a circle. What is its radius?
- Do no algebra. Type
exactly as written and Desmos draws the circle. - Click the circle, then click its highest and lowest points and export both. Never use the left and right points; they often sit on the x-axis and are hard to click. Do not confuse the y-intercept (0, 2) with the maximum (3, 3); compare the y-values.
- Name the points by typing in front of them:
and.gives 10, the diameter, sois the radius.gives the center, (3, −2), and plots it.
Answer: The radius is 5. To see whether a point is inside the circle, type it and look. If the equation holds an unknown, like through , graph first, then regress: gives r = 5.
What is the sum of the solutions of ?
- Type
exactly as written. Desmos graphs an equation with only one variable as vertical lines, one per solution. - Click each line and read its x-value: −1 and 5. The y-value is just where you clicked, so ignore it.
- Set each solution to a constant,
and, then type.
Answer: 4. Regression cannot do this: it returns one number, so it cannot add solutions or count them. For how-many-solutions questions, graph both sides as separate lines and count the intersections, zooming in if two lines seem to merge.
Always split an equation at the equals sign when counting solutions: on one line, on the other. On one line, a no-solution equation and an identity both show nothing; split, you see parallel lines or one line sitting on top of the other. A lone number still gets its own line, as . Splitting also makes a slider readable, which one line never is. Never drag that slider to find a constant, either: if the question lists choices for k, type them in one at a time; if it does not, narrow the number by hand the way the course does, 0.2, then 0.3, then 0.25, and zoom out at the end to check no second crossing is hiding off screen.
Which of the following is equivalent to ? (A) (B) (C) (D)
- Type
, then every choice with y = in front:,,,. - Look for the choice whose curve disappears under the original. Click the colored circle beside
to switch it off and on; the matching curve is still there underneath.
Answer: B. If the expressions contain a constant, watch the slider trap: Desmos starts a new slider at 1, and with a = 1 the choices and sit on the same curve. Type in its place and the wrong choice lifts off.
is divisible by . What is the value of k? (A) 1 (B) −1 (C) 4 (D) −4
- Two expressions that share a factor share an x-intercept, and x − 3 is 0 at x = 3. Type
so that intercept is on screen. - Type
and add the slider for k. Do not drag it: type each choice into k until the parabola crosses the x-axis exactly at 3. If the question says k > 0, honor it. - The regression route: x = 3 makes the whole expression 0, so
solves it directly, with a new letter because k already has a slider.
Answer: k = 1 by either route. Use whichever is faster for the question in front of you.
That leaves the function question, the second chapter of Section 2 and the one pattern where you barely look at the graph. If the only equals sign in the whole question defines the function, define it and type exactly what is asked: , then , which gives 21. Count the equals signs, because a second one, as in f(a) = 21, what is a?, turns it into a regression: gives a = 4.
Regression questions: let the tilde solve it
Section 3, Regression, is the highest-leverage technique in the course; the curriculum's estimate puts these question types at 28.31% of SAT Math. The idea fits in one sentence: Desmos estimates the undefined constants in a line until both sides of the tilde are equal. Follow its rules and it solves equations for you.
- Constants, not variables. Lowercase x and y throw an error next to a tilde; use a subscript like
. - One tilde per line, and nothing about the regression may spill onto the next line. A second tilde on the same line is an error however you arrange it, so give each equation a line of its own.
- Only undefined constants get solved. If
is already in your list,solves for m only; rename b if you meant a different one. - One solution only, favoring whole numbers and the smaller absolute value.
reports 3;on a separate line forces −3. When a question involves several solutions, graph instead. - Read the output. A messy decimal instead of a whole number or clean fraction usually means the setup is wrong:
gives 2.333, your cue to reread the question.
If 3(x + 2) − 5 = 2x + 7, what is the value of 4x − 1?
- Every x becomes and the equals sign becomes a tilde:
. Desmos reports x₁ = 6. - The question asked for 4x − 1, so type
on the next line. Desmos uses the value it just found.
Answer: 23. The phrase is equivalent to counts as an equals sign.
2(x + 3) + kx = 5x + 6 for all values of x. What is the value of k?
- Set it up as usual:
. The first answer is wrong, because Desmos treats both x₁ and k as unknowns and picks any pair that happens to work. - On its own line, type
. Now the regression must hold for all ten values at once, which only the true constant can do: k = 3.works too. - The check: when you solve for a constant, a variable should never appear under regression parameters. If x₁ is listed there, you forgot the list.
Answer: k = 3. The list needs more entries than there are constants to solve, and it must not contradict the question. If the question already gives x, skip the list and type . For a stated condition like k > 0, add to the line.
3(x + 2) = ax + 6 has infinitely many solutions. What is the value of a?
- Infinitely many solutions means both sides draw the same line, so they agree for every x. Type
. - On the next line,
. Desmos returns the a that works for every number in the list.
