Algebra Definitions: Part 9

Te following is Math Made Easy's final  list of Algebra Definitions. Math Made easy, math help is a phone call away.



Sample space: The set of all possible outcomes of a random experiment.

satisfy an open sentence:  Any solution of the sentence satisfies the sentence.

scientific notation: A positive number in scientific notation is expressed as the product of a
number greater than or equal to 1 but less than 10, and an integral power of 10.

sides of an angle:  The two rays that form the angle.

sides of an equation:  The two expressions joined by the equals sign.

sides of an inequality: The expressions joined by an inequality symbol.

sides of a triangle:  The three segments that form the triangle.

similar terms:  Two monomials that are exactly alike or are the same except for their numerical coefficients.

similar triangles:  Two triangles are similar if the measures of two angles of one triangle equal the measures of two angles of the other. Angles with equal measures are called corresponding
angles. Sides opposite corresponding angles are called corresponding sides.

simple event:  An event that involves a single member of a sample space.

simplest form of an algebraic fraction:  A form of the fraction in which the numerator and
denominator have no common factor other than 1 and �1.

simplest form of an expression having a square-root radical:  The form of the expression in which no integral radicand has a square factor other than 1; no fractions are under a radical sign; no radicals are in a denominator.

simplest form of a polynomial:  A polynomial is in simplest form when no two of its terms are similar.

simplifying an expression:  Replacing an expression containing variables by an equivalent
expression with as few terms as possible.

simplifying a numerical expression: Replacing the expression by the simplest name for its value.

simultaneous equations:  See under system of (simultanwous) equations.

sine:  The sine of an acute angle A in a right triangle = the length of the leg of the opposite of
angle A divided by the length of the hypotenuse.

slope of a line:  If (x1 , y1) and (x2 , y2) are two different points on a line, the slope of the line is given by the difference in the y�s divided by the difference in the x�s. A horizontal line has slope 0;
a vertical line has no slope.

slope-intercept form of an equation: The equation of a line in the form y = mx + b, where m is the slope and b is the y-intercept.

solution of an equation in two variables:  An ordered pair of numbers that make the sentence true.

solution of a sentence:  Any value of a variable that turns an open sentence into a true
statement.

solution of a system of two equations in two variables:  An ordered pair that satisfies both equations at the same time.

solution set of an open sentence:   The set of all solutions of the sentence.

solve a conjunction:  To find the values of the variable for which both open sentences in the
conjunction are true.

solve a disjunction:  To find the values of the variable for which at least one of the open
sentences in the disjunction is true.

solve an equation:  To find the set of all solutions of the equation.

solve an open sentence:  To find the solution set of the sentence.

solve a system of two equations in x and y:  To find all ordered pairs (x , y) that make both equations true.

square root: If a2 = b, then a is a square root of b.

standard deviation:  In a frequency distribution, the principal square root of the variance.

standard form of a linear equation: ax + by = c, where a, b, and c are integers and a and b are not both zero.

standard form of a polynomial equation:  A form of the equation in which one side is zero and the other is a simplified polynomial arranged in order of decreasing degree of the variable.

stem-and-leaf plot: A way of displaying a frequency distribution.

straight angle:  An angle with measure 180 degrees.

substitution method:  A method of solving a system of linear equations in two variables.

subtraction:  For all real numbers a and b, the difference a � b is defined by a � b = a + (-b).

supplementary angles:  Two angles are supplementary if the sum of their measures is 180
degrees. Each angle is a supplement of the other.

system of (simultaneous) equations:  Two or more equations in the same variables.

tangent: The tangent of an acute angle A in a right triangle = the length of the leg of the
opposite to angle A divided by the length of the leg adjacent  to angle A.

terminating decimal:  When a common fraction is written as a decimal by dividing the numerator by the denominator, the result is a terminating decimal if the remainder is zero. Also called ending decimal or finite decimal.

terms:  In the sum a + b , a and b are called terms.

theorem:  A statement that is shown to be true by use of a logically developed argument.

transformations: Operations on an equation or an inequality that produce a simpler
equivalent statement.

triangle:  A figure formed by three segments joining three points not on the same line. Each
segment is a side, and each point is a vertex, or the triangle.

trigonometric functions:  The functions sine, cosine, and tangent, each having the set of acute angles as domain.

trigonometric ratios:  Ratios of the lengths of the sides of a right triangle.

trinomial:  A polynomial of only three terms.

uniform motion: Motion without change in speed, or rate.

union of sets:  For any two sets A  and B, the set whose members belong to at least one of  the sets A and B.

unit price:  The price of one unit of a given item.

value of a numerical expression:  The number named by the expression.

values of a function:  Members of the range of the function.

values of a variable:  The numbers that can be represented by the variable.

variable:  A symbol used to represent one or more numbers.

variable expression: An expression that contains a variable.

variance:  a frequency distribution, the mean of the squares of the distance of each score
from the mean.

vertex of an angle:  The common endpoint of the rays forming the angle.

vertex of an parabola:  The maximum point of the graph.

vertical angles:  Two angles whose sides are rays in the same line, but in opposite directions.

vertical axis:  The vertical number line in a coordinate plane.

.

whole numbers:  The set consisting of zero and all the positive integers.

work rate:  The fractional part of a job done in a given unit of time.

x-axis:  The horizontal axis in the coordinate plane.



x-intercept: The x-coordinate of a point where a graph intersects the x-axis.




y-intercept:  The y-coordinate of a point where a graph crosses the y-axis.

zeros of a quadratic function:  The members of the solution set of the related quadratic equation.