formulas Flashcards
slope formula
m = (y1 - y2)/(x1 - x2)
standard form
ax + by = c
vertex
-b/2a (for quadratics)
circle graph equation
(x - h)^2 + (y - k)^2 = r^2
ellipse graph equation
(x - h)^2/a^2 + (y - k)^2/b^2 = 1
discriminant
b^2 - 4ac, >0 = 2 solutions, =0 = 1 solution, <0 = 2 imaginary solutions/no real solution
distance formula
√(x1 - x2)^2 + (y1 - y2)^2
kite area
1/2 lw
square area
s^2
rectangle area
lw
diameter
2r
volume of rectangular prism
lwh
volume of cylinder
πr^2h
triangle area
1/2bh
circle area
πr^2
circumference
πd or 2πr
parallelogram area
bh
trapezoid area
1/2h(b1 + b2)
surface area of cylinder
2πr^2 + 2πrh
surface area of sphere
4πr^2
volume of sphere
4πr^3/3
volume of cube
s^3
sum of angles in n-sided polygon
180(n - 2)
angle measure of each angle in n-sided polygon
180(n - 2)/n
45 45 90 triangle
x, x, x√2
30 60 90 triangle
x, 2x, x√3
determinants
this is supposed to be a matrix but it looks weird ok [ab ] = ad - bc
[cd ]
qualifications for matrices to be multipled
number of columns of first matrix must be the same as number of rows of second one
qualifications for matrices to be added/subtracted
must have the same dimensions
i^2
-1
i^3
-i
i^4
1
arithmetic sequences
- common difference
- terms are added/subtracted to get to next term
geometric sequences
- common ratio
- terms are multiplied/divided to get to next term
union
collection of elements in 2 or more sets
intersection
collection of elements that are shared by 2 or more sets
null set
empty set, set without elements
