The
following is a list of information that each student must transfer (hand
written) to
flashcards. The front and back of the flashcards should each be
written in a different color.
The
front of each card should also have a small number in the upper right hand
corner
identifying
which chapter it belongs to.
Front 
Back 
Chapter 1 

a letter used to
represent an unknown number 
variable 
to rewrite an
expression in its simplest form [solve] 
simplify 
to replace
variables with numbers and then simplify 
evaluate 
The ____________
says that an expression may be replaced by another expression that has the
same value. 
substitution
principle 
words that mean
addition 
sum, plus, and,
increased, more than 
words that mean
subtraction 
difference, minus,
decreased, less than, remainder 
words that mean
multiplication 
product, times,
of, by 
words that mean
division 
quotient, divided,
ratio, parts of 
When translating
less than 
reverse the order 
translate: a number is six
less than twice another number 
x = 2y 6 
When translating
__________, __________, and __________ you
probably use ( ). ex.
translate: twice the sum of a and b. 
the sum of __ and
__, the quantity, which is 2(a+b) 
In a word problem
the verb (usually is) represents _______ 
= 
The order of
operations used to simplify an expression is _______________ 
G grouping (),
[], 1+2 E exponents 3 M multiplication D division A addition S subtraction 
Represents two
things that are equal to one another [problem with an = sign] 
Equation 
An equation with
one or more variables 
Open Sentence 
Any value of a
variable that turns an open sentence into a true statement [solution to an
equation] 
Root 
One or more terms
connected by plus or minus sign. [problem with out an = sign] (Ex. 3 + a, 4y 
z) 
Expression 
The given set of
numbers that a variable may represent. [input values] Written with the
symbol ______ 
Domain Є 
The set of
corresponding positive and negative numbers and zero (Ex.
, 2, 1, 0,
1, 2,
) 
Integers 
The entire
collection of integers and positive and
negative fractions 
Rational numbers 
Numbers that
cannot be expressed as the ratio of two integers 
Irrational numbers 
The set of
rational and irrational numbers 
Real numbers 
The representation
of real numbers as points on a line 
Number line (or number scale) 
The distance
between a number and zero on the number line 
Absolute value 
Symbol used to represent
the absolute value of a number, n 
n 
If one number is
greater than another 
Then it is higher
or further to the right on a number line 
The value of a
number 
a numbers
distance and direction from zero 
The absolute value
is 
Absolutely
positive! 
Chapter 2 

Commutative
Property 
the order in which
you add or multiply real numbers does not affect the result. a + b = b + a ab = ba (for all real numbers a,b) 
Associative
Property 
if you are only
adding or multiplying real numbers the grouping of the numbers does not
affect the result (a + b) + c = a +
(b + c) and (ab)c = a(bc) (for all real numbers a,b,c) 
________________
sometimes makes adding or multiplying groups of numbers much easier. ex. 4*17*25*10 = ______ 
Associative
property 17,000 
Distributive
Property 
a(b + c) = ab +
ac (for all real numbers a,b,c) 
We use the
distributive property for two reasons: 
1. when we get
stuck simplifying with GEMDAS [to destroy parenthesis] 2. to simplify
addition and multiplication. 
Use the
distributive property to multiply
3*6.3 
3*6.3 = 3(6 + 0.3) =
18 + 0.9 = 18.9 
Use the
distributive property to solve 75*17 + 25*17 
17(75 + 25) 17(100) = 1,700 
If equals are +, , *, / to equals 
The results are equal 
Either a single number or letter or the product (or quotient) of several numbers or letters. [Things added together] ex. 7, 5ax,
2(a+b), 3yz/2. 
Term 
What happens when
you divide a number by zero? (Ex. 5/0, y/0, or
3/x if x = 0) 
Undefined (meaningless) 
Expressions that
are equal to the same quantity are 
Equal 
To add numbers
with the same sign 
add the numbers
and keep the sign 
To add numbers
with different signs 
subtract the
numbers and keep the sign of the larger number. 
Rules for
Multiplication: For any real
number a a*1 = _____, a*0 = _____, a(1) = _____ If two numbers
have the same sign, their product is If two numbers
have different signs their product is 
a, 0,
a positive negative 
A negative times a
negative = 
a positive 
If you multiply an
even number of negatives the answer will be _________ 
positive 
If you multiply an
odd number of negatives the answer will be _________ 
negative 
The reciprocal of
3/4 is ________ 
4/3 
Any real number
divided by itself is _____ 
1 
Fill in the
blanks: a) 1 + ____ =
0 b) 2 + ____ = 0 c) 3/4 + ____ =
0 d) 1(____) = 1 e) 2(____) =
1 f) 3/4(____) = 1 
a) 1 b) 2 c) Ύ d) 1 e) ½ f) 4/3 
dividing by 2 is
the same as multiplying by _____ 
½ 
Rules for
division: If two numbers
have the same (different) sign, their quotient is __________ (___________) 
positive
(negative) 
Chapter 3 

