The formulas the SAT gives you
The reference sheet opens from a button on every Math question in Bluebook, so you never have to memorize anything on it. Look at the list and one pattern jumps out: almost every formula here is geometry. Areas, volumes, the Pythagorean theorem, the two special right triangles, and a couple of angle facts. If a question needs one of these, the value is one click away, which is why geometry questions rarely fail because a student forgot a formula. They fail on setup and on arithmetic instead.
Given to you on test day
| Concept | Formula |
|---|---|
| Area of a circle | A = pi r^2 |
| Circumference of a circle | C = 2 pi r |
| Area of a rectangle | A = l w |
| Area of a triangle | A = (1/2) b h |
| Pythagorean theorem | c^2 = a^2 + b^2 |
| Special right triangle 30-60-90 | sides x, x sqrt(3), 2x |
| Special right triangle 45-45-90 | sides s, s, s sqrt(2) |
| Volume of a rectangular box | V = l w h |
| Volume of a cylinder | V = pi r^2 h |
| Volume of a sphere | V = (4/3) pi r^3 |
| Volume of a cone | V = (1/3) pi r^2 h |
| Volume of a pyramid | V = (1/3) l w h |
| Angle measure of a circle | A circle has 360 degrees, which is 2 pi radians |
| Angles in a triangle | The angles in a triangle sum to 180 degrees |
That is the entire geometry toolkit the test hands you, and it maps directly onto the geometry and trigonometry domain. Because these are provided, the smart move is to learn how to set up the shapes rather than to memorize the fourteen expressions above.
The formulas you have to memorize
You must memorize these
| Concept | Formula | Note |
|---|---|---|
| Slope | m = (y2 - y1) / (x2 - x1) | The core of every linear question. |
| Slope intercept form | y = m x + b | Here m is the slope and b is the y-intercept. |
| Quadratic formula | x = (-b +/- sqrt(b^2 - 4ac)) / 2a | Solves any quadratic when factoring fails. |
| Vertex form | y = a(x - h)^2 + k | The vertex sits at the point (h, k). |
| Discriminant | b^2 - 4ac | Tells the number of real solutions. |
| Distance between two points | sqrt((x2-x1)^2 + (y2-y1)^2) | The Pythagorean theorem on a grid. |
| Midpoint | ((x1+x2)/2, (y1+y2)/2) | Average the x values, average the y values. |
| Equation of a circle | (x - h)^2 + (y - k)^2 = r^2 | Center (h, k) and radius r. |
| Exponential growth or decay | y = a(1 +/- r)^t | Plus for growth, minus for decay. |
| Percent change | (new - old) / old times 100 | A negative result means a decrease. |
| Probability | favorable outcomes / total outcomes | Read the table or set carefully. |
| Average | sum / count | Rearranges to sum = average times count. |
| Exponent rules | x^a times x^b = x^(a+b) | Add exponents to multiply, subtract to divide. |
This is the list that actually decides scores. Everything here is algebra, functions, and data analysis, and none of it is on the reference sheet. When a student loses points they thought they had, it is almost always one of these: a half remembered quadratic formula, a slope with the subtraction flipped, an exponential model set up as growth when it should have been decay. Most of these live in the advanced math domain, which is exactly why that domain rewards memorized fluency more than any other part of the test.
How to actually use the sheet
Do not lean on the reference sheet during the test. Opening it, scanning for the formula, and clicking back costs ten to fifteen seconds each time, and on a timed section those seconds add up fast. Treat the sheet as a safety net for a rare blank moment, not as a place you visit on every geometry question. The students who use it least are usually the ones scoring highest, because they already know the shapes cold.
Know the memorized list cold instead. The thirteen formulas in the second table are the ones worth drilling until they are automatic. Write them from memory once a day for a week and the recall becomes free. Once you can produce the quadratic formula and the equation of a circle without pausing, a whole class of questions stops being about memory and starts being about method.
Let Desmos carry the graphing. The built in Desmos calculator can solve much of what these formulas describe. Type a quadratic and read the roots straight off the graph instead of running the formula by hand. Plot two lines and find the intersection instead of solving the system on paper. Knowing a formula and knowing when to graph it instead are both part of a good test day plan, and the strongest scorers switch between the two without thinking about it.
Know the sheet. Memorize the rest.
Drill the formulas free →Questions students ask
- Does the digital SAT give you a formula sheet?
- Yes. A reference sheet with common geometry formulas is available on every Math question in Bluebook, but it does not include algebra or advanced math formulas.
- What formulas are not on the SAT formula sheet?
- Slope, the quadratic formula, the equation of a circle, exponential growth and decay, percent change, and most algebra and function formulas are not given, so you must memorize them.
- Do I need to memorize the quadratic formula for the SAT?
- Yes. It is not on the reference sheet, and it appears often, so know it cold or be ready to graph with Desmos.
- Are the special right triangles on the SAT formula sheet?
- Yes. The 30-60-90 and 45-45-90 side ratios are included on the reference sheet.
Keep going
Put the sheet to work, or drill the formulas you have to memorize.
The reference sheet contents follow the digital SAT's provided formula sheet. Formulas not on it must be memorized. Facts align with College Board Math specifications.