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All Math Formulas (A-Z)

Every formula row from this site's 10 formula sheets, sorted by the concept name inside each letter group, with a link to the sheet each one is listed on.

SAT Math ACT Math 145 formula rows

This page lists every formula row published on the formula sheets of this site, collected into one A-Z index; the records are the formula tables on those sheets, and each row links back to the table it was copied from.

Jump to letter: 0-9 · A · C · D · E · F · G · H · I · L · M · N · O · P · Q · R · S · T · U · V

0-9

Concept	Formula	Sheet
2×2 determinant	\|a b; c d\| = ad − bc	ACT Intermediate Algebra Formula Sheet — Free
30-60-90 triangle	sides 1 : √3 : 2	SAT Geometry & Trigonometry Formula Sheet — Free
30-60-90 triangle	1 : √3 : 2	ACT Plane Geometry Formula Sheet — Free
45-45-90 triangle	sides 1 : 1 : √2	SAT Geometry & Trigonometry Formula Sheet — Free
45-45-90 triangle	1 : 1 : √2	ACT Plane Geometry Formula Sheet — Free

A

Concept	Formula	Sheet
Addition rule (mutually exclusive)	P(A or B) = P(A) + P(B)	SAT Problem-Solving & Data Analysis Formula Sheet — Free
Amplitude of y=a sin(bx)	\|a\|	ACT Trigonometry Formula Sheet — Free
Arc length	s = r θ	SAT Geometry & Trigonometry Formula Sheet — Free
Arc length	s = r θ	ACT Plane Geometry Formula Sheet — Free
Area of circle	A = π r²	SAT Geometry & Trigonometry Formula Sheet — Free
Area of circle	A = π r²	ACT Plane Geometry Formula Sheet — Free
Area of equilateral triangle	A = (√3 / 4) s²	ACT Plane Geometry Formula Sheet — Free
Area of parallelogram	A = b h	ACT Plane Geometry Formula Sheet — Free
Area of rectangle	A = ℓ w	SAT Geometry & Trigonometry Formula Sheet — Free
Area of trapezoid	A = ½ (b₁ + b₂) h	SAT Geometry & Trigonometry Formula Sheet — Free
Area of trapezoid	A = ½ (b₁ + b₂) h	ACT Plane Geometry Formula Sheet — Free
Area of triangle	A = ½ b h	SAT Geometry & Trigonometry Formula Sheet — Free
Area of triangle	A = ½ b h	ACT Plane Geometry Formula Sheet — Free
Arithmetic sequence	aₙ = a₁ + (n − 1)d	ACT Intermediate Algebra Formula Sheet — Free

C

Concept	Formula	Sheet
Change of base	log_b(x) = log(x)/log(b)	ACT Intermediate Algebra Formula Sheet — Free
Circumference of circle	C = 2 π r	SAT Geometry & Trigonometry Formula Sheet — Free
Circumference of circle	C = 2 π r = π d	ACT Plane Geometry Formula Sheet — Free
Combine like terms	3x + 2x = 5x	ACT Elementary Algebra Formula Sheet — Free
Complex add	(a+bi) + (c+di) = (a+c)+(b+d)i	ACT Intermediate Algebra Formula Sheet — Free
Complex multiply	(a+bi)(c+di) = (ac−bd)+(ad+bc)i	ACT Intermediate Algebra Formula Sheet — Free
Conditional probability	P(A \| B) = P(A and B) / P(B)	SAT Problem-Solving & Data Analysis Formula Sheet — Free
Convert percent ↔ decimal	÷100 / ×100	ACT Pre-Algebra Formula Sheet — Free
Convert percent ↔ fraction	% / 100, simplify	ACT Pre-Algebra Formula Sheet — Free
Cosine	cos θ = adjacent / hypotenuse	SAT Geometry & Trigonometry Formula Sheet — Free
Cosine	cos θ = adjacent / hypotenuse	ACT Trigonometry Formula Sheet — Free
Cosine of common angles	cos 30° = √3/2 ; cos 45° = √2/2 ; cos 60° = ½	ACT Trigonometry Formula Sheet — Free

