Reference Sheet and Test Day

The SAT Math reference sheet: provided formulas and required knowledge

The test hands you a small sheet of geometry and asks you to carry everything else in your head. Knowing exactly which is which saves you twice: you stop memorizing what the screen already shows, and you stop hunting the screen for what was never on it.

On test day a reference sheet sits one tap away, open the whole time, in both modules. The sheet covers one corner of the test only, geometry, and not a single line of algebra. This page sorts the two: the short list the screen carries for you, and the shorter list you carry yourself.

Math tools provided in Bluebook

Everything below appears on the reference sheet, so there is nothing here to memorize. The single use of knowing it is to never derive, or hunt for, something the test already shows you. It is all area, volume, right triangles, and angle facts.

• Areas. Circle $A = \pi r^2$, circumference $C = 2\pi r$. Rectangle $A = \ell w$. Triangle $A = \frac{1}{2}bh$.
• Volumes. Box $V = \ell wh$. Cylinder $V = \pi r^2 h$. Sphere $V = \frac{4}{3}\pi r^3$. Cone $V = \frac{1}{3}\pi r^2 h$. Pyramid $V = \frac{1}{3}\ell wh$.
• Right triangles. Pythagorean theorem $c^2 = a^2 + b^2$. A 45-45-90 triangle has sides in the ratio $s : s : s\sqrt{2}$; a 30-60-90 triangle, $x : x\sqrt{3} : 2x$.
• Angles. A full circle is $360$ degrees, or $2\pi$ radians. The angles of a triangle sum to $180$ degrees.

Math facts and relationships not supplied by the reference sheet

None of the following is on the sheet, and most of the test draws on it. The list is shorter than it looks, because each line is an idea you already worked through in its chapter, not a fact to cram. Keep these as ready as your own address.

• Lines. Slope $m = \frac{y_2 - y_1}{x_2 - x_1}$. Slope-intercept $y = mx + b$; point-slope $y - y_1 = m(x - x_1)$. Parallel lines share a slope; perpendicular slopes multiply to $-1$ when both lines have a defined, nonzero slope. A vertical line and a horizontal line are perpendicular without that product rule applying, since a vertical line has no slope.
• Quadratics. Quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. Vertex at $x = -\frac{b}{2a}$. Sum of roots $-\frac{b}{a}$, product $\frac{c}{a}$. The discriminant $b^2 - 4ac$ is positive for two real roots, zero for one, negative for none. Difference of squares $a^2 - b^2 = (a + b)(a - b)$.
• Exponents. $a^m \cdot a^n = a^{m+n}$, $(a^m)^n = a^{mn}$, $a^{-n} = \frac{1}{a^n}$, and $a^{1/n}$ is the $n$th root. A percent change of $r$ each period multiplies by $(1 + r)$ for growth or $(1 - r)$ for decay.
• Data. Percent change is $\frac{\text{new} - \text{old}}{\text{old}}$. Mean is the sum divided by the count. Probability is the favorable outcomes divided by the total.
• Coordinate and trigonometry. Circle $(x - h)^2 + (y - k)^2 = r^2$, with center $(h, k)$ and radius $r$. Distance $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$; the midpoint is the average of the coordinates. Arc length and sector area are the angle's fraction of the whole circle, times circumference or area. And SOH-CAH-TOA: sine is opposite over hypotenuse, cosine adjacent over hypotenuse, tangent opposite over adjacent, with $\sin\theta = \cos(90^\circ - \theta)$.

Use the reference sheet efficiently

Open the reference sheet once at the start of each module, glance over it, and close it. That single look fixes in mind what you can lean on, so you never spend a question deriving a cone's volume from scratch. After that, rely on memory and reach for the sheet only to confirm a shape's formula. Use the sheet when a question calls for one of the formulas or angle facts actually printed there. For lines, quadratics, exponent rules, statistics, probability, most circle theorems, and coordinate relationships, rely on the relationships reviewed above rather than searching the sheet.

Digital SAT test day: device, Bluebook, and Math tools

By test day the work is behind you. What is left is not more math; it is arriving rested and running a steady rhythm, so that everything you built has room to show. A plan made now means no decisions to make on the morning itself.

One week before the test

The week before is for tapering, not cramming. Your skills map from the full-length test already names the few rows still worth a pass; spend short, light sessions there and nowhere else. Take that timed test three or four days out, not the night before, so you arrive fresh rather than spent. Keep your sleep on its normal schedule rather than shifting it. Settle the logistics early: the Bluebook app installed and updated, your device charged, your admission ticket and photo identification ready, and the route and arrival time known.

What to bring

The admission-ticket and photo-identification requirements below describe SAT Weekend, the national Saturday administration most students register for individually. If you are testing through a School Day administration arranged by your school, follow your school's own check-in process, since requirements such as ticketing and ID can differ.

