Panlilio 2008-2009

Panlilio 2008-2009

Section 1.1 & 1.2 ObjectivesUse the order of operations to evaluate

experationsUse formulasDetermine the sets of numbers to which a

given number belongsUse the properties of real numbers to

simplify expressions

Panlilio 2008-2009

Please Excuse My Dear Aunt SallyThe Order:

1. ___________ (and other groupings like brackets or fraction bars)

2. ___________3. All Multiplication and Division from _____ to

______4. All Additions and Subtractions from _____ to

_____

Order of Operations

Panlilio 2008-2009

Order of OperationsTry these problems

10− 4 + 3⋅2( )2⎡⎣

⎤⎦

6 + 23 −7⋅47−3− 5⋅2( )4 7 −14( )

Panlilio 2008-2009

Using FormulasWhen given a formula, just Plug AND Chug!

The formula for the volume of a rectangular prism is . Find the volume of each cylinder given the following values:

l=7, w=22, h=3 l=2.25, w=4.1, h=3 Cube with sides of length 8

V =lwh

Panlilio 2008-2009

Properties of Real Numbers

Q I

Z

WN

R =

I =

Q =

Z =

W =

N =

Reals, R

Rational numbers can be expressed as a ratio m

n

Panlilio 2008-2009

Properties for Addition and Multiplication

Addition Multiplication

Commutatitve

Associative

Identity

Inverse

Distributive

Panlilio 2008-2009

Name the Propertyx + y+ z=y+ z+ x

4(h−2k) =4h−8k

7 −0 =7

12 ⋅3=3⋅12

18(8) =1

Panlilio 2008-2009

Section 1.4 & 1.5 ObjectivesTranslate verbal expressions and sentences

into algebraic expressions and equationsSolve equations by using the properties of

equalitySolve equations for a specific variableSolve equations containing absolute value

Panlilio 2008-2009

Translating Words into MathTwice the cube of a number

Three less than a number is -7

Four times the sum of a number and 2

A number divided by 4 is 2/3

The product of a number and its square

Panlilio 2008-2009

Properties of EqualityFor any real number a, a=a

For all real numbers a and b, if a=b, then b=a

For all real numbers a, b, and c, if a=b and b=c, then a=c

If a=b, then a may be replaced by b

For any numbers a, b, and c, if a=b then a+c=b+c and a-c=b-c

For any real numbers a, b, and c, if a=b, then ab=b c and, if c0,

a

c=

bc

Panlilio 2008-2009

Solving EquationsSolve each equation:4n−5 =11 2

3y +

12=−3 t + 2t−3t+ 4t=10

1.4c−9 =2.3c+ 55

6−38

y=124−10 = 4 5 − 3x( )

Panlilio 2008-2009

Absolute Value EquationsAbsolute Value of a Number --> The number

of units it is from 0 on the number lineAbsolute Value Equations --> Two Possible

Scenarios: 1. The number inside is positive, or 2. The number inside is negative. Either way, when you take the absolute value, you get a __________.2x−3 =5 x−14 =7 9x + 4 =−8

Panlilio 2008-2009

Section 1.6 & 1.7 ObjectivesSolve inequalities and graph the solution setsSolve compound inequalities using and and or

Solve inequalities involving absolute value and graph the solutions

Panlilio 2008-2009

Solve each inequality. Graph the solution.

Solving Inequalities

Reminder! When solving inequalities: if you multiply or divide by a negative number, you have to ________ the inequality sign.

5y−3≤2y+ 9 −.5m >14 −x ≥x − 3

4

Panlilio 2008-2009

Compound Inequalities“And” --> Must make

both inequalities true. Shade the ___________.

“Or” --> Can make either inequality true. Shade ______________.

5 ≤2x−3 <122

5x > 4 and 8 −x> −4

x + 33

≤2 or 1.2x−3.3 < 2.3x+1.1

Panlilio 2008-2009

Absolute Value InequalitiesAbsolute Value Inequalities are Compound Inequalities.

x−2 < 4 4x−3 ≥9 x +1 −x≤1

Panlilio 2008-2009

Homework1.1 & 1.2: P.10 #19-51 EOO,54,56,58; P.17

#21-57 EOO,581.4 & 1.5: P.31 #19-53 Odd,56,60; P.41 #17-

41 EOO,45,461.6 & 1.7: P.47#15-43 EOO,49,50,57-59; P.53

#15-43 EOO,45,46,49-55 OddChapter Review P.56 #1-27 Odd, #33-69 Odd