The Digital SAT math section is 44 questions across two 35-minute modules, and you are given a reference sheet of formulas inside Bluebook on every one of them. Knowing precisely what that sheet does and does not contain is worth real points — most students memorize formulas they are handed, and go hunting for ones that were never there. Here is the exact split:
The short version: the Digital SAT hands you 12 geometry formulas and three angle facts inside Bluebook, and nothing else. Every formula in Algebra, Advanced Math and Data Analysis — roughly 85% of the math section — you bring yourself. This page separates the two lists precisely, then shows which of the second list you can skip anyway because the built-in Desmos calculator will do it for you.
Download the SAT math reference sheet (free PDF)- Key Math Areas: Algebra (~35%), Advanced Math (~35%), Problem Solving & Data Analysis (~15%), Geometry & Trigonometry (~15%).
- Provided Formulas: Includes geometry basics like area, volume, and the Pythagorean theorem.
- Must-Memorize Formulas: Algebra (e.g., slope-intercept form), advanced math (e.g., exponential growth), and statistics (e.g., mean, probability).
- New Features: Built-in calculator, adaptive testing, and a reference sheet for key formulas.
Quick Tips:
- Focus on Application: Practice using formulas efficiently to save time.
- Memorize Critical Formulas: Some are not provided during the test.
- Organize Scratch Paper: Write formulas and calculations clearly to stay accurate.
Knowing formulas isn’t enough - you need to practice applying them. Start with the basics, then work on mastering problem-solving techniques. Let’s dive into the details.
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Digital SAT Math Formula Bible - 34 ESSENTIAL Formulas ...
Math Formulas by Topic
Knowing how and when to use formulas is essential for solving problems effectively. Here’s a breakdown of key formulas by topic that you'll need on test day.
Algebra
Here are some important algebraic formulas:
| Formula Type | Formula | Common Applications |
|---|---|---|
| Linear Equations | y = mx + b | Finding slope, graphing lines, and predicting values |
| Quadratic Formula | x = (-b ± √(b² - 4ac)) / 2a | Solving quadratic equations |
| Slope | m = (y₂ - y₁) / (x₂ - x₁) | Analyzing rate of change, parallel, or perpendicular lines |
Geometry
These geometry formulas help solve problems involving shapes and measurements:
| Shape | Formula | Additional Applications |
|---|---|---|
| Circle | A = πr² | Circumference: C = 2πr |
| Rectangle | A = l × w | Perimeter: P = 2l + 2w |
| Triangle | A = ½bh | Pythagorean Theorem: a² + b² = c² |
| Right Circular Cylinder | V = πr²h | Surface Area: SA = 2πr² + 2πrh |
| Sphere | V = 4/3πr³ | Surface Area: SA = 4πr² |
Problem Solving and Data
These formulas are useful for analyzing data and solving practical problems:
| Concept | Formula | Use Case |
|---|---|---|
| Mean | Average = Sum/Count | Understanding datasets |
| Probability | P(event) = favorable outcomes/total outcomes | Calculating likelihoods |
| Percent Change | % Change = (Change/Original) × 100 | Measuring growth or reduction |
| Proportion | a/b = c/d | Solving ratios and scaling problems |
Advanced Math
For more complex algebraic concepts, these formulas are key:
| Topic | Key Formula | Application |
|---|---|---|
| Function Notation | f(x) = expression | Understanding input-output relationships |
| Exponential Growth | y = ab^x | Modeling population or compound growth |
| Polynomial Operations | (a + b)² = a² + 2ab + b² | Expanding and simplifying expressions |
| Factoring | a² - b² = (a+b)(a-b) | Simplifying using the difference of squares |
Trigonometry
Some basic trigonometric formulas include:
| Ratio | Formula | Common Angles |
|---|---|---|
| Sine | sin θ = opposite/hypotenuse | sin 30° = ½ |
| Cosine | cos θ = adjacent/hypotenuse | cos 45° = 1/√2 |
| Tangent | tan θ = opposite/adjacent | tan 60° = √3 |
To see these formulas in context, refer to the official SAT formula sheet.
