词汇(P-Z)

P
::P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P

parabola

The characteristic shape of a quadratic function graph, resembling a "U."

parallel

When two or more lines lie in the same plane and never intersect. These lines will always have the same slope.

partial sum

The sum of the 1st $\begin{array}{r}n\end{array}$  terms in an infinite series, where $\begin{array}{r}n\end{array}$  is some positive integer.

Pascal's Triangle

A triangular array of numbers constructed with the coefficients of binomials as they are expanded. The ends of each row of Pascal's Triangle are 1's, and every other number is the sum of the two nearest numbers in the row above.

percent

Percent means "out of 100." It is a quantity written with a % sign.

perfect square

A number whose square root is an integer.

perfect square trinomial

A quadratic expression of the form $\begin{array}{r}{a}^2+2ab+b^2\end{array}$  (which can be rewritten as $\begin{array}{r}(a+b{)}^2\end{array}$ ) or $\begin{array}{r}{a}^2-2ab+b^2\end{array}$  (which can be rewritten as $\begin{array}{r}(a-b{)}^2\end{array}$ ).

perimeter

The distance around a two-dimensional figure.

perpendicular

Lines that intersect at a $\begin{array}{r}{90}^{\circ }\end{array}$ angle. The product of the slopes of two perpendicular lines is -1.

piecewise-defined function

A function that pieces together two or more parts of other functions to create a new function.

place value

The value of a digit in a multi-digit number that is indicated by the place or position of the digit.

plane

A flat, two-dimensional surface. It can be conceptualized as a sheet of paper of infinite area.

plot

The process of graphing.

point

A location in space that does not have size or shape.

point of inflection

The point where the cube root function bends.

point-slope form

The point-slope form of a line is $\begin{array}{r}y-y_1=m(x-x_1),\end{array}$  where m is the slope of the line and $\begin{array}{r}(x_1,y_1)\end{array}$  is a point on the line.

polygon

A simple closed figure with at least three straight sides.

polynomial

A function is a polynomial function if it is of the form $\begin{array}{r}f(x)=a_n{x}^n+a_{n-1}{x}^{n-1}+...+a_2{x}^2+a_{1}x+a_0,\end{array}$ where the $\begin{array}{r}{a}_i\end{array}$  are real numbers and the $\begin{array}{r}n\end{array}$  are non-negative integers.

positive correlation

A positive correlation appears as a recognizable line with a positive slope.

power

Refers to the value of an exponent. For example, $\begin{array}{r}{3}^4\end{array}$  is "three to the fourth power."

power function

A polynomial of the form $\begin{array}{r}f(x)=a{x}^n,\end{array}$  where $\begin{array}{r}a\end{array}$  is a real number and $\begin{array}{r}n\end{array}$  is an integer with $\begin{array}{r}n\ge 1\end{array}$ .

power set

The set of all possible subsets of a set.

prime (algebraic expression)

When an algebraic expression cannot be written as a product of two other algebraic expressions (excluding 1 and -1).

prime factorization

Factoring a number into the product of its prime factors.

prime number

A number that has exactly two factors, one and itself.

principal root

The positive root of a number.

prism

A three-dimensional object with two congruent parallel bases that are polygons.

product

The result after two amounts have been multiplied.

proper fraction

A fraction whose numerator is less in absolute value than its denominator. Proper fractions always represent values between -1 and 1.

proper subset

A subset that contains some of the elements in the larger set, but not all of them.

proportion

An equation that shows two equivalent ratios.

pure imaginary number

A complex number with no real part.

pyramid

A three-dimensional object with a base that is a polygon and triangular faces that meet at one vertex.

Pythagorean Theorem

A mathematical relationship between the sides of a right triangle, given by $\begin{array}{r}{a}^2+b^2=c^2,\end{array}$ where $\begin{array}{r}a\end{array}$  and $\begin{array}{r}b\end{array}$  are legs of the triangle, and $\begin{array}{r}c\end{array}$  is the hypotenuse of the triangle .

