The Official SAT Reference Sheet — What's Provided

The College Board provides the following formulas and facts on the SAT Math reference sheet at the start of each math module. These are printed on the test — you do not need to memorize them. However, you DO need to know how to use them quickly and correctly.

Geometry formulas provided on the SAT reference sheet:

• Circle: Area = πr², Circumference = 2πr
• Rectangle: Area = lw
• Triangle: Area = ½bh
• Right triangle (Pythagorean Theorem): a² + b² = c²
• Special right triangles: 30-60-90 (sides 1, √3, 2) and 45-45-90 (sides 1, 1, √2)
• Rectangular prism: Volume = lwh
• Cylinder: Volume = πr²h
• Sphere: Volume = (4/3)πr³
• Cone: Volume = (1/3)πr²h
• Pyramid: Volume = (1/3)lwh

Geometry facts provided:

• A circle contains 360°
• A circle contains 2π radians
• The sum of angles in a triangle is 180°
• Number of radians in a semicircle: π radians

Important note about provided formulas: Just because a formula is provided doesn't mean the question is easy. SAT geometry questions often require multiple steps — using the formula is only part of the solution. Know what each formula means conceptually, not just mathematically.

Algebra Formulas to Memorize for the SAT

Algebra accounts for the largest portion of SAT math questions. These formulas are NOT on the reference sheet and must be known from memory.

Linear equations and systems:

• Slope: m = (y₂ - y₁) / (x₂ - x₁)
• Slope-intercept form: y = mx + b (m = slope, b = y-intercept)
• Point-slope form: y − y₁ = m(x − x₁)
• Standard form: Ax + By = C
• Parallel lines: same slope (m₁ = m₂), different y-intercepts
• Perpendicular lines: slopes are negative reciprocals (m₁ × m₂ = −1)

Exponents and radicals:

• aᵐ × aⁿ = aᵐ⁺ⁿ
• aᵐ / aⁿ = aᵐ⁻ⁿ
• (aᵐ)ⁿ = aᵐⁿ
• a⁻ⁿ = 1/aⁿ
• a^(1/n) = ⁿ√a (e.g., 8^(1/3) = 2)
• a⁰ = 1 (for any non-zero a)

Quadratics:

• Standard form: y = ax² + bx + c
• Vertex form: y = a(x − h)² + k (vertex at (h, k))
• Factored form: y = a(x − r₁)(x − r₂) (roots at r₁ and r₂)
• Quadratic formula: x = [−b ± √(b² − 4ac)] / 2a
• Discriminant: b² − 4ac (positive = 2 real solutions; zero = 1; negative = no real solutions)
• Sum of roots: r₁ + r₂ = −b/a
• Product of roots: r₁ × r₂ = c/a

FOIL and factoring identities:

• Difference of squares: a² − b² = (a + b)(a − b)
• Perfect square trinomial: (a + b)² = a² + 2ab + b²
• Perfect square trinomial: (a − b)² = a² − 2ab + b²

Geometry Formulas — Beyond the Reference Sheet

The reference sheet covers basic shapes, but SAT geometry questions often require formulas and facts that aren't on the sheet.

Coordinate geometry:

• Distance formula: d = √[(x₂ − x₁)² + (y₂ − y₁)²]
• Midpoint formula: M = [(x₁ + x₂)/2, (y₁ + y₂)/2]
• Circle equation (center-radius form): (x − h)² + (y − k)² = r² (center at (h,k), radius r)

Angle relationships:

• Vertical angles are equal
• Supplementary angles sum to 180°
• Complementary angles sum to 90°
• Interior angles of a polygon: (n − 2) × 180° (n = number of sides)
• Exterior angles of any polygon sum to 360°
• Parallel lines cut by a transversal: corresponding angles equal, alternate interior angles equal

Triangle relationships:

• Exterior angle of a triangle = sum of the two non-adjacent interior angles
• Isosceles triangle: two equal sides = two equal base angles
• Similar triangles: corresponding sides are proportional

Statistics, Probability, and Rates

Statistics formulas (NOT provided):

• Mean (average): sum of all values ÷ count of values
• Median: middle value when sorted; average of two middle values if even count
• Percent: (part / whole) × 100
• Percent change: [(new − old) / old] × 100
• Probability: favorable outcomes / total outcomes

Rate, unit, and proportion formulas:

• Distance = Rate × Time (d = rt)
• Work formula: Work = Rate × Time (e.g., pipes filling tanks)
• Direct proportion: y/x = k (y varies directly with x)
• Inverse proportion: xy = k (y varies inversely with x)

Trigonometry Formulas

Basic trig (SOH-CAH-TOA — NOT provided):

• sin θ = opposite / hypotenuse
• cos θ = adjacent / hypotenuse
• tan θ = opposite / adjacent = sin/cos
• Co-function identity: sin(θ) = cos(90° − θ); cos(θ) = sin(90° − θ)

Unit circle key values:

• sin(0°) = 0, sin(30°) = 0.5, sin(45°) = √2/2, sin(60°) = √3/2, sin(90°) = 1
• cos(0°) = 1, cos(30°) = √3/2, cos(45°) = √2/2, cos(60°) = 0.5, cos(90°) = 0

Radian-degree conversion:

• 180° = π radians
• 1 radian = 180°/π ≈ 57.3°
• To convert degrees to radians: multiply by π/180