Algebra 1 Honors Vocabulary
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Student1997 on April 30, 2012
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150 terms
Terms | Definitions |
|---|---|
 Variable | A letter that is used to represent one or more numbers. |
| Algebraic Expression | An expression that includes at least one variable. |
| Power | An expression that represents repeated multiplication of the same factor. |
| Base of a Power | The number or expression that is used as a factor in a repeated multiplication. |
| Exponent | The number or variable that represents the number of times the base of a power is used as a factor. |
| Order of Operations | Rules for evaluating an expression involving more than one operation. |
| Verbal Model | Describes real-world situation using words as labels and using math symbols to relate the words. |
| Rate | A fraction that compares two quantities measured in different units. |
| Unit Rate | A rate in which the denominator of the fraction is 1 unit. |
| Open Sentence | An equation or an inequality that contains an algebraic expression. |
| Equation | a mathematical sentence formed by placing the = between two expressions. |
| Inequality | A mathematical sentence formed by placing one of the symbols <, >, ≤,or ≥ between two expressions. |
| Solution of an Equation | A number that produces a true statement when substituted for the variable in the equation. |
| Solution of an Inequality | A number that produces a true statement when it is substituted for the variable in the inequality. |
| Formula | An equation that relates two or more quantities. |
| Function | It consists of: 1. A set called the domain containing numbers called inputs, and a set called the range containing numbers called outputs. 2. A pairing of inputs with outputs such that each input is paired with exactly one output. |
| Domain | The set of all inputs of a function. |
| Range | The set of all outputs of a function |
| Independent Variable | The input variable of a function. |
| Dependent Variable | The output variable of a function. |
| Relation | Any pairing of a set of inputs with a set of outputs. |
| Whole Numbers | The numbers 0,1,2,3... |
| Integers | The numbers ...-3,-2,-1,0,1,2,3... |
| Rational Number | A number that can be written as a/b where a and b are integers and b is not equal to 0. |
| Opposites | Two numbers that are the same distance from zero on a number line but are on opposite sides of 0. |
| Absolute Value | The distance between a number and 0 on a number line. |
| Conditional Statement | A statement with a hypothesis and a conclusion |
| Set | A collection of distinct objects. |
| Element of a Set | Each object in a set. |
| Empty Set | A set with no elements. |
| Universal Set | The set of all elements under consideration. |
| Union | Of two sets A and B is the set of all elements in either A or B written in A U B. |
| Intersection | Of two sets A and B is the set of all elements in both A and B written in A (upside down U) B |
| Complement of a Set | Of set A is the set of all elements in the universal set U that are not in A. |
| Cross Product of Two Sets | Of two sets A and B, written as A X B, is the set of all possible ordered pairs of the form (x,y) where x is an element of A and y is an element of B. |
| Additive Identity | The number 0, because the sum of any number and 0 is the number. |
| Additive Inverse | The opposite of a number, the sum of a number and its opposite is 0. |
| Multiplicative Identity | The number 1, because the product of any number and 1 is the number. |
| Equivalent Expressions | Two expressions that have the same value for all values of the variable. |
| Distributive Property | A property that can be used to find the product of a number and a sum or difference. |
| Term | The parts of an expression that are added together. |
| Coefficient | The number part of a term with a variable part. |
| Constant term | A term with a number part but no variable part. |
| Like Terms | Terms that have the same variable parts. |
| Multiplicative Inverse | The reciprocal of a nonzero number. |
| Square Root | A number that when multiplied by itself equals a given number. |
| Radicand | The number or expression inside a radical symbol. |
| Perfect Square | A number that is the square of an integer. |
| Irrational Number | A number that cannot be written as the quotient of two integers. |
| Real Numbers | The set of all rational and irrational numbers. |
| Cube Root | A number that when multiplied three times equals a given number. |
| Inverse Operations | Two operations that undo each other. |