• Device. Know whether you are testing on your own laptop, tablet, or a school-managed Chromebook, and practice on that same device, since the trackpad, keyboard, and screen size all shape how comfortably you move through Bluebook. Keep it fully charged, and pack a cord or a portable charger rather than counting on a free outlet.
• Calculator plan. Desmos is already built into the Math section, and a separate handheld calculator is optional. Decide which you prefer, or whether you will use both, during practice, not after the start code. A handheld calculator must meet the College Board's current calculator policy, which prohibits any calculator with CAS (computer algebra system) functionality. The embedded Desmos calculator remains available on every Math question, so it is a reliable fallback either way.
• Bluebook. Recent updates include a resizable embedded calculator window and improved zoom-and-pan viewing for the reference sheet and other on-screen images. Interface details can change between updates, so a few minutes exploring the current layout during your last practice session is worth more than memorizing a fixed description.
• Scratch paper is provided at the testing site; you do not bring your own. Learn from timed practice roughly how much paper your Math work uses, so you can write economically and raise a hand early if you need more.
• Pack a pen or pencil, your photo identification, and your admission ticket. Leave a smartwatch, a separate timer, earbuds, and notes at home; each is either unnecessary or against the rules.

The night before and the morning of

No new material the night before; it trades rest for almost nothing. A light skim of the reference page and your error log is plenty. Pack what you need, set out your clothes, and sleep at your usual hour. Be unremarkable: a normal evening, an early night.

On test morning, eat the breakfast you usually eat, and give yourself more time than you think you need. Arriving early settles the nerves; arriving late spends them. Warm up with two or three easy problems on the way in, just enough to wake the part of your mind the test will use, so the first real question does not meet a cold start.

During the test

Each module gives you thirty-five minutes for twenty-two questions, a little over a minute and a half apiece on average. Questions are arranged from easier to harder overall within each module, though any individual item may feel easier or harder than its neighbors. Use early routine items to preserve time for later questions that need more work. Work in two passes. On the first pass, answer every question you can solve without strain, and the moment one resists, mark it for review and move on. On the second pass, return to the marked questions with the time you saved.

Test-day sequence

• About ninety seconds a question on average, but spend less early and more late.
• Two passes: the questions you can solve now first, the flagged ones second.
• Flag and move. No single question is worth the clock that the easy ones need.
• Open the calculator when it is faster than you are (graphing, solving, a quick check), not for arithmetic you can see at a glance.
• On grid-ins, re-read what is asked, then enter the answer in a form the grid accepts.

When Module 1 closes

Module 1 sets the difficulty of Module 2, and once you submit it, that is settled; there is nothing to gain by replaying how it went. The break in your testing day falls between the Reading and Writing section and Math, not between the two Math modules themselves, so plan your reset, however brief, with that in mind. Treat the start of Module 2 as a clean page: the same rhythm, the same two passes, the same flag-and-move.

If something goes wrong

A testing room is not immune to a frozen screen, a Wi-Fi hiccup, or a device that stops cooperating. None of these end your test, and none of them are yours to solve alone. If the app freezes or misbehaves, raise your hand; restarting, signing back in, or moving to a backup device is the proctor's job. A brief Wi-Fi drop after testing has started does not invalidate anything; current guidance allows testing to continue through a momentary loss of connection. If a final submission seems to fail, keep the device open and follow the in-app instructions; a failed upload is not the same thing as lost answers, and saved responses can typically be resubmitted. Raising a hand costs seconds and gets you back to the math faster.

After the benchmark and final review

Turn your results into a plan

Score the benchmark out of forty-four. The Math section is reported on a scale from 200 to 800, but there is no single raw-to-scaled conversion that applies to every digital SAT form, so read the raw result for diagnosis, not as a precise official score estimate. Mark every wrong answer by domain (Algebra, Advanced Math, Problem-Solving and Data Analysis, or Geometry and Trigonometry) and by module. Compared with your diagnostic, a domain weak on both is a persistent gap and gets the most remaining time; weak on the diagnostic but clean here is resolved; clean on the diagnostic but weak here is new, so review the specific questions rather than the whole domain.

One domain carrying most of the wrong answers is a knowledge gap: return to its chapters and drill the idea that generates the questions. Scattered single slips across every domain are an accuracy problem: slow down on the setup, re-read what is asked, confirm the answer form, and let the calculator check your hand. A noticeably weaker Module 2 suggests higher-difficulty transfer, pacing, or late-module execution deserves review. Work only the rows your error map names, largest cluster first, then stop adding new material and let what you know settle.

The four domains in one view

• Algebra: read and solve linear relationships. Anything linear is a steady rate added to a starting amount; slope is the rate, the intercept the starting value, and where two lines meet is the solution of their system. The move: undo until the unknown stands alone.
• Advanced Math: recognize the form before solving. A function is a rule from input to output. A quadratic's standard form shows the y-intercept, factored form the roots, vertex form the turning point, and the discriminant counts the real roots (and decides whether a line meets a curve twice, once, or not at all). Radical and rational equations need a check for extraneous or excluded values. Exponentials are repeated multiplication by a fixed factor. The move: name the shape, then read the form that answers the question.
• Problem-Solving and Data Analysis: keep the reference quantity clear. Ratios, rates, and percentages depend on the correct base; percent change uses the original value. The word "given" restricts the sample space. Random sampling supports generalization, random assignment supports causal inference, and a margin of error is the plus-or-minus amount around a sample estimate.
• Geometry and Trigonometry: reuse the core relationships. The Pythagorean theorem, similar figures (sides scale by the ratio, areas by its square), congruence conditions (two sides and a non-included angle do not force it), SOH-CAH-TOA and the unit circle (reference angle sets the size, quadrant sets the sign), a radius meeting a tangent at a right angle, and equal tangents from one point. The move: find the relationship the figure is hiding, and the numbers follow.

On the day, you will rarely meet a question you have never seen; you will meet a structure you know, carrying different numbers. Identify the structure first, then use the method that fits it.