PeezyPrep · Digital SAT Math

The Desmos
Cheat Sheet.

Practice Desmos in the Bluebook app from College Board. It has the exact version of Desmos you'll see on test day.

1

Solve Any Equation in One Variable

Saves 30-60 sec

Example

What value of \(x\) satisfies \(\,5(x - 3) + 8 = 2(2x + 1)\,\)?

A) −7

B) −1

C) 5

D) 9

The move — split into two graphs

Type y = 5(x - 3) + 8

Type y = 2(2x + 1)

Click the intersection. Desmos labels it \((9, 38)\).

Answer: D.

This works for anything. Linear, quadratic, exponential, log, radical. Left side row 1, right side row 2, click the intersection.

Live · drag, zoom, click the intersection

2

Systems (Especially Nonlinear)

Saves 45-75 sec

Example

\(y = x^2 - 6x + 10\), \(\;y = 2x - 5\). The solutions are \((x_1, y_1)\) and \((x_2, y_2)\) where \(x_1 < x_2\). What is \(x_2 - x_1\)?

A) 1

B) 2

C) 4

D) 5

The move

Type both equations exactly as written.

Click both intersections: \((3, 1)\) and \((5, 5)\).

\(5 - 3 = 2\). Answer: B.

3

Square Roots & Rational Equations

Saves 60-90 sec

Example

\(\sqrt{5x + 11} = x + 1\). What is the value of \(x\) that satisfies the equation?

A) −2

B) 1

C) 5

D) −2 and 5

The move — let Desmos throw out the fakes

Type y = sqrt(5x + 11)

Type y = x + 1

Curves cross only at \(x = 5\). Answer: C.

Why this matters — the extraneous trap

Squaring both sides or cross-multiplying creates extraneous solutions: answers that pop out of the algebra but don't actually satisfy the original equation. Algebra gives \(x = 5\) and \(x = -2\), but \(-2\) makes the right side negative while the square root is positive, so it's fake. The SAT puts the extraneous answer in the choices on purpose. Desmos only draws real points, so the fake never shows up — and you won't pick it.

4

Inequalities

Saves 30-60 sec

Example

What is the solution to \(\,-2x + 5 \geq 13\,\)?

A) \(x \leq -4\)

B) \(x \geq -4\)

C) \(x \leq 4\)

D) \(x \geq 4\)

The move — let Desmos shade it

Type the inequality exactly: -2x + 5 >= 13

Desmos shades the region of \(x\) values that work.

Shading sits to the left of \(x = -4\), so \(x \leq -4\). Answer: A.

No mental sign-flip required. Same trick for systems of inequalities: type each one, the dark overlap is the feasible region.

5

How Many Solutions

Saves 45-90 sec

Example

How many real solutions does \(\,x^4 + x^2 - 12 = 0\,\) have?

A) 0

B) 2

C) 3

D) 4

The move

Type y = x^4 + x^2 - 12

Count where the curve crosses the x-axis. You see 2 crossings.

Answer: B.

6

Vertex, Max, or Min

Saves 30-60 sec

Example

A ball's height is modeled by \(h(t) = -16t^2 + 48t + 4\), where \(t\) is time in seconds. What is the maximum height, in feet?

A) 36

B) 40

C) 48

D) 52

The move

Type y = -16x^2 + 48x + 4. Swap \(t\) for \(x\).

Click the peak. Desmos labels it \((1.5, 40)\).

Max height is 40. Answer: B.

The gray dots Desmos auto-marks on a parabola are the vertex and both roots. One click each. Always click the dot, don't eyeball the curve — the SAT loves trap answers that are 0.5 off from what you'd estimate visually.

7

Parameter Problems (Sliders)

Saves 45-75 sec

Example

\(3x + 2y = 12\), \(\;6x + ky = 18\). For what value of \(k\) does the system have no solution?

A) −4

B) 2

C) 4

D) 6

The move — drag the slider

Type 3x + 2y = 12

Type 6x + ky = 18. Tap "add slider: \(k\)?"

Drag \(k\) until the lines look parallel.

Slider lands on \(k = 4\). Answer: C.

Drag the k slider · watch lines go parallel

8

Regression (Tables of Values)

Saves 60-120 sec

Example

The table shows population over time. Which equation best models the data?
x: 0, 1, 2, 3, 4 y: 100, 130, 169, 220, 286

A) \(y = 30x + 100\)

B) \(y = 100(1.3)^x\)

C) \(y = x^2 + 100\)

D) \(y = 100(1.5)^x\)

The move — let Desmos fit the curve

Tap the + button (top of the expressions panel) and choose table. A two-column table appears with headers \(x_1\) and \(y_1\).