| Equivalent Equations | Equations that have the same solution. |
| Identity | An equation that is true for all values of the variable. |
| Ratio | A comparison of two numbers using division. |
| Proportion | An equation that states that two ratios are equivalent. |
| Cross Product | The product of the numerator of one ratio and the denominator of the other ratio. |
| Scale Drawing | A two-dimensional drawing in which the dimensions of the drawing are in proportion to the dimensions of the object. |
| Scale Model | A three-dimensional model in which the dimensions of the model are in proportion to the dimensions of the object. |
| Scale | A ratio that relates the dimensions of a scale drawing or model and the actual dimensions. |
| Percent of Change | A percent that indicates how much a quantity increases or decreases with respect to the original amount. |
| Percent of Increase | The percent of change in a quantity when the new amount of the quantity is greater than the original amount. |
| Percent of Decrese | The percent of change in a quantity when the new amount of the quantity is less that the original amount. |
| Literal Equation | An equation in which letters are used to replace the coefficients and constants of another equation. |
| Quadrant | The four regions into which the coordinate plane is dived by the x-axis and the y-axis. |
| Transformation | It produces an image by applying a rule to the coordinates of each point on the graph. |
| Translation | It moves every point on a graph the same distance in the same direction |
| Vertical Stretch | Moves a point away from the x-axis. |
| Vertical Shrink | Moves a point toward the x-axis. |
| Reflection | Flips a point in a line. |
| Standard Form of a Linear Equation | Ax + By = C, where A,B, and C are real numbers and A and B are not both zero. |
| Linear Function | The equation Ax + By = C provided B does not equal 0. |
| Discrete Function | A function with a graph that consists of isolated points. |
| Continuous Function | A function with a graph that is unbroken. |
| X-Intercept | The x-coordinate of the point where a graph crosses the x-axis. |
| Y-Intercept | The y-coordinate of a point where a graph crosses the y-axis. |
| Slope | The ratio of the vertical change to the horizontal change between any two points (x₁,y₁) and (x₂,y₂) on the line. |
| Rate of Change | A comparison of a change in one quantity with a change in another quantity. |
| Slope-Intercept Form | y=mx+b where m is the slope and b is the y-intercept of the equation's graph. |
| Parallel Lines | Two lines in the same plane that do not intersect. |
| Direct Variation | The relationship of two variable x and y if there is a nonzero number a such that y =ax. |
| Constant of Variation | The nonzero constant a in a direct or inverse variation equation. |
| Function Notation | A way to name a function using the symbol f(x) instead of y. |
| Family of Functions | A group of functions with similar characteristics. |
| Parent Linear Function | The function f(x) = x, which is the most basic function in the family of linear functions. |
| Point-Slope Form | y − y₁= m(x − x₁) that passes through a given point (x₁, y₁) with a slope of m. |
| Sequence | An ordered list of numbers. |
| Arithmetic Sequence | A sequence in which the difference between consecutive terms is constant. |
| Common difference | The constant difference between consecutive terms of an arithmetic sequence. |
| Converse | The statement formed by interchanging the hypothesis and conclusion of the conditional. |
| Perpendicular Lines | Two lines in the same planes that intersect to form a right angle. |
| Scatter Plot | A graph used to determine whether there is a relationship or trend between paired data. |
| Correlation | The relationship between paired data. |
| Line of Fit | A line used model the trend in data having a positive or negative correlation. |
| Best-Fitting Line | The line that most closely follows a trend in data. |
| Linear Regression | The process of finding the best-fitting line to model a set of data. |
| Linear Interpolation | Using a line or its equation to approximate a value between two known values. |
| Linear Extrapolation | Using a line or its equation to approximate a value outside the range of known values |
| Zero of a Function | An x-value for which f(x) = 0. |
| Graph of an Inequality | On a number line, the set of points that represent all solutions of the inequality. |
| Equivalent Inequalities | Inequalities that have the same solution |
| Compound Inequality | Two inequalities joined by "and" or "or" |
