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 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 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) ¾ 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^2yz^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 = 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	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 = 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 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 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 = ax^2 + bx + c, where a not = 0 a parabola. vertex.
The vertex has an x-coordinate, Vx, found by ____ that also tells us ___________________________ The vertex has a y-coordinate, Vy, 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 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 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 x-intercepts
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 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 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 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 ___________	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^m-n
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 slope-intercept form. Use a dashed line if there is no =