Unit 1Â Number Order and Absolute Value
axiom
A statement accepted as true without proof.
closure
The condition that produces a unique element in the sum or product of two original elements.
domain
The set composed of first elements from a set of ordered-pair numbers.
element
One member of a set.
empty set
A set with no elements.
equal sets
Sets whose elements are identical.
equivalent sets
Sets that contain the same number of elements
exponent
A small-sized number placed at the right of and above a symbol that indicates the number of times the symbol appears as a factor.
exponential notation
A shorthand expression for repeated multiplication.
finite set
A set in which the number of elements is possible to reach or exceed by counting
function
A set of ordered-pair numbers such that for each first element there exists a unique second element.
infinite set
A set in which the number of elements is limitless.
integer
Any one of the numbers from negative infinity to positive infinity.
intersection of sets
A set whose elements are common to two other sets.
inverse of a function
A set of ordered-pair numbers in which the range and domain sets are interchanged.
natural numbers
Any one of the numbers from positive one to infinity.
operation
One of two mathematical procedures: addition or multiplication.
range
The set composed of second elements from a set of ordered-pair numbers.
relation
A set or ordered-pair numbers.
set
A collection of objects, concepts, or symbols.
subset
A set whose members are also members of a second set.
theorem
A statement requiring proof.
union of sets
A set whose elements appear in either of two other sets.
whole numbers
Any one of the numbers from zero to infinity.
Unit 2 Numbers, Sentences, and Problems
absolute value
The value of a number, without regard to sign.
compound sentence
A mathematical expression combining two shorter sentences using or or and.
inequality
A mathematical sentence with a verb of > or <.
linear equation
A mathematical sentence of one variable, in which the variable is of the first power or degree.
linear inequality
An inequality in which the variable is of the first power or degree.
trichotomy
A true statement with three independent but related parts.
Unit 3 Linear Equations and Inequalities
coincident lines
Lines that have all points as common solutions.
common solution
The ordered pair that makes two equations true simultaneously.
constant function
A function that has the same second coordinate in all its ordered pairs.
horizontal line
A line with zero slope.
intersecting lines
Lines that have exactly one common solution.
linear programming
A branch of mathematics concerned with solving practical problems involving linear inequalities.
parallel lines
Lines that have equal slopes and no common solution.
point-slope form
The equation of a line in the form y - y 1 = m (x - x 1).
slope
The inclination of a line; the change in y values of two points divided by the change in x values of the points.
slope-intercept form
The equation of a line in the form y = mx + b.
slope-point form
The equation of a line in the form y - y 1 = m (x - x 1).
standard form
The equation of a line in the form Ax + By = c.
two-order system
A pair of equations of one or two variables used to solve a problem.
vertical line
A line with an undefined slope such as 1/0
y-intercept
The point at which a line crosses the y-axis.
Unit 4 Polynomials
associative property
If any three numbers are multiplied or added in a given order, they may be grouped in any way without changing the product or sum.
binomial
The algebraic sum of two monomials.
combined variation
A variation that involves both direct and inverse variations with at least three variables.
commutative property
A law of mathematics stating that the order in which you multiply or add two numbers does not affect the product or sum.
direct variation
Occurs when the quotient of two variables is a constant.
distributive property
For real numbers a, b, and c: a(b + c) = ab + ac.
inverse variation
Occurs when the product of two variables is a constant: xy = c.
joint variation
A variation that involves at least three variables when one of the three varies directly as the product of the other two.
monomial
An integer or variable or the product of an integer and variables.
perfect square trinomial
A polynomial of three terms that can be stated as the product of two equal factors: a 2 + 2ab + b 2 = (a + b) (a + b).
synthetic division
An abbreviated way of dividing a polynomial by a binomial.
trinomial
A polynomial of three terms.
Unit 5 Algebraic Fractions
algebraic fraction
A fraction that contains variables in either the numerator or denominator.
complex fraction
A fraction with numerator or denominator, or both, that contain fractions.
equation
A mathematical sentence with an = sign between two expressions that name the same number.
equivalent fractions
Fractions that have the same value. If reduced or evaluated, they would be the same number.
exclusion
Any value of the variable in a fractional equation that would make the denominator equal to zero.
exponent
Tells how many items a factor occurs in a number with repeated factors.
extraneous root
In the algebraic process used for solving an equation, a number obtained that is not a root of the original equation.
extremes
The first and fourth terms of a proportion.
fractional equation
An equation with at least one fraction with a variable in the denominator.
lowest common denominator
The least number that the given denominators will divide into evenly.
means
The second and third terms of a proportion.
mixed expression
A polynomial that has at least one integral term and one fractional term.
proportion
A statement of equality between two ratios.
reciprocal
Commonly called the multiplicative process. If the product of two numbers is 1, either is the reciprocal of the other.
redundant equation
An equation that has occurred during the solving process and has a root that does not satisfy the original equation.
root
A solution of an equation. If the value of the variable makes the sentence true, that value is called the root.