equation 
a mathematical way
to represent a balanced system. 
operations that
undo each other 
inverse operations 
To solve an
equation for a specific variable we need to _______________________________ 
get the variable
alone on one side of the equal sign. 
Steps for solving
equations 
1) Rewrite the
equation and simplify each side. 2) Write the
inverse operation needed on both sides to get the variable alone and draw a
line underneath. 3) Perform the
inverse operation for each side of the equation always keeping things lined
up. 4) Go back to step
2) as needed(reverse GEMDAS) 5) Check 
Identity 
An equation that
is true for all values of the variable [something = itself] 
To solve
membership problems, write an equation with the cost of the 1^{st}
plan _________________ 
equal to the cost
of the 2^{nd} plan. 
To solve cost,
income, value problems we usually need 2 equations: 
1) # (number of items) 2) $ (cost/value of items) 
Ch. 4 

b^{n} = The b is called
the ____________ The n is called
the ____________ 
b*b*b*b
(b times
itself n times) (if b is any real
number and n is any + integer) base exponent 
(2y)^{3 }=
_______________ 2y^{3 }=
_______________ 
(2y)(2y)(2y) 2*y*y*y 
One of the numbers or letters multiplied together to make up a term. [Things multiplied together] 
factors 
Any factor (or group of factors) is called the _________ of the product of the remaining factors. [The number in front of the
variable(s)] 
coefficient 
In the term 3xy^{2}, 3 is the _____________ of xy^{2} 
numerical
coefficient 
An expression that
is either a numeral, a variable, or the product of a numeral and one or more
viariables. [A polynomial with
one term.] 
monomial 
A monomial that is
just a numeral such as 14 
constant 
A sum of monomials ex. x^{2}
4xy + y^{2} 5 
polynomial 
A polynomial with
two terms ex. 2x 9 or 2ab
+ b^{2} 
binomial 
A polynomial with
three terms ex. x^{2}
4x 5 or a^{2} + 3ab 4b^{2} 
trinomial 
Terms that have
the exact same variable parts. You can only add
_______________ 
like terms 
__________ is the
process of combining the like terms in an expression. (Show by making _____) 
Simplifying Vs 
The number of
times that the variable occurs as a factor in the monomial. (What is the
exponent?) 
degree of a
variable in a monomial 
degree of a
monomial 
the sum of the
degrees of its variables (add the exponents
of the variables) 
degree of a polynomial 
the greatest of
the degrees of its terms after it has been simplified. 
For the monomial
5x^{2}yz^{4} what is the degree
of x? what is the degree
of z? what is the degree
of the entire monomial? 
2 4 7 (because 0 + 2 + 1 + 4 = 7) 
To multiply powers
of the same base: keep the base and
_____________________ 
add the exponents 
a^{m}*a^{n}
= __________ 
a^{m+n} 
b^{2}*b*2b^{6}
= ______ 
2b^{9} 
To find a power of
a power of a base: keep the base and
_____________________ 
multiply the
exponents 
(a^{m})^{n}
= __________ 
a^{mn} 
To multiply
polynomials by monomials we just use
________________________ 
the distributive
property. 
To multiply
polynomials by polynomials we just use
________________________ 
the distributive
property more than once.Officially: 1. distribute each
term of the 1^{st} polynomial 2. Simplify
(combine like terms) 
an equation used
to express a rule in concise form 
formula 
Distance =
______________________ 
Rate * Time 
It is customary to
arrange polynomials with 
1. the variables
of a term in alphabetical order. 2. the terms in
descending powers of one of the variables that appears most frequently. 
Ch. 8 

