learn it, then use it

Updated July 2026

The ultimate Desmos guide

Bluebook gives you Desmos throughout SAT Math. The advantage is not typing everything into a calculator. It is recognizing when a tool can turn a longer solution into a shorter check. Start with the four core moves, practice the path that matches your weakest domain, and use the advanced tools only when they simplify the work.

18SAT-focused moves

4guided learning paths

91 minfor the full guide

Practice progress0 of 18

Mark a move practiced after you can repeat it. Saved on this device.

Jump to a section

Choose your learning path

New to Desmos? Start with the first path. Already comfortable? Jump straight to the SAT domain you want to improve.

Keyboard shortcuts worth learning

You do not need the entire shortcut catalog. These shortcuts reduce keystrokes in the illustrated SAT Math workflows.

What you want	Type this	Notes
Open the current shortcut panel	`Ctrl + / or Cmd + /`	Use the live panel as the final authority when a shortcut changes.
Exponent	`^`	Type x^2 and it auto-raises to a superscript.
Fraction	`/`	Stacks into a real fraction as you type.
Square root	`sqrt`	Type sqrt, then enter the expression under the radical.
Cube or nth root	`cbrt or nthroot`	The keypad also exposes the root templates.
Absolute value	`abs( or \| \|`	The pipe key works too.
Pi	`pi`	Converts to the π symbol.
Regression	`~`	Shift + the backtick key. This is not an equals sign.
Subscript	`_`	Use x_1 and y_1 for table columns and regressions.
New data table	`Ctrl + Alt + T or Ctrl + Cmd + T`	Windows/ChromeOS first, Mac second.
Degrees or radians	`Alt + D or Ctrl + D`	Windows/ChromeOS first, Mac second. Verify the mode before trig.
Undo	`Ctrl + Z or Cmd + Z`	Works like most other apps.
Zoom to fit	`Shift + Alt + Z or Shift + Option + Z`	Useful after pasting a table or when a solution is off-screen.
≤ and ≥	`<= and >=`	Auto-convert to the proper symbols.

build your toolkit

18 SAT-focused techniques

Open a lesson, watch Psychtopus decode the move, practice with 5 or 10 Main Bank questions, then lock in the trick.

watch the move unfold

Watch how Psychtopus decodes it

One thought at a time. This short demo teaches the move before the real question-bank drill.

Guided skill demoCalculator allowed

Find the solution to the system $y = 2x + 3$ and $y = -x + 7$ .

Step 1: Translate

Type each equation on its own line. You do not need slope-intercept form. Desmos accepts standard form, point-slope, anything.

Live Desmos walkthroughStep 1 of 3

Expression 1:

Loading the real Desmos calculator...

Where this setup comes from

Both equations come directly from the question. Graphing each as y shows every ordered pair it satisfies; their intersection is the one pair that satisfies both.

What Desmos is showing

First graph: y = 2x + 3

Desmos draws the rising line from the first equation.

watch the move unfold

Watch how Psychtopus decodes it

One thought at a time. This short demo teaches the move before the real question-bank drill.

Guided skill demoCalculator allowed

How many solutions does the equation $2^{x} = 5x$ have?

Step 1: Translate

Type the equation exactly as written. Desmos marks every x that satisfies it.

Live Desmos walkthroughStep 1 of 3

Where this setup comes from

The equation says two expressions are equal. Writing each side as its own y-expression turns a solution into an x-value where the two graphs have the same height.

What Desmos is showing

Curve 1: y = 2ˣ

Desmos draws the exponential curve.

watch the move unfold

Watch how Psychtopus decodes it

One thought at a time. This short demo teaches the move before the real question-bank drill.

Guided skill demoCalculator allowed

What is the vertex of $f(x) = x^{2} - 6x + 5$ , and what are its zeros?

Step 1: Translate

Type the quadratic. Desmos graphs it and auto-marks the key points as grey dots.

