Mathematics Flashcards
List the most common units
Length - metre (m)
time - seconds (s)
mass - kilograms (kg)
current - ampere (A)
temp - kelvin (K) = celcius + 273.15
amount of substance - mole (mol)
what is the format for scientific notation?
purpose
c x 10^x
allows for easier calculations & recording results
what are the four basic rules of alegbra
associative rule - regroup to get the same answer = (x + y) + z = x + (y + z)
communitive law - move numbers around while multiplying & get the same answer =
(x + y) = (y + x)
distributive law - multiplying numbers added together same as separate multiplication
= (x + y)z = (xz) + (yz)
arithmetic order of operations - BEDMAS
examples of bracket rules
- x - = +
+ x - = -
+ x + = +
what are the fraction rules
(−a)/b=a/(−b)=−a/b
x/u×y/z= xy/uz
x/y ÷ u/z= x/y×z/u=xz/yu
x/y+z/y=(x+z)/y
x/y+z/u=ux/yu+yz/yu=(ux+yz)/yu
examples of exponent rules
x^a x^b=x^(a+b)
〖(x/y)〗^a=x^a/y^a
〖(xy)〗^a=x^a y^a
x^a/x^b =x^(a−b)=1/x^(a−b)
〖(x〗^a)〗^b=x^ab
(x^(1/a) )=√(a&x)
〖(x^(1/a))〗^a=x^(a/a)=x
logarithm rules
logMN=logM+logN
log M/N=logM−logN
log〖M^n 〗=nlogM
〖log〗a x=(〖log〗_b x)/(〖log〗_b a)
trig functions
sin (SOH)
cos (CAH)
tan (TOA)
simplifying small angle rules
if θ «_space;1 then
sin θ approx. θ
cos θ approx. 1
tan θ approx. θ
how does vector addition work?
two vectors add head-to-tail and give a resultant vector
what to do if they don’t form right angled triangles?
split vectors into x and y components and add components together as usual
how does vector subtraction work?
reverse direction of the vector you want to subtract & treat like normal vector addition
what is the purpose signed numbers?
they increase the scope of the numbering system changing how the system works (i.e allowing more calculations with the same numbers)
basic exponential to log rule
x=a^y —-> yloga = x
what are two base numbers where the log conversion rule is useful?
when the base is e (x = e^ y –> y ln x)
when the base is 10 (x = 10^y –> ylog10x)
if not stated the base is assumed to be 10
