Face
Any of the flat surfaces of a solid figure.
Fact family
A group of related addition and subtraction (or multiplication and division) facts that use the same three numbers.
Factor
A number that is multiplied by another to give a product. A factor of a number divides it evenly: 3 and 4 are factors of 12.
Factor pair
Two numbers that multiply to give a certain number. The factor pairs of 12 are 1 × 12, 2 × 6 and 3 × 4.
Factor theorem
A polynomial f(x) has (x − a) as a factor exactly when f(a) = 0.
Factor tree
A diagram that breaks a number into factors step by step until only prime numbers remain.
Factorial
The product of all positive whole numbers from 1 up to n, written n!.
Factoring
Rewriting an expression as a product of its factors, such as x² + 5x + 6 = (x + 2)(x + 3).
Fahrenheit
A temperature scale on which water freezes at 32° and boils at 212° at sea level.
Fair game
A game in which every player has the same chance of winning.
Fibonacci numbers
The sequence 1, 1, 2, 3, 5, 8, 13, … in which each number after the first two is the sum of the two before it.
Figure
A shape in two or three dimensions, such as a square, triangle, cube or sphere.
Finite
Having a definite end or a countable number of elements.
First quartile
The median of the lower half of a data set, written Q1. About 25% of the data fall below it.
Five-number summary
The minimum, first quartile, median, third quartile and maximum of a data set, which are used to draw a box plot.
Flip
A transformation that makes a mirror image of a figure across a line; also called a reflection.
Fluid ounce
A US customary unit of liquid volume. There are 16 fluid ounces in a pint, and 1 fl oz is about 29.6 mL.
Focus
A fixed point used to define a conic section. On a parabola, rays parallel to the axis reflect through the focus.
FOIL method
A way to multiply two binomials: First, Outer, Inner, Last.
Foot
A US customary unit of length equal to 12 inches, about 30.5 cm.
Formula
An equation that states a general rule, such as A = l × w for the area of a rectangle.
Fractal
A pattern in which smaller copies of the whole shape repeat at every scale, such as the Sierpiński triangle.
Fraction
A number that names part of a whole or part of a set, written as a numerator over a denominator.
Fractional exponent
An exponent written as a fraction, which means a root: x^(1/n) is the nth root of x.
Fractional form
A number written as a fraction, such as 3/4 for 0.75 or 75%.
Frequency
The number of times a value or event occurs in a data set.
Frequency polygon
A line graph made by joining the midpoints of the tops of a histogram's bars.
Frequency table
A table that lists each value or category and how often it occurs.
Frustum
The part of a cone or pyramid left after the top is cut off by a plane parallel to the base.
Function
A rule that assigns exactly one output to each input.
Function notation
A way of naming a function and its input, such as f(x) = 2x + 1, read "f of x".
Fundamental counting principle
If one choice can be made in m ways and a second in n ways, the two can be made together in m × n ways.
Fundamental theorem of algebra
Every polynomial of degree n has exactly n roots, counting complex and repeated roots.
Fundamental theorem of arithmetic
Every whole number greater than 1 is either prime or can be written as a product of primes in exactly one way.
Fundamental theorem of calculus
Connects derivatives and integrals: the definite integral of f from a to b equals F(b) − F(a), where F is an antiderivative of f.