Desmos guide

The SAT Desmos guide

The digital SAT puts a graphing calculator on screen for every math question. These are the twelve ways of using it that save the most time, with the exact thing to type for each and the mistake that costs the question.

Desmos is the graphing calculator built into the digital SAT, available on every question of the math section.

The short answer

Learn a small set of moves until reaching for them is the first instinct and not the fallback: graph both sides of an equation and click the crossing, put a letter in an equation and slide it, enter a table and read the line of best fit. Each technique below says what it solves, when it applies, what to type and what to watch for.

The twelve techniques

What to type is shown in this style. A line that describes something you do with the interface, such as opening the table, is written as plain text.

1. Graph and click the intersection

Solves any system of equations without algebra.

Use it when: Two equations that share a solution — linear, quadratic, or mixed.

Type:

  • y = 2x + 1
  • y = -x + 7
  1. Type each equation on its own line.
  2. Desmos draws both immediately.
  3. Gray dots appear where they cross — click one.
  4. It shows the exact coordinates, e.g. (2, 5).

Watch for: If the intersection is off-screen you will think there isn't one. Zoom out before concluding.

2. Zeros and vertex of a parabola

Reads roots and the turning point straight off the graph.

Use it when: Any quadratic asking for roots, minimum, maximum, or the vertex.

Type:

  • y = x^2 - 6x + 8
  1. Type the quadratic.
  2. Click where the curve meets the x-axis for the roots.
  3. Click the lowest or highest point for the vertex.
  4. Read the coordinates directly.

Watch for: The question may want the minimum VALUE (the y) rather than where it occurs (the x). Read which.

3. The regression tilde

Fits a line or curve to data and returns the coefficients.

Use it when: Scatterplots, line-of-best-fit questions, and 'which model fits' items.

Type:

  • x_1 = [1,2,3,4]
  • y_1 = [3,5,7,9]
  • y_1 ~ m x_1 + b
  1. Create two lists with the data.
  2. Type y_1 ~ m x_1 + b using the tilde, not equals.
  3. Desmos returns values for m and b underneath.
  4. Use them to answer or to predict.

Watch for: The tilde is not an equals sign. Typing = gives an error instead of a regression.

4. Sliders for 'how many solutions'

Turns a parameter into a dial you can move and watch.

Use it when: Questions asking for what value of k a system has one, none, or infinitely many solutions.

Type:

  • y = x^2 + k
  • y = 4
  1. Type the equation with the unknown letter in it.
  2. Desmos offers 'add slider' — click it.
  3. Drag the slider and watch the graph move.
  4. Find the value where the curves touch, cross twice, or miss.

Watch for: Sliders are slow if you flail. Predict roughly where the answer sits, then confirm.

5. Back-solve with a table

Tests all four answer choices at once instead of one at a time.

Use it when: 'Which value of x satisfies…' and any question with numeric choices.

Type:

  • Table → x: 2, 5, 7, 9
  • y_1 = expression
  1. Add a table and type the four answer choices in the x column.
  2. Replace the y_1 header with the expression from the question.
  3. Desmos evaluates every row at once.
  4. The row producing the target value is your answer.

Watch for: Only worth it when the choices are plain numbers. With algebraic choices, graph them instead.

6. Overlap check for equivalent expressions

Confirms two expressions are the same by seeing one curve, not two.

Use it when: 'Which expression is equivalent to…' questions.

Type:

  • y = (x+2)(x-5)
  • y = x^2 - 3x - 10
  1. Type the original expression as y = …
  2. Type an answer choice as a second equation.
  3. If they are equivalent only ONE curve appears — the second sits exactly on the first.
  4. If you can see two curves, that choice is wrong.

Watch for: Identical curves hide each other. Toggle one off and on to be sure Desmos drew both.

7. Statistics on a list

Computes mean, median and standard deviation without arithmetic.

Use it when: Any question giving a data set and asking for a center or spread.

