Section 1
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zero product property
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Cards (105)
Section 1
(50 cards)
zero product property
Any number multiplied by zero equals zero.
extraneous solution
A result that does not satisfy the original equation or inequality.
additive inverse
The opposite of a number. When added together, the sum is zero.
multiplicative identity property
Multiplying a number by one equals that number.
linear equation
An equation whose variables have an exponent of one and whose graph creates a straight line.
integer
All whole numbers and their opposites.
commutative property
Changing the order of addition or multiplication does not change the value. Ex: a+b+c = c+a+b
axis of symmetry
The line that divides a graph into two symmetrical parts.
deductive reasoning
The process of using logic to draw conclusions.
associative property
The grouping of terms within expressions involving addition or multiplication does not change the value. Ex: (a+b) + c = a + (b+c)
grouping symbols
Symbols such as parentheses and brackets, which separate terms within an expressions. Others include fraction bars, absolute value, square root, braces, etc.
consistent system
A system of equations with at least one solution.
irrational number
Numbers that cannot be expressed as fractions or terminating/repeating decimals.
inequality
A sentence using greater than or less than symbols. Also, greater than or equal to, or less than or equal to.
discriminant
The expression inside the radical of the quadratic formula.
algebraic expression
A collection of numbers and variables with at least one arithmetic operation.
absolute value
The distance between a real number and zero on a number line.
exponent
The number of times a base is multiplied by itself. Also called a power.
opposites
Numbers that have the same absolute value.
isolate the variable
Collecting like terms and using inverse operations to get a variable by itself on one side of a relation.
no solution
When there is no answer to an equation or inequality.
compound inequality
Two inequalities combined in one statement by the word and or or.
inconsistent system
A system of equations that has no solution.
like terms
Terms with the same variables raised to the same exponents.
factor
An integer that divides another integer with no remainder.
function notation
When the output (y) of a relation is renamed f(x). Read "f of x".
denominator
The lower half of a fraction.
constant
A term with no variables.
graphing
The act of plotting points on a plane to represent a function or relation.
function
A relation in which every input (x) has exactly one output (y).
multiplicative inverse
Two numbers multiplied together that equal one.
combine like terms
Adding or subtracting terms that have the same variable(s) and exponent(s).
difference of two squares
A binomial whose terms are perfect squares being subtracted.
coefficient
The numerical value of a term.
direct variation
An equation in the form y=kx, where k does not equal zero.
base
The repeated factor of a number written in exponential form.
independent system
A system of equations that has exactly one solution.
order of operations
The rules for evaluating an expression.
evaluate
To find the value of an expression by following the order of operations.
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
dependent system
A system of equations that has infinite solutions.
natural number
The set of counting numbers starting with one.
coordinates
Ordered pairs that identify points on a plane.
numerator
The upper half of a fraction.
binomial
A two-term polynomial.
coordinate plane
Formed by two number lines that cross each other at zero.
monomial
An expression with a one term.
greatest common factor
The largest number that divides into two terms.
equation
A mathematical sentence with an equal sign.
difference
The answer to a subtraction problem.
Section 2
(50 cards)
x-axis
The horizontal number line of a coordinate plane.
quadrant
One of four regions of a coordinate plane.
y-intercept
The point where a graph touches the y-axis. Sometimes represented by the letter b.
quadratic expression
An expression in this form with a, b and c being numbers.
dependent variable
The y-value, or output, of a relation, whose value depends on the input.
ratio
The relationship of two quantities, often shown using division.
property
A law that governs mathematics.
standard form of an equation
An equation in this form, where A, B and C are integers and A is positive.
sum
The answer to an addition problem.
parallel
Lines or planes that never intersect.
rational expression
A fraction that has polynomials in the numerator and denominator.
degree
The sum of the exponents in a monomial.
solve
The process of finding all values of a variable that make an equation or inequality true.
ordered pair
A pair of numbers used to identify a point (x, y) on a coordinate plane.
term
A number and/or variable(s), or a combination of both being multiplied or divided.
rise
The difference between two y-values on a linear graph.
y-axis
The vertical number line of a coordinate plane.
slope-intercept form
An equation of a line in this form, with m as the slope and b as the y-intercept.
variable
Symbols, usually letters, used to represent unspecified values.
standard form of polynomials
When terms are placed in descending order according to their degree.
real number
All rational and irrational numbers.
perfect square
A number with a square root that is rational.
domain
The set of x-values in a relation.
range
The set of y-values in a relation.
perpendicular
Lines or planes that intersect at right angles.
slope
A measure of steepness of a line. Often represented by the letter m. Calculated by finding the ratio of the change in y-coordinates (rise) to the change in x-coordinates (run).
reciprocal
The multiplicative inverse of a number. Created by switching the numerator and the denominator.
simplify
To reduce an expression to as few terms as possible.
replacement set
A set of solutions that can replace a variable.
parabola
A U-shaped graph created by a quadratic function. Can also be upside down.
trinomial
An expression with three terms.
rate
The ratio that compares two quantities in different units.
counterexample
A specific case that makes a statement false.
origin
The intersection of the axes in a coordinate plane.
line of best fit
A line drawn through a scatter plot to best represent the data.
undefined
No solution.
whole number
All natural (counting) numbers and zero.
terminating decimal
A rational number that does not repeat or continue indefinitely after the decimal.
x-intercept
The point where a graph touches the x-axis. Also referred to as roots or zeros.
polynomial
An expression with one or more monomials being added or subtracted.
product
The answer to a multiplication problem.
quotient
The answer to a division problem.
quadratic formula
A method of finding roots of a quadratic function by replacing a, b and c with numbers.
simplest form
An expression that contains no like terms or parentheses.
rational number
Any number that can be written as a fraction.
repeating decimal
A rational number that has a block of one or more numbers after the decimal that continually show up.
system of equations
A set of two or more equations with two or more variables.
run
The difference between two x-values on a linear graph.
point-slope form
An equation of a line in this form:
independent variable
The x-value, or input, of a relation, which determines the output.
Section 3
(5 cards)