Integrated Algebra B GLOSSARY |
| A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z |
A |
Absolute value
|
A number's distance from zero on a number line (The absolute value of –4 is 4; the absolute value of 4 is 4.)
|
Absolute value equation
|
Equation whose graph forms a V that opens up or down. |
Absolute value inequality
|
Inequalities involving absolute value |
Additive inverse
|
The opposite of a number (The additive inverse of 3 is –3. The sum of a number and its additive inverse is zero.)
|
Algebra
|
A generalization of arithmetic in which symbols represent members of a specified set of numbers and are related by operations that hold for all numbers in the set
|
Algebraic expression
|
An expression that contains a variable Ex. X – 2
|
Algebraic fraction
|
A fraction that contains a variable
|
Algorithms
|
A mechanical procedure for performing a given calculation or solving a problem through step-by-step procedures such as those used in long division
|
Array
|
A rectangular arrangement of objects in rows and columns
|
Associative Property
|
If three are more numbers are added or multiplied, the numbers can be regrouped without changing the results. Ex. 4 + (6 + 5) = (4 + 6) + 5
|
Axis
|
Either of two number lines used to form a coordinate grid
|
B |
Bar graph
|
A graph in which horizontal or vertical bars represent data
|
Binomial
|
An expression consisting of two terms connected by a plus or minus sign, such as 4a + 6
|
Box-and-whisker plot
|
A graphic method for showing a summary of data using median, quartiles, and extremes of data (A box-and-whisker plot makes it easy to see where the data are spread out and where they are concentrated. The longer the box, the more the data are spread out.)
|
C |
Central tendencies
|
A single number that is used to describe a set of numbers (Ex. mean, median, mode, etc.)
|
Chance
|
The probability of an outcome in an uncertain event (Ex. In tossing a coin, there is an equal chance of getting heads or tails.)
|
Coefficient
|
The numerical factor when a term has a variable (Ex. In the expression 3x + 2y = 16, 2 and 3 are coefficients.)
|
Commutative Property
|
If two numbers are added or multiplied, the operations can be done in any order. Ex. 4 x 5 = 5 x 4
|
Composite number
|
Any integer that is not a prime number (evenly divisible by numbers other than one and itself)
|
Consecutive
|
Following one another in an uninterrupted order (Ex. 6, 7, 8, and 9 are consecutive numbers.)
|
Constant
|
In an algebraic expression, the number without the variable (Ex. In the expression 2x + 5, 5 is the constant.)
|
Coordinate
|
A set of numbers that locates the position of a point usually represented by (x, y) values
|
Coordinate system/Cartesian Plane
|
A method of locating points in the plane or in space by means of numbers (A point in a plane can be located by its distances from both a horizontal and a vertical line called the axes. The horizontal line is called the x-axis. The vertical line is called the y-axis. The pairs of numbers are called ordered pairs. The first number, called the x-coordinate, designates the distance along the horizontal axis. The second number, called the y-coordinate, designates the distance along the vertical axis. The point at which the two axes intersect has the coordinates (0,0) and is called the origin.)
|
D |
Data
|
Information gathered by observation, questioning, or measurement
|
Dependent variable
|
A variable that provides the output values of a function
|
Difference
|
The result of subtraction
|
Direct variation
|
A linear function of the form y = kx, where k is the constant of variation and k is not equal to zero
|
Distributive Property
|
A property that relates two operations on numbers, usually multiplication and addition, or multiplication and subtraction Ex. a(x + y) = ax + ay
|
Domain
|
The set of all first coordinates from the ordered pairs of a relation
|
E |
Equation
|
A mathematical sentence containing an equal sign
|
Explicit equation
|
An equation that relates the inputs to the outputs
|
Exponent
|
A number showing how many times the base is used as a factor
Ex. 3² = 3 x 3 or 9
|
Exponential Function
|
A function in the form of f(x) = a x , where x is a real number, and a is positive and not 1
|
Expression
|
A mathematical statement that does not contain an equal sign
|
Extrapolate
|
To extend and estimate data based on given information
|
F |
Factor
|
Any numbers multiplied by another number to produce a product
|
Factoring
|
A method used to solve a quadratic equation that requires using the zero product property (Factoring is a process of rewriting a number or expression as product of two or more numbers or expressions.)
|
Formulas
|
Specific equations giving rules for relationships between quantities
|
Function
|
A relation in which each member of the domain is paired with one, and only one, member of the range
|
Function Notation
|
To write a rule in function notation, you use the symbol f(x) in place of y.
