Chapter 12. Appendix
12.1. Table of Symbols*
| ( ) | Parentheses (grouping symbols) |
| [ ] | Brackets (grouping symbols) |
| { } | Braces (grouping symbols) |
| = | equal |
| ≠ | not equal to |
| ≈ | approximately equal to |
| > | greater than |
| < | less than |
| ≥ | greater than or equal to |
| ≤ | less than or equal to |
| x | variable or constant |
| – x | negative of x (opposite of x ) |
| | x | | absolute value of x |
| reciprocal of x |
| ( a , b ) | ordered pair with component a and second component b |
| π | the irrational number pi, often approximated by 3.14 |
| the principal square root of a |
| the secondary square root of a |
12.2. Properties of Real Numbers*
Rule 12.1. Commutative Property
a + b = b + a 3 + 4 = 4 + 3
a b = b a 4 · 3 = 3 · 4
Rule 12.2. Associative Property
a + ( b + c ) = ( a + b ) + c 4 + ( 3 + 5 ) = ( 4 + 3 ) + 5
a ( bc ) = ( ab ) c 4 ( 3 · 5 ) = ( 4 · 3 ) 5
Rule 12.3. Distributive Property
a ( b + c ) = a b + a c 4 ( x + 3 ) = 4x + 12 ( b + c ) a = a b + b c ( x + 3 ) 4 = 4x + 12
Rule 12.4. Properties of Zero
a
·
0
=
0
0
·
a
=
0
If
a
≠
0, then
and
is undefined.
Rule 12.5. Double Negative Property
– ( – a ) = a
12.3. Important and Useful Rules/Formulas*
Exponents (Assume each expression is defined.)
a n a m = a n + m
( ab ) n = a n b n
a 0 = 1
Factorization and special product formulas
ab + ac = a ( b + c )
a 2 + 2ab + b 2 = ( a + b ) 2
a 2 – 2ab + b 2 = ( a – b ) 2
Formulas
12.4. The 5-Step Method of Solving Applied Problems*
Let x (or some other letter) represent the unknown quantity.
Translate the English to mathematics and form an equation.
Solve this equation.
Check this result by substituting it into the original statement of the problem.
Write a conclusion.