Pith thing for factors/multiples
Factors are few. Multiples are many.
Repeated percent increase formula
Final amount = original (1+ Rate) ⁿ =original (1+ Rate) ^ (number of changes)
Repeated percent decrease formula
Final amount = original (1- Rate) ⁿ =original (1- Rate) ^ (number of changes)
Definition of a logarithim
logbN= x <--> b^x= N
Change of base formula
work done formula
work done= rate of work *time
Area of an equilateral triangle formula
A=(s²√3) / 4
Area of a triangle formula (two)
Area of a parallelogram
Area of a square
A=s²= d²/2 (diagonal)
Area of a trapezoid
A= average of basesheight= (b₁b₂/2)h
Sum of angles of n-sided regular polygon
Inscribed angle is...
1/2 the central angle
The long diagonal of a rectangular solid is (super Pythagorean theorem)
The face diagonal of a cube is
face diagonal= s√2
The long diagonal of a cube is
long diagonal= s√3
Volume of a prism?
Volume of a cylinder?
Surface area of a cylinder?
SAcylinder= 2Πr² + 2Πrh= 2Πr² +ΠDh=2Πr² +Ch
Volume of a cone?
Surface area of a cone (include the base)
SA= ΠrL *Πr² (L=slant height/slanted side of the cone)
Volume of a PYRAMID?
Geometry question about the volume of a solid of all lengths are increased...
When lengths of a solid increase by certain factor, surface area increase by square of that factor, and volume increases by cube of that factor.
d=√(x₂-x₁)² + (y₂-y₁)²
Standard formula for equation of a circle
(x-h)² + (y-k)²= r²
Equation for a horizontal ellipse
(x-h)² /a² + (y-k)²/b² = 1 a>b (the larger under the x)
Equation for a vertical ellipse
(x-h)² /b² + (y-k)²/a² = 1 a>b (the larger under the y)
Major axis, minor axis, distance btw. focis for ellipse?
Maj axis=2A, Min axis= 2B, distance btw foci= 2c
Equation for a horizontal hyperbola
(x-h)² /a² - (y-k)²/b² = 1 (y is negative=horizontal)
Equation for a vertical hyperbola
(y-k)²/b² - (x-h)² /a² = 1 (x is negative= vertical)
distance in a 3d space?
d=√(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²
1/sinx = ?
tan 2x= 2tanx / (1-tan²x)
sin (A+B)= sinAcosB +cosAsinB
cos (A+B)= cosAcosB - sinAsinB (notice opposite sign)
amplitude=a, period= 360/b or 2Π/b when y=asinbx
Use law of sines when
S-S-A opp (two sides and one of their opposite angles) or A-A-Sany (two angles and any side)
(ASS or AAS)
Use law of cosines when
S-S-S (all three sides) or S-A-S (two sides and angle between them)
(SSS or SAS)
Converting from rectangular to polar
x²+y²=r² and tanθ=y/x
Converting from polar to rectangular
To find inverse function
1. Rewrite f(x) as y 2. switch y's and x's 3. solve for new y
f(-x)=f(x) y-axis symmetry. (think x=y, -x=y)
f(-x)= - f(x) origin symmetry (think x=y, -x= -y)
Degree of polynomial tells us..
the maximum amount of zeroes/roots, and (n-1) is the number of extremas or min/max
Number of standard deviations above/below?
Mean-number/Standard deviation= # (of SDs)
order does not matter (like choosing groups/committees)
Total= Group 1+ Group 2 + Neither - Both
Finding the nth term of an arithmetic sequence
Sum of the first n terms of an arithmetic sequence
Sum arith= n (a₁ + an/2) = number of terms *average of 1st and An
Finding nth term of a geometric sequence
an= a₁ * r ⁿ⁻¹
Sum of first n terms of a geometric sequence
sum geo= a₁ (1- r ⁿ)/ 1-r
Sum of infinite geometric sequence
sum geo= a₁/ 1-r
You can only multiply matrices if the first matrix has the same number of columns as the second matrix has..
rows. (1st matrix columns=2nd matrix rows)