Live Desmos walkthroughStep 1 of 3

Where this setup comes from

The rule f(x) = x² - 6x + 5 becomes y = x² - 6x + 5 so Desmos can graph its outputs. Zeros occur where y = 0, and the turning point is the vertex.

What Desmos is showing

Graph: y = x² - 6x + 5

Desmos draws an upward-opening parabola.

watch the move unfold

Watch how Psychtopus decodes it

One thought at a time. This short demo teaches the move before the real question-bank drill.

Guided skill demoCalculator allowed

Which region satisfies both $y > 2x + 3$ and $y < -x + 5?$

Step 1: Translate

Type each inequality on its own line. Desmos shades each region for you.

Live Desmos walkthroughStep 1 of 3

Where this setup comes from

Each inequality is copied directly from the question. Desmos shades every point that makes it true, so the region shaded by both inequalities is the solution set.

What Desmos is showing

Shade above y = 2x + 3

A dashed line appears because the first inequality is strict.

watch the move unfold

Watch how Psychtopus decodes it

One thought at a time. This short demo teaches the move before the real question-bank drill.

Guided skill demoCalculator allowed

How many solutions does $|2x - 5| = 7$ have, and what are they?

Step 1: Translate

Type the absolute-value equation directly. Desmos draws a vertical line at each solution.

Live Desmos walkthroughStep 1 of 3

Where this setup comes from

The bars around 2x - 5 mean absolute value, which Desmos accepts as abs(2x - 5). Setting it equal to 7 asks where that distance from zero is exactly 7.

What Desmos is showing

Relation: |2x - 5| = 7

Desmos plots every x-value that makes the two sides equal.

watch the move unfold

Watch how Psychtopus decodes it

One thought at a time. This short demo teaches the move before the real question-bank drill.

Guided skill demoCalculator allowed

For what value of $k$ does $y = kx$ intersect $y = x^{2}$ exactly once?

Step 1: Translate

Type the line with the unknown as a letter. Desmos offers to add a slider for k. Accept it.

Live Desmos walkthroughStep 1 of 3

Where this setup comes from

The question already gives y = kx and y = x². Because k is the unknown slope, Desmos turns k into a slider so you can find when the line touches the parabola once.

What Desmos is showing

Line family: y = kx

Desmos creates a slider so k can change the line's slope.

watch the move unfold

Watch how Psychtopus decodes it

One thought at a time. This short demo teaches the move before the real question-bank drill.

Guided skill demoCalculator allowed

What are the mean and median of the data set ${12, 7, 5, 15, 9}?$

Step 1: Translate

Define your data as a list with square brackets.

Live Desmos walkthroughStep 1 of 3

Where this setup comes from

L is just a short name for the five values in the question. Commands such as mean(L) and median(L) ask Desmos to calculate those statistics from the stored list.

What Desmos is showing

List stored: [12, 7, 5, 15, 9]

Desmos treats the five values as one reusable list.

watch the move unfold

Watch how Psychtopus decodes it

One thought at a time. This short demo teaches the move before the real question-bank drill.

Guided skill demoCalculator allowed

Find the center and radius of $x^{2} + y^{2} - 6x + 4y - 3 = 0$ .

Step 1: Translate

Type the equation in its expanded form, exactly as given. No rearranging.

Live Desmos walkthroughStep 1 of 3

Where this setup comes from

The expanded circle equation is copied exactly as given. Every point Desmos draws satisfies that equation, letting the graph reveal the center and radius without rewriting it first.

What Desmos is showing

Graph the expanded circle equation

Desmos recognizes the relation without completing the square first.

watch the move unfold

Watch how Psychtopus decodes it

One thought at a time. This short demo teaches the move before the real question-bank drill.

Guided skill demoCalculator allowed

For the points $(1, 3), (2, 7), (3, 13), (4, 21)$ , and $(5, 31)$ , which model fits better: linear or quadratic?

Step 1: Translate

Press Ctrl/Cmd + Alt + T to open a table. Put the x values in the x_1 column and the y values in y_1.

