On the Digital SAT you may use a calculator on every Math question, and the Bluebook testing app has a Desmos calculator built in. Many students use it only for arithmetic. For some question types, though, graphing gets you to the answer much faster than solving by hand. For others, the calculator just slows you down.
Below are 12 common question types, each with an example written by Clever Academy and the exact input to use. If you are sitting the 7 November SAT, the registration deadline is 23 October, so there is still time to build the habit.
What Desmos in Bluebook gives you
- Two modes: graphing and scientific. You can switch between them at any point in the Math section.
- A movable window that you can drag anywhere on screen so it does not cover the question.
- Your own handheld calculator is allowed as long as it has no CAS (computer algebra system). Models such as the TI-Nspire CAS, TI-89, HP Prime and Casio ClassPad are prohibited. If your handheld fails mid-test, you can carry on with Desmos in Bluebook.
- No calculators in Reading and Writing. A handheld must stay under your desk during those modules.
- A reference sheet is available on Math questions, and scratch paper is provided.
Four moves worth knowing before test day:
- Click a graph to reveal grey points: intersections, vertices and intercepts. Click a grey point to see its coordinates.
- Sliders: type an unfamiliar letter such as k or c and Desmos offers to add a slider.
- Tables: enter data in columns x₁ and y₁.
- The ~ symbol runs a regression on table data.
College Board suggests getting familiar with Desmos through the Math section of the Bluebook test preview, full practice tests in Bluebook, or the Desmos website. Practising inside Bluebook is best, because the screen layout matches test day.
Solving systems by graphing
1. Two linear equations
Example: 3x + 2y = 16 and x − y = 2. Find x + y.
Type both equations as written, on separate lines. There is no need to solve for y. Click the intersection: (4, 2). So x + y = 6.
2. A system with a parameter and no solution
Example: for what value of k does the system 2x + 3y = 7 and 4x + ky = 10 have no solution?
Type the second equation with k and add the slider. Drag k until the lines are parallel: k = 6. Confirm algebraically: no solution when 2/4 = 3/k but 7/10 ≠ 1/2, so k = 6. The slider shows you the answer; the algebra makes sure of it.
3. A line meeting a parabola
Example: y = x² − 4x + 3 and y = x − 1 intersect at two points. What is the sum of their x-coordinates?
Graph both and click the two intersections: (1, 0) and (4, 3). The sum is 5.
4. Systems of inequalities
Example: which point satisfies both y > 2x − 1 and y ≤ −x + 5: (3, 1), (1, 3), (0, −2) or (2, 4)?
Desmos shades each solution region. A strict inequality is drawn dashed, a non-strict one solid. Add the four points on new lines; the one inside the overlap is the answer: (1, 3).
Quadratics: vertex, roots and intersections
5. Maximum or minimum value
Example: a ball's height in metres after t seconds is h(t) = −5t² + 20t + 1. What is its maximum height?
Type y = −5x² + 20x + 1 (Desmos uses x). Zoom until the vertex is visible and click it: (2, 21). Maximum height is 21 m, reached after 2 seconds. Read carefully whether the question asks for the time or the height.
6. Roots of a quadratic
Example: find the positive solution of 2x² − 7x − 15 = 0.
Type y = 2x² − 7x − 15 and click the x-intercepts: x = −1.5 and x = 5. The positive root is 5. If a root is irrational, Desmos gives a decimal while the answer choices use radicals. Type each choice into Desmos and compare decimals.
7. A constant that gives exactly one solution
Example: x² − 6x + c = 0 has exactly one real solution. Find c.
Type y = x² − 6x + c and add a slider for c. Drag until the parabola just touches the x-axis: c = 9. Check: the discriminant 36 − 4c = 0 gives c = 9. Set the slider step to 1 so it stops on whole numbers.
8. Equivalent expressions
Example: which expression is equivalent to x² + 2x − 15? A. (x − 5)(x + 3) B. (x + 5)(x − 3) C. (x − 15)(x + 1) D. (x + 15)(x − 1)
Graph y = x² + 2x − 15, then graph each choice. The one that lies exactly on top is correct: B. This works for any "which expression is equivalent" question.
9. Circles: centre and radius
Example: find the radius of the circle x² + y² − 6x + 4y − 12 = 0.
Type the equation as given and Desmos draws the circle. Reading the grid: centre (3, −2), radius 5. To be certain, complete the square: (x − 3)² + (y + 2)² = 25.
Regression and statistics
10. Mean and median
Example: the data are 12, 15, 15, 18, 20, 22, 38. If 38 is removed, how do the mean and median change?
Type L = [12, 15, 15, 18, 20, 22, 38], then mean(L) = 20 and median(L) = 18. Remove 38 and recalculate: mean 17, median 16.5. The mean falls by 3 and the median by 1.5. Desmos also has stdev() for questions about spread.
11. A linear function from a table
Example: a linear function f has f(1) = 4, f(3) = 10 and f(6) = 19. Find f(10).
Create a table with x₁ = 1, 3, 6 and y₁ = 4, 10, 19. Type y₁ ~ mx₁ + b and Desmos returns m = 3, b = 1. So f(10) = 31. With scattered data, the same command gives the line of best fit and the correlation r.
12. An exponential model from a table
Example: a town's population, in thousands, is 200, 240 and 288 after 0, 1 and 2 years. Using an exponential model, what is it after 3 years?
Enter the table and type y₁ ~ a·b^x₁. Desmos returns a = 200 and b = 1.2, a 20% annual increase. After 3 years: 200 × 1.2³ = 345.6 thousand.
When not to use Desmos
College Board itself notes that some Math questions are better done without a calculator. Solve by hand when:
- The algebra is one line. If 3x + 5 = 20, what is 6x + 10? Double both sides: 40. Typing only costs time.
- The question asks for meaning. "What does 1.2 represent in the model?" is a reading question, not a calculation.
- Geometry needs a sketch, such as angles or similar triangles. Use scratch paper and the reference sheet.
- You have been typing for 30 seconds with nothing to show. Stop, solve by hand, and mark the question for review if you want to come back.
A practice routine that works: take the questions you missed on practice tests and redo each one twice, by hand and with Desmos, noting which was faster for that type. After two or three weeks you will know at a glance when to open the calculator.
Sources
- SAT Suite of Assessments Calculator Policy — College Board
- Bluebook Testing Tools — College Board
- Bluebook — College Board
- Desmos Graphing Calculator — Desmos
Information on the Bluebook calculator and calculator rules is from College Board, checked on 25 September 2026. The maths examples were written by Clever Academy for illustration.