Notesale: Turn your study into money

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Key Concepts & Things to Remember
The Real Numbers
Rational Number: any number that can be written in the form ab, where ‘a’ and ‘b’ are integers and b 0
...

Irrational Number: any number that cannot be written in the form ab, where ‘a’ and ‘b’ are integers and
b 0
...
(ex: is an irrational
number 3
...
)

Absolute Value


Answer is always a positive number, it is impossible to be negative

On a coordinate plane:
any number that can be written in the form ab, where ‘a’ and ‘b’ are integers and b 0
...

When multiplying radicals,, remember you multiply the outsides with the outsides, and the insides with the
insides
...
008

Zero exponent
 always equal to 1

Exponent Laws
 When multiplying powers with the same base, you ADD the exponents
 When dividing powers with the same base, you SUBTRACT the exponents
 When you have power of a power, you MULTIPLY the exponents and keep the base the same
 If a rational number (fraction) has an exponent, both the numerator and the denominator have the exponent
Fractional Exponents



Exponents of a power can be written as a fraction
stands for the root (ie: square root)
...

Factoring Quadratics
Factoring Trinomials in the Form of x2 + bx + c
o factor any common factor (if possible)
o write two sets of brackets with x as the first term in each bracket
o find two numbers that add to give you the middle term b AND multiply to give you the last term c
o write the two numbers as the second term in each bracket (one number in each bracket)
Factoring Trinomials in the Form of ax2 + bx + c
o If you have a trinomials in the form of ax2 + bx + c, where a 1, you can factor it by following the
steps below
 factor any common factor (if possible)

o












find two numbers that add to give you the middle term and multiply to give you the
product of the first and third term ac
replace the middle term with the the two terms you found just before
group the first two terms together, and group the other two together, then find a common
factor for each group
...
This is your
final answer!

Common Identities
a2 - b2

=

(a+b)(a-b)

a2 + 2ab + b2

=

(a+b)(a+b)

a2 - 2ab + b2

=

(a-b)(a-b)

a3 + b3

=

(a+b)(a2-ab+b2)

a3 - b3

=

(a-b)(a2+ab+b2)

a3+3a2b+3ab2+b3

=

(a+b)3

a3-3a2b+3ab2-b3

=

(a-b)3

Equations and Inequalities





Solving equations is trying to find the value of the variable
Remember what you do on one side you do to the other side of the equation ( ‘=’ sign)
o ex: (4x = 16) divide x by 4 and 16 by 4
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if there are brackets in the equation, remove them by using the distributive property
you always want to try to find the value of a POSITIVE VARIABLE

Solving Inequalities
 are similar to equations



instead of an equal sign, there is an inequality sign (<, >, , )
to graph using a number line, put a circle on the number of that value of an inequality
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o *tip: just follow the place it points
 ex: if the sign is ‘>’ then arrow points right so the number line should draw the line right
until the number line ends
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o Restrictions are basically any value of a variable that makes the denominator of a term 0
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o This is when you multiply the numerator of the RHS equation with the denominator of the LHS
equation, and the denominator of the RHS equation with the numerator of the LHS equation
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o Ex
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4x/5 = 6y → 4x = (6y)(5)
Graphing Linear Equations With 2 Variables
 A linear equation is an equation that graphs as a straight line
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Isolate for y (if necessary)
b
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Plot and join the points
Graphing Linear Inequalities
 To graph a linear inequality you must:
1
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Plot the points
3
...
Solid line, if you have a ‘’ or ‘’
b
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Pick a point that is not on the line
5
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True, shade the area the point is found in
a
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 Line segments falling to the left have negative slopes
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 Vertical line segments have an undefined slope
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o
o

m = RiseRun
m = y2 - y1x2 - x1

Parallel and Perpendicular Slopes
 When two lines have the same slope, they’re parallel
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o E
...
If two lines have the slopes 5 and -1/5 then they’re perpendicular
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o The equation would be in y=mx form where ‘m’ is the constant of proportionality
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 Partial Variation is a line where y varies partially as x
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o The graph would be a straight line which doesn’t pass through the origin
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Standard Form
 Ax + By + C = 0
o Where A, B, and , C are integers with no common factors between them
o A must be positive
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o To find the y intercept using this equation, substitute 0 for x and solve for y
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o Cross multiply and move all of the coefficients and variable to one side of the equations to get the
equation in standard form
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 In order to solve this by graphing, you must graph the two lines, and plot the point at which the two lines
intersect
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o Add or subtract the two equations and solve for the remaining variable
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Solving Linear Systems by Substitution
 In order to solve linear systems by substitution:
o Solve one equation for one of its variables
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Solving Word Problems
 To solve a word problem using linear systems:
o Identify the unknowns, and assign variables to them using let statements
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o Solve the systems using either elimination or substitution
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 Remember to use concluding statements when answering these word problems

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