Digital SAT Math
SAT Math Formulas
The digital SAT gives you a reference sheet with area, volume and triangle formulas. Here is everything on it, plus the formulas it leaves out that are worth memorizing.
Formulas on the Reference Sheet
You can open these during the Math section, so you do not need to memorize them.
Circle
A = πr² · C = 2πr
Rectangle
A = ℓw
Triangle
A = ½bh
Pythagorean theorem
c² = a² + b²
30-60-90 triangle
Sides x, x√3 and 2x
45-45-90 triangle
Sides s, s and s√2
Rectangular solid
V = ℓwh
Cylinder
V = πr²h
Sphere
V = (4/3)πr³
Cone
V = (1/3)πr²h
Rectangular pyramid
V = (1/3)ℓwh
Angle facts
A circle has 360° or 2π radians. A triangle's angles add up to 180°.
Formulas to Memorize
These are not on the reference sheet.
Slope
m = (y₂ − y₁) / (x₂ − x₁)
Slope-intercept form
y = mx + b
Parallel and perpendicular lines
Parallel lines have equal slopes. Perpendicular slopes are negative reciprocals.
Quadratic formula
x = (−b ± √(b² − 4ac)) / 2a
Discriminant
b² − 4ac: positive means 2 real solutions, zero means 1, negative means none
Vertex of a parabola
x = −b / 2a, or y = a(x − h)² + k with vertex (h, k)
Sum and product of roots
Sum = −b/a · Product = c/a
Distance
d = √((x₂ − x₁)² + (y₂ − y₁)²)
Midpoint
((x₁ + x₂)/2, (y₁ + y₂)/2)
Equation of a circle
(x − h)² + (y − k)² = r²
Arc length and sector area
Arc = (θ/360) · 2πr · Sector = (θ/360) · πr²
Right triangle trig
sin = opposite/hypotenuse · cos = adjacent/hypotenuse · tan = opposite/adjacent
Complementary angles
sin x° = cos (90 − x)°
Percent change
(new − old) / old × 100
Exponential growth
y = a(1 + r)ᵗ
The Tools Are One Click Away
On every SAT Math question here, Desmos and the reference sheet open in windows you can move anywhere, so you can get used to them before test day.
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Common Questions
Does the SAT give you a formula sheet?
Yes. A reference sheet is available during the Math section, with area and volume formulas, the Pythagorean theorem and special right triangles.
What formulas are not on the SAT reference sheet?
Slope, the quadratic formula, the vertex of a parabola, the equation of a circle, arc length and sector area, sine, cosine and tangent, and percent change, among others. It is worth memorizing these.
Do I need to memorize SAT math formulas?
Not the ones on the reference sheet, though knowing them saves time. Memorize the ones that are not on it.
Can Desmos replace some formulas?
Often. Desmos can find the zeros and vertex of a parabola, or the intersection of two lines, without the formula. See the SAT Desmos calculator practice page.
How do I practice using these formulas?
The SAT Math practice page has 1,925 official questions with the reference sheet and Desmos one click away, and the SAT Math course teaches each topic.
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