Math 3 EOC

Quadratic Formula

x \= -b ± √(b² - 4ac)/2a

Difference of Squares Formula

(a+b)(a-b) \= a^2 - b^2

Negative Exponents

1 / x^b \= x^(-b)

Degree to Radian

degree\# · (pi / 180 degrees)

Radian to Degrees

radian * 180/pi

Cos

x-coordinate

Sin

y-coordinate

Log Form

exponential form

a number written with a base and an exponent

Volume of a Cone

V(cone) \= 1/3 Bh

*B \= area of the circular base
*h \= height of the cone

Area of a Cone

πr* slant height + area of the base

Distance Formula

d \= √[( x₂ - x₁)² + (y₂ - y₁)²]

(x1, y1), (x2, y2)

45 - 45 - 90 Triangle

x, x, x√2

the measure of the hypotenuse is (√2) times the measure of a leg

30 - 60 - 90 Triangle

x, x√3, 2x

a right triangle that consists of a right angle, a 30 degree angle, and a 60 degree angle

Fundamental Theorem of Algebra

The degree shows the \# of solutions

Standard Form of a Circle

(x-h)² + (y-k)² \= r²

Incenter

equidistant from each side of the triangle.

Area of Trapezoids

A\=1/2(b1+b2)h

Arc Length

a/360 * (2πr)

Area of a Sector

(degree / 360) · pi · r^2

Sphere Volume

Volume(sphere) \= 4/3 * pi * r^3

Dividing Fractions (Functions)

Keep Change Flip no matter how ugly each fraction looks

Point of Discontinuity

- Holes
- Vertical Asymptotes
- (denominator \= 0)

Centroid

- A median is created by a vertex connected to the midpoint of the opposite side.
- Center of Mass: Balance Point

Incenter

- The incenter is equidistant from each side of the triangle

DG \= EG \= FG

Circumcenters

- The circumcenter is equidistant from each vertex of the triangle

AG \= BG \= CG

Simple Interest Formula (no compounding)

I \= P(1 + r)^t

P \= Principle Original
R \= Rate
T \= Time in Years

Remainder Theorem

when a polynomial p(x) is divided by a linear polynomial (x - a), then the remainder is equal to p(a).

Pythagorean Theorem

a²+b²\=c²

Volume of a Prism

V(prism) \= Bh

*B \= Area of the base
*h \= height of the prism

Area of a Triangle

A\= 1/2 bh

Vertex Form

y\=a(x-h)²+k

Volume of Cylinder

Volume(cylinder) \= Bh

*B \= Area of the cylinder base
*h \= height of the cylinder

Central Angle

an angle with its vertex at the center of a circle

Inscribed Angle

measure of angle x \= 1/2 measure of arc length n

Angle Inside Circle

arc+arc/2

Angle Outside Circle

m angle k \= 1/2 (large arc - small arc)

Segments Inside Circle

a * b \= c * d
(multiply measures on the same line)

Segments Outside Circle

Outside * Whole \= Outside * Whole

Secant Tangent

whole * outside \= tangent^2

5 \# Summary in Calculator

* Go to STAT
* Edit
* Clear list of L1 if needed
* Enter data in List 1
* Go back to STAT
* Calculate 1-Var Stats
* Use Sx for the sample standard deviation

Orthocenter

An altitude is created by a vertex connected to the opposite side so that it is perpendicular to that side.

Circumference of a circle

C\=2πr

Area of a circle

A\=πr²

sine curve

Starts at midline y\=Asin(Bx) + D

cosine curve

Starts at maximum if positive function
Starts at minimum if negative function
y \= Acos(Bx) + D

Continuosly Compounded Interest

A\=Pe^rt

Compound Interest Formula

A\=P(1+r/n)^nt

30 degrees unit circle

(√3/2, 1/2)

45 degrees on unit circle

(√2/2, √2/2)

60 degrees on unit circle

(1/2, √3/2)

Unit Circle

a circle with a radius of 1, centered at the origin

Base of Common Log

10

base of natural log

amplitude of a wave

Height of a wave from midline

Period of a wave

Time for one complete waveform to travel

midline of wave

horizontal shift of wave.
y\=Asin(Bx) + D y\= D is the midline
y\=Acos(Bx) + D y\= D is the midline