Precalculus Memorization List

Area of a Triangle

A= ½ bh

Area of a circle

A = πr²

Circumference of a circle

C = 2πr

Area of a Trapezoid

A = ½ h (b₁ + b₂)

Surface area of a sphere

SA = 4πr²

Volume of a sphere

V= 4/3 πr³

Equation of circle centered at (h,k) and radius r

(x-h)²+(y-k)²=r²

Midpoint formula

(x_{1 + x₂)/2}, (y₁ + y₂)/2

Distance Formula

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Point-slope equation of a line

y-y₁= m(x - x₁)

Slope intercept equation of a line

y=mx+b

log_bx=y

b^y=x

ln e

1

ln 1

0

Change of base

log_bx = log x / log b

expand log_bxy

log_b x + log_b y

Expand log_b x/y

log_bx-log_by

Expand log_bxⁿ

n⋅log_bx

Average (mean)

sum of terms / # of terms

Median

number in the middle

Mode

number that occurs the most

Domain

set of all possible x-values for a function

Range

set of all possible y-values for a function

Quadratic Formula

x = (-b ± √(b^2 - 4ac)) / (2a)

Ratio sides 30-60-90 triangle

x:x√3:2x

Ratio of sides 45-45-90 triangle

x:x:x√2

a²-b²

(a+b)(a-b)

(a+b)²

a²+2ab+b²

(a-b)²

a²-2ab+b

a³-b³

(a-b)(a²+ab+b²)

a³+b³

(a+b)(a²-ab+b²)

Shift down c units

y=f(x)-c

Shift left c unit

y=f(x+c)

shift right C units

Y=f(x-c)

reflect over X axis

Y=-f(x)

reflect over Y-axis

Y=f(-x)

Vertical stretch by factor a

axf(x)

sin²0+cos²0

1

tan0

sin0/cos0

cot0

Cos0/sin0

Sin0

1/csc0

cos0

1/sec0

tan0

1/cot0

sin²0

1-cos²0

Cos²0

1-sin²0

tan0

Cot(90-0)

cot0

tan(90-0)

sec0

csc(90-0)

Csc0

sec(90-0)