3/30/2011
Definition
Scientific Notation
Objectives: To express numbers
using scientific notation and to
convert numbers to and from
scientific notation.
Steps for Converting to
Scientific Notation
Move the decimal so that the number is between 1
and 10.
Linear Equation in one Variable
Addition Property of
Equality
Objectives: To identify linear
equations and to use the addition
property of equality.
VOCABULARY Review
Equation - math sentence with an equal
sign; equal sign divides the equation into two
si
8/31/2009
The Golden Rule of Solving Equations
Multiplication Property of Equality
Do unto one side of
an equation as you
an equation as you
would do unto the
other side.
More PROPERTIES
Review of Properties
Addition Property of Equality
For every real n
8/31/2009
Solve and check.
More on Solving Equations
OBJECTIVE: TO USE ADDITION,
SUBTRACTION, MULTIPLICATION, AND
DIVISION TO SOLVE EQUATIONS.
a) h 4 = 10
b) 8p - 3 = 13
Add 4 to both sides.
h = 14
CHECK
14 4 = 10
10 = 10
Add three to both sides.
8p = 16
VOCABULARY
FORMULAS
Objective: To solve equations
by working with formulas.
Example 1
The width w is 75 feet and the
perimeter P is 300 feet. Use the
formula P = 2l + 2w to find the length l.
300 = 2l + 2(75)
300 = 2l + 150
150 = 2l
75 = l = length
RE-WRI
Vocabulary and Signs
Linear Inequalities
Objective: To graph intervals and
solve inequalities.
Linear inequality Ax + B < C
Solution of an inequality- any number that
makes the inequality true.
Signs
< Less than
< Less than or equal to
> Greater than > Gr
8/21/2009
VOCABULARY
Term a number, a variable, or a product of
a number & variable(s)
Constant a term that has no variable (a
Simplifying Expressions
number by itself)
number by itself)
Coefficient a numerical factor of a term
Objectives: To use the
Dist
Vocabulary
Equations of Lines
Todays objective: To write and
graph lines in slope-intercept
form and point-slope form.
Find the slope and y-intercept of each
equation.
a) y= -2x + 1
b) y = -(4/5)x
c) y=(7/6)x 3/4
Linear equation: an equation whose
graph i
Review: Base and Exponent
Integer Exponents Rules
OBJECTIVE: TO USE
EXPONENT RULES TO
SIMPLIFY
EXPRESSIONS .
Identify the base and the exponent in each of the
following. Pay close attention to parenthesis.
EXAMPLES
A) 32
B) -32
7
C) (-3)
D) x4
9
E) (-x)
F
Square of a binomial
SPECIAL PRODUCTS
Objective: To use patterns to find
(a + b)2
(a - b)2
(a + b)(a - b)
(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 2ab + b2
Do you notice a pattern here?
Steps for squaring a binomial
Watch and think
1. Square the first term.
Zero Exponent
n0 = 1
-n0 = -1
(-n) 0 = 1
In other words, when raising a base to the
zero power, that part becomes 1.
Integer Exponents Rules
Objective: To use Exponent rules to simplify expressions.
Zero Exponent
EXAMPLES
P) 30
S) x0
Zero Exponent
R) (-3)
Think of the problem this way:
Separate the numerator into individual
fractions over the denominator and simplify.
Objective: To divide a polynomial by a
monomial.
5a 2b 15ab 3 + 10a 3b 4 5a 2b 15ab3 10a 3b 4
+
=
5ab
5ab
5ab
5ab
Reduce fractions and use e
Definitions
Variable a symbol, usually a letter,
that represents one or more numbers
Al
Algebraic expression a math phrase
that can include numbers, variables,
and operation symbols
Equation math sentence with an
equal sign
Variables, Expressions, & Equat
Definitions
Exponents and Order of
Operations
Objective: To use exponents, the
order of operations, and grouping
symbols.
variable a symbol, usually a letter,
that represents one or more numbers
algebraic expression a math phrase
l b i
i
th h
with numbers
Reminder
FACTORING TRINOMIALS
ax2 + bx + c
FACTORING REVERSES
MULTIPLICATION.
For example: What can you multiply to get
4? x2? 6x2?
Answer: 1 times 4 or 2 times 2;
x times x
2x(3x) or 6x(x)
OBJECTIVE: TO FACTOR TRINOMIALS WHEN
A IS NOT EQUAL TO 1.
Review
Review
Special Factoring
Objectives: To factor the difference
of two squares and to factor Perfect
Square Trinomials.
Multiply using FOIL: (x 3) (x + 3).
x2 + 3x 3x - 9
Answer: x2 9
Remember: the outside/inside terms cancel b/c they
are opposite terms.
Mu
Solving Quadratic Equations by
Factoring
Objective: To use the zero factor
property to solve equations.
Steps for Solving Quadratic
Equations w/ Factoring
Zero Factor Property
If ab = 0, then a = 0 or b = 0 or
both a and b = 0.
1.
2.
In other words, if a
Review
Solving Equations
Applications of Quadratic
Equations
Objectives: To write equations from given
information and use the six steps in solving an
applied problem.
IMPORTANT INFO!
Verbal Expressions and Mathematical
Expressions: twice, sum, product, l
Rule: top x top
bottom x bottom
Objective: To multiply and divide
rational expressions.
Want to Cancel before Multiplying? Fine!
(Its like reducing first!) But
Cancel only top to bottom!
For Example:
=
1.
2.
3.
4.
a)
FACTOR, if possible.
Cancel out common
Adding & Subtracting
Rational Expressions
Review - adding or subtracting
fractions
EXAMPLE :
14 15
+
35 35
Objective: To add and subtract
rational expressions with like or
different denominators.
Examples with Like
Denominators
a)
3
2
x+2 x+2
b)
5n
2n
+
n
Joke of the Day
Systems of Linear Equations in Two
Variables Elimination Method
Objective: To solve systems of
equations using the elimination
method.
Are the given ordered pairs solutions of
the given systems?
Definitions
System 2 or more equations
toget
Product Rule for Radicals
If n a and n b are real numbers and
n is a natural number, then
Simplifying Radicals
Objective: To simplify radical
To simplify radical
expressions using the product
and quotient rules.
n
a
( b) =
n
n
ab .
In other words, the pro
Joke of the Day: Top Ten Excuses for
not Doing Quizzes or Homework
10. I locked the paper in my trunk but a four
dimensional dog got in and ate it.
9. I couldn't figure out whether I am the square of
negative one or am the square root of negative
negative