| Absolute Value Equation | An equation that contains an absolute value expression. |
| Absolute Deviation | A number x from a given value is the absolute value of the difference of x and the given value. |
| Linear Inequality in Two Variables | An inequality that is the result of replacing the = sign in a linear equation with <, ≤, >, or ≥. |
| Graph of an Inequality in Two Variables | In a coordinate plane, the set of points that represent all solutions of the inequality. |
| System of Linear Equations | Two or more linear equations in the same variables. |
| Solution of a System of Linear Equations | An ordered pair that is a solution of each equation in the system. |
| Consistent Independent System | A linear system with exactly one solution. |
| Inconsistent System | A linear system with no solution. |
| Consistent Dependent System | A linear system with infinitely many solutions. |
| System of Linear Inequalities | Two or more linear inequalities in the same variables. |
| Solution of a System of Linear Inequalities | An ordered pair that is a solution of each inequality in the system. |
| Graph of a System of Linear Inequalities | The graph of all solutions of the system. |
| Order of Magnitude | The power of 10 nearest the quantity. |
| Scientific Notation | Numbers are written in the form c x 10^n where 1≤c<10 and n is an integer. |
| Monomial | A number, variable, or the product of a number and one or more variables with whole number exponents. |
| Degree of a Monomial | The sum of the exponents of the variables in the monomial |
| Degree of a Polynomial | The greatest degree of the terms of the polynomial. |
| Polynomial | A monomial or sum of monomials. |
| Leading Coefficient | The coefficient of the forest term. |
| Binomial | A polynomial with two terms. |
| Trinomial | A polynomial with three terms. |
| Roots | The solutions of a polynomial equation. |
| Vertical Motion Model | A model for the height of an object that is propelled into the air but has no power to keep itself up in the air. |
| Perfect Square Trinomial | Trinomials of the form a²+2ab+b² or a²- 2ab+b². |
| Factor by Grouping | Factor a common monomial from pairs of terms and then look for a common binomial factor. |
| Factor Completely | A factorable polynomial with integer coefficients when it is written as a product of unfactorable polynomials with integer coefficients. |
| Quadratic Function | A nonlinear function that can be written in the standard form y=ax²+bx+c where a≠0. |
| Parabola | The U-shaped graph of a quadratic function. |
| Parent Quadratic Function | The function y=x². |
| Vertex | The lowest or highest point on a parabola. |
| Axis of Symmetry | The line that passes through the vertex and divides the parabola into two symmetric parts. |
| Minimum Value | The y-coordinate of the vertex for y= ax²+bx+c, where a>0. |
| Maximum Value | The y-coordinate of the vertex for y=ax²+bx+c when a<0. |
| Intercept Form of a Quadratic Function | A quadratic function in the form y=a(x-p)(x-q). |
| Quadratic Equation | An equation that can be written in the standard form ax² + bx + c = 0, where a ≠ 0. |
| Completing the Square | The process of rewriting a quadratic expression so that it is a perfect square trinomial. |
| Vertex Form of a Quadratic Function | A quadratic function in the form y=a(x-h)²+k. |
| Quadratic Formula | The formula x=(-b±√b²-4ac)/2a can be used to find the solutions of the quadratic equation ax²+bx+c=0 where a≠0 and b²-4ac≥0 |
| Discriminant | The expression b² - 4ac of the associated equation ax² + bx + c = 0. |
| Simplest Form of Radical Expression | A radical expression that has no perfect square factors other than 1 in the radicand, no fractions in the radicand, and no radicands appearing in the denominator of the fraction. |
| Rationalizing the Denominator | The process of eliminating a radical from an expression's denominator. |
| Inverse Variation | The relationship of two variables x and y if there is a nonzero number a such that y=a/x |
| Hyperbola | The graph of the inverse variation equation y=a/x. |
| Branches of a Hyperbola | The two symmetrical parts of a hyperbola. |
| Asymptotes of a Hyperbola | Lines that a hyperbola approaches but does not intersect. |
| Rational Expression | An expression that can be written as the ratio of two polynomials where the denominator is not 0. |
| Excluded Value | A number that makes a rational expression undefined. |
| Simplest Form of a Rational Expression | A rational expression whose numorator and denominator have no factors in common other that 1. |
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