Physics Quiz Math Review

area

m²

volume

m³

velocity

m/s

acceleration

m/s²

Force

N (kg m/s²)

Density

kg/m³

Rule for converting units

Make sure units cancel by num/denom

SIgfig + - rule

= - .5 of last sigfig

Sig fig with decimal rules

last column of sig fig

find 10 raised to x equals y

log(y)

e raised to x equals y

ln(y)

get rid of ln

e both sides

get rid of positive e

multiply by negative e both sides

1/x² to 1

multiple both sides by x²

graph line

y=mx+b

distance between two points

square root (x2-x1²-y2-y1²)

y=x²

parabola

circle circumference

2piR

circle area

piR²

sphere surface area

4piR²

volume

(4/3)piR³

cylinder surface area

2piRL

cylinder volume

piR²L

angles of a triangle equal

180

right triangle 3rd angle

90-theta

triangle side lengths (pythag theorem)

a²+b²=c²

90-30-60 triangle

opp 30 1/2h, opp 60 (sqr(3)/2)h

45 45 90 triangle

both sides are sqr(2)/r * h

intersecting lines angle

both theta

parallel lines alternate interior angles

both theta

unit circle

o degree = o rad, 90 = pi/2, 180 = pi, 270 = 3/2 pi

arc length on circle

R theta in radians

theta adjacent

hcostheta

theta opposite

hsintheta

cos negtheta

costheta

sin neg thata

neg sin theta

sintheta

opp/h

costheta

adj/h

tantheta

sintheta/costheta, opp/adj

if v(t)=t^n

dV/dt = nt^n-1

if v(t) = c

derivative is zero

if v(t) = e^t

derivative = e^t

if v(t) = ln(t)

derivative = 1/t

if v(t) = sin(t)

derivative = cos(t)

if v(t) = cos(t)

derivative = -sin(t)

if c*f(t)

derivative = c * df-dt

addition rule

df/dt + dg/dt

product rule

df/dt g + f * dg/dt

functional composition/the chain rule

df(g(t))/dt * dg/dt

graphing a derivative

0 at min/max, above x where pos, below x where neg

what is an integral

“inverse” of a derivative

definite integral

integral x - integral y