Type:

  • L = [3,4,4,6,33]
  • mean(L)
  • median(L)
  • stdevp(L)
  1. Put the data in a list with square brackets.
  2. Type mean(L) on the next line.
  3. Add median(L) and stdevp(L) as needed.
  4. Desmos prints each value instantly.

Watch for: stdev and stdevp differ. The SAT means the population version, stdevp.

8. Circles in any form

Finds the center and radius without completing the square.

Use it when: Circle equations, especially in expanded form.

Type:

  • x^2 - 6x + y^2 + 4y = 12
  1. Type the equation exactly as printed, expanded or not.
  2. Desmos draws the circle.
  3. Click the center point to read its coordinates.
  4. Measure or read the radius from the axis crossings.

Watch for: Zoom so the whole circle is visible before reading the center by eye.

9. Inequalities and shaded regions

Shows the solution region of a system without sketching.

Use it when: Systems of inequalities and 'which point satisfies both' questions.

Type:

  • y > 2x - 3
  • y <= -x + 4
  1. Type each inequality with > < >= or <=.
  2. Desmos shades each region automatically.
  3. The darker overlap is the solution set.
  4. Test any answer point by typing it as (a, b).

Watch for: A strict inequality excludes its boundary line. Desmos draws it dashed — check which you need.

10. Function values and composition

Evaluates f(3) or g(f(3)) without substitution errors.

Use it when: Function notation, composite functions, and table look-ups.

Type:

  • f(x) = 2x + 1
  • g(x) = x^2
  • g(f(3))
  1. Define each function on its own line using f(x) = …
  2. Type the expression you want, such as g(f(3)).
  3. Desmos prints the value.
  4. Works for any depth of nesting.

Watch for: Defining f(x) and then typing f=3 overwrites the function. Use f(3) to evaluate.

11. Solve any single-variable equation

Turns algebra into a picture by graphing each side.

Use it when: Radical, rational, absolute value or exponential equations.

Type:

  • y = sqrt(5x - 4)
  • y = 6
  1. Graph the left side as one equation.
  2. Graph the right side as a second.
  3. Click where they cross.
  4. The x-coordinate is your solution.

Watch for: Graphing catches extraneous roots that squaring both sides would invent.

12. Degree mode for trigonometry

Makes sin, cos and tan read degrees instead of radians.

Use it when: Any trig question stated in degrees.

Type:

  • Settings (spanner icon) → Degrees
  • sin(30) = 0.5
  1. Click the spanner in the top right of the graph.
  2. Switch the angle setting to Degrees.
  3. Now sin(30) returns 0.5 rather than −0.988.
  4. Switch back if a question uses radians.

Watch for: This is the most expensive setting on the calculator. Check it before your first trig question.

Making it the first instinct

Reading about a technique does not make it fast. A technique you have to remember to use is not yet a technique, so the work is repetition on real questions with the calculator open beside them, until the first thing your hands do is type. The course teaches these twelve as a subject of their own, with the keystrokes drilled and questions built to be solved with the calculator; the argument for why is in Desmos is a skill, not a shortcut.

To try the calculator itself, the public version is at desmos.com/calculator. The College Board describes the test, and the calculator it includes, at satsuite.collegeboard.org/sat.

Common questions

Can I use Desmos on the whole SAT math section?

Yes. The graphing calculator is built into the test application and is on screen for every question in both math modules, so there is no question where it is unavailable.

Does Desmos make SAT math easier?

It changes which questions are hard. An equation that takes a page of algebra can be a crossing point on a graph, so the questions that stay difficult are the ones that need a model built from words, not a calculation.

Do I still need to know the algebra?

Yes. Graphing needs a correct equation to type, and some questions are faster to reason through than to plot. The point of the twelve techniques is to know, for each question, which of the two is quicker.

Last reviewed . The techniques are the ones the course teaches; test details are checked against College Board’s published specification each term.