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. 




Chapter 1


a letter used to represent an unknown number


to rewrite an expression in its simplest form [solve]


to replace variables with numbers and then simplify


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


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”


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]


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]


One or more terms connected by plus or minus sign. [problem with out an = sign]

(Ex. 3 + a, 4y - z)


The given set of numbers that a variable may represent. [input values]

Written with the symbol ______




The set of corresponding positive and negative numbers and zero

(Ex. …, -2, -1, 0, 1, 2, …)


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


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 number’s 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



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.


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


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



A negative times a negative =

a positive

If you multiply an even number of negatives the answer will be _________



If you multiply an odd number of negatives the answer will be _________



The reciprocal of –3/4 is ________


Any real number divided by itself is _____


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 _____


Rules for division:

If two numbers have the same (different) sign, their quotient is __________ (___________)



positive (negative)

Chapter 3



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


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 1st plan _________________


equal to the cost of the 2nd plan.

To solve cost, income, value problems we usually need 2 equations:

1) #  (number of items)

2) $  (cost/value of items)

Ch. 4


bn =


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)



(2y)3 = _______________

2y3 = _______________



One of the numbers or letters multiplied together to make up a term. 

[Things multiplied together]



Any factor (or group of factors) is called the _________ of the product of the remaining factors.

[The number in front of the variable(s)]




In the term –3xy2,  -3 is the _____________ of xy2

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.]


A monomial that is just a numeral such as 14


A sum of monomials

ex. x2 – 4xy + y2 – 5


A polynomial with two terms

ex. 2x – 9 or 2ab + b2


A polynomial with three terms

ex. x2 – 4x – 5 or a2 + 3ab – 4b2


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 _____)



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 5x2yz4

what is the degree of x?

what is the degree of z?

what is the degree of the entire monomial?




7  (because 0 + 2 + 1 + 4 = 7)

To multiply powers of the same base:

keep the base and _____________________


add the exponents

am*an = __________


b2*b*2b6 = ______


To find a power of a power of a base:

keep the base and _____________________


multiply the exponents

(am)n = __________


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 1st polynomial

2. Simplify (combine like terms)

an equation used to express a rule in concise form


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.


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 =

rise  =  vertical change       =  y2 – y1

run       horizontal change       x2 – x1

When reading from left to right:

lines that go up have ___________ slope

lines that go down have ___________ slope




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


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 =  y2 – y1

                                                            x2 – x1

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 y-intercept, 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 Addition-or-Subtraction 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


3. Solve the resulting equation for the remaining


4. Substitute this value into either original equation

    to find the value of the first variable.

5. Check.

Ch. 5


Things added together.


Things multiplied together.


Canceling, any number divided by itself = ______


You may cancel any common ________ but not

common _______.

factors, terms.

The largest shared factors (numeral and literal)

GCF (Greatest Common Factor)


[what can each term be divided by?]

(expressing a number (or algebraic expression) as a

product of certain factors.)


A fraction bar is a _____________.  When you get

stuck with GEMDAS you must ______________.



(x – 3) and (3 – x) are __________.  To make them factorable (the same) rewrite (3 – x) as _________


-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 ax2 + 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 A2 – B2 ?

(A + B)(A – B)        [the good times and the bad times]

but A2 + B2   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


1. rewrite in standard form (ex. ax2 + 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 x2 + 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 ± √ b2 – 4ac


completing the square.

Graphing Non-Linear 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 = ax2 + bx + c, where a not = 0

a parabola.


The vertex has an x-coordinate, Vx, found by ____

that also tells us ___________________________

The vertex has a y-coordinate, Vy, found by _____


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 Vx

3. Make a table of x & y values, using x-values to

    the left and right of Vx

4. Plot the ordered pairs and connect with a smooth


a,b,c effects on the graph:






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 _______________


algebraically, graphically


The discriminant, ________________,

tells us _________________________________

b2 – 4ac

the number of solutions (+ = 2, 0 = 1, – = none)

Be able to describe the graphs of:

y = x2

y = x3

y = x4

y = √x



Bipolar parabola (½ happy, ½ sad)

Skinnier parabola

Parabola opening to the right

Be able to describe the graphs of:

y = 2x

y = (½)x

y = |2x – 4|

y = 2/(x+1)


Exponential growth

Exponential decay



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 ______________


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




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 can’t = 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


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.



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 1st and 4th terms are the ______ and the 2nd and 3rd terms are the ______.



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 non-zero constant)

The equation for inverse variation

y = k/x     (k is a non-zero 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 ___________




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 ____________


(a/b)m =

am/bm        (for every positive integer m)

A nonzero number to the zero power is ____


Negative exponents mean ______________

     Ex.  a-n = ____

take the reciprocal


To divide powers of the same base:

keep the base and _____________________

am/an = __________


subtract the exponents


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)]


Scientific Notation is used to

write very big or small numbers.

Numbers in Scientific Notation have the form

             x.xx * 10n

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







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



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 slope-intercept form.

Use a dashed line if there is no =