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What's on the official SAT reference sheet
Every Digital SAT math module opens with a reference sheet you can pull up at any time inside Bluebook. The SAT reference sheet contains 12 geometry formulas and three angle facts — nothing else. Knowing exactly what is on it is worth real points, because every formula on this list is one you do not need to memorize.
Provided on test day — do not spend memorization time here
| Group | What the reference sheet gives you |
|---|---|
| Area & circumference | Rectangle A = lw · Triangle A = ½bh · Circle A = πr² · Circle C = 2πr |
| Right triangles | Pythagorean theorem a² + b² = c² · 30-60-90 ratio 1 : √3 : 2 · 45-45-90 ratio 1 : 1 : √2 |
| Volume | Rectangular prism V = lwh · Cylinder V = πr²h · Sphere V = (4/3)πr³ · Cone V = (1/3)πr²h · Pyramid V = (1/3)Bh |
| Stated facts | 360° in a circle · 2π radians in a circle · 180° in a triangle |
Two things students get wrong about this list. First, rectangle perimeter is not on it — P = 2l + 2w is simple enough to reconstruct, but it is not on the SAT reference sheet, so do not expect to look it up. Second, the volumes of spheres, cones and pyramids are on it, as are both special right triangles. A lot of prep material tells students to memorize those. That is wasted effort.
Not provided — these are the ones to memorize
Everything outside geometry is on you. These are the formulas the SAT reference sheet will not help with, ordered by how often they actually appear:
| Area | Memorize |
|---|---|
| Linear | Slope m = (y₂ − y₁)/(x₂ − x₁) · Slope-intercept y = mx + b · Point-slope y − y₁ = m(x − x₁) |
| Quadratic | Standard ax² + bx + c · Vertex y = a(x − h)² + k · Quadratic formula · Discriminant b² − 4ac · Axis of symmetry x = −b/2a |
| Exponential | Growth/decay y = ab^x · Percent change (new − old)/old · Compound interest |
| Statistics | Mean · Median · Range · Standard deviation (conceptual) · Margin of error (conceptual) |
| Circles in the plane | Standard form (x − h)² + (y − k)² = r² · Arc length · Sector area |
| Trigonometry | SOHCAHTOA · Complementary angle identity sin θ = cos(90° − θ) · Radian conversion |
The split matters more than the list. Geometry is the one domain where the test hands you the tools — and it is only about 15% of the math section. Algebra and Advanced Math are roughly 35% each, and the reference sheet helps with neither.
The other half of this is knowing which of these you never have to compute by hand at all, because the built-in Desmos calculator will do it faster. Vertex, discriminant, standard deviation and circle centre are all faster to read off a graph than to calculate — see the Desmos guide for the exact keystrokes.
Why the SAT reference sheet helps less than you think
Every formula on the sheet is a geometry or trigonometry formula. Geometry & Trigonometry is about 15% of the Digital SAT math section — roughly 5 to 7 questions out of 44. So the reference sheet is silent on the other ~85%.
| Domain | Share of the math section | Questions | Does the reference sheet help? |
|---|---|---|---|
| Algebra | ~35% | 13–15 | No |
| Advanced Math | ~35% | 13–15 | No |
| Problem-Solving & Data Analysis | ~15% | 5–7 | No |
| Geometry & Trigonometry | ~15% | 5–7 | Yes — this is the whole sheet |
There is a wrinkle worth knowing, though, and it cuts the other way. In our College-Board-grounded concept taxonomy, 14 of the 47 math concepts flagged as frequent on Module 2 Hard are Geometry & Trigonometry — far above that domain's 15% share of the test. Advanced Math contributes 17, Algebra only 7.
So the sheet is close to useless across the bulk of the test, and disproportionately useful on the hard adaptive module. That is a real argument for knowing it cold rather than glancing at it: the questions where it matters are the ones deciding whether you finish at 1400 or 1550.
Using Formulas During the Test
How you use formulas during the test can make a big difference in your performance. Let’s break it down.
