Rules that apply for addition, subtraction, multiplication, or division of real numbers
Commutative
Associative
Identity
Inverse
Distributive
Commutative
You can change the order of the terms or factors.
a + b = b + a
ab = ba
Associative
You can regroup the terms as you like.
a + (b + c) = (a + b) + c
a(bc) = (ab)c
Identity
Finding a number so that when added to a term results in that number; finding a number such that when multiplied by a term results in that number.
a + 0 = a
a x 1 = a
Inverse
Finding a number such that when added to the number it results in zero; or when multiplied by the number results in 1.
a - a = 0
a x (1/a) = 1
Distributive
This technique allows us to perate on tems with parentheses without first perfoming operations with the parentheses. This is especially helpful when terms within the parentheses cannot be combined.
a (b + c) = ab + ac
Arithmetic Sequence
a (sub n) = a (sub 1) + (n - 1)d
a (sub 1) is the first term in the sequence
d = common difference between the terms
n = the nth term
Net
Two-dimensional figure that can be cut out and folded up to make a three-dimensional solid
Cube
Six square net
Tetrahedron
4 equilateral triangle net
Octahedron
8 equilateral triangle net
Icosahedron
20 equilateral triangle net
Dodecahedron
12 regular pentagon net
Tessellation
An arrangement of glosed shapes that completely covers the plane without overlapping or leaving gaps; unlike tilings, tessellations do not require the use of regular polygons
Four basic tranformational symmetries that can be used in tessellations
1) 2) 3) 4)
1) Translation
2) Rotation
3) Reflection
4) Glide Reflection
Sum of the Squares
Sum of the squares of the differences between each item and the mean
(Each number - average)(Same number - average)
Variance
The sum of the squares quanitity divided by the number of items