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# alg. midterm vocab

### vocabulary for chapters 1-6

Question | Answer |
---|---|

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