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Exam Review
By: John Misiewicz
Jeremiah Johnson
1st Power Equations
-Has no exponents
-Make the equation equal the variable
1st Power Examples
Ex1: x-2=3 Answer: x= 5
Ex2: x+12=x+12
Answer=x so the answer is All real numbers
1st power Examples cont.
Ex3: 5  x  25 Answer: x= 20
2
Properties
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Addition/ Subtraction property of Equality- If the
same number is added/ subtracted to equal
numbers the sums/ differences are equal
a+c=b+c; a-c=b-c
Multiplication/ Division property of Equality- If
equal number are multiplied/ divided by the same
[(non zero) in the case of division] number the
products/ quotients are equal
ca=cb; a b
c

c
Properties
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Reflexive property- all numbers equal
themselves. a=a
Symmetric Property- If one number equals
another than the other number equals the
first number. a=b, b=a
Transitive Property- If a=b and b=c than,
a=c
Properties
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Associative Property of Addition(a+b)+c=a+(b+c)
Associative Property of Multiplication(ab)c=a(bc)
Commutative property of Additiona+b=b+a
Commutative Property of Multiplicationab=ba
Properties
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Distributive Property-a(b+c)=ab+ac
Property of Opposites- a+(-a)=0; -a+a=0
1
Property of Reciprocals- a   1
a
Identity Property of Addition- a+0=a; 0+a=a
Identity Property of Multiplication- a 1  a
Multiplicative property of zero- a  0  0
Closure property of addition-a+b
Closure property of multiplication- ab
Properties
Power of a product property-(2t)2 = 22 x t2
 Product of a power property- 84 x 46
 Power of a power property- (84)5
x6
 Quotient of powers propertyx2
2
 Power of a quotient property- 3
 Zero power property-(x+5)(x-8)=0
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Properties
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Negative power property- -3-3=1/27
Zero product property-(x+10)(x-15)=0 x=10 or x=+15
Product of roots property-√9 x√5 = √45
Quotient of roots property-√225=√9x25
=3x5 = 15
Inequalities in one variable
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x-8<15 solve and graph
3x-5>1 solve and graph
13-7n<8 solve and graph
4y+3>7 solve and graph
2x+7>3 solve and graph
Conjunctions
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2m<4 and 12+2m<0 solve and graph
2d-5>-8 and -2d-5<d-3 solve and graph
-3+2<x-2+2<4+2 solve and graph
5-2p>-8 and -2d-5<d-3 solve and graph
Disjunction
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2w-1<3 or 3w>w+10 solve and graph
5-2p>11 or 5-2p<-1 solve and graph
-6>18 or 12+3r>0 solve and graph
H+5<-2 or h+5>2 solve and graph
IMPORTANT!!!!!!!!!!!!!!!!!!!!!!
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When solving these equations conjunctions
join the sentences together using the word
and (just like in a sentence in english
class). In a conjunctions you will find that
both of the sentences are true. In a
disjunction the word or is used. This means
that at least ONE sentence is true and it
cancels out the other sentence.
Linear Equations in Two Variables
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4x+3y=10 here are a list of ordered pairs
(4,-2) (-2,6) (2,3) (8,5) plug these in to see
which one fits the equation.
All Equations For All Lines
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Standard/General- ax+by=c
Point slope form- y-y1=m(x-x1)
Slope intercept form- y=mx+b
equation of a horizontal line-y=b
Equation of a vertical line- x=a
Slopes for all lines
The slope for a rising line is positive.
The slope of a falling line is negative.
A line that is parallel with the bottom of the
graph has a slope of zero because it never
rises.
A verticle line has a slop that is undefined
because it it has no run.
How to Graph
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Using the equation y=mx+b
y= the equation of the line
mx= the rise over the run or the slope of
the line
And b is the where the line crosses the
y-axis
Linear System
Substitution Method- 2x+y=25
4x+3y=32
Solution- y=25-2x (plug this equation into
your second one)
4x+3(25-2x)=32
X=21 y=67
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Linear Systems cont.
Addition/Subtraction Method- 5-y=12
3x+y=4
solution is- 8x=16
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Final solution is: x=2 y=-2
Linear Solution Commonalities
Solution- Null set
Inconsistent System
Solution- Intercept point
Solution- A.R.N.
Consistent System
Dependent System
4
4
2
2
-2
-2
-4
-4
4
2
-2
-4
Factoring Polynomials
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5a3+b3 Solution is :
5(a3+b3)
ax+bx-bx-by solution is:
a(x+y)-b(x-y)
5a3-5a2+10a-10 solution is:
(a-1) (5a2+10)
Quadratic Equations
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Factoring- 20x2-49x+30
(5x-6) (4x-5)
Quadratic Equation-ax2+bx+c=0
Functions
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Quadratic Functions-Graphing the Parabola y = ax2 + bx + c
1. Determine whether the parabola opens upward or downward.
a. If a > 0, it opens upward.
b. If a < 0, it opens downward.
2. Determine the vertex.
a. The x-coordinate is .
b. The y-coordinate is found by substituting the x-coordinate,
from
Step 2a, in the equation y = ax2 + bx + c.
3. Determine the y-intercept by setting x = 0.
4. Determine the x-intercepts (if any) by setting y = 0, i.e., solving the
equation
ax2 + bx + c = 0.
5. Determine two or three other points if there are no x-intercepts.
Remember point slope form and domains and ranges
Simplifying expressions with exponents
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(2r3s2)(-5r5s)
Solutions is –
10r8s3
Important to note that the powers add
together not multiply only the numbers
multiply together
Simplifying Expression with Radicals
Rationalizing Denominators-
2
2 2 2
*

 2
2
2
2
Now Onto
the Word
Problems
One rectangle’s length is five more (ft.) than
twice as long as the width. If the area of the
rectangle is 35ft what is the width
2w+5
w
So your
equation is
2w2+5=35
And your
solution is
W=the
square root
of 15
The sum of two numbers is
100. Five times the
smaller is 8 more than the
larger. Find the number(s)
The numbers are
18 and 82
A $200 coat is on sale for $166.
What is the percent of discount..
17%
You put $1000 into an investment
yielding 6% annual interest; you left
the money in for two years. How
much interest do you get at the end
of those two years?
I=Prt
I=Prt
$120
I=Prt
The sum of two numbers is
100. Five times the
smaller is 8 more than the
larger. Find the number(s)
The numbers are
18 and 82
Line of Best Fit
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Use this when- you have a linear
regression and you need to find a general
estimate of the best line.
Your Calculator helps by having the
technology to find the exact estimate and
pick any one of the x or y axis’s.
For extra help try these websiteshttp://www.mathtv.com/
http://www.coolmath.com/