Memorizing Key Formulas
The SAT provides some geometry formulas, but others - especially in algebra, advanced math, statistics, and probability - must be memorized. Here’s how to prioritize:
| Knowledge Level | Action Plan | Priority |
|---|---|---|
| Know Well | Review once a week | Low |
| Sorta Know | Practice 2-3 times a week | Medium |
| Don’t Know | Practice daily until mastered | High |
By focusing on these crucial formulas, you’ll be able to quickly identify and apply the right one during the test.
How to Choose the Right Formula
1. Analyze the Question
Pay attention to the details. Look for shapes in geometry problems, variables in algebra questions, or data in statistics scenarios. These clues will guide your formula choice.
2. Check for Efficiency
Think about the fastest way to solve the problem:
- Compare using a formula versus a different strategy.
- Pick the method you’re most comfortable with.
- Always aim for the approach that saves time without sacrificing accuracy.
3. Know Common Scenarios
Be ready for these frequent problem types:
- Circle problems often need area or circumference formulas.
- Linear equations rely on the slope-intercept form.
- Word problems may call for growth or decay formulas.
Using Scratch Paper Effectively
Once you’ve picked the right formula, how you organize your work on scratch paper can help you stay accurate and efficient.
1. Organize Your Work
Divide your scratch paper into sections:
- Top: List commonly used formulas for quick reference.
- Middle: Do your calculations here.
- Bottom: Write your final answers clearly.
2. Document Your Steps
Write out every part of the process:
- Start with the formula.
- List the values you’re using.
- Show your substitutions.
- Highlight your final answer.
3. Manage Your Time
Stay efficient with these tips:
- Write down the formula as soon as you start a problem.
- Cross out mistakes instead of erasing to keep your work clear.
- Use arrows to connect related calculations for better flow.
These strategies will help you stay organized and focused, even under time pressure.
The formulas to memorize, by domain
Because the SAT math reference sheet stops at geometry, the memorize list is organised here the way the test is: by College Board domain, heaviest first. If you are triaging with limited time, work top down — Algebra and Advanced Math are 70% of the section between them.
Algebra — ~35% of the section, 13–15 questions
Nothing in this domain appears on the reference sheet.
- Slope
m = (y₂ − y₁)/(x₂ − x₁)— the single most reused formula on the test. - Slope-intercept form
y = mx + b, and point-slopey − y₁ = m(x − x₁)when you are given a point rather than an intercept. - Parallel and perpendicular — equal slopes; negative reciprocal slopes. Frequently the whole question.
- Systems — know that no solution means equal slopes with different intercepts, and infinitely many means the two equations are multiples of each other. This phrasing appears constantly.
Advanced Math — ~35% of the section, 13–15 questions
- Standard form
ax² + bx + c, vertex formy = a(x − h)² + k, factored formy = a(x − r₁)(x − r₂)— and what each form tells you at a glance. - Quadratic formula and the discriminant
b² − 4ac: positive means two real solutions, zero means one, negative means none. - Axis of symmetry
x = −b/2a. - Exponential growth and decay
y = ab^x, and reading the growth rate out ofb. - Exponent and radical rules —
x^(a/b) = ᵇ√(x^a)is the one most often missed.
Problem-Solving & Data Analysis — ~15%, 5–7 questions
- Percent change
(new − old)/old, and percent-of versus percent-more-than. - Mean, median, range, and conceptually what moves standard deviation — the SAT asks you to reason about spread far more often than to compute it.
- Probability as favourable over total, including conditional probability read from a two-way table.
- Margin of error and sampling — conceptual, but reliably one question.
Geometry & Trigonometry beyond the sheet — ~15%, 5–7 questions
The reference sheet SAT candidates are given covers the basics here, but not these:
- Circle in the plane
(x − h)² + (y − k)² = r²— not on the sheet, and common. - Arc length and sector area, and radian–degree conversion.
- SOHCAHTOA, plus the complementary identity
sin θ = cos(90° − θ), which shows up as a standalone question type. - Similar triangles and the scale factor rule: lengths scale by k, areas by k², volumes by k³.
