Desmos for the SAT · Technique 8 of 15
Build a Table to Test Several x-values at Once
Stop plugging in one number at a time. Evaluate the whole list in one shot.
Some questions ask you to find an x-value that satisfies more than one condition at once, like a specific output AND a range restriction. Checking each candidate by hand is slow and easy to mess up.
Define the function once, list every candidate x-value in a table, and Desmos fills in the output for all of them in one column. Then you just scan the table for the row that fits every condition.
There is a second mode built for the answer choices: back-solving. To test which choice solves an equation, first move everything to one side so it reads expression = 0. That is the Target Zero rule. Type the four choices down the x1 column, put the expression in the y1 header, and the row whose y1 comes out to 0 is your answer. For 2x2 - 3x = 5, use the header 2x12 - 3x1 - 5 and look for the row that gives 0.
Nova
Stop plugging in one number at a time. Build a table, list every candidate x-value, and Desmos evaluates the whole column in one shot. This is gold when a question stacks two conditions on you, like a specific output AND a range, and it turns a slow hunt into a quick scan.
The algebra way vs the Desmos way
This technique sidesteps plugging in each x-value by hand, one at a time.
The algebra way
- Substitute
x = 0intof(x) = x^2 - 5x + 6and check the conditions. - Do it again for
x = 1, thenx = 2, thenx = 3, and so on throughx = 6. - Seven separate substitutions, each an arithmetic step where a slip can hide the right answer.
The Desmos way
- Define
f(x) = x^2 - 5x + 6once. - List the candidate x-values as
x_1 = [0, 1, 2, 3, 4, 5, 6]. - Type
f(x_1)to evaluate every candidate at once, then scan the column forf = 0andx > 2, which isx = 3.
The payoff: You evaluate seven inputs in one shot instead of running seven by-hand substitutions.
See the move, live
That same example, already loaded in the real calculator, the one built into Bluebook on test day. Try the move yourself.
Quick reference
When to reach for a table
| The equation looks like... | Do this |
|---|---|
| x + 5 = 12 (a quick mental solve) | Solve it in your head, do not open a table |
| 2x2 - 3.4x = 1.2 (messy quadratic) | Back-solve: test the choices in a table |
| The answer is a fraction or radical | Back-solve: Desmos simplifies the result for you |
Before you start: set up Desmos
Convert decimals to fractions
Desmos shows decimals like 1.333. SAT choices are usually fractions. Click the round fraction-converter button next to a value to turn 1.333 into 4/3.
Use subscripts for tables
When building a table for a regression, name the columns x_1 and y_1 so the regression binds to the right data.
Step by step
Nova
Follow along one step at a time, hit Next as you go. I'll flag the spots where people slip.
Type the function into the expression list, e.g. f(x) = x2 - 5x + 6.
Now try it on a real SAT question
The equation x2 - 3x = 10 is given.
Which of the following is a solution to the equation?
Pick an answer to get instant coaching from Nova.
Rewrite it as expression = 0, drop all four choices down one column, and the row that reads 0 is your answer. No re-solving the quadratic by hand.
Move everything to one side so the equation reads x2 - 3x - 10 = 0, then test each choice in that expression. Only x = 5 gives 52 - 3(5) - 10 = 0, so it is the solution.
In the app, drills like this adapt to your level, and your AI coach can walk you through any step you get stuck on.
Nova
Rewrite it as expression = 0, drop all four choices down one column, and the row that reads 0 is your answer. No re-solving the quadratic by hand.
Set it up yourself in the blank calculator, then read the answer straight off the graph. Muscle memory beats watching.
Watch it
The Desmos trap: when to close the calculator
- If you only need to check one x-value, plugging it into the equation by hand is faster than setting up a table.
- Table mode is most useful when a question gives you the answer choices themselves as the candidates, plug all four choices into one column instead of testing them one at a time.
- The table header has to be an expression, not an equation. Type 2x1 - 5, never 2x1 - 5 = 0, which just throws an error.
- Use the x1 and y1 subscripts in the header, like 2x1 - 5, or the column has nothing to evaluate and stays blank.
- The tilde ~ is for regressions, not back-solving, so leave it out here. A plain expression in the y1 header is all you need.
Nova
Quick gut-check though: if you only need to test one value, just do that in your head. It's faster than building a whole table. Tables earn their keep when you have a list of candidates to check, like all four answer choices, not for a single input.
Put this move into real practice
"Build a Table to Test Several x-values at Once" shows up all over the real SAT. SAT Prep Quest drills the skill at your level, so reaching for it becomes automatic by test day.
Practice freeSAT is a registered trademark of the College Board, which was not involved in producing, and does not endorse, this product. Score estimates are Learner Labs projections, not official College Board scores.