(Ex. f(x) = 3x – 8 is in functional notation.)
|
G |
Graph of a function
|
A pictorial way to display a function
|
H |
Histogram
|
A graphic representation of the frequency distribution of a continuous variable (Rectangles are drawn in such a way that their bars lie on a linear scale representing different intervals (bin width), and their heights are proportional to the frequencies of the values within each of the intervals.)
|
I |
Independent variable
|
A variable that provides the input values of a function
|
Inequality
|
A mathematical statement that one quantity is less than (<) or greater than (>) another
|
Inference
|
Reasoning from data, premises, graphs, and incomplete and inconsistent sources to from sensible conclusions
|
Integers
|
The set of whole numbers and their opposites
|
Interest
|
Amount paid for the use of money
|
Interpolate
|
To interpret and estimate data between given values
|
Irrational numbers
|
Real numbers that cannot be expressed in the form a/b (a fraction) where a and b are integers
|
Inverse variation
|
A function that can be written in the form xy = k or y = k/x (The product of the quantities remains constant, so as one quantity increases, the other decreases.)
|
L |
Linear function
|
A function that has a constant rate of change and can be modeled by a straight line
|
Line graph
|
A means of displaying statistical information by connecting graphs of ordered pairs to show changes in quantities
|
Line of best fit
|
The most accurate trend line on a scatter plot showing the relationship between two sets of data
|
Lines
|
A set of points (x, y) that satisfy the equation ax + by + c = 0 where a and b are not both zero
|
Literal equation
|
An equation involving two or more variables
|
M |
Mapping diagram
|
A diagram that maps an input value to an output value to determine whether a relation is a function (See diagram)
|
Matrices
|
Ordered tables or listings of numerical data
|
Maximum
|
The greatest value of the function if is has such an extreme value
|
Mean
|
The sum of a set of numbers divided by the number of numbers in that set
|
Median
|
In a list of data ordered from least to greatest or greatest to least, the middle number or the average of the middle two numbers
|
Minimum
|
The least value of the function if is has such an extreme value
|
Mode
|
In a list of data, the number or item occurring most frequently
|
Monomial
|
An expression that is a number, a variable, or a product of a number and variable (Ex. 7, x and 8xy are all monomials.)
|
N |
Natural Numbers
|
One of the numbers 1, 2, 3, 4… also called counting numbers
|
Number sense
|
The ability of the learner to make logical connections between new information and previously acquired knowledge to understand the meanings, relationships, and magnitudes of numbers and common measurements
|
Number Theory
|
Concepts of numbers such as prime, composite, squares, factors and multiples
|
P |
Parabola
|
The graph of a quadratic function
|
Patterns
|
Repeated sequences
|
Perfect Square Trinomial
|
Any trinomial in the form a² + 2ab + b²
|
Point slope form
|
A linear equation of a non-vertical line written as y – y 1 = m (x – x 1 )
|
Polynomial
|
In algebra, a n expression consisting of two or more terms (Ex. x² -2xy + y²)
|
Powers
|
Numbers that can be expressed using exponents
|
Prime Numbers
|
A whole number greater than one having exactly two distinct factors, one and itself
|
Probability
|
How likely it is that an event will occur (Written formally as P(event))
|
Proportion
|
An equation that states that two ratios are equal
|
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. Ex. a² + b² = c²
|
Q |
Quadratic formula
|
The solutions of a quadratic equation of the form ax² + bx + c = 0 where a ¹ 0 are given by the quadratic formula which is
|
Quadratic function
|
A function that has an equation of the form y = Ax² +Bx + C where ‘A' does not equal 0 |
R |
Radicals
|
A radical symbol ( Ö ) and its radicand
|
Radical Equation
|
An equation that has a variable in a radicand
|
Radical expression
|
An expression with a radical in it
|
Radicand
|
An expression under the radical sign
|
Range
|
The set of all the second coordinates from the set of ordered pairs of a relation
|
Range (statistics)
|
The difference between the greatest and least numbers in a set of numerical data
|
Ratio
|
A comparison of two numbers, represented in one of the following ways: 2 to 5, 2 out of 5, 2:5, or 2/5
|
Rational Numbers
|
A number in the form of an a/b, where a and b are integers and b is not equal to zero
|
Real Roots
|
The zeros of an equation that occur at x-intercepts of the graph of the related function
|
Recursive function
|
A recursive formula has two parts: the value(s) of the first term(s), and a recursion equation that shows how to find each term from the term(s) before it
|
Reflection
|
Mirror image of a figure (Objects remain the same shape, but their positions change through a flip.)