a set of
coordinates that serve to locate a point on a coordinate system 
ordered pair 
Tell whether each
is + or In quadrant I x is _____ and y is ______ In quadrant
II x is _____ and y is ______ In quadrant
III x is _____ and y is ______ In quadrant
IV x is _____ and y is ______ 
+, + , + ,  +,  
If an ordered pair
is a solution to an equation it will produce ____________ 
an identity 
Special points at
which a line cuts the axes. 
intercepts 
How do you find
the x intercept 
set y = 0 and
solve the resulting equation for x 
How do you find
the y intercept 
set x = 0 and
solve the resulting equation for y 
Linear equations
in standard form 
ax + by = c a, b, and c are integers. 
The steepness of a
line 
slope 
slope = 
rise
= vertical change = y_{2} y_{1} run horizontal change x_{2} x_{1} 
When reading from
left to right: lines that go up
have ___________ slope lines that go down
have ___________ slope 
positive negative 
The steeper the
line 
The greater the
absolute value of the slope 
If a line is
straight 
Then its slope is
constant 
The slope of a
horizontal line 
zero 
The slope of a
vertical line 
no slope 
Slope Intercept
Form of a linear equation 
y = mx + b m = slope, b = y intercept (for all
real numbers m and b) 
If the lines have
the same slope 
Then they are
parallel. 
If the lines have
 reciprocal slope 
Then they are perpendicular. 
The three steps to
write the equation of a line in slope intercept form are: 
1. find slope
(m) m = y_{2} y_{1} x_{2}
x_{1} 2. find y
intercept (b) substitute x, y, and
m
into y = mx + b and
solve for b 3. write the
equation substitute m and b
into y
= mx + b 
In a function, the
independent variable is ________ technically know
as _________ 
the input the domain 
In a function, the
dependent variable is _________ technically know
as __________ 
the output the range 
Ch. 9 

Two or more
equations in the same variable form 
a system of linear
equations 
To solve a system
of two equations with two variables, you must 
find all ordered
pairs (x, y) that make both equations true. 
We have learned
three methods for solving a system of linear equations, they are 
the graphing
method, the substitution method, and the addition or subtraction method. 
The three possible
solutions to a system of linear equations. 
1. point or
ordered pair  the lines cross 2. no solution
the lines are parallel 3. infinite
solutions the same line (equation) 
The steps of the
Graphing Method are 
1. Solve each
equation for y to get y = mx +b form. 2. Find b, the
yintercept, on the graph. 3. Use m, the
slope, to graph the line. 4. Write the
solution 5. Check 
The steps of the
Substitution Method 
1. Solve one equation
for one of the variables. 2. Substitute this
expression into the other equation and solve for the other variable. 3. Substitute this
value into the equation in Step 1 to find the value of the first variable. 4. Check 
The steps of the
AdditionorSubtraction Method 
1. Multiply one or
both equations to get the same or opposite coefficients for one of the
variables. 2. Add or Subtract
the equations to eliminate one variable. 3. Solve the
resulting equation for the remaining variable. 4. Substitute this
value into either original equation to find the value of the first variable. 5. Check. 
Ch. 5 