Q
::质 质

quadrant

One-fourth of the coordinate plane. The four quadrants are numbered using Roman numerals I, II, III, and IV, starting in the top right and increasing counterclockwise.

quadratic equation

An equation that can be written in the form $\begin{array}{r}a{x}^2+bx+c=0\end{array}$ , where $\begin{array}{r}a\end{array}$ , $\begin{array}{r}b\end{array}$ , and $\begin{array}{r}c\end{array}$  are real constants and $\begin{array}{r}a\ne 0\end{array}$ .

quadratic formula

For any quadratic equation in the form $\begin{array}{r}a{x}^2+bx+c=0\end{array}$ , $\begin{array}{r}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\end{array}$ .

quadratic in form

An algebraic expression that has two or three terms and can be factored like a quadratic expression.

quotient

The result after two amounts have been divided.

R
::R R

radical

The $\begin{array}{r}\sqrt{}\end{array}$ , or square root, sign.

radicand

The number under the radical.

radius

The distance from the center of the circle to the edge of the circle.

range

The set of $\begin{array}{r}y\end{array}$ -values or output values for a function.

rate

A special kind of ratio that compares two quantities.

rate of change

The quantity we use to compare changes in the dependent values to the independent values.

ratio

A comparison of two quantities that can be written in fraction form, with a colon or with the word "to."

rational expression

A fraction with polynomials in the numerator and denominator.

rational function

Any function that can be written as the ratio of two polynomial functions.

rational numbers

Any number that can be written as a fraction  $\begin{array}{r}\frac{p}{q}\end{array}$ , where $\begin{array}{r}p\end{array}$  and $\begin{array}{r}q\end{array}$  are integers. In decimal form, these are terminating decimals, and non-terminating, repeating decimals.

Rational Root Theorem

For a polynomial,  $\begin{array}{r}f(x)=a_n{x}^n+a_{n-1}{x}^{n-1}+\cdots +a_{1}x+a_0,\end{array}$  where $\begin{array}{r}{a}_n,a_{n-1},\cdots ,a_0\end{array}$  are integers, the rational roots can be determined from the factors of $\begin{array}{r}{a}_n\end{array}$  and $\begin{array}{r}{a}_0\end{array}$ . More specifically, if $\begin{array}{r}p\end{array}$  is a factor of $\begin{array}{r}{a}_0\end{array}$  and $\begin{array}{r}q\end{array}$  is a factor of $\begin{array}{r}{a}_n\end{array}$ , then all the rational factors will have the form $\begin{array}{r}\pm \frac{p}{q}\end{array}$ .

rationalizing the denominator

Rewriting a fraction so the denominator no longer contains a radical.

real number line

A line used to represent the real numbers graphically.

real numbers

Any number that can be expressed as a decimal.

real part

The real part of a complex number $\begin{array}{r}a+bi\end{array}$  is $\begin{array}{r}a\end{array}$ .

reciprocal

The number you multiply another number by to get one. The reciprocal of 2 is 1/2. It is also called the multiplicative inverse, or just inverse.

rectangular coordinate system

The system in which a point is written using rectangular coordinates, if it is written in terms of $\begin{array}{r}x\end{array}$  and $\begin{array}{r}y\end{array}$  and can be graphed on the Cartesian plane.

recursive sequence

The recursive formula for a sequence allows you to find the value of the $\begin{array}{r}{n}^{th}\end{array}$  term in the sequence if you know the value of the $\begin{array}{r}(n-1{)}^{th}\end{array}$  term in the sequence.

reflection

A transformation that flips a figure on the coordinate plane across a given line without changing the shape or size of the figure.

relation

Any set of ordered pairs $\begin{array}{r}(x,y)\end{array}$ . A relation can have more than one output for a given input.

relative maximum/minumum

The relative extrema (maximum/minimum) of a function are the points of the function with $\begin{array}{r}y\end{array}$  values that are the highest or lowest of a local neighborhood of the function.

remainder

The value left over if the divisor does not divide evenly into the dividend.

removable discontinuity

Removable discontinuities, also known as holes, occur when factors can be algebraically canceled from rational functions.

rigid transformation

A transformation that preserves distance and angles; it does not change the size or shape of the figure.

roots

The roots of a function are the values of $\begin{array}{r}x\end{array}$  that make $\begin{array}{r}y\end{array}$  equal to zero.

