Digital SAT Math Formulas: The 20 You Need, and 12 You Don't

The Digital SAT's Bluebook app includes a reference sheet visible on every math question. A lot of 'must-memorize' lists still circulating online were written for the paper SAT, back when no reference sheet existed. For the test you're actually taking, memorizing what's already on the reference sheet is wasted effort.

This article sorts every formula you might encounter into three groups: already on the reference sheet (don't memorize), worth memorizing (do memorize), and over-studied (skip).

On the Bluebook reference sheet: don't memorize

These 12 formulas are always visible during the test. Know what they mean and when to reach for them, but don't burn flashcard time on them.

The 20 formulas worth memorizing

These aren't on the reference sheet, and they come up often enough that reaching for them fluently is a meaningful speed advantage.

Algebra (6)

• Slope from two points: m = (y₂ − y₁) / (x₂ − x₁).
• Point-slope form: y − y₁ = m(x − x₁). Faster than slope-intercept for building a line through a known point.
• Parallel lines share the same slope. Perpendicular lines have slopes that are negative reciprocals.
• Distance between two points: d = √((x₂ − x₁)² + (y₂ − y₁)²). A Pythagorean application, worth having as a one-step memory.
• Midpoint: ((x₁ + x₂)/2, (y₁ + y₂)/2).
• For a system of two linear equations to have no solution, the lines are parallel (same slope, different intercepts). For infinitely many solutions, they're identical (one equation is a scalar multiple of the other).

Advanced math (7)

• Quadratic formula: x = (−b ± √(b² − 4ac)) / (2a).
• Discriminant: b² − 4ac. Positive means two real solutions, zero means one repeated solution, negative means no real solutions.
• Vertex form: a(x − h)² + k has vertex (h, k). Positive a opens up (min at k), negative a opens down (max at k).
• Sum and product of roots (Vieta's): for ax² + bx + c = 0, sum = −b/a, product = c/a.
• Factor theorem: (x − r) is a factor of p(x) if and only if p(r) = 0.
• Difference of squares: a² − b² = (a + b)(a − b).
• Exponential growth or decay: y = a · b^x. When b > 1 it's growth; when 0 < b < 1 it's decay. Growth rate r as a percent: multiplier is 1 + r.

Problem-solving and data (4)

• Percent change: (new − old) / old × 100%. Always divide by the original value, never the new one.
• Mean from sum: mean × count = sum. Most 'find the missing value' mean problems resolve to this one line.
• Probability: favorable outcomes / total outcomes. For conditional probability P(A|B), the denominator is total(B), not total overall.
• Margin of error interpretation: the confidence interval applies to the population parameter, not the sample. 'We are 95% confident the true percentage is in [X, Y].'

Geometry and trig (3)

• SOH-CAH-TOA: sin = opposite / hypotenuse, cos = adjacent / hypotenuse, tan = opposite / adjacent. Complements: sin(x) = cos(90° − x).
• Arc length: s = (θ/360°) × 2πr. Sector area: A = (θ/360°) × πr². Both are the whole-circle formula scaled by the angle fraction.
• Circle equation: (x − h)² + (y − k)² = r², with center (h, k) and radius r. Watch the sign of h and k. An equation written with (x + 3)² has center x = −3, not x = 3.

The 12 formulas you can skip

These appear so rarely on the Digital SAT that memorizing them is poor return on study time. If one shows up, you can derive it or flag and skip.

• Heron's formula for triangle area.
• Law of cosines and law of sines. Non-right-triangle problems are almost never set up requiring these.
• Arithmetic-sequence sum formulas. SAT-style sequences are short enough to add by hand.
• Compound interest in full form. It's almost always a plain exponential problem in disguise.
• Most matrix operations.
• Volume of any regular polyhedron beyond the standard shapes on the reference sheet.
• Trapezoid area via midsegment.
• Polar coordinates.
• Binomial expansion beyond (a ± b)².
• The standard-deviation formula. You need to understand what SD measures, not compute it.
• Z-scores.
• Log change-of-base. If it shows up, use Desmos.

How to memorize formulas that don't stick

Flashcards of the formula alone don't work. What actually works: write each formula on a sticky note, then solve two problems that use it. One where the formula is the direct tool, one where it's applied inside a word problem. The problem-solving step is what forms the retrievable memory.

If a formula hasn't stuck after a week of doing that, it almost certainly means you don't yet have the conceptual hook for it. Slope through two points, for example, clicks once you see it as rise-over-run on a specific graph. It never clicks as a symbolic rule.

Rivie's practice tests tag every missed math item with its trap pattern (slope_inversion_or_sign, percent_change_base, vertex_x_vs_y_coordinate, and so on). When you review, you find out not just that you missed a formula question, but which specific formula trap keeps catching you. Those names match the ones in the reference sheets above.