Live Desmos walkthroughStep 1 of 3

Where this setup comes from

The table names its columns x₁ and y₁. The tilde tells Desmos to choose the coefficients that best fit those points, first for a line and then for a quadratic.

What Desmos is showing

Table: (1,3), (2,7), (3,13), (4,21), (5,31)

The points bend upward instead of following a constant slope.

watch the move unfold

Watch how Psychtopus decodes it

One thought at a time. This short demo teaches the move before the real question-bank drill.

Guided skill demoCalculator allowed

For what value of $k$ does the system $y = 4x + k$ and $y = 2x^{2} - 5$ have exactly one solution?

Step 1: Translate

Graph the line with the parameter as a letter and add the slider Desmos offers.

Live Desmos walkthroughStep 1 of 3

Where this setup comes from

The line and parabola come directly from the system. The unknown k is the line's vertical shift, so changing k shows when two intersection points merge into one tangent point.

What Desmos is showing

Line family: y = 4x + k

The k slider moves the line up and down without changing its slope.

watch the move unfold

Watch how Psychtopus decodes it

One thought at a time. This short demo teaches the move before the real question-bank drill.

Guided skill demoCalculator allowed

Which value is a solution to $2x^{2} - 7x + 3 = 0?$ A $) -1$ B $) 1$ C $) 5/2$ D $) 3$

Step 1: Translate

Press Ctrl/Cmd + Alt + T for a table. Put all four answer choices in the x_1 column.

Live Desmos walkthroughStep 1 of 3

Where this setup comes from

The answer choices become the x₁ column. The y₁ formula is the original left side with x replaced by x₁, so each row checks one choice against the target value 0.

What Desmos is showing

x₁ column: -1, 1, 5/2, 3

All four choices go into the table at once.

watch the move unfold

Watch how Psychtopus decodes it

One thought at a time. This short demo teaches the move before the real question-bank drill.

Guided skill demoCalculator allowed

Which expression is equivalent to $(x + 2)(x - 3)?$

Step 1: Translate

Graph the original expression on line one.

Live Desmos walkthroughStep 1 of 3

Where this setup comes from

The original expression and a candidate answer are each set equal to y. Equivalent expressions return the same output for every x, so their graphs overlap completely.

What Desmos is showing

Original: y = (x + 2)(x - 3)

Desmos draws the original expression as a parabola.

watch the move unfold

Watch how Psychtopus decodes it

One thought at a time. This short demo teaches the move before the real question-bank drill.

Guided skill demoCalculator allowed

If $f(x) = x^{2} - 4x + 3$ , what is $f(7)$ , and how does $y = f(x - 2) + 1$ change the graph?

Step 1: Translate

Define the rule with f(x)= so Desmos stores it as a function.

Live Desmos walkthroughStep 1 of 3

Where this setup comes from

The first line stores the rule exactly as f(x). Then f(7) substitutes 7 for x, while f(x - 2) + 1 copies the transformation written in the question.

What Desmos is showing

Stored: f(x) = x² - 4x + 3

Defining f once lets Desmos reuse the full rule.

watch the move unfold

Watch how Psychtopus decodes it

One thought at a time. This short demo teaches the move before the real question-bank drill.

Guided skill demoCalculator allowed

A population starts at $800$ and grows $6\%$ each year. What is the population after $9$ years?

Step 1: Translate

Convert the percent to a decimal and build the multiplier: 1+r for growth or 1-r for decay.

Live Desmos walkthroughStep 1 of 3

Where this setup comes from

The initial population gives 800. A 6% yearly increase creates the multiplier 1 + 0.06 = 1.06, and the exponent t counts the number of yearly growth periods.

What Desmos is showing

Growth multiplier: 1 + 0.06 = 1.06

A multiplier above 1 represents a 6% increase each year.

watch the move unfold

Watch how Psychtopus decodes it

One thought at a time. This short demo teaches the move before the real question-bank drill.

