math 2

Perimeter of Any Polygon

P=Sum of all side lengths

Triangle Angle Sum

The angles in any triangle sum to 180∘.

Isosceles Triangle

Has exactly two sides of equal length.

Equilateral Triangle

Has three sides of equal length and all angles are 60∘.

Square Perimeter

P=4s

Square Area

A=s²

Rectangle Perimeter

P=2ℓ+2w

Rectangle Area

A=ℓ⋅w

Triangle Perimeter

P=side1 + side2 + side3

Triangle Area

A=½⋅base⋅height

Trapezoid Area

A=½(b₁ + b₂)⋅h

Greatest Common Divisor (GCD)

The largest integer that divides evenly into both. Example: gcd(6,10)=2

Least Common Multiple (LCM)

The smallest integer that is evenly divisible by both. Example: lcm(6,10)=30

Order of Operations

PE(MD)(AS): Parentheses, Exponents, (Multiplication and Division equal priority, left to right), (Addition and Subtraction equal priority, left to right).

Squares (1² to 12²)

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144

Cubes (1³ to 5³)

1, 8, 27, 64, 125

Decimal Equivalents

1/5=0.2, 1/4=0.25, 1/3≈0.3̅, 1/2=0.5, 2/3≈0.6̅, 3/4=0.75

Simple Interest

I=P⋅r⋅t (Interest = Principal ⋅ rate ⋅ time)

Uniform Motion/Rate of Change

d=r⋅t (Distance = rate ⋅ time) or New Amount=Start+rate⋅time

Percent Change Formula

New Amount=Original±(% change)⋅Original

Product Rule

a^m⋅a^n=a^(m+n)

Quotient Rule

a^m/a^n=a^(m−n)

Power Rule

(a^m)^n=a^(m⋅n)

Zero Exponent

a^0=1

Exponent of One

a^1=a

Negative Exponent

a^(-n)=1/a^n

Negative Exponent (Inverse)

a^(-n)=1/a^n

Root-Exponent Relationship

n√a=a^(1/n)

Radical Distribution (Product)

n√(a⋅b)=n√a⋅n√b

Radical Distribution (Quotient)

n√(a/b)=n√a/n√b

Caution! (Sum)

n√(a+b)≠n√a+n√b

Distance Formula

d=√((x₂−x₁)²+(y₂−y₁)²)

Pythagorean Theorem

a²+b²=c² (for legs a,b and hypotenuse c)

Circle Area

A=πr²

Circle Circumference

C=2πr

Rectangular Prism Volume

V=ℓ⋅w⋅h

Rectangular Prism Surface Area

SA=2ℓw+2ℓh+2wh

Cube Volume

V=s³

Cube Surface Area

SA=6s²

Sphere Volume

V=(4/3)πr³

Sphere Surface Area

SA=4πr²

Cylinder Volume

V=πr²h

Cylinder Surface Area

SA=2πrh+2πr²

Interval Notation

Uses brackets [ and ] to include endpoints (≤,≥) and parentheses ( and ) to exclude endpoints (<,>). ∞ and −∞ always use parentheses.

Interval Examples

2≤x<5 is [2,5) x>−3 is (−3,∞) x≤3.2 is (−∞,3.2]