Things added
together. 
Terms 
Things multiplied
together. 
Factors 
Canceling, any
number divided by itself = ______ 
One 
You may cancel any
common ________ but not common _______. 
factors, terms. 
The largest shared
factors (numeral and literal) 
GCF (Greatest
Common Factor) 
Undistributing [what can each
term be divided by?] (expressing a
number (or algebraic expression) as a product of certain
factors.) 
Factoring 
A fraction bar is
a _____________. When you get stuck with GEMDAS
you must ______________. 
grouping distribute 
(x 3) and (3
x) are __________. To make them
factorable (the same) rewrite (3 x) as _________ 
opposites 1(x 3) 
The first step of
factoring is to ___________ 
take out the GCF
if possible. 
To factor 4 terms 
1. Consider factor
by grouping. 2. Then factor the
common polynomial factors 
To factor 3 terms
of the form ax^{2} + bx + c 
1. Find 2 factors
of a*c that add to b. 2. Use these
factors to rewrite the trinomial with 2 x terms (4 terms total)* then follow
the steps for 4 terms * if a = 1,
then only 1 step (x )(x ) 
To factor 2 terms 
Is it A^{2}
B^{2} ? (A + B)(A
B) [the good times and the
bad times] but A^{2}
+ B^{2 } is forever. 
Zero Product
Property: If the product of
factors = 0 ab = 0 
Then one or more
of the factors = 0 a or b = 0. 
Factoring is often
used to _________ polynomial equations by using
these 3 steps 
solve 1. rewrite in
standard form (ex. ax^{2} + bx + c = 0) 2. factor
completely 3. set each factor
= 0 and solve. 
Ch.11 & 12


Radical Rules: √a*b = ___________, √a/b = ____________, you
can only add __________________ 
√a * √b, √a/√b like √ 
Simplifying
Radicals: 
1. No perfect squares inside √ 2. No fractions inside √ 3. No √ in
the denominator 
( )^{2} and √ are ____________________ they ____________ each other. 
inverse operations undo each other. 
To solve √ equations 
1. get the √ alone 2. ( )^{2} both sides. 
Now we can solve unfactorable (prime) quadratic equations by ___________________________ 
completing the square. 
Completing the
square will solve ______ quadratic equation using
these 5 steps. 
1. Get into x^{2} + bx = c form. 2. Add (b/2)^{2} to both sides. 3. Factor into the perfect square, (x + b/2)^{2} 4. √ both sides 5. Solve for x 
The quadratic
formula =_____________________ We derive it by
____________________________ 
b ± √ b^{2} 4ac 2a completing the
square. 
Graphing NonLinear Equations 

A quadratic function is one that can be written in the standard form _____________________. When graphed it forms ______________. with a turning point called the ___________. 
y = ax^{2}
+ bx + c, where a
not = 0 a parabola. vertex. 
The vertex has an xcoordinate, V_{x}, found by ____ that also tells us ___________________________ The vertex has a ycoordinate, V_{y}, found by _____ 
b/2a the axis of
symmetry (x = b/2a) substituting x
back into the function. 
To graph quadratic functions by hand: 
1. Get it in
standard form. 2. Find V_{x} 3. Make a table of
x & y values, using xvalues to the left and right of V_{x}_{} 4. Plot the
ordered pairs and connect with a smooth curve. 
a,b,c effects on the graph: a b c 
Smile if positive
and frown if negative. Big number if
skinny and small number if wide. Moves the vertex
side to side and up and down. Moves the vertex
up and down only. 
The solutions of a quadratic equation are the _____ They can be found ___________ or ____________ by identifying the _______________ 
roots algebraically,
graphically xintercepts 
The discriminant, ________________, tells us _________________________________ 
b^{2}
4ac the number of
solutions (+ = 2, 0 = 1, = none) 
Be able to describe the graphs of: y = x^{2} y = x^{3} y = x^{4} y = √x 
Parabola Bipolar parabola
(½ happy, ½ sad) Skinnier parabola Parabola opening
to the right 
Be able to describe the graphs of: y = 2^{x} y = (½)^{x} y = 2x 4^{} y = 2/(x+1) 
Exponential growth Exponential decay V Reflection 
The exponential growth model 
FV = PV(1 + r)^{t} 
The exponential decay model 
FV = PV(1  r)^{t} 
Rational Expression 
Algebraic Fraction 
Anything divided by 0 is ______________ 
undefined 
Any x or y values that make the denominator of a rational expression 0 create _________________ The graph of the rational function will _________ but never ________ them. 
asymptote lines. get close intersect 
Ch.6 