Guided skill demoCalculator allowed

Which input in ${-2, -1, 1, 3, 4}$ makes $3x^{2} - 7x$ equal to $20?$

Step 1: Translate

Add a table and enter all candidate inputs in the x_1 column.

Live Desmos walkthroughStep 1 of 3

Where this setup comes from

The listed candidates become x₁. The derived y₁ column copies 3x² - 7x with x₁ in place of x, so Desmos evaluates the same rule for every candidate.

What Desmos is showing

x₁ column: -2, -1, 1, 3, 4

The candidate inputs are stored as a reusable table column.

watch the move unfold

Watch how Psychtopus decodes it

One thought at a time. This short demo teaches the move before the real question-bank drill.

Guided skill demoCalculator allowed

For the points $(1, 2), (2, 5), (3, 10), (4, 17)$ , and $(5, 26)$ , is a linear or quadratic model more appropriate?

Step 1: Translate

Fit a model with the tilde and keep its parameter names visible.

Live Desmos walkthroughStep 1 of 3

Where this setup comes from

The regression mx₁ + b predicts y for each x₁. A residual is observed minus predicted, so R = y₁ - (mx₁ + b) measures each point's vertical error from the fitted line.

What Desmos is showing

Linear fit: y = 6x - 6

Desmos fits a line, but the data do not scatter randomly around it.

watch the move unfold

Watch how Psychtopus decodes it

One thought at a time. This short demo teaches the move before the real question-bank drill.

Guided skill demoCalculator allowed

Points $A(-2, 3)$ and $B(6, -1)$ are endpoints of a segment. What are its slope, midpoint, and length?

Step 1: Translate

Create the two points so the diagram and coordinates stay connected.

Live Desmos walkthroughStep 1 of 3

Where this setup comes from

A and B store the endpoints from the question. Their coordinate properties feed the midpoint average and distance formula, so every later calculation comes from those two points.

What Desmos is showing

Points: A = (-2, 3), B = (6, -1)

Desmos stores each point's x- and y-coordinates for reuse.

watch the move unfold

Watch how Psychtopus decodes it

One thought at a time. This short demo teaches the move before the real question-bank drill.

Guided skill demoCalculator allowed

If sin $(x) = 0.6$ and $0^{\circ} < x < 90^{\circ}$ , what is $x$ to the nearest tenth of a degree?

Step 1: Translate

Read the question's angle unit before typing anything, then switch Desmos to degrees or radians.

Live Desmos walkthroughStep 1 of 3

Where this setup comes from

The equation sin(x) = 0.6 is copied from the question. Arcsin reverses sine to recover x, and degree mode comes from the degree symbols in the stated interval.

What Desmos is showing

Angle mode: Degrees

The calculator must match the degree symbol in the interval.

The test-day workflow

A calculator method is only good when it protects accuracy. Run this four-step check before you lock an answer.

1. Translate before you type
Name the unknown, preserve the units, and decide what the answer should represent. Desmos can calculate the wrong model perfectly.
2. Pick the shortest reliable route
Use mental math for a quick computation, a direct expression for arithmetic, a graph for intersections, and a table for repeated values.
3. Read the full graph
Check the window, every visible intersection, axis scale, boundary type, and degree or radian mode before trusting the display.
4. Return to the question
Attach units, answer what was asked, respect the interval, and round only once at the end.

Copy-ready SAT templates

Treat these as starting points. Replace the placeholder values and keep the mathematical meaning visible.

Define and evaluate

Functions and transformations

Restrict a graph

Domains, intervals, and graph cleanup

Piecewise function

Absolute value and multi-rule models

Candidate list

Test several values at once

Linear regression

Fit a line to table data

Quadratic regression

Fit a curved quadratic model

Residual plot

Check whether a linear model misses a pattern

Percent growth

Repeated percent increase

Percent decay

Repeated percent decrease

Coordinate distance

Distance between two points

Keyboard and Audio Trace support

Desmos supports keyboard navigation, screen-reader output, Braille modes, reverse contrast, and Audio Trace.

