Homework: p. 17-18 9-15 odd, 21-33 odd, 91-

95 odd, 117-119 odd, and 121-127 odd

P.1 Algebraic Expressions, Mathematic Models, and

Real Numbers

Chapter P has a lot of review topics from your previous math years! • Variable – represents various numbers• Algebraic expression – combination of variables and numbers• Exponential Notation:

• Order of operations: PEMDAs; left to right• Equations – general rule of thumb…variables on the left when

reporting the solution – values on the right. Solutions should always be identified and “boxed”.

• Model – develop a model means to write an equation that represents a set of data

...

base

exponent

nb b b b b

b

n

Guided Practice…Evaluate the algebraic expression: 37 5( 4) for 6x x (6) 47f

SetsSet – collection of objects whose contents can be clearly determined.• Elements: objects of a set• { 1,2,3,4,5…} – brackets illustrate a set – called the roster

method when individual elements are separated by a comma• Set-builder notation: {x|x is a counting number less than 6} =

the set of all x such that x is a counting number less than 6• Intersecting sets: the intersection of sets A and B , written

, is the set of elements common to both set A and set B.

={x|x is an element of A and x is an element of B}

A B

A B

A B

Guided Practice…Find the intersection of two sets:

{7,8,9,10,11} {6,8,10,12}8 and 10 are the common elements (and)

{8,10}

More set info…• The union of sets A and B, written , is the set of elements that

are members of set A or of set B. This expression can be expressed in set-builder notation as:

A B

{ | is an element of A OR is an element of B}A B x x x

Guided Practice…Find the union of two sets:

{7,8,9,10,11} {6,8,10,12}

Information to remember:and = intersection (what sets have in common)or = union (everything in each of the sets)

The Set of Real Numbers:Name/Symbol Description Examples

Natural Numbers(N)

Counting numbers 2,3,5,17

Whole Numbers(W)

The set of whole numbers includes 0 and the natural numbers.

0,2,3,5,17

Integers(Z)

The set of integers includes the negatives of the natural numbers and the whole numbers.

-17,-5,-2,0,2,3,5,17

Rational Numbers(Q)

The set of rational numbers includes numbers that can be expressed as a quotient of 2 integers (denominator not 0). Terminating or repeating decimals.

2/5=0.4-2/3 = -0.666666…

(calculator tricks!!)

Irrational Numbers(I)

The set of irrational numbers is the set of numbers whose decimal representations are neither repeating or terminating. Cannot be expressed as a quotient of integers.

Real Numbers (R)

The set that includes rational and irrational numbers

The union of rational and irrational numbers.

More algebra stuff to remember…

(this is the tricky statement, the

Definition of absolute value:

if

key beinng

being that -x means t

0

if

he opposite of

0

x)

x x x

x x x

Properties of absolute value: for all real numbers and ,

0

, 0

(called the triangle inequality)

a b

a

a a

a a

ab a b

aab

b b

a b a b

Guided Practice…Evaluate:

a. 3 1 b. 2

c. if 0x

xx

And even more algebra stuff to remember…If and are any two points on a real number line,

then the distance between and is given by:

or

a b

a b

a b b a

Guided Practice…Find the distance between -5 and 3 on the real number line:

Solution:

Remember: distance can't be negative!

Properties of Real Numbers:Name Meaning

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

Distributive Property of Multiplication over Addition

Identity Property of Addition

Identity Property of Multiplication

Inverse Property of Addition

Inverse Property of Multiplication 1( ) 1, 0a aa

( ) ( )a b c a b c

( ) ( )ab c a bc

( )a b c ab ac

0a a (1)a a

( ) 0a a

Guided Practice…2 2Simplify: 6(2 4 ) 10(4 3 )x x x x 2Solution: 52x 54x

Simplify: 8 2[5 ( 3)]x x Solution: 6x+16