Math reference sheet
Two lists. The first is what Bluebook shows you on every Math question — you don't need to memorize it. The second is what Bluebook does not give you — memorize this list cold.
What Bluebook gives you on every Math question
The in-app reference sheet is always one click away. Don't waste working memory on these formulas — pull them up if you forget.
| Shape | Formula |
|---|---|
| Circle | Area A = πr² · Circumference C = 2πr |
| Rectangle | Area A = ℓw |
| Triangle | Area A = (1/2)bh |
| Right triangle | Pythagorean theorem a² + b² = c² |
| Special right triangle 30-60-90 | Sides in ratio 1 : √3 : 2 |
| Special right triangle 45-45-90 | Sides in ratio 1 : 1 : √2 |
| Rectangular prism | Volume V = ℓwh |
| Cylinder | Volume V = πr²h |
| Sphere | Volume V = (4/3)πr³ |
| Cone | Volume V = (1/3)πr²h |
| Pyramid | Volume V = (1/3)ℓwh |
| Constants | Sum of angles in triangle = 180°. Full circle = 360° = 2π radians. |
What you have to memorize
Algebra
- Slope-intercept:
y = mx + b - Point-slope:
y − y₁ = m(x − x₁) - Standard form:
Ax + By = C→ slope= −A/B, y-intercept= C/B - Slope between two points:
m = (y₂ − y₁)/(x₂ − x₁) - Parallel: same slope. Perpendicular: slopes multiply to
−1. - Distance between (x₁,y₁) and (x₂,y₂):
√((x₂−x₁)² + (y₂−y₁)²) - Midpoint:
((x₁+x₂)/2, (y₁+y₂)/2)
Quadratics
- Standard:
ax² + bx + c - Vertex form:
a(x − h)² + kwith vertex (h, k) - Factored:
a(x − r₁)(x − r₂)with roots r₁, r₂ - Vertex x-coordinate:
x = −b/(2a) - Quadratic formula:
x = (−b ± √(b² − 4ac)) / (2a) - Discriminant
D = b² − 4ac: D>0 two real roots, D=0 one (double) root, D<0 no real roots - Sum of roots =
−b/a; product of roots =c/a
Exponents & logs
aᵐ · aⁿ = aᵐ⁺ⁿ;aᵐ / aⁿ = aᵐ⁻ⁿ;(aᵐ)ⁿ = aᵐⁿ;a⁰ = 1;a⁻ⁿ = 1/aⁿa^(1/n) = ⁿ√a;a^(m/n) = ⁿ√(aᵐ)- Exponential growth:
y = a · bˣ; "doubles every k" → exponentx/k; "halves every k" → exponent−x/k - Compound: successive % changes multiply: a +20% then −10% is
1.20 · 0.90 = 1.08 → +8%, not +10%. - Logarithm:
logₐ(b) = c ⇔ aᶜ = b;logₐ(xy) = logₐ(x) + logₐ(y);logₐ(xⁿ) = n logₐ(x)
Functions & transformations
f(x) + k: shift up by k.f(x + k): shift left by k.−f(x): reflect over x-axis.f(−x): reflect over y-axis.a · f(x): vertical stretch by factor |a|.(f ∘ g)(x) = f(g(x))
Percentages & statistics
- Percent change:
(new − old) / old × 100% - Mean: sum ÷ count.
- Adding constant
kto every value: mean and median shift by k; SD unchanged. - Multiplying every value by
k: mean, median, SD all scale by|k|(sd bykif k>0). - Median is robust to outliers; mean is not.
- Independent events:
P(A ∩ B) = P(A) · P(B). - Mutually exclusive:
P(A ∪ B) = P(A) + P(B). - Conditional:
P(A | B) = P(A ∩ B) / P(B); on a two-way table, divide by the row/column total for the given.
Geometry & trigonometry
- Triangle area from base and height:
(1/2)bh - Triangle area from two sides and included angle:
(1/2)ab sin C - Similar figures: areas scale as
(ratio)²; volumes scale as(ratio)³ - Circle area sector:
A = (θ/360°) · πr²(degrees) or(θ/2) · r²(radians) - Arc length:
s = rθ(radians) - SOH-CAH-TOA:
sin = O/H,cos = A/H,tan = O/A - Complementary:
sin(90° − θ) = cos θ - Pythagorean identity:
sin²θ + cos²θ = 1 - Radians ↔ degrees:
π rad = 180° - Circle in coordinates:
(x − h)² + (y − k)² = r²with center (h, k), radius r
Bluebook Desmos quick reference
- Graph two functions, find intersection — read coordinates for system solutions.
- Type
y = x² − 5x + 6to plot. Click intersections with the x-axis to read roots. - Use a slider:
a = 1with a slider, then ploty = ax + 2; tweakato see slope changes. - For "between which two values does f equal zero", graph and click x-intercepts.
- Regression:
y₁ ~ a*x₁ + bin a table for linear fit.
Desmos is allowed on every Math question. Practice with it during all your Bluebook tests so the controls become muscle memory.