Formulas you can skip because Desmos does them
The memorize list above is the standard answer. It is also longer than it needs to be. The Digital SAT gives you a full Desmos graphing calculator on every math question, and several formulas people grind into flashcards are faster to read off a graph than to recall and apply.
| Formula | What to do instead | Time saved |
|---|---|---|
Vertex x = −b/2a | Graph the parabola and click the grey vertex dot | ~15s |
| Quadratic formula | Type the equation and click where it crosses the x-axis | ~30s |
Discriminant b² − 4ac | Graph it and count the x-intercepts | ~60s |
| Circle centre and radius | Type the equation in any form — no completing the square | ~40s |
| Standard deviation | stdev(L) on a list | ~90s |
| Distance between two points | distance((1,2),(4,6)) | ~15s |
Try it on a real one. This is the quadratic y = x² − 6x + 5 — the grey dots Desmos marks automatically are its two zeros and its vertex, which is every value a typical SAT question about this parabola can ask for:
And a circle in the ugly expanded form that normally costs a minute of completing the square:
The full set of calculator techniques, with the exact keystrokes for each, is in the SAT Desmos cheat sheet.
How to actually use the reference sheet on test day
The panel is two clicks away inside Bluebook, which sounds free but is not. Opening it, scanning twelve formulas and closing it costs perhaps ten seconds. Do that six times and you have spent a minute you needed for the last hard question.
- Know the sheet before test day. Not to memorize it — to know what is on it, so you never open it hoping for a formula that was never there. Rectangle perimeter, the quadratic formula and slope are the three people most often go looking for in vain.
- Open it deliberately, once. If a question is clearly a cone or sphere problem, pull the panel, take the formula, close it. Do not browse.
- Write the formula down before you substitute. Copying
V = (1/3)πr²honto scratch paper and then filling in numbers catches the transcription errors that cost more points than the formula itself. - Check your calculator mode for trigonometry. Desmos defaults to radians and the SAT asks in degrees. The reference sheet will not warn you.
Take both lists with you. The free SAT math reference PDF puts what the test provides and what you have to know side by side, then works through real questions applying them — with a Desmos check on each one.
Download the free 10-page PDFSAT reference sheet FAQ
Is the SAT reference sheet the same as the SAT formula sheet?
Yes. College Board calls it the reference sheet; most students and prep sites call it the formula sheet or a math cheat sheet. They all mean the same panel of 12 geometry formulas inside Bluebook.
Do I get the reference sheet on both math modules?
Yes. It is available on every math question in both Module 1 and Module 2, and there is no limit on how often you open it.
Is the quadratic formula on the SAT reference sheet?
No. Neither is slope, vertex form, the exponential growth model, nor any statistics formula. The sheet is geometry only.
Is rectangle perimeter on the sheet?
No — and this is a common misconception, including in some published prep material. Rectangle area is on it; perimeter is not.
Do I need to memorize the volume of a sphere?
No. Sphere, cone and pyramid volumes are all printed on the sheet, as are both special right triangles. Memorizing them is wasted preparation time.
How many formulas are on the SAT reference sheet?
Twelve formulas plus three stated facts: 360 degrees in a circle, 2π radians in a circle, and 180 degrees in a triangle.
Can I bring my own formula sheet to the SAT?
No. You may not bring notes of any kind. The only reference material available is the built-in panel.
Conclusion
Get a strong grip on SAT math formulas with focused daily practice. Group formulas based on how well you know them, and spend 5-10 minutes on each topic, focusing on areas where you can make the most progress. Remember, simply knowing a formula isn’t enough - you need to know how to use it effectively.
Leverage Pursu’s tools to sharpen your skills. Its topic-specific tests and performance analytics can help you track your progress and fine-tune your study plan.
Here are some key strategies to include in your prep:
- Use Pursu’s topic-based tests for targeted practice.
- Focus on the most critical formulas before moving on to less essential ones.
- Write down formulas and practice explaining them to solidify understanding.
- Solve problems that closely resemble actual SAT questions.
What kind of mistakes are costing you points?
7 questions, ~3 minutes. After each, tell us what happened — we'll surface the *pattern* that's keeping your score down (it's almost never knowledge).
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