These nine Desmos SAT practice problems come from the real October 2026 SAT, as rebuilt in our question bank. Each one shows what to type into Desmos, where the answer appears on the graph, and the trap answer to avoid. Answers hide behind a toggle, so try each problem first.
Short answer: Desmos is built into Bluebook for the whole Math section, so you can use it on every problem below. The problems run from Easy to Hard, using the difficulty labels in our bank. For the full technique library and a practice calculator, use our Desmos for the SAT page.
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Question banks: October 2026 Math question bank
Notes and practice need a free account: one click with Google, and you land straight on the lesson.
How to use these Desmos SAT practice problems
Open a Desmos graphing calculator next to this page. Our Desmos SAT hub loads Desmos's testing calculator, the same one inside Bluebook. Then follow three rules:
- Try first. Read the problem and guess the Desmos move before you open the steps.
- Check the last line. Several of these ask for something other than x. Desmos finds the point. You still answer the question.
- Time yourself. On the real test, Math has 44 questions in 70 minutes, per College Board. That is about 95 seconds a question.
College Board says students can use their own approved calculator "or take advantage of the Desmos calculator embedded in Bluebook," per its calculator policy. If you are new to Desmos, start with is Desmos allowed on the SAT.
The nine problems at a glance
| # | Skill | Bank difficulty | Desmos move |
|---|---|---|---|
| 1 | Systems of equations | Intermediate | Graph both lines, click the crossing point |
| 2 | Systems of equations (grid-in) | Intermediate | Graph both lines, read x |
| 3 | System with no solution | Hard | Slider for the constant |
| 4 | Quadratic equation | Easy | Click the x-intercepts |
| 5 | Maximum of a quadratic | Easy | Click the vertex |
| 6 | Number of solutions | Easy | Count the x-intercepts |
| 7 | Quadratic word problem (grid-in) | Hard | Graph a curve and a flat line |
| 8 | Quadratic from a table | Intermediate | Table plus regression |
| 9 | Circle equation | Hard | Test the answer choices |
All nine are from the October 2026 SAT Math Question Bank, which has 106 questions. We solved each one by hand and checked that our answer matches the bank's key.
Desmos practice problems on systems of equations
A system's solution is the point where its graphs cross. Desmos finds it for you. Its FAQ says that when you click a line, "gray dots will appear at intercepts, intersection points, maximums, and minimums."
Problem 1 (Intermediate)
Practice Desmos under test timing. A free account includes one full-length adaptive SAT test with a likely score range.
Start 1-day free trial →2x + 3y = 19
x − y = 2
What is the value of x + y?
A) 5 B) 7 C) 8 D) 11
Show the Desmos steps and answer
Type both equations as written, one per line. Desmos accepts equations "that are not solved for y," says its FAQ. Click the crossing point: (5, 3). So x + y = 5 + 3 = 8.
Answer: C) 8. Choice A, 5, is x alone. You found the point but skipped the last step.
If the point shows no numbers, retype each line as y = something. The Desmos FAQ says coordinates are easiest to see when you "enter the expression explicitly."
Problem 2 (Intermediate, grid-in)
2x − 2y = 8
−3y = 18
The solution to the given system of equations is (x, y). What is the value of x?
Show the Desmos steps and answer
The second equation has no x, so it graphs as a flat line at y = −6. The two lines cross at (−2, −6).
Answer: −2. By hand: y = −6, so 2x + 12 = 8 and x = −2. On a grid-in, type the minus sign. Do not enter −6, which is y.
Problem 3 (Hard)
18x + 6y = 8y + 9
ty = 1⁄5 + 9x
In the given system of equations, t is a constant. If the system has no solution, what is the value of t?
Show the Desmos steps and answer
Type both equations. Desmos sees the letter t and offers a slider. Its sliders guide says that "any time you have free variables in an expression, the calculator will prompt you to define them with sliders."
Drag t until the two lines never meet. "No solution" means parallel lines, so look for the moment the lines stop crossing. That happens at t = 1.
Answer: 1. By hand: the first equation becomes y = 9x − 4.5, slope 9. The second becomes y = (9/t)x + 1/(5t). The slopes match when 9/t = 9, so t = 1. Then the y-intercepts are 0.2 and −4.5, so the lines are parallel and never touch.
Desmos practice problems on quadratics
A parabola shows you its zeros and its vertex. Click the curve, and Desmos marks both with gray dots.
Problem 4 (Easy)
What is the positive solution to the equation x2 − 7x − 18 = 0?
See which question types are costing you points
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A) 2 B) 6 C) 9 D) 18
Show the Desmos steps and answer
Type y = x^2 − 7x − 18. Click the curve. It crosses the x-axis at (−2, 0) and (9, 0).
Answer: C) 9. By hand: (x − 9)(x + 2) = 0. Choice A, 2, is the negative root with its sign dropped. Choice D, 18, is the constant term.
Problem 5 (Easy)
The function f is defined by f(x) = −2(x − 3)2 + 8. What is the maximum value of f(x)?
A) −2 B) 3 C) 6 D) 8
Show the Desmos steps and answer
Type f(x) = −2(x − 3)^2 + 8. Click the top of the curve. The vertex is (3, 8).
Answer: D) 8. The maximum value is the y-value of the vertex. Choice B, 3, is the x-value of the vertex, so it answers a different question.
Problem 6 (Easy)
x2 − 25⁄9 = 0
How many distinct real solutions does the given equation have?
A) Zero B) Exactly one C) Exactly two D) Infinitely many
Show the Desmos steps and answer
Type y = x^2 − 25/9. Count where the curve crosses the x-axis. It crosses twice, near −1.667 and 1.667.
