ap pre calc - formulas

apparently ms noll hates all her students!

slope intercept form of line

y = mx + b

point slope form of line

y - y₁ = m(x - x₁)

standard form of line

Ax + By = C

rate of change

(y1 - y2) / (x1 - x2) = (f(a)-f(b))/ a - b

quadratic equation

ax² + bx + c = 0

quadratic formula

x = (-b ± √(b² - 4ac)) / 2a

discriminant rules

• x² - 4ac > 0 then 2 distinct real roots

• x² - 4ac = 0 then 1 repeated real root

• x² - 4ac < 0 then 0 real roots (2 imaginary roots

volume/surface area of sphere

• V = (4/3)πr³

• SA = 4πr²

volume of cone

V = (1/3)πr²h

area of trapezoid

A = (1/2)h(b₁ + b₂)

right triangle - sin x

opp/hyp

right triangle - cos x

adj/hyp

right triangle - tan x

opp/adj

circular function, radius r - sin x

y/r

circular function, radius r - cos x

x/r

circular function, radius r - tan x

y/x

reciprocal identity: csc x

1/sin x

reciprocal identity: sec x

1/cos x

reciprocal identity: cot x

cos x/sin x = 1/tan x

reciprocal identity: 1

• sin x csc x

• cos x sec x

• tan x cot x

pythagorean identities: 1 =

sin²x + cos²x

pythagorean identities: sec²x

1 + tan²x

pythagorean identities: csc²x

1 + cot²x

lim of sin x as x approaches c

sin c

lim of cos x as x approaches c

cos c

f(c) is continuous at point (c, f(c) ) when

• f(c) exists

• lim of f(c) as x approaches c exists

• lim of f(c) as x approaches c = f(c)

even function

• symmetric to x=0

• f(x) = f(-x)

odd function

• symmetry with respect to origin

• -f(x) = f(-x)

lim of (sin x)/x as x approaches 0

1

lim of (1 - cos x)/x as x approaches 0

0

domain of √s(t)

s(t) >= 0

domain of 1/g(m)

all reals, g(m) ≠ 0

domain of ln(s(x))

s(x)>0

lim f(x) as x approaches a +- lim g(x) as x approaches a =

lim[f(x)+-g(x)] as x approaches a

lim f(x) as x approaches a * lim g(x) as x approaches a =

lim[f(x) * g(x)] as x approaches a

lim f(x) as x approaches a / lim g(x) as x approaches a

lim[f(x)/g(x)] as x approaches a

(a + b)²

a² + 2ab + b²

(a - b)²

a² - 2ab + b²

(a + b)³

a³ + 3a²b + 3ab² + b³

(a - b)³

a³ - 3a²b + 3ab² - b³

vertex form of parabola

y = a(x-h)²+k

w^a * w^b

w^(a+b)

polar to rectangular, y =

r sin theta

rectangular to polar, theta =

tan^-1 (y/x)

m^g/m^h

m^(g-h)

sin(a-b) =

sin a cos b - cos a sin b

cos(a+b)

cos a cos b - sin a sin b

types of polar graphs

rose curve, spiral, circle, leminscate

factor a³ + b³

(a+b)(a²-ab+b²)

sin(a + b)

sin a cos b + cos a sin b

double angle for sin 2theta

2 sin theta cos theta

sqrt of -1

i

common log

log base 10

cos(a-b)

cos a cos b + sin a sin b

polar to rectangular, x =

r cos theta

rectangular to polar, r =

sqrt of x² + y²

cos 2x

• cos²x-sin²x

• 2cos²x-1

• 1-2sin²x

factor a³-b³

(a-b)(a²+ab+b²)

given f(x) = ax^m+…/bx^m+… what are three rules for HA

• m>n then no HA

• m=n then y=a/b

• m<n then y=0

rule for oblique asymptote

n+1=m/m-1=n

tan(a-b)

tan a - tan b/1 + tan a tan b

trig form of complex number

r cos theta + i r sin theta

tan (a + b)

tan a + tan b/1 - tan a tan b