Use the keyboard

Focus the graph with Ctrl + Alt + P on Windows/ChromeOS or Ctrl + Cmd + P on Mac, then move through interactive points with Tab and Shift + Tab.

Hear the graph

Audio Trace can describe and sonify curves. Open it with Alt + T on Windows or Option + T on Mac, then press H to hear the selected graph.

Verify the embedded version

Bluebook may expose fewer public-site features. Open the calculator's own shortcut panel and practice inside Bluebook before test day.

When not to use Desmos

The calculator is a tool, not a reflex. Opening it when a faster mental or algebraic route is already clear can add steps. Skip it when:

The 15-second rule

If you can finish it in your head in under fifteen seconds, just do it. Opening the calculator for simple arithmetic costs more time than it saves.

Symbolic algebra

Desmos is not a computer algebra system. It graphs and computes with numbers, but it will not factor, expand, or simplify an expression symbolically for you.

Exact radical or fraction forms

A decimal approximation may not match an answer written as a radical or fraction. Use Desmos to check the value, then return to the requested exact form before answering.

Conceptual questions

Which statement must be true and similar items have nothing to graph. Reason them out.

Know your own calculator policy

Desmos is built into Bluebook, so it is always allowed. If you also bring a handheld, check the current College Board approved-calculator list for your specific model rather than assuming.

Quick reference

All eighteen at a glance.

#	Path	When to use it	Rough PsychSAT time estimate
1	Start here	Any system of equations.	about a minute
2	Start here	Exponential or other equations with no clean algebra.	about 90 seconds
3	Start here	Parabola questions where the graph exposes zeros, a vertex, or a minimum or maximum.	about 90 seconds
4	Algebra and functions	Inequality systems and shaded-region questions.	about 90 seconds
5	Algebra and functions	Absolute-value equations and piecewise functions.	about a minute
6	Algebra and functions	Tangent, parallel, and one-solution parameter questions.	two minutes or more
7	Data and regression	Any mean, median, spread, or quartile question.	about a minute
8	Geometry and trig	Circle center and radius from a general equation.	about two minutes
9	Data and regression	Scatterplot and best-fit line or curve questions.	about three minutes
10	Algebra and functions	Parameter questions about how many solutions.	two minutes or more
11	Start here	Numerical multiple-choice and SPR checks.	about 90 seconds
12	Algebra and functions	Which is equivalent and factoring questions.	about 45 seconds
13	Algebra and functions	Function evaluation, composition, and graph transformations.	about a minute
14	Algebra and functions	Repeated percent change, exponential growth, and decay.	about a minute
15	Data and regression	Answer-choice testing, sequences, and repeated evaluations.	about 90 seconds
16	Data and regression	Model comparison and line-of-best-fit questions.	about two minutes
17	Geometry and trig	Slope, midpoint, distance, and coordinate-geometry questions.	about 90 seconds
18	Geometry and trig	Right-triangle trig and trig equations with stated intervals.	about a minute

These are unmeasured PsychSAT estimates for the illustrated comparison, not benchmark results. Your time will vary with the question, method, and calculator fluency.

Frequently asked questions

Is Desmos available on every SAT math question?

Yes. College Board allows calculator use throughout SAT Math, and Bluebook includes Desmos graphing and scientific options. The assessment version may not include every feature on the public Desmos website, so practice inside Bluebook before test day.

What is the single most useful Desmos technique?

Graphing a system and inspecting its intersection can be useful when the equations graph cleanly. In those cases, it can replace a longer substitution workflow. Practice that move first, then add parabola key points and the regression tilde.

How do you run a regression on Desmos?

Open a table with Ctrl/Cmd + Alt + T, put your data in the x_1 and y_1 columns, then on a new line type the model using a tilde: y_1 ~ mx_1 + b for a line or y_1 ~ ax_1^2 + bx_1 + c for a quadratic. Desmos fits it and reports the coefficients and r-squared. The tilde is Shift + backtick, and you must use x_1, not x.