S
::S S 级

scatter plot

A plot of the dependent variable versus the independent variable. It is used to investigate whether or not there is a relationship or connection between two sets of data.

scientific notation

A means of representing a number as a product of a number that is at least 1, but less than 10 and a power of 10.

sequence

An ordered list of numbers or objects.

series

The sum of the terms of a sequence.

set

A collection of objects.

set-builder notation

A notation in which the 1st part indicates the number system we are using, and the 2nd part indicates the condition or restriction on that number system.

sigma notation

A way to represent a sum of numbers. It is especially useful when the numbers have a specific pattern or would take too long to write out without abbreviation. It is  also known as summation notation.

simple interest

Interest calculated on the original principal only. It is calculated by finding the product of the the principal, the rate, and the time.

slope

A measure of the steepness of a line. A line can have positive, negative, zero (horizontal), or undefined (vertical) slope. The slope of a line can be found by calculating "rise over run" or "the change in the $\begin{array}{r}y\end{array}$  over the change in the $\begin{array}{r}x\end{array}$ ." The symbol for slope is  $\begin{array}{r}m\end{array}$ .

slope-intercept form

The slope-intercept form of a line is $\begin{array}{r}y=mx+b\end{array}$ , where $\begin{array}{r}m\end{array}$  is the slope and $\begin{array}{r}b\end{array}$  is the $\begin{array}{r}y\end{array}$ -intercept.

smooth

A smooth function is, as the word implies, smooth. There are no corners or cusps.

solid figure

A three-dimensional figure with height, width, and depth.

solution

A solution to an equation or inequality should result in a true statement when substituted for the variable in the equation or inequality.

solution set

A set of numbers that are solutions to an equation or inequality.

solving

The process of finding solutions to an equation or inequality.

sphere

A round, three-dimensional solid. All points on the surface of a sphere are equidistant from the center of the sphere.

square root

A value that must be multiplied by itself to equal the specified term. The square root of 9 is 3, since $\begin{array}{r}3\times 3=9\end{array}$ .  

square root method

If $\begin{array}{r}{a}^2=b\end{array}$ , then $\begin{array}{r}a=\pm \sqrt{b}\end{array}$ .

standard form of a cube root function

  $\begin{array}{r}y=a\sqrt[3]{x-h}+k\end{array}$

standard form of a logarithmic function

  $\begin{array}{r}f(x)={\log }_b(x-h)+k,\end{array}$  where $\begin{array}{r}h\end{array}$  and $\begin{array}{r}k\end{array}$  are real numbers.

standard form of a quadratic function

  $\begin{array}{r}y=f(x)=a(x-h{)}^2+k,\end{array}$  where $\begin{array}{r}a\end{array}$ , $\begin{array}{r}h\end{array}$ , and $\begin{array}{r}k\end{array}$  are real numbers and $\begin{array}{r}a\ne 0\end{array}$ .

standard form of a reciprocal function

  $\begin{array}{r}f(x)=\frac{a}{x-h}+k\end{array}$

standard form of a square root function

  $\begin{array}{r}y=a\sqrt{x-h}+k\end{array}$

standard form of an exponential function

A function whose variable is in the exponent. The standard form is $\begin{array}{r}y=a\cdot b^{x-h}+k\end{array}$ .

subset

A collection of numbers or objects within a larger set.

substitute

In algebra, to substitute means to replace a variable or term with a specific value.

sum

The result after two or more amounts have been added together.

sum of two cubes

The sum of cubes formula is $\begin{array}{r}{a}^3+b^3=(a+b)(a^2-ab+b^2)\end{array}$ .

summation notation

The notation used as a shorthand to indicate the sum of a sequence of numbers.

surface area

The total area of all of the surfaces of a three-dimensional object.

symmetry

A figure has symmetry if it can be transformed and still look the same.

synthetic division

A shorthand version of polynomial long division in which only the coefficients of the polynomial are used.

system of equations

A set of two or more equations.

