Studied by 33 peopleCircumference of a Circle
π*d (d=diameter)
Area of a Circle
πr² (r=radius)
Area of a Square w/ Diagonal
d²/2 (d=diagonal)
Area of a Parallelogram
b*h (b=base & h=height)
Area of a Trapezoid
1/2h(b₁+b₂) (b₁ is the bottom edge and b₂ is the top edge)
Area of a Triangle
bh/2
Area of a Rhombus
d₁*d₂/2 (d₁=up and down diagonal) (d₂=left and right diagonal)
Area of Scalene Triangle (Heron's Formula)
√s(s - a)(s - b)(s - c) (abc - sides of triangle, s- semiperimeter)
Semipermeter
a+b+c/2
Area of an Equilateral Triangle (w/ Side)
(s²*√3)/4
Area of an Equilateral Triangle (w/ Height)
(h²√3)/3
Height of an Equilateral Triangle (given side)
(s√3)/2
Diagonal of a Square
side√2
Area of Any Regular Polygon (w/number and length of sides)
ns²/4 tan(180/n) (n=number of sides and s= length of sides)
Area of Any Regular Polygon (w/perimeter and apothem)
pa/2 (p=perimeter and a= apothem)
Inner Diagonal of cube
side√3
Surface Area of a Cube (w/ edge)
6e² (e=edge)
Surface Area of a Cube (w/ inner diagonal)
d²*2 (d=inner diagonal)
Surface Area of a Cube (w/ volume)
6v²/3 (volume)
Surface Area of Rectangular Prism
2(lw+lh+wh)
Inner Diagonal of a Rectangular Solid
√L²+w²+h²
Lateral Surface Area of a Cylinder
2πrh (r=radius and h=height)
Lateral Surface Area of a Cone
√r²+h²
Total Surface Area of a Cylinder
2πr(r+h)
Total Surface Area of a Cone (given slant height
πr(r+s) (s=slant height)
Surface Area of a Sphere
4πr²
Surface Area of a Hemisphere
3πr²
Volume of a Cube (given edge)
e³ (e=edge)
Volume of a Rectangular Prism
lwh
Volume of a Cylinder
πr²h
Volume of a Cone (given radius & height)
πr²h/3 (h= height, r=radius)
Volume of a Cone (given diameter & height)
1/12*πd²h (h=height, d=diameter)
Volume of a Sphere
4πr^3/3
Volume of a Hemisphere
(2/3)πr^3
Volume of a Pyramid
bh/3 (b=area of base and h=height)
Total Number of Subsets or Power Set
2^n (number of elements)
Number of Proper Subsets
2^n-1 (number of elements)
Permutations (Ways something can be arranged in an order)
n! ÷ (n-r)! (n=total number of objects and r=number of objects selected)
Total of Sequences
n(n+2)/4 (n=last number)
Combinations (Ways something can be arranged w/o order in mind)
n!/r!(n-r)! (n=total number of objects and r=number of objects selected)
Work of Two People Combined
n*n/n+n
Sum of roots in Quadratic
-b/a
Product of Roots in Quadratics
c/a
Axis of Symmetry
-b/2a
Volume of a cube (given Inner diagonal)
(3√d)*3 (d=inner diagonal)
Midpoint of two points
(x1 + x2)/2, (y1 + y2)/2
Midrange
Highest number+Lowest number/2
Interior Angle of a Regular Polygon
(n-2)180 (number of sides)
Number of Diagonals in a Polygon
((n-3)n)/2 (n=number of vertices or sides)
Geometric Mean
√ab (a=one number, b=second number)
Exterior angle of a regular polygon
360/number of sides
Number of diagonals from one vertex
n-3 (n=number of sides or vertices)
Simple Interest
prt
Triangular Number
n(n+1)/2
Note
Flashcard