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Panlilio 2008-2009
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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
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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
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Panlilio 2008-2009
Order of OperationsTry these problems
10− 4 + 3⋅2( )2⎡⎣
⎤⎦
6 + 23 −7⋅47−3− 5⋅2( )4 7 −14( )
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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
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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
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Panlilio 2008-2009
Properties for Addition and Multiplication
Addition Multiplication
Commutatitve
Associative
Identity
Inverse
Distributive
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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
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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
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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
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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
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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( )
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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
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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
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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
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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
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Panlilio 2008-2009
Absolute Value InequalitiesAbsolute Value Inequalities are Compound Inequalities.
x−2 < 4 4x−3 ≥9 x +1 −x≤1
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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