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Algebra

Terms in this set (105)

absolute value
The distance between a real number and zero on a number line.
additive inverse
The opposite of a number. When added together, the sum is zero.
algebraic expression
A collection of numbers and variables with at least one arithmetic operation.
associative property
The grouping of terms within expressions involving addition or multiplication does not change the value. Ex: (a+b) + c = a + (b+c)
axis of symmetry
The line that divides a graph into two symmetrical parts.
base
The repeated factor of a number written in exponential form.
binomial
A two-term polynomial.
coefficient
The numerical value of a term.
combine like terms
Adding or subtracting terms that have the same variable(s) and exponent(s).
commutative property
Changing the order of addition or multiplication does not change the value. Ex: a+b+c = c+a+b
compound inequality
Two inequalities combined in one statement by the word and or or.
consistent system
A system of equations with at least one solution.
constant
A term with no variables.
coordinate plane
Formed by two number lines that cross each other at zero.
coordinates
Ordered pairs that identify points on a plane.
deductive reasoning
The process of using logic to draw conclusions.
denominator
The lower half of a fraction.
dependent system
A system of equations that has infinite solutions.
difference
The answer to a subtraction problem.
difference of two squares
A binomial whose terms are perfect squares being subtracted.
direct variation
An equation in the form y=kx, where k does not equal zero.
discriminant
The expression inside the radical of the quadratic formula.
distributive property
Used to clear parentheses by multiplying a term on the outside by two or more terms inside the parentheses. Ex: a(b - c) = ab - ac
equation
A mathematical sentence with an equal sign.
evaluate
To find the value of an expression by following the order of operations.
exponent
The number of times a base is multiplied by itself. Also called a power.
extraneous solution
A result that does not satisfy the original equation or inequality.
factor
An integer that divides another integer with no remainder.
function
A relation in which every input (x) has exactly one output (y).
function notation
When the output (y) of a relation is renamed f(x). Read "f of x".
graphing
The act of plotting points on a plane to represent a function or relation.
greatest common factor
The largest number that divides into two terms.
grouping symbols
Symbols such as parentheses and brackets, which separate terms within an expressions. Others include fraction bars, absolute value, square root, braces, etc.
inconsistent system
A system of equations that has no solution.
independent system
A system of equations that has exactly one solution.
inequality
A sentence using greater than or less than symbols. Also, greater than or equal to, or less than or equal to.
integer
All whole numbers and their opposites.
irrational number
Numbers that cannot be expressed as fractions or terminating/repeating decimals.
isolate the variable
Collecting like terms and using inverse operations to get a variable by itself on one side of a relation.
like terms
Terms with the same variables raised to the same exponents.
linear equation
An equation whose variables have an exponent of one and whose graph creates a straight line.
monomial
An expression with a one term.
multiplicative identity property
Multiplying a number by one equals that number.
multiplicative inverse
Two numbers multiplied together that equal one.
zero product property
Any number multiplied by zero equals zero.
natural number
The set of counting numbers starting with one.
no solution
When there is no answer to an equation or inequality.
numerator
The upper half of a fraction.
opposites
Numbers that have the same absolute value.
order of operations
The rules for evaluating an expression.
ordered pair
A pair of numbers used to identify a point (x, y) on a coordinate plane.
origin
The intersection of the axes in a coordinate plane.
parabola
A U-shaped graph created by a quadratic function. Can also be upside down.
parallel
Lines or planes that never intersect.
perfect square
A number with a square root that is rational.
perpendicular
Lines or planes that intersect at right angles.
point-slope form
An equation of a line in this form:
polynomial
An expression with one or more monomials being added or subtracted.
product
The answer to a multiplication problem.
property
A law that governs mathematics.
quadrant
One of four regions of a coordinate plane.
quadratic expression
An expression in this form with a, b and c being numbers.
quadratic formula
A method of finding roots of a quadratic function by replacing a, b and c with numbers.
quotient
The answer to a division problem.
rate
The ratio that compares two quantities in different units.
ratio
The relationship of two quantities, often shown using division.
rational expression
A fraction that has polynomials in the numerator and denominator.
rational number
Any number that can be written as a fraction.
real number
All rational and irrational numbers.
reciprocal
The multiplicative inverse of a number. Created by switching the numerator and the denominator.
repeating decimal
A rational number that has a block of one or more numbers after the decimal that continually show up.
replacement set
A set of solutions that can replace a variable.
rise
The difference between two y-values on a linear graph.
run
The difference between two x-values on a linear graph.
simplest form
An expression that contains no like terms or parentheses.
simplify
To reduce an expression to as few terms as possible.
slope
A measure of steepness of a line. Often represented by the letter. Calculated by finding the ratio of the change in y-coordinates (rise) to the change in x-coordinates (run).
slope-intercept form
An equation of a line in this form, with m as the slope and b as the y-intercept.
solve
The process of finding all values of a variable that make an equation or inequality true.
standard form of an equation
An equation in this form, where A, B and C are integers and A is positive.
standard form of polynomials
When terms are placed in descending order according to their degree.
sum
The answer to an addition problem.
system of equations
A set of two or more equations with two or more variables.
terminating decimal
A rational number that does not repeat or continue indefinitely after the decimal.
term
A number and/or variable(s), or a combination of both being multiplied or divided.
trinomial
An expression with three terms.
undefined
No solution.
variable
Symbols, usually letters, used to represent unspecified values.
whole number
All natural (counting) numbers and zero.
x-axis
The horizontal number line of a coordinate plane.
x-intercept
The point where a graph touches the x-axis. Also referred to as roots or zeros.
y-axis
The vertical number line of a coordinate plane.
y-intercept
The point where a graph touches the y-axis. Sometimes represented by the letter b.
line of best fit
A line drawn through a scatter plot to best represent the data.
counterexample
A specific case that makes a statement false.
degree
The sum of the exponents in a monomial.
dependent variable
The y-value, or output, of a relation, whose value depends on the input.
independent variable
The x-value, or input, of a relation, which determines the output.
domain
The set of x-values in a relation.
range
The set of y-values in a relation.
radical
A root symbol. The most common is square root, but can also be cubed, fourth root, fifth root, etc.
geometric sequence
A pattern in which each term is found by multiplying the previous term by a common ratio (r). Ex: 3, 6, 12, 24, 48, 96...
arithmetic sequence
A pattern that increases or decreases at a constant rate (d). Ex: 5, 10, 15, 20, 25...
roots
The solution(s) of a quadratic equation, where the parabola crosses the x-axis. Also called zeros.
scientific notation
A way to represent very large or very small numbers by multiplying a number (at least one but less than 10) by 10 to the nth power.
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