The SAT Math Reference Sheet

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. It is worth knowing precisely what lives there, because 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. You have met every item on both lists in the chapters; here they stand together, so the split is plain before test day.

▸ 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. Notice the theme: it is all area, volume, right triangles, and angle facts.

AREAS Circle A = πr², circumference C = 2πr. Rectangle A = lw. Triangle A = (1/2)bh.

VOLUMES Box V = lwh. Cylinder V = πr²h. Sphere V = (4/3)πr³. Cone V = (1/3)πr²h. Pyramid V = (1/3)lwh.

RIGHT TRIANGLES Pythagorean theorem c² = a² + b². A 45-45-90 triangle has sides in the ratio s : s : s√2; a 30-60-90 triangle, x : x√3 : 2x.

ANGLES A full circle is 360 degrees, or 2π 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 = (y₂ − y₁)/(x₂ − x₁). Slope-intercept y = mx + b; point-slope y − y₁ = m(x − x₁). 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 = (−b ± √(b² − 4ac))/(2a). Vertex at x = −b/(2a). Sum of roots −b/a, product c/a. The discriminant b² − 4ac is positive for two real roots, zero for one, negative for none. Difference of squares a² − b² = (a + b)(a − b).

EXPONENTS a^m · aⁿ = a^m+n, (a^m)ⁿ = a^mn, a⁻ⁿ = 1/aⁿ, and a^1/n is the nth root. A percent change of r each period multiplies by (1 + r) for growth or (1 − r) for decay.

DATA Percent change is (new − old) / old. Mean is the sum divided by the count. Probability is the favorable outcomes divided by the total.

COORDINATE & TRIG Circle (x − h)² + (y − k)² = r², with center (h, k) and radius r. Distance √((x₂ − x₁)² + (y₂ − y₁)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 θ = cos(90° − θ).

▸ 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.

Test day