Answer: a = 3. Use this only when the question states there are infinitely many solutions, never when it is an answer choice, and never for no, one or two solutions; those are graphed.
2x + 3y = 12 and x − y = 1. What is the value of x + y?
- Two separate regressions do not work, because Desmos does not link the x₁ on one line to the x₁ on another. Put every left side in one list and every right side in another:
, first equation first in both lists. - Desmos solves both at once: x₁ = 3, y₁ = 2. Type
to get what the question asked for.
Answer: 5. Percent word problems are systems in disguise: replace is and was with equals signs and type the question almost verbatim. A jacket's price was 20% more than its cost, and the price was $60, becomes ; the cost is 50.
Two limits with brackets. You cannot also set a variable equal to a list, so check a constant by hand: set , then , and confirm it did not move. And do not over-constrain: pin both variables and the constant, and Desmos cannot solve it. When a constant will not stay constant, substitute: if y = 2x + n and y = 5x − 4 meet where x = 2, type with , and n = 2.
f is a linear function with f(2) = 8 and f(5) = 17. What is f(10)?
- Function notation is just points: f(2) = 8 is the point (2, 8). Type
tableand enter 2 and 5 under x₁ with 8 and 17 under y₁. Never enter the point you are solving for, so leave 10 out. - Type the line through the points, y = mx + b, in regression format with the table column names:
. Desmos reports m = 3, b = 2. Add regression on the table, in the edit list, writes the same line for you. - Type
on the next line; Desmos reuses m and b from the regression.
Answer: f(10) = 32. A table is really just and , which is why your subscripts must match the column headers. A second table uses x₂ and y₂.
If the drop-down does not offer the form in the question, type the regression yourself: for y = a(x − h), type . Only two equations need memorizing: circle standard form, , whose center is and whose radius is the square root of the right side, and quadratic vertex form, , whose vertex is the maximum or the minimum. Vertex form earns its place because it cuts the unknowns down. When the question hands you the vertex, put h and k straight into the model before you regress, and a is the only letter left for Desmos to find.
Give a regression at least as many points as it has constants: a line needs two, a standard-form parabola three. If a regression refuses to pass through your points, check under Statistics; it has to be exactly 1. The exception is the standard form of a line, Ax + By = C, which no number of points pins down: force one value with and fit . Regressions do not draw a curve; to see one, duplicate the line and change to and to x on the copy.
If F = (P − Q)/R, which of the following expresses R in terms of P, Q and F?
- Type the equation exactly as given, swapping the equals sign for a tilde:
. Do not rearrange anything. - Give every constant except R a different value, never 0 or 1:
,,. R is the only undefined letter, so Desmos solves for it: R = 4. - Type each answer choice and see which one equals 4.
gives 4;gives 2.5.
Answer: The choice R = (P − Q)/F. Equal values would make different choices look identical.
| If the question... | Tool | Chapter |
|---|---|---|
| Has no equation, only words to reason about | Stays on paper | Choosing Your Method |
| Hands you an equation and asks for a point on it | Graph, click the point | Basic Graphing |
| Defines f(x) and nothing else is set equal to anything | Function notation | Functions |
| Contains < or > | Graph, read the shaded region | Inequalities |
| Gives a circle equation | Graph, top and bottom points | Circle Equations |
| Asks for the sum, greatest or least solution, or how many | Graph, read or count | Multiple Solutions |
| Asks which expression is equivalent | Graph, find the curve on top | Equivalent Expressions |
| Asks whether one expression is a factor of another | Graph, line up the x-intercepts | Factoring |
| Asks to express one letter in terms of the others | Regression, isolation | Isolation |
| Gives points, or a graph you can pull points from | Table regression | Given Points |
| Has more than one equation | Bracket regression | Systems of Equations |
| Has one equation and asks for the variable | Regression with | Single Variable Equations |
| Has one equation and asks for a constant | Regression with | Constants |
The rule of thumb: regression solves for one unknown number; the graph shows shapes, counts and comparisons. Behind everything is one framework from the last chapter: meet every condition the question states, then type in what is asked and read the answer. Take with , and , what is ? Define , then put both function values into one bracket regression with the constraint on the end: . Desmos gives a = 110 and b = 90, so is 200. When the question wants an expression instead, pick any two values that satisfy the constraint, such as and , type the expression, then move the values and confirm it does not change. The Desmos regression guide walks through every pattern.
Statistics, fractions, sliders and tables
The Prerequisites section has twelve short chapters, and several are pure time-savers on questions that are neither graphing nor regression.
Statistics. Type the function name, open a bracket, and list the numbers: is 7, is 6, is 1.63. is 5, and is (2.5, 4), which Desmos also plots. is 12, is 12, is 2. max, min, floor, ceil and round do what their names say. Store a list first and the functions take it whole: , then .
