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alg. midterm vocab

vocabulary for chapters 1-6

Symbols of Inclusion ( ), { }, [ ], or a vinculum.
Vinculum The fraction bar that is a symbol of inclusion but also can mean do whatever is underneath first.
Opposite Two numbers (that are the same but with a different sign) that add up to zero.
Absolute Value On a number line, the positive distance from the origin.
Positive Numbers A number greater than zero.
Negative numbers A number less than zero,
Integers A whole number or it's opposite, not including the fraction in between.
Real Numbers Any number on a number line including negative and positive numbers, fractions, decimals, and 0.
Subtraction To add the opposite.
Multiplicative Inverse to multiply by the reciprocal to get the answer of one
Reciprocal what you multiply a number by to get the answer of one
Dividing Multiply by the reciprocal
Commute to interchange to numbers in an expression
Binary addition and multiplication
Associate To group numbers with parentheses without changing their positions
Distance d=rt, measure of horizontal motion
Multiplication by -1 x times -1 = -x
Sign of a product The sign of a product will be negative if it has an uneven amount of negative factors, and positive if it has an even amount of negative factors.
Sign of a power and a negative number A negative number in parentheses raised to an odd exponent is negative, and to an even exponent is positive. If it is not in parentheses, it will always be negative no matter what the exponent is.
Commuting terms You can commute terms in a sum
Commuting factors You can commute factors in a product
Associating terms You can associate any two terms in a sum
Associating factors You can associate any two factors in a product
Arithmetic Operations add, subtract, multiply, and divide
expression a group of constants, variables, symbols of inclusion, and operation signs.NOT = though.
evaluate to find the number for which the expression stands
variable a letter that represents a constant
constants symbols that always stand for the same number
substitute to replace a variable with a constant
Terms numbers that are added or subtracted from each other
factors numbers that are multiplied together
Power A base raised to an exponent
Exponent A number that tells how many times to multiply the base
base A constant or variable that tells what number is to be multiplied
order of operations PEMDAS
Equation two expressions set equal to each other
Solution A number you can switch with the variable to make the equation true
Transforming an equation do the same thing to each member
perimeter the distance around a figure
area the measure of space inside a polygon
right member the expression on the right side of the equation
left member the expression on the left side of the equation
simple interest the amount of money you earn on a deposit yearly
Property a fact that is true concerning a mathematical system
Axiom a property assumed to be true without proof
Distributive axiom Multiplication distributes over addition: x(y+z)= xy+xz. Multiplication distributes over subtraction: x(y-z)=xy-xz.
Like terms two terms are like terms if they the SAME variables raised to the SAME powers.
Numeral coefficient the constant multiplied by the variable.
Common factor the common factor of each term in an expression, finding them is called factoring; the opposite of distributing
Commutative axiom of addition x+y=y+x
Commutative axiom of multiplication xy=yx
Associative axiom of addition (x+y)+z=x+(y+z)
Associative axiom of multiplication (xy)z=x(yz)
Additive identity axiom x+0=x
Multiplicative identity axiom y x 1= y
Multiplicative inverse axiom y x 1/y =1
Additive inverse axiom x+(-x)= 0
Multiplication Property of -1 -1 x X= -x
Multiplication property of zero X x 0= 0
Transitive axiom of equallity if x=y and y=z then x=z
Symmetric axiom of equality if x=y then y=x
Reflexive axiom of equality x=x
Additive property of equality if x=y then x+z=y+z
Multiplicative property of equality if x=y then xz=yz
Identity solution an equation that is true for all variable values
conditional equation an equation that is true for some variable values
literal equation an equation that uses letters in the place of one or more constants
formula an equation that tells what one variable or constant can be found by solving the equation on the other member
Polynomial an expression that has no operations other than addition, subtraction, or multiplication by or of the variable, or an expression with more than three terms.
Monomial a polynomial with one term
binomial a polynomial with two terms
trinomial a polynomial with three terms
degree the degree of a polynomial is the highest power of that variable
linear a first degree polynomial
quadratic a second degree polynomial
cubic a third degree polynomial
Multiplying two binomials first multiply each term of one binomial by each of the other then combine like terms
factoring a polynomial to transform a polynomial to a product of two or more factors
prime polynomial A polynomial whose only factors are one and itself
leading coefficient a term that has a coefficient other than one
conjugate binomials binomials that are the same except for the sign between the terms
difference of two squares the factors of a difference of two squares are conjugate binomials;a^2 -b^2
Binomial square pattern first square the first term then add twice the product if the two terms then add the square of the last term
trinomial square the first and last terms must be perfect squares so they can be factored
square root the square root of n gives n for an answer when it is squared
radical a square root symbol, a vinculum, and a radicand
rational number a number that can be written as a ratio of two integers
irrational number a number that cannot be written as the ratio of two inegers
closure under x a set of real numbers is closed under multiplication if any number in the set times another number in that same set will give you a unique number in that set
closure under + a set of numbers is closed under addition if any given number in a set added to another number in that same set will give you a unique number in that set
closure a given set of numbers is closed under an operation if there is just one answer and that answer is in the set whenever that operation is performed with that set
not a real number a number not found anywhere on a number line
Quadratic formula x equals the opposite of b plus or minus the square root of the quantity b squared minus four ac all divided by two a
radicand a number that appears under the vinculum
solution set the set of all solutions to an equation
solving an equation writing the equation's solution set
empty set a solution with no numbers in it
square root property of equality if two numbers are equal then their positive square roots are equal
Square root of a perfect square the square root of a number squared = | number |
completing the square if the coefficient equals one then to complete the square you do the following: take half the coefficient of x, square it, and change the third term to that number by transforming
quadratic formula 2 If ax^2+bx+c=0 and a does not =0 then (the quadratic formula). The restriction a does not equal 0 is needed for 2 reasons; 1 if a were 0 then the equation would not be quadratic and you would not need the formula. 2, if a were 0 it would lead to / by 0.
Vertical motion formula d=rt-5t2; if an object is thrown into the air with and initial upward velocity of r meters per second the its distance, d meters, above it's starting point at time, t seconds, after it is thrown.
discriminant b^2-4ac which appears in the quadratic formula.
velocity the amount of thrust put onto an object
initial velocity the amount of thrust put on an object that you start with.
Created by: Eliseyo