|
Regression
|
Statistical technique that predicts the equation that best fits the data
|
Relation
|
A set of ordered pairs of data
|
S |
Scale
|
The numeric ratio used to produce an enlarged or reduced drawing of a picture or an object
|
Scalar multiplication
|
Multiplication of a matrix by a constant (scalar)
|
Scatter plot
|
A graph of the points representing a collection of data
|
Scientific Notation
|
A means of expressing a number as a product of a number between one and ten and a power of ten
Ex. 1100 = 1.1 x 10³
|
Simultaneous (Systems) Equations
|
Pair of equations of the first degree upon which two different conditions are put on the same variables at the same time (Ex. Find two numbers whose sum is 7 and whose difference is 1. x + y = 7 and x – y = 1.)
|
Slope
|
The ratio of the vertical change to the horizontal change
|
Slope-intercept form
|
A linear equation in the form y = mx + b, where m is the slope of the graph of the equation and b is the y-intercept
|
Square root
|
That number which, when multiplied by itself, produces the given number (Ex. 5 is the square root of 25, because 5x5=25.)
|
Standard form of a linear equation
|
The form of a linear equation Ax + By = C where A, B, and C are real numbers and A and C are not both zero (Ex. 6x – y = 12)
|
Standard form of a polynomial
|
The form of a polynomial in which the degree of the terms decreases from left to right (descending order)
|
Stem-and-leaf display
|
A means of organizing data in which certain digits are uses as stems, and the remaining digits are leaves
|
T |
Table
|
A display of data, usually arranged in rows and columns
|
Term
|
A number, variable, or the product or quotient of a number and one or more variables
|
Theoretical probabilities
|
Probabilities determined without performing an experiment
|
Trinomial
|
An expression containing three terms connected by a plus or minus sign (Ex. 5x² + 3x – 6)
|
U |
Units of measure
|
Inches, meters, pounds, grams, etc.
|
| Unit rates |
Any fixed amount, quantity, etc., used as a standard
|
V |
Variable
|
A letter that can assume different values
|
Vertex
|
The maximum or minimum value of a parabola
|
Vertical Line Test
|
A method used to determine if a relation is a function or not (If a vertical line passes through a graph more than once, the graph is not the graph of a function.)
|
Vertical Shift
|
Movement of a graph up or down the y-axis
|
W |
Whole numbers
|
The set of natural numbers and zero
|
X |
X-axis
|
The horizontal axis of a coordinate plane
|
X-coordinate
|
The location on the x-axis of a point on the coordinate plane
|
X-intercept
|
The x-coordinate of the point where a line crosses the x-axis
|
Y |
Y-axis
|
The vertical axis of a coordinate plane
|
Y-coordinate
|
The location on the y-axis of a point on the coordinate plane
|
Y-intercept
|
The y-coordinate of the point where the line crosses the y-axis
|
Z |
Zeros
|
The x-intercepts of a quadratic equation that crosses the x-axis
|
+ 7 
and 4 
* 2 