If a fraction is in simplest form 
Then the numerator and denominator have no common factor other than 1 and 1 
To simplify an algebraic fraction To multiply algebraic fractions 
1. factor the numerator and denominator (remember to look for opposites) 2. state restrictions (denominator cant = 0) (set each factor in denominator = 0 and solve) 3. cancel any common factors 
To multiply algebraic fractions 
Use the same rules as simplifying. 
To divide algebraic fractions 
Multiply by its reciprocal. 
To find the GCF 
1. find the prime factorization (factor tree) 2. circle and multiply the common factors 
To find the LCM 
multiply the GCF by all the leftovers in the factor trees. 
If we multiply the numerator and denominator of a fraction by the same non zero number or ________ Then we get an ___________ in a _____________. 
adjustment fraction equivalent fraction different form 
To + or  fractions with common denominators: 
1. + or the numerators 2. keep the common denominator. 3. simplify. 
To + or  fractions with different denominators: 
1. rewrite with factored denominators and space for adjustment fractions 2. find the LCD (LCM of the denominators) and write it off to the side. 3. write in the adjustment fractions needed to produce the LCD. 4. follow the rules for + or  fractions with common denominators. 
Ch.7 

A ratio is just a ____________ 
fraction (of 2
quantities measured in the same units) 
I say the ratio is 3:2, you say ________ 
3x, 2x 
A proportion is just ___________ 
equal ratios. (We use them to solve problems containing
four terms that compare similar objects or situations.) 
In a proportion the 1^{st} and 4^{th} terms are the ______ and the 2^{nd} and 3^{rd} terms are the ______. 
extremes means 
To solve a proportion ______________ 
cross multiply (product of the
means = product of the extremes) 
To eliminate fractions from an equation 
Multiply
everything by the LCD 
% increase (decrease) = 
1. amount of
increase (decrease) original amount 2. covert the
decimal to a percent. 
discount (markup/sales tax) = new price = 
original price *
rate of discount (markup/sales tax) original price
discount (or + markup/sales tax) 
commission earned = 
sales * commission
rate 
profit = 
revenues 
expenses 
The equation for direct variation 
y = kx (k is a nonzero constant) 
The equation for inverse variation 
y = k/x (k is a nonzero constant) (x not = 0) 
The law of levers 
(weight)(distance) = (weight)(distance) Left Right 
Mixture problems are just like _______ problems. We need to write 2 equations, 1 for the _________ and 1 for the ___________ 
coin amount value 
Work problems are set up using ______________ and solved with the fact that _________________ 
Rate of work * Time = work Done work done by A + work done by B = 1 job. 
The rate of work is expressed as a ____________ 
reciprocal. 
(a/b)^{m} = 
a^{m}/b^{m} (for every positive integer m) 
A nonzero number to the zero power is ____ 
One 
Negative exponents mean ______________ Ex. a^{n }= ____ 
take the reciprocal 1/a^{n} 
To divide powers of the same base: keep the base and _____________________ a^{m}/a^{n} = __________ 
subtract the exponents a^{mn} 
To find a power of a quotient __________ (a/b)^{m} = __________ 
Find the power of the numerator and denominator then divide. [distribute the power (top & bottom)] a^{m}/b^{m} 
Scientific Notation is used to 
write very big or small numbers. 
Numbers in Scientific Notation have the form 
x.xx * 10^{n} one
digit before the decimal, no extra zeros, 10 to nth power 
The exponent, n, tells you 
how many places to move the decimal point 
With Scientific Notation the exponent n is __________ for large numbers n is __________ for small numbers 
positive negative 


Ch.10 

When solving linear inequalities if you multiply or divide by a negative number you must ________ 
Reverse the inequality symbol 
To solve compound inequalities 
solve two separate problems 
and means or means 
overlap all 
To solve absolute value equations and inequalities: 
Get the absolute value alone then Solve two separate problems, a positive and negative version. 
To graph linear inequalities in two variables 
Use slopeintercept form. Use a dashed line if there is no = 























