Desmos basics for the test

Practice on the free College Board version of Desmos so nothing in it is new on test day. Do this lesson on a laptop or tablet with that page open, and type each example as you go. On a phone, save the steps for later.

In a math moduleOne of the two timed parts of each SAT section, each with its own clock.Read the lesson, click Calculator near the right end of the top toolbar, between Reference and More. The panel opens over the question on the Graphing tab, with a Scientific tab beside it. Drag the six dots at the top to move it and the bottom corner to resize it, so you can still read the question.

On test day the graph sits on top and the numbered rows sit under it. The practice site puts the rows to the left of the graph instead.

The on-screen keypad has arrow keys, letters behind its ABC key, and more math under funcs. With a keyboard you can type it all, including the words sqrt, abs, nthroot and pi. You don't need * to multiply, since 2x and 3(x+1) work as written.

Click Calculator again to close the panel. Moving to another question doesn't clear it, so your rows and settings stay for the whole module. Delete old rows when you start a new question, so an old graph doesn't cross your new one.

Typing / starts a fraction and puts the cursor in the bottom. Everything you type after that stays down there, even +, = and another /, until you press the right arrow. Typing ) won't get you out.

Skip step 2 and the whole 3+1/6 lands in the bottom, so the row prints about 0.316.

To see the answer as a fraction, click the small round fraction button on the result row. The 0.5 turns into $\frac12$, and a second click turns it back. Clicking the number itself only selects it. With no mouse, the Tab key reaches the button.

When the top of a fraction has more than one term, type the top in parentheses before the slash, as in (2x+6)/4. Typed as 2x+6/4, only the 6 goes over the 4. Try this once on the practice site and check that the row shows the whole top over the 4.

The ^ key raises the cursor. Digits and letters you type next stay raised, but +, - and = drop back to the main line by themselves. So x^2+5 gives $x^2+5$ with no arrow needed.

That also means 2^x+1 gives $2^x+1$. For $2^{x+1}$, put the power in parentheses, 2^(x+1), and check the row the first time you try it. If a letter or digit after a power belongs on the main line, press the right arrow before you type it.

For a square root, type sqrt or use the keypad key. For a cube root, nthroot puts the cursor in the small raised number first:

After a root, press the right arrow before typing anything that belongs outside it. Group with parentheses, never { or }, which Desmos prints as braces.

Each row gets its own graph. Type an equation the way it's printed, even $2x+3y=12$, since Desmos doesn't need $y$ alone. Click a graph and gray dots appear where it crosses another graph, where it crosses each axisOne of the two lines a graph is measured against, one running across and one running up., and at its highest or lowest point. Click a dot to see its coordinates.

If the question asks for the greater of the two $x$-values, the answer is 4.414. The 4.828 is the $y$-coordinate, and the crossing on the left, at $x=1.586$, is the smaller solution. Check which coordinate the question asks for before you answer.

Clicking the parabolaThe U-shaped curve a quadratic draws, opening either up or down.Read the lesson also shows $(1,0)$ and $(3,0)$ on the $x$-axis, $(2,-1)$ at its lowest point, and $(0,3)$ on the $y$-axis.

For an equation with only $x$ in it, such as $\frac{15}{6}=\frac{40}{x}$, type 15/6, press the right arrow, then type =40/x. Desmos draws a vertical line at the solution, and clicking where it meets the $x$-axis shows 16. The solving by graphing lesson has more of these.

Gray dots show rounded decimals and have no fraction button, so a dot at 1.333 may stand for $\frac43$. For a grid-inA question where you type your own answer instead of picking one of four.Read the lesson, enter 4/3 or 1.333. Don't shorten it to 1.3, which is a different number.

If a graph you expect isn't on screen, its numbers may be too big for the starting view, so zoom out. Find the zoom controls once on the practice site.

On "Which expression is equivalent to $2x^2+7x-15$?" type y=2x^2+7x-15 on the first row. Then type each choice after y= on its own row. The right choice lands exactly on top of the original, and a wrong one pulls away somewhere.

Say two of the choices are $(2x-3)(x+5)$ and $3x^2+6x-15$. Plug in $x=0$ and $x=1$ and both look right, since each gives $-15$ and $-6$ like the original. On the graph, $3x^2+6x-15$ pulls away everywhere else, while $(2x-3)(x+5)$ stays on top the whole way.

Click the circle again to bring the original back. Find it once on the practice site before test day.

When a question needs several values of one functionA rule that takes in one number and gives back one number, like f(x) = 5x - 7.Read the lesson, define it once. Type f(x)=7x-12 on one row, then f(5) on the next, and the row prints = 23. Put each value you need on its own row.

Type y=kx+1. Desmos doesn't know what $k$ is, so it offers "add slider: k" with a button. One click makes a slider, and dragging it shows how $k$ changes the line.

Use a slider to see a condition, such as the point where a line stops crossing a parabola twice and only touches it. Then find the exact value by hand, because a number read off a slider is only as exact as where you let go.

A slider you didn't ask for means a typo. If you meant y=2x+1 and typed y=2s+1, Desmos offers a slider for $s$.

The graphing calculator starts in radians, so sin(30) prints about $-0.988$. For an angle in degrees, open the wrench at the top right of the graph and switch to Degrees. Then sin(30) prints $0.5$. Nothing warns you when the setting is wrong.

The setting stays when you move to another question. For a later angle in radians, such as $\frac{\pi}{4}$, switch back to Radians first. On the Scientific tab, RAD and DEG are keys on the keypad.

Open the + menu at the top of the rows and choose table. The columns start as $x_1$ and $y_1$. Type one pair of numbers per row, and Desmos plots each point.

For a regressionHaving Desmos find the equation that best fits a set of points once you tell it the shape, such as a line or a parabola.Read the lesson line through the points, type y1~mx1+b on a new row. Desmos lowers each 1 by itself, and ~ needs Shift. With the points (2, 58) and (6, 38), a "Regression Parameters" box shows $m=-5$ and $b=68$.

Don't type _ for the small 1. It starts a subscript that keeps everything after it small until you press the right arrow, so y_1~mx_1+b puts the whole row in the subscript.

For the mean of a column you've typed, use mean(y1). For loose numbers, put them in square brackets, as in mean([3,5,10]), which prints 6. The data and regression lesson covers curved fits.

Typing takes time before Desmos tells you anything. Open it when typing is shorter than the hand work, or when it checks a step you'd worry about. That usually means an equation with $x^2$ or fractions, two equations together, a question about how many solutions there are, or "Which expression is equivalent."

A figure, a survey, a probabilityHow likely something is, written as a number from 0 to 1, like 1/2 for heads on a coin flip.Read the lesson table, or "What does 45 represent?" gives you nothing to graph, so use Desmos there only for arithmetic. Skip it too when the equation is factored already or one step from solved, like $4x=36$.

Work through the three examples, then try five more questions. Before you open Desmos on each one, say what you'll type and which number you'll read off the screen.