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)