When is mental math actually faster?

Whenever the problem is a sub-fifteen-second one: simple arithmetic, a clean fraction, spotting a perfect square. The trap is reaching for the calculator on every question out of habit. If you can already see the path, just take it.

Which shortcuts should I memorize before test day?

Four carry most of the weight: the table shortcut, undo, the caret for exponents, and Shift + backtick for the regression tilde. Also know that the slash makes a fraction and how to switch between degrees and radians. Press Ctrl + / on Windows/ChromeOS or Cmd + / on Mac to open the current shortcut panel.

Should I practice with Desmos before the SAT?

Yes, and on the right version. Use Desmos Test Mode, the same interface embedded in Bluebook, so the layout is muscle memory on test day and you can spend your attention on the math instead of hunting for buttons. A few full practice sessions with it is plenty.

Sources and version note

This guide is SAT-focused and was reviewed against current College Board and Desmos documentation on July 17, 2026. Assessment versions can expose fewer features than the public calculator. If a shortcut differs, open the calculator's live shortcut panel. The quick-reference time figures are unmeasured PsychSAT estimates, not benchmark results.

Practice these on digital SAT questions

PsychSAT embeds a Desmos practice surface alongside SAT-style math questions. College Board controls the assessment version in Bluebook, so use official practice to confirm its test-day tools and limits.

Start practicing free →

keep reading

Related SAT resources

SAT Math Formula Guide

Search formulas by question pattern, see which appear on the current SAT reference sheet, and know when to use each one.

The Digital SAT, Explained

Format, timing, tested domains, and the limits of public information about adaptive scoring.

Bluebook Practice Tests

What the official app offers and a structured review cycle after each test.

Manage SAT Test Anxiety

A carefully scoped guide to preparation, worry, and low-risk test-day strategies.

Choose your learning path

Keyboard shortcuts worth learning

18 SAT-focused techniques

1Solve a system by graphing, then click the intersectionStart here·Difficulty: Easy4 min practice

Watch how Psychtopus decodes it

2Count solutions to a messy equation by graphing both sidesStart here·Difficulty: Easy4 min practice

3Read a parabola's zeros and vertex straight off the graphStart here·Difficulty: Easy4 min practice

4Shade inequalities and read the overlapAlgebra and functions·Difficulty: Medium4 min practice

5Absolute value and piecewise without splitting into casesAlgebra and functions·Difficulty: Medium5 min practice

6Sliders for tangent, parallel, and exactly-one-solutionAlgebra and functions·Difficulty: Hard6 min practice

7One-line statistics: mean, median, standard deviationData and regression·Difficulty: Easy5 min practice

8Drop a circle's general equation in and read center plus radiusGeometry and trig·Difficulty: Medium5 min practice

9Regression with the ~ tilde for scatterplots and tablesData and regression·Difficulty: Medium7 min practice

10Sliders for how-many-solutions parameter questionsAlgebra and functions·Difficulty: Hard6 min practice

11Back-solve all four answer choices at once in a tableStart here·Difficulty: Easy4 min practice

12Check equivalent expressions by overlapping graphsAlgebra and functions·Difficulty: Medium4 min practice

13Define a function once, then evaluate or transform itAlgebra and functions·Difficulty: Easy5 min practice

14Model percent growth and decay with a reusable multiplierAlgebra and functions·Difficulty: Medium5 min practice

15Use tables and derived columns to test many values at onceData and regression·Difficulty: Easy5 min practice

16Check residuals before trusting a regression modelData and regression·Difficulty: Hard7 min practice

17Turn coordinate geometry into points, segments, and equationsGeometry and trig·Difficulty: Medium6 min practice

18Set the angle mode first, then solve trig equations visuallyGeometry and trig·Difficulty: Easy5 min practice

The test-day workflow

Copy-ready SAT templates

Keyboard and Audio Trace support

When not to use Desmos

Quick reference

Frequently asked questions

Sources and version note

Related SAT resources