SAT Math formulas: what to memorize and what you don't need to

The digital SAT includes a reference sheet available throughout the Math section in Bluebook. Clicking it brings up a set of geometry formulas: areas, volumes, angle relationships, the Pythagorean theorem, and properties of special right triangles. Students who don't know this exists waste time re-deriving things that are sitting right there. Students who rely on it too heavily miss the formulas it doesn't include, which are just as important.

The practical split is this: the reference sheet handles most geometry. Everything else (algebra identities, quadratic relationships, exponential functions, circle equations, trigonometry) needs to be memorized.

What the reference sheet gives you

The reference information in Bluebook includes: area and circumference of a circle, area of a rectangle, triangle, and trapezoid, volume of a rectangular prism, cylinder, sphere, cone, and pyramid, the Pythagorean theorem, and the side ratios for 30-60-90 and 45-45-90 special right triangles.

It also includes three geometry facts: the number of degrees in a circle (360), in a straight line (180), and in a triangle (180).

The reference sheet is your friend on geometry questions. Before setting up any area or volume problem, check whether the formula is already there. Most of the time it is.

What you need to memorize

Algebra

Exponent rules. These come up constantly across Algebra and Advanced Math questions:

• x^a · x^b = x^(a+b)
• x^a / x^b = x^(a-b)
• (x^a)^b = x^(ab)
• x^0 = 1 (for any nonzero x)
• x^(-a) = 1/x^a
• x^(1/2) = √x

Algebraic identities. The SAT tests these repeatedly, both in expanding and in factoring:

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• a² - b² = (a + b)(a - b) ← difference of squares; appears constantly

Slope formula. m = (y₂ - y₁) / (x₂ - x₁). Keep subtraction in the same order in numerator and denominator; reversing one but not the other is one of the most common arithmetic errors on slope questions. You also need slope-intercept form (y = mx + b) and the relationships for parallel lines (equal slopes) and perpendicular lines (negative reciprocal slopes, so if one slope is m the other is -1/m). Beyond calculating slope, the SAT frequently asks what a slope means in context: if a line models distance over time, the slope is the speed; if it models cost over quantity, the slope is the price per unit. Interpreting slope in a word problem is just as commonly tested as computing it.

Percent change. % change = (change / original) × 100. Increasing by 20% means multiplying by 1.2. Decreasing by 20% means multiplying by 0.8. "150% more than x" means x + 1.5x = 2.5x, not 1.5x.

Distance, rate, and time. d = rt. Rearranges to r = d/t and t = d/r.

Quadratics

Quadratics have more formulas attached to them than any other topic on the SAT. These are all worth memorizing.

Standard form: ax² + bx + c = 0. In this form, c is the y-intercept, and the sign of a determines whether the parabola opens up (positive) or down (negative).

Vertex form: a(x - h)² + k. The vertex is at (h, k). The a is the same as in standard form. This form makes it easy to read off the vertex, identify transformations, and write the equation when you're given the vertex and a point.

Vertex x-coordinate: x = -b/2a. Useful when you have standard form and need the vertex without converting to vertex form or using Desmos.

Sum of solutions: -b/a. When a quadratic has two solutions (roots), their sum equals -b/a. The SAT tests this directly.

Product of solutions: c/a. The product of the two solutions equals c/a. Also tested directly.

The discriminant: b² - 4ac (from the quadratic formula). The discriminant tells you how many real solutions a quadratic has: positive means two solutions, zero means exactly one, negative means none. You don't need to solve the full quadratic formula on most questions; the discriminant alone answers questions about the number of intersections or solutions.

Difference of squares is worth repeating here because it's one of the most common factoring patterns in Advanced Math: a² - b² = (a + b)(a - b).

Circles

Circle equation: (x - h)² + (y - k)² = r². The center is (h, k) and the radius is r. The signs inside the parentheses feel backwards at first: if the equation reads (x + 2)², the center is at x = -2, not x = 2. This is among the most commonly missed traps on circle questions, so read the signs carefully. If the equation isn't in standard form, complete the square to find the center and radius.

Arc length and sector area. Rather than memorizing separate formulas, think proportionally: an arc or sector is just a fraction of the full circle. A 60° arc is 60/360 = 1/6 of the circumference. A 90° sector is 1/4 of the total area. Both formulas on the sheet become unnecessary once you understand this.

Inscribed angle theorem. An inscribed angle (an angle formed by two chords meeting on the circle) is half the central angle that subtends the same arc. If a central angle is 80°, the inscribed angle is 40°.

Tangent lines. A line tangent to a circle is perpendicular to the radius at the point of tangency. Use this with the negative reciprocal slope rule to find the equation of a tangent line.

Trigonometry

SOH CAH TOA. For a right triangle: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent. This is the foundation of every trig question on the SAT.

Complementary angle identity. sin(x) = cos(90° - x). The sine of an angle equals the cosine of its complement. The SAT tests this frequently, often in ways that look more complicated than they are.

Radians. 180° = π radians. Use this conversion to move between degrees and radians. Key values: π/6 = 30°, π/4 = 45°, π/3 = 60°, π/2 = 90°, π = 180°.

Pythagorean triples. Right triangles with integer sides come up often: 3-4-5, 5-12-13, 8-15-17. Multiples also work (6-8-10, 10-24-26). Recognizing these saves time on calculation.

Exponential functions

The standard form is y = a · b^x, where a is the initial value and b is the growth or decay factor. If something grows by 4% per year, b = 1.04. If it decays by 10% per year, b = 0.90. The SAT also tests variations like y = a · b^(x/k), where k changes the rate; if k = 2, the growth happens every 2 units instead of every 1.

Statistics

These aren't really formulas but they're tested conceptually:

Mean vs. median. Mean is sensitive to outliers; median is not. In a skewed distribution (like wealth), the mean is pulled toward the extreme values while the median stays near the center. When a data set is symmetric, mean and median are equal.

Standard deviation measures the spread of a data set. You'll never need to calculate it, but you need to know that a tighter cluster of data means lower standard deviation, and a more spread-out data set means higher.

Margin of error. A sample mean plus or minus the margin of error gives a confidence interval for the population mean. Values outside the interval are possible but not plausible; that's the language the SAT uses. Increasing the sample size reduces the margin of error.

The formulas most students forget

A few that consistently trip people up:

The vertex x-coordinate formula (-b/2a) is often neglected in favor of always using Desmos. Know it for questions where Desmos is slower or where the answer needs to be in exact algebraic form.

The sum and product of solutions (−b/a and c/a) are tested directly on harder questions and aren't as widely known as the quadratic formula. They're worth thirty seconds to memorize.

The complementary angle identity (sin x = cos(90° - x)) is tested in ways that disguise what's being asked. Knowing it makes those questions immediate.

The difference of squares pattern (a² - b² = (a + b)(a - b)) appears across factoring, simplification, and advanced algebra problems more than almost any other single identity.

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