Answer: C) Exactly two. By hand: x2 = 25/9, so x = 5/3 or −5/3. To see a decimal as a fraction, the Desmos FAQ says to click its "Convert" button.
Problem 7 (Hard, grid-in)
A rectangle has a width of n yards and a length of (n + 7) yards. If the rectangle has an area of 198 square yards, what is the value of n?
Show the Desmos steps and answer
Area is width times length, so n(n + 7) = 198. Desmos graphs in x, so use x for n. Type y = x(x + 7) on line 1 and y = 198 on line 2. The graphs cross at x = −18 and x = 11.
Answer: 11. A width cannot be negative, so drop −18. Check: 11 × 18 = 198.
Desmos practice problems with tables and regression
When a question gives a table, put the table in Desmos. The Desmos tables guide says the first two columns, x1 and y1, plot by default. Then fit a model with the tilde key (~). For more on this move, read when to use regression on the SAT.
Problem 8 (Intermediate)
| x | 25 | 27 | 29 |
|---|---|---|---|
| f(x) | −4 | −4 | 4 |
For the quadratic function f, the table shows three values of x and their corresponding values of f(x). Which equation defines f?
A) f(x) = (x − 25)(x − 27) + 2
B) f(x) = (x − 25)(x − 27) − 4
C) f(x) = (x − 4)(x − 29) + 16
D) f(x) = (x − 4)(x − 29) − 16
Show the Desmos steps and answer
Way 1, regression. Make a table with the three points. On a new line type y1 ~ ax1^2 + bx1 + c. Three points fix one parabola, so the fit is exact: a = 1, b = −52, c = 671.
Way 2, test the choices. Type each choice as a graph and see which one passes through all three table points. Only B does.
Answer: B. Check: (29 − 25)(29 − 27) − 4 = 8 − 4 = 4. Choice A matches the shape but gives f(25) = 2, not −4.
Desmos practice problems on circles
Desmos graphs a circle from its equation as written. When the choices are equations, graph them and test the points you know.
Problem 9 (Hard)
A circle in the xy-plane has a diameter with endpoints (2, 6) and (12, 16). Which equation represents this circle?
A) (x + 7)2 + (y + 11)2 = 200
B) (x − 7)2 + (y − 11)2 = 200
C) (x + 7)2 + (y + 11)2 = 50
D) (x − 7)2 + (y − 11)2 = 50
Show the Desmos steps and answer
Type the points (2, 6) and (12, 16). Then type each choice. The right circle passes through both points. For an exact check, type (2 − 7)^2 + (6 − 11)^2. Desmos shows 50.
Answer: D. The center is the midpoint, (7, 11). The radius squared is 52 + 52 = 50. Choice B uses 200, which is the diameter squared. Choices A and C flip the signs of the center.
Where can you find more Desmos SAT practice problems?
Use real test questions first. They show you how the SAT words each type.
- Our question banks. The SAT question bank hub lists every bank by test month, for Math and Reading and Writing. You can try 5 sample questions from any test in our practice test catalog with no account.
- Technique pages. Read how to solve for x on Desmos, ratios and percentages on Desmos, and the complete guide to Desmos on the SAT.
- Know when to skip it. Some questions are faster by hand. See when not to use Desmos on SAT Math.
- "Save Me Desmos." Many students search for savemedesmos.com. On October 13, 2026, that address redirected to a page on Bedrock, a math prep site. The page had a Desmos guide video and 27 listed problems. We compare that site in our Bedrock review.
How do you practice Desmos under real test conditions?
Take a timed, adaptive Math section. Problems in a list feel easy. A clock and harder second module feel different.
A free account on The Test Advantage includes one full-length adaptive test with a likely score range. Our Math adaptive tests use two 22-question, 35-minute modules, the same lengths as the real test. The free account also includes Targeted Practice. Create your free account to take it. You do not need a card. When you want the full October 2026 Math bank and the rest of the catalog, see Premium plans.
How we built this page
All nine problems come from test 4235, our October 2026 SAT Math Question Bank, read from our database on October 13, 2026. We solved each by hand, and every answer matched the bank's key. Choices appear in the bank's stored order. We quote Desmos behavior from the Desmos Help Center and College Board facts from its own pages. We did not run these problems in Desmos ourselves. All facts verified 2026-10-13.
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Frequently Asked Questions
Where can I find Desmos SAT practice problems?
Use real SAT questions where possible. This page has nine from the October 2026 SAT Math bank with Desmos steps and answers. College Board's Bluebook practice tests include the same built-in Desmos calculator, and The Test Advantage's question banks group more questions by test month.
Can you use Desmos on every SAT Math question?
Yes. College Board's calculator policy says students can use the Desmos calculator embedded in Bluebook and can switch between graphing and scientific options at any point in the Math section. Some questions are still faster by hand.
How do you solve a system of equations on Desmos?
Type each equation on its own line, exactly as written. Click one of the lines, and Desmos shows gray dots at intersection points. Click the dot where the lines cross to read the solution (x, y).
How do you use a slider for a constant on Desmos?
Type the equation with the letter in it. Desmos prompts you to add a slider for any free variable. Drag the slider until the graphs show what the question asks for, such as parallel lines for no solution.
How do you do a regression on Desmos for the SAT?
Enter the table values in a Desmos table, then on a new line type the model with a tilde instead of an equals sign, for example y1 ~ a x1^2 + b x1 + c. Desmos fits the constants to the table data.
What is savemedesmos.com?
On October 13, 2026, savemedesmos.com redirected to a videos page on Bedrock, a SAT Math prep site. That page showed a Desmos guide video and a list of 27 practice problems.