D

Concept	Formula	Sheet
Degree ↔ radian	180° = π rad	ACT Trigonometry Formula Sheet — Free
Degree-radian conversion	180° = π rad	SAT Geometry & Trigonometry Formula Sheet — Free
Difference of squares	a² − b² = (a − b)(a + b)	SAT Advanced Math Formula Sheet — Free
Difference of squares	a² − b² = (a − b)(a + b)	ACT Elementary Algebra Formula Sheet — Free
Discriminant	Δ = b² − 4ac	SAT Advanced Math Formula Sheet — Free
Discriminant	Δ = b² − 4ac	ACT Intermediate Algebra Formula Sheet — Free
Distance formula	d = √((x₂−x₁)² + (y₂−y₁)²)	SAT Algebra Formula Sheet — Free
Distance formula	d = √((x₂−x₁)² + (y₂−y₁)²)	ACT Coordinate Geometry Formula Sheet — Free
Distance, rate, time	d = r · t	SAT Algebra Formula Sheet — Free
Distributive property	a(b + c) = ab + ac	ACT Elementary Algebra Formula Sheet — Free

E

Concept	Formula	Sheet
Each interior angle (regular)	(n − 2) · 180° / n	SAT Geometry & Trigonometry Formula Sheet — Free
Ellipse (centred at origin)	x²/a² + y²/b² = 1	ACT Coordinate Geometry Formula Sheet — Free
Equation of a circle	(x − h)² + (y − k)² = r²	ACT Coordinate Geometry Formula Sheet — Free
Equation of a circle	(x − h)² + (y − k)² = r²	SAT Geometry & Trigonometry Formula Sheet — Free
Exponent product	xᵃ · xᵇ = xᵃ⁺ᵇ	SAT Advanced Math Formula Sheet — Free
Exponent quotient	xᵃ / xᵇ = xᵃ⁻ᵇ	SAT Advanced Math Formula Sheet — Free
Exponent rules	xᵃ · xᵇ = xᵃ⁺ᵇ ; (xᵃ)ᵇ = xᵃᵇ	ACT Pre-Algebra Formula Sheet — Free
Exponential growth/decay	A = P(1 + r)ᵗ ; A = Pe^(rt)	SAT Advanced Math Formula Sheet — Free

F

Concept	Formula	Sheet
Fractional exponent	x^(a/b) = ᵇ√(xᵃ)	SAT Advanced Math Formula Sheet — Free
Function composition	(f ∘ g)(x) = f(g(x))	SAT Advanced Math Formula Sheet — Free

G

Concept	Formula	Sheet
General addition rule	P(A or B) = P(A) + P(B) − P(A and B)	SAT Problem-Solving & Data Analysis Formula Sheet — Free
Geometric sequence	aₙ = a₁ · rⁿ⁻¹	ACT Intermediate Algebra Formula Sheet — Free

H

Concept	Formula	Sheet
Heron's formula	A = √(s(s−a)(s−b)(s−c))	ACT Plane Geometry Formula Sheet — Free
Hyperbola (centred at origin)	x²/a² − y²/b² = 1	ACT Coordinate Geometry Formula Sheet — Free

I

Concept	Formula	Sheet
Imaginary unit	i = √(−1) ; i² = −1	ACT Intermediate Algebra Formula Sheet — Free
Inequality flip rule	flip ≥ ↔ ≤ when × or ÷ by a negative	ACT Elementary Algebra Formula Sheet — Free
Inscribed angle	½ × central angle	ACT Plane Geometry Formula Sheet — Free
Inverse function check	f(f⁻¹(x)) = x and f⁻¹(f(x)) = x	SAT Advanced Math Formula Sheet — Free

L

Concept	Formula	Sheet
Law of cosines	c² = a² + b² − 2ab cos C	ACT Trigonometry Formula Sheet — Free
Law of sines	a/sin A = b/sin B = c/sin C	ACT Trigonometry Formula Sheet — Free
Linear inequality flip	Multiply or divide by a negative ⇒ flip the inequality sign.	SAT Algebra Formula Sheet — Free
Log power rule	log_b(Mᵏ) = k·log_b M	SAT Advanced Math Formula Sheet — Free
Log product rule	log_b(MN) = log_b M + log_b N	SAT Advanced Math Formula Sheet — Free
Log quotient rule	log_b(M/N) = log_b M − log_b N	SAT Advanced Math Formula Sheet — Free
Log to exponential	log_b(x) = y ⇔ bʸ = x	ACT Intermediate Algebra Formula Sheet — Free
Logarithm definition	log_b(x) = y ⇔ bʸ = x	SAT Advanced Math Formula Sheet — Free

