Algebra 2 Chapter 1 Quiz Study Guide
Factors vs Terms
Factors- multiplication Terms- addition
Subtraction
For all real #s a and b: a - b = a + (-b)
Division
For all real #s a and b: a divided by b = a x 1 over b (1/b)
Transitive Property
If a = b, & b=c, then a = c Ex: if y+x=z, then z=y+x z = a + 2 & a + 2 = 3, then z = 3
Subtraction Property of Equality
If a = b, then a - c = b - c 10 - 2 = 10 - 2
Division Property of Equality
If a = b, then a / c = a / b 18 / 2 = 18 / 2
Multiplication Property of Equality
If a = b, then ac = bc and ca = cb Ex: x + 4 = 3, then 2(x = 4) = 6
Addition Property of Equality
If a=b, then a + c = b, then c + a = c + b Let's say a = 15 (a - 2) + 2 = 13 + 2 a - 2 = 13
Symmetric property
If a=b, then b=a 7 + 8 = 15 15 = 7 + 8 4 - x = y y = 4 - x
Substitution Property
If x=y, then y can be substituted for x at any given time Let's say x=2, a=3, & 1=n 2x + 5a - 6n = (2 x 2) + (5 x 3) - (6 x 1) = 13
One to one correspondence
It's I think when 1=a, 2=b, 3=c, etc.
Associative
Multiplication: (a x b) x c = a x (b x c) Addition: (a+b) + c = a+(b+c)
Commutative
Multiplication: a x b = b x a Addition: a+b += b+a
Order of Operations
When you use PEMDAS to solve a problem
Additive Inverses (opposites)
[a + (-a)= 0] 4 + -4 = 0
Additive Identity
a + 0 = a 89+0 = 89
Reflexive Property
a = a 5 = 5, 4 + 5 = 4 + 5, 2x + 6 = 2x + 6
Multiplicative Identity
a x 1 = a 5x 1 = 5
(.) any number repeating
#/9 ( 5 over nine is .5 repeating)
Multiplicative inverses (reciprocals)
(a x 1/a = 1) 3 x 1/3 = 1
Distributive
(works for addition as well as multiplication) 2(3+4) = 2 x 3 + 2 x 4
Integers
-2, -1, 0, 1, 2....
Whole Numbers
0, 1, 2, 3....
Natural Numbers
1, 2, 3, 4......
This is the end
2 = 1 n stuff
Rational Numbers
2.4, 8/3, -6.25 (terminating decimal or repeating)
Numerical Expressions vs Algebraic Expressions
A numerical would be limited to numerals whereas in an Algebraic expression there are variables
Definition of Absolute value
l a l = {-a if a< 0 l a l = { a if a >0 l a l = { 0 if a = 0
Irrational Numbers
the square root of 7, pi (no terminating decimal)