SAT Math — complete formula and topic reference sheet

SAT Math — formulas & topics

Digital SAT · 44 questions · 70 min · calculator allowed throughout

Algebra 35% Advanced Math 35% Problem Solving & Data 15% Geometry & Trig 15%
① Algebra
Linear equations
slope-intercepty = mx + b
slope from two pointsm = (y₂−y₁)/(x₂−x₁)
point-slope formy−y₁ = m(x−x₁)
parallel / perpendicularparallel: same m
perp: m₁·m₂ = −1
Systems of equations
no solution (parallel)a₁/a₂ = b₁/b₂ ≠ c₁/c₂
infinite solutionsa₁/a₂ = b₁/b₂ = c₁/c₂
one solutionintersection point (x, y)
Inequalities & absolute value
flip sign when ÷ or × negative−2x > 4 → x < −2
absolute value|ax + b| = c
→ ax+b = c or ax+b = −c
② Advanced Math
Quadratic equations
standard formax² + bx + c = 0
quadratic formulax = (−b ± √(b²−4ac)) / 2a
discriminantD = b²−4ac
D>0 two roots · D=0 one · D<0 none
vertex x-coordinatex = −b / 2a
vertex formy = a(x−h)² + k
Polynomial identities
(a+b)² = a²+2ab+b²
(a−b)² = a²−2ab+b²
(a+b)(a−b) = a²−b²
remainder theoremf(x)÷(x−a): remainder = f(a)
factor theoremf(a)=0 ⟺ (x−a) is a factor
Exponents & radicals
aᵐ · aⁿ = aᵐ⁺ⁿ
(aᵐ)ⁿ = aᵐⁿ
a⁻ⁿ = 1/aⁿ
a^(m/n) = ⁿ√(aᵐ)
√a · √b = √(ab)
③ Problem Solving & Data
Statistics
meanmean = Σx / n
IQRIQR = Q3 − Q1
outlier cutoffsbelow Q1 − 1.5·IQR
above Q3 + 1.5·IQR
outlier effectmean shifts · median stable
spreadlarger SD = more spread out
Probability
P(A) = n(A) / n(S)
P(Aᶜ) = 1 − P(A)
independent eventsP(A and B) = P(A)·P(B)
Growth models
lineary = mx + bconstant rate of change
exponential growthy = a(1+r)ᵗa = initial, r = rate, t = time
exponential decayy = a(1−r)ᵗ
compound interestA = P(1+r/n)ⁿᵗn = compounding periods/year
percent change(new − old) / old × 100
④ Geometry & Trig
Triangles
Pythagorean theorema² + b² = c²
30-60-90sides: 1 : √3 : 2
45-45-90sides: 1 : 1 : √2
areaA = ½ b h
interior angles sum180°
Trigonometry
SOH-CAH-TOAsin = opp/hyp
cos = adj/hyp
tan = opp/adj
Pythagorean identitysin²θ + cos²θ = 1
complementary anglessin θ = cos(90°−θ)
Circles & coordinate geometry
area / circumferenceA = πr² · C = 2πr
arc lengths = (θ/360) · 2πr
circle equation(x−h)²+(y−k)²=r²center (h,k), radius r
distance formulad = √((Δx)²+(Δy)²)
midpointM = ((x₁+x₂)/2, (y₁+y₂)/2)
Volume (given on test)
cylinder: πr²h
cone: ⅓πr²h
sphere: 4/3 πr³