# How to use Desmos on the SAT

Canonical: https://duckyhelper.com/learn/sat-math/desmos-calculator/
Updated: 2026-10-01

The digital SAT has a Desmos graphing calculator built into Bluebook, and calculators are allowed on every Math question. You may also bring an approved handheld calculator. Desmos is fastest for systems of equations, the vertex and zeros of a parabola, counting solutions, checking equivalent expressions and fitting a table. It is slower than mental math for simple arithmetic, so use it on purpose, not out of habit.

## What College Board allows

- Bluebook has an embedded Desmos calculator with a graphing and a scientific mode, and you can switch between them at any point in the Math section.
- The Math directions say calculator use is permitted for all questions, in both modules.
- You may bring your own calculator instead, as long as it is not a CAS (computer algebra system) model or another prohibited device. Check College Board's calculator policy before test day.
- College Board links the free Desmos graphing calculator at desmos.com/calculator for practice, and the full-length practice tests in Bluebook use the same built-in tool.

## The moves worth learning

**Desmos moves for SAT math**

| Question type | What to type | What to look at |
| --- | --- | --- |
| System of equations | Both equations, as written | Tap the crossing point |
| Solve any one-variable equation | \(y = \) left side, \(y = \) right side | x value of each crossing |
| Vertex or zeros of a parabola | \(y = 3x^2 - 21x + 30\) | Tap the curve: gray dots show vertex and zeros |
| How many solutions | Both sides as graphs | Count the crossings |
| Equivalent expressions | The original and each choice | The match lies exactly on top |
| Table to equation | A table, then \(y_1 \sim mx_1 + b\) or \(y_1 \sim ab^{x_1}\) | The fitted values of m, b or a, b |
| Mean, median, spread | \(\text{mean}([\ldots])\), \(\text{median}([\ldots])\), \(\text{stdev}([\ldots])\) | The value printed on the right |
| A constant like k | The equation with k, then add a slider | Watch the graph change as k moves |

> **Watch out: When Desmos is slower**
>
> Simple arithmetic, word problems you still have to set up, and "what does this number mean" questions. Typing also adds risk: one missing parenthesis gives a wrong graph that looks fine. For a two-step equation, plain algebra is faster.

## Worked examples

**Example 1: a system with decimals**

Problem: Solve the system \(0.4x + 1.3y = 7.3\) and \(2.5x - 0.6y = 2\).

1. Type the first equation exactly as written on line 1, and the second on line 2. Desmos draws two lines.
2. Tap the point where they cross. Desmos shows \((2, 5)\).
3. Check in the first equation.

   $$
   0.4(2) + 1.3(5) = 7.3
   $$
4. Check in the second equation.

   $$
   2.5(2) - 0.6(5) = 2
   $$

Answer: \((2, 5)\)

**Example 2: the minimum of a parabola**

Problem: What is the minimum value of \(y = 3x^2 - 21x + 30\)?

1. Type \(y = 3x^2 - 21x + 30\) and tap the curve. Gray dots appear at the zeros, \((2, 0)\) and \((5, 0)\), and at the vertex, \((3.5, -6.75)\).
2. Check the vertex by hand: it sits halfway between the zeros, at \(x = 3.5\).

   $$
   3(3.5)^2 - 21(3.5) + 30 = -6.75
   $$

Answer: \(-6.75\)

**Example 3: fit a table**

Problem: A table has the points \((0, 5)\), \((1, 7.5)\), \((2, 11.25)\) and \((3, 16.875)\). Find an equation for the data and predict y when \(x = 5\).

1. Add a table in Desmos and enter the points in the \(x_1\) and \(y_1\) columns.
2. The y values multiply by 1.5 each step, so try an exponential fit: type \(y_1 \sim ab^{x_1}\). Desmos shows \(a = 5\) and \(b = 1.5\).
3. Predict at \(x = 5\).

   $$
   5(1.5)^5 = 37.96875
   $$

Answer: \(y = 5(1.5)^x\), and at \(x = 5\), y is about 37.97

**Example 4: check an equivalent expression**

Problem: Which expression is equivalent to \((x + 3)^2 - (x - 3)^2\)?