T
::T T T T T

tangent line

A line that "just touches" a curve at a single point.

term

A group of variables and constants not separated by addition or subtraction.

term of a sequence

A sequence is a numbered collection of terms.

test point

A point to test a solution set of an inequality.

three space

Coordinate geometry in three dimensions: length, width, and height or depth.

transformation

A transformation moves a figure in some way on the coordinate plane.

translation

A transformation that slides a figure on the coordinate plane  left, right, up, and/or down  without changing its shape, size, or orientation.

transverse axis

For a hyperbola with equation of the form $\begin{array}{r}\frac{(x-h{)}^2}{a^2}-\frac{(y-k{)}^2}{b^2}=1\end{array}$  or $\begin{array}{r}\frac{(y-k{)}^2}{a^2}-\frac{(x-h{)}^2}{b^2}=1\end{array}$ , the transverse axis travels from vertex to vertex and has length $\begin{array}{r}2a\end{array}$ .

trinomial

A polynomial with three terms.

two-step equation

An algebraic equation with two operations in it that requires two steps to solve.

two-step inequality

An algebraic inequality that requires two steps to solve.

U
::U U

unbounded interval

Intervals with only one endpoint or no endpoints—those that continue forever in at least one direction.

undefined

An expression in mathematics that has no meaning. Division by zero is undefined.  

union

The union of two sets is the set that contains all the elements in both sets.  $\begin{array}{r}\cup \end{array}$  is the symbol that is used. The operation of union is associated with the logical term OR.

unit

A quantity used in measurement.

unit rate

A ratio that compares a quantity to one.

universal set

The set of all the elements in a given situation.

upper nappe

The surface of the upper cone in a double right-circular cone.

V
::五五

variable

A symbol used to represent an unknown or changing quantity.

Venn diagram

A pictorial representation of the relationships between sets.

vertex

The points of intersection of the conic section with the axis.

vertex angle

The angle between the axis and the generator of a double right-circular cone.

vertical asymptote

A vertical line marking a specific value toward which the graph of a function may approach, but will never reach.

vertical line test

If a vertical line drawn anywhere through the graph of a relation intersects the relation in more than one location, then the relation is not  a function.

vertices

The plural of vertex.

volume

The amount of space inside the bounds of a three-dimensional object.

W
::西 西

whole numbers

All positive counting numbers and zero. The whole numbers are 0, 1, 2, 3, ...

X
::X 十

x-axis

The horizontal axis is also referred to as the x-axis of a coordinate graph. By convention, we graph the input variable on the x-axis.

x-coordinate

The 1st term in a coordinate pair, commonly representing the value of the input or independent variable.

x-intercept

A location where a graph crosses the x-axis. As a coordinate pair, this point will always have the form $\begin{array}{r}(x,0).\end{array}$  x-intercepts are also called solutions, roots, or zeros.

Y
::Y Y Y

y-axis

The vertical axis is also referred to as the y-axis of a coordinate graph. By convention, we graph the output variable on the y-axis.

y-coordinate

The 2nd term in a coordinate pair, commonly representing the value of the output or dependent variable.

y-intercept

A location where a graph crosses the y-axis. As a coordinate pair, this point will always have the form $\begin{array}{r}(0,y)\end{array}$ .

Z
::兹

z-axis

A 3rd axis in three-dimensional space that is perpendicular to the x- and y-axes.

zero-product property

If $\begin{array}{r}ab=0\end{array}$ , then either $\begin{array}{r}a=0\end{array}$  or $\begin{array}{r}b=0\end{array}$ .

zeros of the function

The zeros of a function $\begin{array}{r}f(x)\end{array}$  are the values of $\begin{array}{r}x\end{array}$  that cause $\begin{array}{r}f(x)\end{array}$  to be equal to zero.