i
The imaginary unit, defined so that i² = −1, or i = √−1.
Identity property
Adding 0 or multiplying by 1 leaves a number unchanged: a + 0 = a and a × 1 = a.
Image
The figure that results from a transformation, labeled with primes, such as A′B′C′.
Imaginary number
A number that is a real number times i, such as 3i. Its square is negative.
Impossible event
An event that cannot happen. Its probability is 0.
Improper fraction
A fraction whose numerator is greater than or equal to its denominator, such as 7/4 or 5/5.
Incenter
The point where the three angle bisectors of a triangle meet. It is the center of the circle that fits inside the triangle and touches all three sides.
Inch
A US customary unit of length. There are 12 inches in a foot, and 1 inch equals 2.54 cm.
Included angle
The angle formed between two given sides of a triangle.
Increasing function
A function whose output values go up as the input values go up.
Indefinite integral
The family of all antiderivatives of a function, written with ∫ and a constant C, such as ∫ 2x dx = x² + C.
Independent events
Events where the outcome of one does not change the probability of the other, such as two separate coin flips.
Independent variable
The variable you choose or change, usually x, shown on the horizontal axis. The dependent variable responds to it.
Inductive reasoning
Reaching a general conclusion from patterns in specific examples. The conclusion is likely but not certain.
Inequality
A statement that two quantities are not equal, using <, >, ≤, ≥ or ≠.
Infinite
Without end or limit, such as the set of counting numbers.
Infinity
The idea of a quantity larger than any number, written ∞. It is not itself a number.
Inflection point
A point on a curve where it changes from curving up (concave up) to curving down, or the reverse.
Input-output table
A table that lists inputs and the outputs a rule gives for them.
Inscribed angle
An angle whose vertex is on a circle and whose sides are chords. It is half the central angle that intercepts the same arc.
Integers
The whole numbers and their opposites: …, −3, −2, −1, 0, 1, 2, 3, …
Interest
Money paid for the use of money, either earned on savings or charged on a loan. Simple interest is I = Prt.
Interior angle
An angle inside a polygon, formed by two sides that meet at a vertex.
Interquartile range
The difference between the third and first quartiles, IQR = Q3 − Q1. It measures the spread of the middle half of the data.
Intersecting lines
Lines that cross at exactly one point.
Intersection
The set of elements that belong to both of two sets, written A ∩ B. In geometry, the point or points where figures meet.
Interval notation
A way to write a set of numbers between two endpoints using brackets for included ends and parentheses for excluded ends, such as [2, 5).
Inverse function
A function that undoes another, written f⁻¹. Its graph is the reflection of f across the line y = x.
Inverse operations
Operations that undo each other, such as addition and subtraction, or multiplication and division.
Inverse variation
A relationship where one quantity goes down as the other goes up so their product stays the same: xy = k, or y = k/x.
Invert
To flip a fraction by swapping its numerator and denominator. Inverting 2/5 gives 5/2, its reciprocal.
Irrational number
A number that cannot be written as a fraction of two integers. Its decimal goes on forever without repeating, like √2 or π.
Irregular polygon
A polygon whose sides and angles are not all equal.
Isosceles trapezoid
A trapezoid whose two non-parallel sides (legs) are equal in length.
Isosceles triangle
A triangle with at least two equal sides. The angles opposite those sides are also equal.