M

Concept	Formula	Sheet
Margin of error idea	wider sample interval ⇒ less precise estimate	SAT Problem-Solving & Data Analysis Formula Sheet — Free
Matrix add	add term-by-term, same dimensions	ACT Intermediate Algebra Formula Sheet — Free
Mean	sum / count	ACT Pre-Algebra Formula Sheet — Free
Mean (average)	mean = sum / count	SAT Problem-Solving & Data Analysis Formula Sheet — Free
Median	middle of sorted list	ACT Pre-Algebra Formula Sheet — Free
Median	middle value of sorted data	SAT Problem-Solving & Data Analysis Formula Sheet — Free
Midpoint formula	M = ((x₁+x₂)/2, (y₁+y₂)/2)	SAT Algebra Formula Sheet — Free
Midpoint formula	((x₁+x₂)/2, (y₁+y₂)/2)	ACT Coordinate Geometry Formula Sheet — Free
Mixture (concentration)	C₁V₁ + C₂V₂ = Cₘ(V₁+V₂)	SAT Algebra Formula Sheet — Free
Mode	most frequent value	ACT Pre-Algebra Formula Sheet — Free
Multiplication (independent)	P(A and B) = P(A) · P(B)	SAT Problem-Solving & Data Analysis Formula Sheet — Free

N

Concept	Formula	Sheet
Negative exponent	x⁻ᵃ = 1 / xᵃ	SAT Advanced Math Formula Sheet — Free
Negative exponent	x⁻ᵃ = 1/xᵃ	ACT Pre-Algebra Formula Sheet — Free

O

Concept	Formula	Sheet
Order of operations	PEMDAS	ACT Pre-Algebra Formula Sheet — Free

P

Concept	Formula	Sheet
Parallel lines	m₁ = m₂	SAT Algebra Formula Sheet — Free
Parallel lines	m₁ = m₂	ACT Coordinate Geometry Formula Sheet — Free
Percent change	(new − old) / old × 100%	SAT Algebra Formula Sheet — Free
Percent change	(new − old) / old × 100%	ACT Pre-Algebra Formula Sheet — Free
Percent change	(new − old) / old × 100%	SAT Problem-Solving & Data Analysis Formula Sheet — Free
Percent of	percent · whole	SAT Problem-Solving & Data Analysis Formula Sheet — Free
Percent of a number	% × number	ACT Pre-Algebra Formula Sheet — Free
Perfect-square trinomial	(a ± b)² = a² ± 2ab + b²	SAT Advanced Math Formula Sheet — Free
Period of sin/cos	2π (or 360°)	ACT Trigonometry Formula Sheet — Free
Period of y=a sin(bx)	2π / \|b\|	ACT Trigonometry Formula Sheet — Free
Perpendicular lines	m₁ · m₂ = −1	SAT Algebra Formula Sheet — Free
Perpendicular lines	m₁ · m₂ = −1	ACT Coordinate Geometry Formula Sheet — Free
Point-slope form	y − y₁ = m(x − x₁)	SAT Algebra Formula Sheet — Free
Point-slope line	y − y₁ = m(x − x₁)	ACT Elementary Algebra Formula Sheet — Free
Power of a power	(xᵃ)ᵇ = xᵃᵇ	SAT Advanced Math Formula Sheet — Free
Probability	favourable / total	ACT Pre-Algebra Formula Sheet — Free
Probability of an event	P(A) = favourable / total	SAT Problem-Solving & Data Analysis Formula Sheet — Free
Proportion	a/b = c/d ⇔ ad = bc	SAT Algebra Formula Sheet — Free
Pythagorean identity	sin² θ + cos² θ = 1	SAT Geometry & Trigonometry Formula Sheet — Free
Pythagorean identity	sin² θ + cos² θ = 1	ACT Trigonometry Formula Sheet — Free
Pythagorean theorem	a² + b² = c²	SAT Geometry & Trigonometry Formula Sheet — Free
Pythagorean theorem	a² + b² = c²	ACT Plane Geometry Formula Sheet — Free

Q

Concept	Formula	Sheet
Quadratic factoring	x² + (p+q)x + pq = (x+p)(x+q)	ACT Elementary Algebra Formula Sheet — Free
Quadratic formula	x = (−b ± √(b² − 4ac)) / 2a	SAT Advanced Math Formula Sheet — Free
Quadratic formula	x = (−b ± √(b² − 4ac)) / 2a	ACT Intermediate Algebra Formula Sheet — Free
Quotient identity	tan θ = sin θ / cos θ	ACT Trigonometry Formula Sheet — Free

R

Concept	Formula	Sheet
Range	max − min	ACT Pre-Algebra Formula Sheet — Free
Range	range = max − min	SAT Problem-Solving & Data Analysis Formula Sheet — Free
Reciprocal identities	csc = 1/sin ; sec = 1/cos ; cot = 1/tan	ACT Trigonometry Formula Sheet — Free

