SAT® math formulas: what’s on the reference sheet and what to memorize
The digital SAT gives you a reference sheet with basic geometry formulas on every Math question. Most of the algebra, function and statistics formulas you need are not on it. Here is the full list, sorted into what you are given and what you need to know by heart.
The short version
- Given on the reference sheet: area of a circle, rectangle and triangle; circumference; the Pythagorean theorem; 30-60-90 and 45-45-90 triangles; volumes of a box, cylinder, sphere, cone and pyramid; 360° (2π radians) in a circle; 180° in a triangle.
- Not given, memorize these: slope and line forms, the quadratic formula and discriminant, vertex form, exponent rules, percent change and growth, circle equations, arc length and sector area, SOH-CAH-TOA, mean and median.
- A graphing calculator is allowed on every Math question.
On the reference sheet (you don’t need to memorize these)
| What | Formula | Note |
|---|---|---|
| Area of a circle | A = πr² | |
| Circumference | C = 2πr | |
| Area of a rectangle | A = ℓw | |
| Area of a triangle | A = ½bh | |
| Pythagorean theorem | a² + b² = c² | c is the hypotenuse |
| 30-60-90 triangle | x, x√3, 2x | short leg, long leg, hypotenuse |
| 45-45-90 triangle | s, s, s√2 | |
| Rectangular box | V = ℓwh | |
| Cylinder | V = πr²h | |
| Sphere | V = (4/3)πr³ | |
| Cone | V = (1/3)πr²h | |
| Rectangular pyramid | V = (1/3)ℓwh | |
| Angles | 360° = 2π radians in a circle; 180° in a triangle |
Knowing these by heart still saves time, but you can always check them.
Lines and linear functions (memorize)
| What | Formula | Note |
|---|---|---|
| Slope | m = (y₂ − y₁) / (x₂ − x₁) | |
| Slope-intercept form | y = mx + b | b is the y-intercept |
| Point-slope form | y − y₁ = m(x − x₁) | |
| Standard form | Ax + By = C | slope is −A/B |
| Parallel lines | equal slopes | |
| Perpendicular lines | slopes multiply to −1 | e.g. 2 and −1/2 |
| Systems with no solution | same slope, different intercepts | |
| Systems with infinitely many solutions | same line |
Quadratics and exponents (memorize)
| What | Formula | Note |
|---|---|---|
| Quadratic formula | x = (−b ± √(b² − 4ac)) / 2a | for ax² + bx + c = 0 |
| Discriminant | b² − 4ac | positive: 2 real solutions; zero: 1; negative: none |
| Vertex form | y = a(x − h)² + k | vertex at (h, k) |
| Vertex x-coordinate | x = −b / 2a | |
| Sum and product of roots | sum = −b/a, product = c/a | |
| Exponent rules | xᵃ·xᵇ = xᵃ⁺ᵇ, xᵃ/xᵇ = xᵃ⁻ᵇ, (xᵃ)ᵇ = xᵃᵇ, x⁻ᵃ = 1/xᵃ, x^(1/n) = ⁿ√x | |
| Exponential growth or decay | y = a(1 ± r)ᵗ | r is the rate per period as a decimal |
Percentages and data (memorize)
| What | Formula | Note |
|---|---|---|
| Percent change | (new − old) / old × 100 | |
| Successive changes | multiply the factors | up 20% then down 20% is 1.2 × 0.8 = 0.96 |
| Mean | sum ÷ number of values | |
| Median | middle value in order | average the middle two if the count is even |
| Probability | favorable outcomes ÷ total outcomes | |
| Conditional probability | P(A given B) = count of A and B ÷ count of B | read the row or column of the table that B names |
Circles and trigonometry (memorize)
| What | Formula | Note |
|---|---|---|
| Equation of a circle | (x − h)² + (y − k)² = r² | center (h, k), radius r |
| Arc length | (θ / 360°) × 2πr | |
| Sector area | (θ / 360°) × πr² | |
| Degrees to radians | multiply by π / 180 | |
| SOH-CAH-TOA | sin = opp/hyp, cos = adj/hyp, tan = opp/adj | |
| Complementary angles | sin x° = cos(90° − x°) | |
| Similar triangles | corresponding sides are in the same ratio |
Worked example: completing the square
A circle has the equation x² − 6x + y² + 4y = 12. What is its radius?
Complete the square on each variable: x² − 6x + 9 + y² + 4y + 4 = 12 + 9 + 4, so (x − 3)² + (y + 2)² = 25. The center is (3, −2) and the radius is √25 = 5.
Calculator tips
The digital SAT lets you use a calculator on every Math question, and the testing app includes the Desmos graphing calculator in Bluebook™. Graphing is often the fastest way to find where two equations meet, the vertex of a parabola, or the number of solutions. Practice with the calculator you will use on test day. Peakscor’s own Peak Calculator is built into every Peakscor Math question.
Practice the formulas
Peakscor’s Learn course has a module for every Math skill, from linear functions to circles, each with worked examples. Then drill any Math skill at the difficulty you need.
Peakscor is an independent practice tool and is not affiliated with College Board. Its questions are original practice in the style of the digital SAT.
Questions
Does the SAT give you a formula sheet?
Yes. In the digital SAT testing app you can open a reference sheet on every Math question. It covers basic area and volume formulas, special right triangles and the Pythagorean theorem, plus a few facts about angles and circles. It does not cover algebra, functions, statistics or trigonometry formulas.
Do I need to memorize formulas for the SAT?
Yes, the ones the reference sheet leaves out: slope, the forms of a line, the quadratic formula and discriminant, vertex form, exponent rules, percent change, the equation of a circle, and SOH-CAH-TOA.
Can I use a calculator on the whole SAT Math section?
Yes. On the digital SAT a calculator is allowed on every Math question, and a graphing calculator is built into the testing app. You can also bring an approved calculator of your own.
What is the equation of a circle on the SAT?
(x − h)² + (y − k)² = r², where (h, k) is the center and r is the radius. If the equation is given in expanded form, complete the square on x and on y to find the center and radius.
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