1. Type \(y = (x + 3)^2 - (x - 3)^2\). The graph is a straight line through the origin, and the point \((1, 12)\) is on it.
2. A line through the origin with slope 12 is \(y = 12x\). Type it: it lies exactly on top. The algebra agrees:

   $$
   (x + 3)^2 - (x - 3)^2 = 12x
   $$

Answer: \(12x\)

## Common mistakes

- **Missing parentheses.** \(y = 2^x + 3\) and \(y = 2^{x + 3}\) are different graphs. Fix: use the exponent key and check that the graph looks right.
- **Reading a gray point with rounded values.** Desmos may show 2.444 for a value that is not a nice number. Fix: match it to the answer choices or round as the question asks.
- **Using Desmos before setting up a word problem.** Desmos cannot read the story for you. Fix: write the equation on scratch paper first.
- **Trusting the window.** A crossing can be off screen. Fix: zoom out once before you count solutions.
- **Degree mode for trig.** The graphing calculator can be set to radians or degrees in its settings. Fix: check the mode before evaluating \(\sin\) or \(\cos\).

## Practice

**5 questions to try with Desmos, then by hand**

1. What is the solution to the system \(y = 1.5x - 2\) and \(y = -0.5x + 6\)?
   A. \((2, 1)\)
   B. \((4, 2)\)
   C. \((4, 4)\)
   D. \((8, 10)\)

   Answer: \((4, 4)\). The lines cross at \((4, 4)\). By hand: \(1.5x - 2 = -0.5x + 6\) gives \(2x = 8\), \(x = 4\), \(y = 4\). \((2, 1)\) and \((8, 10)\) are on the first line only.

2. How many real solutions does \(x^3 - 4x = 1\) have?
   A. 0
   B. 1
   C. 2
   D. 3

   Answer: 3. Graph \(y = x^3 - 4x\) and \(y = 1\). The horizontal line crosses the curve three times: once left of \(-1\), once between \(-1\) and 0, and once right of 2.

3. What is the minimum value of \(f(x) = 2x^2 - 7x + 3\)?
   A. \(-3.125\)
   B. \(-2.5\)
   C. \(1.75\)
   D. \(3\)

   Answer: \(-3.125\). The vertex is at \(x = \frac{7}{4} = 1.75\), and \(f(1.75) = -3.125\). 1.75 is where the minimum happens, not its value, and 3 is the y-intercept.

4. What is the median of 12, 15, 15, 18, 22, 30?
   A. 15
   B. 16.5
   C. 18
   D. 18.67

   Answer: 16.5. In Desmos, \(\text{median}([12, 15, 15, 18, 22, 30])\) gives 16.5, the mean of the middle values 15 and 18. 18.67 is the mean.

5. Student-produced response: the graphs of \(y = 2^x\) and \(y = x + 3\) cross at a point with a positive x-coordinate. What is that x-coordinate, rounded to the nearest tenth?

   Answer: 2.4. Graph both and tap the crossing on the right: Desmos shows about \((2.444, 5.444)\). Rounded to the nearest tenth, x is 2.4. This one is very hard to do by hand, which is exactly when Desmos earns its place.

## Frequently asked questions

### Is Desmos allowed on the SAT?

Yes. Bluebook has a Desmos calculator built in, with graphing and scientific modes, and College Board's math directions say a calculator is permitted for all questions. You can also bring an approved handheld calculator instead.

### Can I bring my own calculator to the SAT?

Yes, if it follows College Board's calculator policy. Graphing and scientific calculators are allowed, but models with a computer algebra system (CAS) are not. If your calculator fails, you can keep going with the built-in Desmos.

### How do I practice with the SAT's Desmos?

Use the free graphing calculator at desmos.com/calculator, which College Board links, and take the full-length practice tests in Bluebook so you use the same built-in version under time pressure. Practice the moves in the table above until they take seconds.

### Should I use Desmos on every question?

No. Use it when it saves time or catches mistakes: systems, parabolas, counting solutions, tables and checks. For quick arithmetic or reading a word problem, it usually slows you down.

## Sources

- [College Board: SAT Suite calculator policy](https://satsuite.collegeboard.org/sat/what-to-bring-do/calculator-policy), accessed 2026-10-01
- [College Board: Bluebook testing tools](https://bluebook.collegeboard.org/students/tools), accessed 2026-10-01
- [College Board: SAT Bluebook test directions (math directions)](https://satsuite.collegeboard.org/media/pdf/english-sat-test-directions-bb.pdf), accessed 2026-10-01

## Related

- [Systems of linear equations on the SAT](https://duckyhelper.com/learn/sat-math/systems-of-equations/)
- [Quadratics on the SAT](https://duckyhelper.com/learn/sat-math/quadratics/)
- [The hardest SAT math question types, and how to beat them](https://duckyhelper.com/learn/sat-math/hardest-questions/)
- [SAT Math study guides](https://duckyhelper.com/learn/sat-math/)

## Try asking Ducky

- "Show me how to find where these two graphs cross in Desmos."
- "Is it faster to do this one in Desmos or by hand?"
- "How do I make a slider for k?"

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