S

Concept	Formula	Sheet
Scientific notation	a × 10ⁿ, 1 ≤ \|a\| < 10	ACT Pre-Algebra Formula Sheet — Free
Sector area	A = ½ r² θ	SAT Geometry & Trigonometry Formula Sheet — Free
Sector area	A = ½ r² θ	ACT Plane Geometry Formula Sheet — Free
Sine	sin θ = opposite / hypotenuse	SAT Geometry & Trigonometry Formula Sheet — Free
Sine	sin θ = opposite / hypotenuse	ACT Trigonometry Formula Sheet — Free
Sine of common angles	sin 30° = ½ ; sin 45° = √2/2 ; sin 60° = √3/2	ACT Trigonometry Formula Sheet — Free
Slope	(y₂ − y₁)/(x₂ − x₁)	ACT Coordinate Geometry Formula Sheet — Free
Slope from two points	(y₂ − y₁)/(x₂ − x₁)	ACT Elementary Algebra Formula Sheet — Free
Slope of a line	m = (y₂ − y₁) / (x₂ − x₁)	SAT Algebra Formula Sheet — Free
Slope-intercept form	y = mx + b	SAT Algebra Formula Sheet — Free
Slope-intercept form	y = mx + b	ACT Coordinate Geometry Formula Sheet — Free
Slope-intercept line	y = mx + b	ACT Elementary Algebra Formula Sheet — Free
Solve linear equation	isolate x using inverse ops	ACT Elementary Algebra Formula Sheet — Free
Square root product	√(ab) = √a · √b	ACT Pre-Algebra Formula Sheet — Free
Standard form	Ax + By = C	SAT Algebra Formula Sheet — Free
Standard form of a line	Ax + By = C	ACT Coordinate Geometry Formula Sheet — Free
Sum of arithmetic series	Sₙ = n(a₁ + aₙ)/2	ACT Intermediate Algebra Formula Sheet — Free
Sum of interior angles	(n − 2) · 180°	SAT Geometry & Trigonometry Formula Sheet — Free
Sum of interior angles	(n − 2) · 180°	ACT Plane Geometry Formula Sheet — Free
Sum/product of roots	r₁ + r₂ = −b/a; r₁r₂ = c/a	SAT Advanced Math Formula Sheet — Free
Surface area of sphere	A = 4 π r²	ACT Plane Geometry Formula Sheet — Free

T

Concept	Formula	Sheet
Tangent	tan θ = opposite / adjacent	SAT Geometry & Trigonometry Formula Sheet — Free
Tangent	tan θ = opposite / adjacent	ACT Trigonometry Formula Sheet — Free

U

Concept	Formula	Sheet
Unit rate	quantity / 1 unit	SAT Problem-Solving & Data Analysis Formula Sheet — Free

V

Concept	Formula	Sheet
Vertex form (parabola)	y = a(x − h)² + k	SAT Advanced Math Formula Sheet — Free
Vertex from standard form	x = −b/(2a)	ACT Coordinate Geometry Formula Sheet — Free
Vertex of a parabola (vertex form)	y = a(x − h)² + k	ACT Coordinate Geometry Formula Sheet — Free
Volume of cone	V = ⅓ π r² h	SAT Geometry & Trigonometry Formula Sheet — Free
Volume of cone	V = ⅓ π r² h	ACT Plane Geometry Formula Sheet — Free
Volume of cylinder	V = π r² h	SAT Geometry & Trigonometry Formula Sheet — Free
Volume of cylinder	V = π r² h	ACT Plane Geometry Formula Sheet — Free
Volume of pyramid	V = ⅓ ℓ w h	SAT Geometry & Trigonometry Formula Sheet — Free
Volume of rectangular prism	V = ℓ w h	SAT Geometry & Trigonometry Formula Sheet — Free
Volume of sphere	V = ⁴⁄₃ π r³	SAT Geometry & Trigonometry Formula Sheet — Free
Volume of sphere	V = ⁴⁄₃ π r³	ACT Plane Geometry Formula Sheet — Free

Which sheet has which formulas

SAT Advanced Math Formula Sheet — Free18 rows
SAT Algebra Formula Sheet — Free13 rows
ACT Coordinate Geometry Formula Sheet — Free12 rows
ACT Elementary Algebra Formula Sheet — Free9 rows
SAT Geometry & Trigonometry Formula Sheet — Free23 rows
ACT Intermediate Algebra Formula Sheet — Free12 rows
ACT Plane Geometry Formula Sheet — Free18 rows
ACT Pre-Algebra Formula Sheet — Free14 rows
SAT Problem-Solving & Data Analysis Formula Sheet — Free12 rows
ACT Trigonometry Formula Sheet — Free14 rows