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Algebra One Math Vocabulary

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**A number’s distance from zero on a number line.**

Absolute Value A number’s distance from zero on a number line. Examples: 3

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Algebraic expression A mathematical phrase that can include numbers, variables, and operation symbols Examples: 3x2 + 2y + 7xy + 5 3x + 12 – x + 2 or 2x + 14 Write an algebraic expression For the sum of six and a number: 6 + x Evaluate the algebraic expression if x = 2:

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**Coefficient The numerical factor of a variable term**

A number that multiplies a variable in a term Examples: The coefficients are in red coefficient variable exponent

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**Combinations An arrangement of the elements of a set**

without regard to order Examples In how many different ways can three letters be chosen from the letters A, B, C, D, and E? ( The order of the three letters is not important: so, {A,B,C} and {C,B,A} are the same) {A, B, C} {A, B, E} {A, C, E} {B, C, D} {B, D, E} {A, B, D} {A, C, D} {A, D, E} {B, C, E} {C, D, E}

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**A term that has no variable factor**

Constant A term that has no variable factor Examples Constant Constant Constant Coefficient Variable Constant

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**Coordinate Plane A plane formed by a horizontal number line (x-axis)**

and a vertical number line (y-axis) Example:

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**Distance Formula The distance d between any two points and is Examples**

The distance between (-3,2) and (0,-2) is: (-3,2) (0,-2) 4 3 5

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Domain and Range Domain: The set of all x-coordinates in the ordered pairs (x,y) of a relation Range: The set of all the y-coordinates in the ordered pairs (x,y) of a relation Examples x y 1 -1 Domain: {1,2,3,4} Range: {2.4,6,8} Domain: {1,0,-1} Range: {1,0}

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**Equations (solving) An equation is a mathematical sentence**

containing an equal sign To solve an equation, find a value for the variable that makes the sentence true Examples

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**Equations (graphing) The graph of an equation contains ordered pairs**

that make the equation true Examples x Y=2-x 2 1 -2 4 x y=x-3 -3 3 -2 -5

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**Equations (slope-intercept)**

The slope-intercept form of an equation is y = mx + b Where m is the slope of the line and b is its y-intercept Examples slope = -1 y-int = 2 slope = 1 y-int = -3 slope = 2 y-int = -3

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Factoring To write an expression (or number) as a product of two or more expressions (or numbers ) Examples Factor 3x+6 = 3(x+2) x2-2x-15 = (x-5)(x+3) Factor tree Factor x2 + 3x + 2 (x + 1) (x + 2) (x + 1)(x + 2)

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Function notation A way to write an equation or rule that is a function, use the symbol f (x) in place of y f(x) is read “f of x” and means that the value of the function depends on the value of x f(x) is the output of the function with input x (Given an x, you get f(x) or y) Examples f(x) = x+3 f(2) = 2+3= 5 when x=2, y=5 (2,5) f(x) = x2 f(-3)=(-3)2 = 9

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**using <, >, <, >, or**

Inequalities (number line) The graph of a mathematical sentence showing the relationship between quantities that are not equal, using <, >, <, >, or Examples

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**Inverse Examples Addition and subtraction are inverse operations**

Operations that undo each other Examples Addition and subtraction are inverse operations (undo adding 3 by subtracting 3) Multiplication and division are inverse operations (undo multiplying by 2 by dividing by 2) To solve an equation: x + 3 = 5 x + 3 – 3 = 5 – 3 x = 2

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**Irrational Numbers A number that cannot be written**

as a ratio of two integers Numbers in decimal form that are non-terminating and non-repeating Examples Real Numbers Rational Numbers Irrational numbers Integers Whole Natural

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Line of best fit A straight line that best fits the data on a scatter plot (This line may pass through some, none, or all of the points) Examples

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**Linear systems: Elimination A method of solving a system of equations**

with two variables to reduce it to an equation with only one variable by eliminating one of the variables by addition/multiplication Examples

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**Linear systems: Substitution**

Example To solve a system by substitution, solve one equation for one variable in terms of the other, Substitute into the other equation to obtain an equation with only one variable

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**The midpoint of a line segment with endpoints and**

Midpoint formula The midpoint of a line segment with endpoints and is Examples A B A: (-4,3) and B(2,-5)

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**Permutations An arrangement of elements in which order is important**

Examples MATH: how many ways can two letters be arranged from the four letters M, A, T, and H? 12 possible permutations: MA, AM, MT, TM, MH, HM, AT, TA, AH, HA, TH, HT CAT: How many permutations are there of the letters C A T ? 6 possible permutations: CAT, CTA, ATC, ACT, TAC, TCA

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Polynomial An expression that is the sum (or difference) of more than one term, each of these having variables with whole number exponents (A quotient with a variable in the denominator is not a polynomial) Some polynomials have special names Examples Not a polynomial

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**Pythagorean Theorem In a right triangle, the sum of the squares of the**

length of the legs is equal to the square of the length of the hypotenuse: 5 3 4 5 13 15 8 17 12

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**An equation of degree two: ax2 + bx + c = 0**

Quadratic Equation An equation of degree two: ax2 + bx + c = 0 Example To solve:

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**Discriminant Quadratic formula The part of the quadratic formula**

Examples The part of the quadratic formula that is under the radical: It tells the nature of the roots: how many and whether they are real (D>0) or not (D<0)

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**Ratio, Proportion Ratio: A comparison of two numbers by division.**

Proportion: An equation stating that two ratios are equal. If the cross products of the two ratios are equal, then the pair forms a proportion Examples is a proportion because 12x1 = 3x4 do not form a proportion because 15x2 5x7

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**The ratio used to enlarge or reduce**

Scale Factor The ratio used to enlarge or reduce similar figures Examples Drawings: if the Eiffel Tower is 1000 feet tall and the drawing of it was 1 foot tall, the scale factor would be Models: if a car is 204” in length and the length of a model of the car is 12” long, the scale factor would be

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**Real Number A number that is either rational or irrational.**

Real numbers include natural numbers, whole numbers, integers, rational numbers and irrational numbers Examples Real Numbers Rational Numbers Irrational numbers Integers Whole Natural

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**Slope A measure of the steepness of a line**

The ratio of the vertical change (rise) to the horizontal change (run) The change in y over the change in x Slope = = = where The symbol for slope is m rise = -2 run = 4 (-2,3)

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**Subset A set whose elements are all elements of another set**

A set contained within a another set The symbol for subset is Examples The set {a,b,c} has subsets: {a}, {b}, {c}, {ab}, {ac}, {bc},{a,b,c} and { } The set of Rational numbers is a subset of the set of Real numbers, All Rational numbers are Real numbers

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