Introduction to Desmos: your SAT calculator

Desmos is one of the biggest advantages you have on the digital SAT. For a large share of Math questions, it's the fastest way from what the question gives you to the answer.

It does a lot more than arithmetic. Give it an equation or a system, and it finds the solutions. Graph something, and it shows you the key points. It can also evaluate a function, organize data, and fit a model to it. And it can test answer choices and handle messy arithmetic, all without pages of algebra.

So don't save it for a last check. When Desmos fits the problem, it's usually faster than a long handwritten solution, and you're less likely to make an arithmetic slip. Your job is the part it can't do for you: typing in every condition correctly and reading off exactly what the question asks for.

Each numbered row in Desmos is an expression line. Put one equation or calculation on each line. With your steps stacked one above the other, you can compare them at a glance and catch a typing mistake before it costs you a question.

Graph with lowercase x and y. Desmos treats most other letters as constants. So a stray letter, like the $a$ in y=ax, can bring up a slider, a bar you drag to change a value, instead of the graph you expected.

Dragged or zoomed the graph somewhere unhelpful? The home button snaps it back to the standard view, so you never have to hunt for it.

Before you start a new problem, clear the old one. Click the gear to open edit mode, then choose Delete All. Leftover lines crowd the graph, and they can clash with your new work. If an old line already defines $f$, for example, Desmos flags a second $f$ as an error.

You'll see a Scientific mode too, but the Graphing calculator is the one to learn. It handles the same calculations, and it can also graph equations, build tables, fit models, and show where graphs meet.

Type the equation as written

You can type many equations exactly the way the question shows them. For $2y-4x=8$, type 2y-4x=8. You don't have to solve for $y$ first, and Desmos still graphs the line. That's one less step, and one less place to slip.

Desmos uses the same order of operations as the SAT. Parentheses tell it which parts belong together. You need them most in two places: around a negative number, and around any part of a fraction, power, or root that has more than one term, like the $x-2$ in $\frac{1}{x-2}$.

Here's the classic trap. $-3^2$ and $(-3)^2$ look almost the same, but they aren't. In $-3^2$, the exponent acts only on the $3$, so you get the negative of $9$, which is $-9$. In $(-3)^2$, the parentheses put the whole $-3$ under the exponent, so you get $(-3)(-3)=9$.

Fractions, roots, and exponents need the same care:

• In $\frac{4+5}{3^2}$, the whole sum sits above the fraction bar.
• In $\sqrt{\frac{100}{49}}$, the whole fraction sits under the root.
• In $5^{1+3}$, both terms are in the exponent.

Type / for a fraction, ^ for an exponent, and sqrt for a square root. Press Tab to leave a denominator, exponent, or root before you type the rest of the expression. Otherwise, the next thing you type lands inside it.

If Desmos shows a decimal, click the fraction-conversion button next to the result to see whether there's an exact fraction. A strange decimal where you expected a clean answer is a warning sign. Compare what's on the screen with the question before you trust it.

Keep each pair in one row

Tables show up all over the SAT, for functions, scatterplots, and data. In Desmos, click Add → Table and type one value in each cell. Each row holds one pair, an $x$-value and the $y$-value that goes with it, and Desmos plots every row as a point. So as soon as the table is in, you can see its shape.

Read the pattern down the columns

Look at $(0,2)$, $(1,5)$, and $(2,8)$. Each time $x$ goes up by $1$, $y$ goes up by $3$. That steady change is what makes the pattern linear, and it's why the three points line up on the graph.

Read the unit first

Trig questions can measure angles in degrees or in radians, and Desmos has a setting for each. The same $\sin(30)$ gives two very different answers depending on that setting. So before you evaluate anything, check which unit the question uses and set Desmos to match.

Switch modes before calculating

Say the angle is $30^\circ$. Open Graph Settings, choose Degrees, and type $\sin(30)$. Desmos gives $0.5$, which is $\frac12$. Leave it in radians and you'd get about $-0.988$, the sine of $30$ radians. That's the right sine of the wrong angle.