Fraction to decimal. When a result is a decimal, look at the icon on the left of the row. shows 0.625; click the icon and it flips to 5/8. The button only appears when the decimal converts cleanly: and get it, but and never do. If you do not see the button, the SAT answer is probably the decimal.
Sliders. Type and Desmos adds a slider. The classic use is dragging until a graph passes through a given point: with and on screen, drag a until the line sits on the point, at a = 3. For a precise value, especially a small decimal like 0.03, type it instead of dragging.
Tables and factor pairs. For factor pairs, type , turn it into a table with the table icon in the edit list, then click the last x value and hold Enter. Each new row adds 1 to x, and the rows where both numbers are whole are the pairs: 1 and 24, 2 and 12, 3 and 8, 4 and 6. A table also converts forms: turn into a table, add a quadratic regression, and a = 1, b = −4, c = 3 is the standard form.
When not to reach for Desmos
The course is upfront about its limits. Its own estimate is that the graphing and regression methods address 53.55% of SAT Math question types (Graphing 25.24% + Regression 28.31%), so a large share of the test still runs on ordinary math. Here is when the calculator is the wrong tool, or the right tool used the wrong way.
- No equation, no Desmos. Pure word reasoning, with nothing in the question you could type, stays on paper. The course says that is the only kind of question that does.
- Never use regression to count solutions or add them up. It returns one number and hides the rest. Graph the equation and read the vertical lines.
- Never use regression on an inequality. A tilde only compares two things that are supposed to be equal.
- Never use the infinite-solutions regression when infinitely many is one of the answer choices, or for no solution, one solution or two solutions. Desmos will still print a number, and it is meaningless.
- Do not regress f(4) when nothing is set equal to anything. There is no second side to balance; define f and type f(4).
- Do not trust the default view. A parabola that looks like it touches the axis may not, and parallel lines can look like one line. Zoom in before you decide.
Ten habits to drill before test day
- Practice in the SAT version. Search SAT Desmos and use the testing-app version with the green bar, or the calculator inside a Bluebook practice test.
- Keyboard, not keypad. Keep the keypad closed and type everything:
sqrt,,^,~, brackets. - Start every question clean. Edit list, Delete All, Done, so a constant left over from the last question cannot collide with a new one.
- Check the trig mode. Radians is the default. If the question is in degrees, open the wrench and switch before you type.
- Put y = in front. Anything you want graphed gets
in front. Only lowercase x graphs. - Split at the equals sign. For solution-counting questions, left side on one line, right side on the other. A lone number still gets its own line:
. - x becomes , equals becomes tilde. That is a single-equation regression. Add
if the question asks for a constant, andfor any stated condition. - Never 0, never 1, never equal. When you pick values for constants yourself, use something like
and. Retype a slider's default of 1. - Zoom before you trust. Zoom in on near-misses and merges. Zoom out when the question asks for a greatest value.
- Answer what was asked. Read x₁, then type the expression the question wants, like
. For a typed-in answer, click the fraction button if it appears; if it does not, the decimal is your answer.
Questions students ask before test day
- Do I have to bring a calculator at all? No. College Board encourages you to use whichever calculator is most familiar to you, and names the embedded Desmos calculator as one of the two choices. If you do bring a handheld, check the model against the calculator policy page on collegeboard.org rather than a forum thread.
- Does any of this change on an iPad or a Chromebook? The calculator does not; the typing does. College Board says Bluebook supports Mac and Windows devices, iPads and school-managed Chromebooks. Every method here assumes keys under your fingers. The on-screen keypad exists for an iPad with no keyboard attached, and it is slower for every symbol on it.
- Do I have to work through the chapters in order? Section 1 is where the four symbols the rest of the course is built from arrive: the subscript in
, the tilde, the square-bracket list and the curly-bracket condition. Skip them and the Section 3 chapters read like a foreign language. - Graph or regression, when both would work? Count keystrokes. A point the graph already draws costs one click; the same value through a regression costs retyping the whole expression. Reach for the tilde when the graph will not show you what you need.
- Does Desmos solve every SAT Math question? No, and the course does not claim it does. The curriculum's own estimate is that its graphing and regression methods address 53.55% of SAT Math question types, Graphing 25.24% plus Regression 28.31%. That is a count of question types, not a score, and the mix shifts from one exam to the next. Learn Desmos is free and independent; it is not affiliated with College Board or Desmos.
- Will the policy still read like this on my test date? Rules change, and this page is a summary, not the rule. Open the calculator policy page on collegeboard.org before you test and read the current wording there.
Ready to practice? The full curriculum has 27 chapters, each with a short video and guided practice inside a live Desmos calculator; Graphing and Regression chapters end with original hard SAT-style questions. Create a free account to start with chapter 1, skim the cheat sheet for the keystrokes on one page, or check the FAQ for how the course itself works.