 # Algebra One Math Vocabulary.

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Algebra One Math Vocabulary

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

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:

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

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}

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

Coordinate Plane A plane formed by a horizontal number line (x-axis)
and a vertical number line (y-axis) Example:

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

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}

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

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

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

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)

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

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

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

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

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

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

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

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)

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

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

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

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

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)

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

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

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

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)

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