Math Formula Vault

The digital reference sheet is geometry-only — so the formulas behind ~70% of the test (Algebra + Advanced Math) are exactly the ones you must carry in your head. This vault is that finite list. Own it cold and you remove an entire class of avoidable losses: the "I knew the method but forgot the formula" miss.

Sources: College Board reference sheet (Bluebook directions); Piqosity, College Panda. Point convention: each Math item = 1 of ~44; a Module-1 miss is a ceiling-risk miss.

---

#WHAT'S ALREADY ON THE SHEET (do NOT waste memory here)

Provided in Bluebook on every Math question: circle area πr² & circumference 2πr; rectangle ℓw; triangle ½bh; Pythagorean a²+b²=c²; special right triangles 30-60-90 (x, x√3, 2x) and 45-45-90 (s, s, s√2); volumes of box ℓwh, cylinder πr²h, sphere 4/3·πr³, cone 1/3·πr²h, pyramid 1/3·ℓwh; 360°/2π radians in a circle; triangle angles sum to 180°. Know they're there; don't burn revision time memorising them.

---

#MUST-MEMORISE — ALGEBRA

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

System of two linear equations — number of solutions:

• different slopes → one solution (lines cross)
• same slope, different intercept → no solution (parallel)
• same slope, same intercept → infinitely many (same line) Why it matters: "no solution / infinitely many" questions are pure slope-intercept comparisons — recognise them instantly. Desmos alt: graph both; one intersection / parallel / overlapping tells you directly.

---

#MUST-MEMORISE — ADVANCED MATH (the highest-value block)

Quadratic formula   x = (−b ± √(b² − 4ac)) / (2a)
Discriminant        D = b² − 4ac
   D > 0 → two real roots      D = 0 → one (tangent)      D < 0 → none
Vertex form         y = a(x − h)² + k     vertex (h, k)
Axis of symmetry    x = −b/(2a)           (also the vertex x)
Sum / product roots −b/a  and  c/a
Factored form       y = a(x − r₁)(x − r₂)  → zeros at r₁, r₂
Difference of squares  a² − b² = (a + b)(a − b)

Exponent & radical rules:

xᵃ·xᵇ = xᵃ⁺ᵇ      xᵃ/xᵇ = xᵃ⁻ᵇ      (xᵃ)ᵇ = xᵃᵇ
x⁻ᵃ = 1/xᵃ        x^(1/n) = ⁿ√x       x⁰ = 1

Exponential growth / decay:

y = a(1 + r)ᵗ  (growth by rate r)     y = a(1 − r)ᵗ  (decay)
y = a·bˣ        b > 1 growth · 0 < b < 1 decay · a = initial value

Why it matters: discriminant/tangency, vertex, and growth-vs-linear are the staples of the hard Module 2. Desmos alt: roots = x-intercepts (grey dots); vertex = auto-marked; "how many solutions"/tangent = slider on a/c until the condition holds.

---

#MUST-MEMORISE — PROBLEM-SOLVING & DATA ANALYSIS

Percent change      (new − old) / old × 100
Percent of          part = (percent/100) × whole
Mean                sum ÷ count            Median = middle value (order first)
Probability         favourable / total
Conditional prob.   favourable / (the conditioning subgroup's total)   ← right denominator!
Margin of error     interval = estimate ± MOE
Unit rate           quantity ÷ units (set up a proportion)

Why it matters: the most-misread Math domain — errors come from the wrong denominator (conditional probability) or percent-of vs percent-change. Desmos alt: mean(...), median(...), and 20%700-style percent computations.

---

#MUST-MEMORISE — GEOMETRY & TRIG (beyond the sheet)

Equation of a circle   (x − h)² + (y − k)² = r²   center (h,k), radius r
   (from general form: complete the square)
Arc length             (θ/360) · 2πr
Sector area            (θ/360) · πr²
SOHCAHTOA              sin = opp/hyp · cos = adj/hyp · tan = opp/adj
Cofunction             sin(x) = cos(90° − x)
Radians ↔ degrees      radians = degrees · π/180 ;  degrees = radians · 180/π
Similar triangles      corresponding sides proportional; trig ratios preserved

Why it matters: the circle equation and radian/degree conversion are common and not on the sheet. Desmos alt: type the circle equation to see center/radius; graph to read intercepts.

---

#RECALL DRILL (cover the answers · self-marked)

Drill 1 — Blank recall (target 18/20, ≤4 min). Cover the vault. Write from memory: slope formula · perpendicular-slope rule · quadratic formula · discriminant cases (3) · vertex form + vertex · sum/product of roots · difference of squares · 3 exponent rules · exponential growth model · percent change · conditional-probability denominator rule · circle equation · arc length · sector area · SOHCAHTOA · cofunction · radians↔degrees. PASS: ≥18/20 correct. FAIL: the missed formulas go straight into Anki; re-drill daily until 20/20.

Repetition protocol: recall daily for a week, then space to every few days. Goal: every formula retrievable in <3 seconds without the sheet.

---

#REFERENCE CARD — FORMULA VAULT

SHEET HAS: areas/volumes, Pythagoras, special triangles, 360°/180°.  YOU CARRY THE REST:
ALG: m=(Δy/Δx) · y=mx+b · ⟂ = neg-recip · #solutions by slope/intercept
ADV: x=(−b±√(b²−4ac))/2a · D=b²−4ac (>0,=0,<0) · vertex (h,k) y=a(x−h)²+k ·
     a²−b²=(a+b)(a−b) · exponent rules · y=a(1±r)ᵗ
PSDA: %change=(new−old)/old · P=fav/total · conditional = right denominator · est±MOE
GEO: (x−h)²+(y−k)²=r² · arc (θ/360)2πr · sector (θ/360)πr² · SOHCAHTOA · rad=deg·π/180
Desmos replaces memory for: roots, vertex, intersections, "how many solutions", circles, mean/median.

---

MERIDIAN™ · © 2026 · For Neo's personal study use. Not affiliated with or endorsed by the College Board. SAT® is a trademark of the College Board.

MERIDIAN · CODEX · MATH FORMULA VAULT | v1.0