Type the values from the question into the table, one per row.

On a new expression line below the table, type: y_1 ~ ab^{x_1}. The tilde \(\sim\) tells Desmos to fit. Desmos auto-formats the subscripts.

Look at the panel: Desmos returns \(a \approx 100\), \(b \approx 1.3\). Match to the choices. Answer: B.

Match the shape to the answer choices. Linear: y_1 ~ mx_1 + b. Quadratic: y_1 ~ ax_1^2 + bx_1 + c. Exponential: y_1 ~ ab^{x_1}. Type each model on its own line and compare.

Live · table on the left, regression coefficients filled in

9

Mean, Median & Standard Deviation

Saves 30-60 sec

Example

What is the median of the data set: \(\,12, 7, 5, 15, 9, 11, 8\,\)?

A) 7

B) 8

C) 9

D) 11

The move

Type median(12, 7, 5, 15, 9, 11, 8). Desmos returns 9.

Answer: C.

Same syntax for mean(...), stdev(...), stdevp(...), total(...), min(...), max(...), and quantile(L, 0.25) for quartiles. Drop the values straight into the parentheses, no list definition needed.

10

Absolute Value Equations

Saves 45-75 sec

Example

How many real solutions does \(\,|2x - 5| + 3 = 10\,\) have?

A) 0

B) 1

C) 2

D) 3

The move

Type y = abs(2x - 5) + 3. The V opens upward.

Type y = 10. A horizontal line.

Count intersections: 2 (at \(x = -1\) and \(x = 6\)). Answer: C.

The pipe key works too: |2x - 5| + 3. Either way, "no solution" questions come down to whether the horizontal line sits below the V's vertex.

⚡

4 Mistakes That Quietly Cost Points

Habits to fix before test day

1

Wrap fractions in parentheses. Typing x+1/x-2 gives Desmos \(\,x + \frac{1}{x} - 2\,\), not \(\,\frac{x+1}{x-2}\,\). Always type (x+1)/(x-2). Desmos reads exactly what you enter.
2

Sliders show up when there's an unknown letter. If your equation has a letter that isn't \(x\) or \(y\) (like \(k\), \(b\), or \(a\)), Desmos asks "add slider?" right under the row. Tap yes. You get a draggable bar — drag it left and right to watch the graph move in real time, and stop where the graph satisfies the question. The default slider goes from \(-10\) to \(10\) in steps of \(1\). If your answer choices are outside that range or need decimals, click the small numbers at each end of the bar to change the range, and tap the gear to change the step size.

Live · drag the m slider, watch the line tilt
3

Swap any other variables for \(x\) and \(y\). Desmos graphs in \(x\) and \(y\). If the problem uses \(h(t)\), \(f(p)\), or anything else, just retype the equation with \(x\) and \(y\). The answer is identical.
4

Recognize when a decimal is really a fraction. Desmos shows \(1.4142...\) Your answer choices say \(\sqrt{2}\). Same number. Same for \(0.5 = \tfrac{1}{2}\), \(0.333... = \tfrac{1}{3}\), \(1.732... = \sqrt{3}\). Don't reject a correct answer because it's written in a different form.

⌨️

Keyboard Shortcuts That Save Time

Type these instead of hunting for buttons

^

Exponent. x^2 → \(x^2\)

_

Subscript. x_1 → \(x_1\)

/

Fraction. Auto-stacks. Wrap top & bottom in parens.

sqrt

Square root. sqrt(x) = \(\sqrt{x}\)

nthroot

Nth root. nthroot(27, 3) = 3

abs

Absolute value. abs(x-3) or |x-3|

pi

Pi. Type the letters → \(\pi\)

> then =

Inequalities. Type the angle bracket, then the equals sign. > then = → \(\geq\). Same with < then = for \(\leq\).

~

Regression. y_1 ~ mx_1 + b fits a line.

— Michelle

I'm a Columbia Business School alum and a former AI PM at Meta, and I've been tutoring SAT math for 10 years. I built PeezyPrep because the prep resources I had as a student weren't honest about what the test actually rewards: pattern recognition, trap awareness, and knowing when not to reach for the calculator.

If this sheet helped, the full course covers every question pattern the digital SAT reuses. Videos, trap analysis, and practice modeled on the College Board question bank. It lives at peezyprep.com whenever you want it.

The DesmosCheat Sheet.

The Desmos
Cheat Sheet.