This math glossary gathers the words students meet from 6th to 12th grade: numbers, ratios, expressions, equations, functions, geometry, statistics, probability, trigonometry and calculus. Each entry gives a one-sentence definition, an explanation and a worked example, then links to the Math Made Easy lesson where the term is taught.
Terms are sorted by topic. Pick a topic, then a word, to check the exact meaning of a term before a worksheet, a quiz or a test. The definitions follow the Common Core State Standards and the AP courses: a 6th grader finds “ratio” or “mean absolute deviation”, while an AP student finds “derivative” or “p-value”. When a word grows from one grade to the next, the entry says so and gives an example at the right level.
To go further, each entry leads to the lessons , the worksheets and the tests of the chapter where the term is taught. Read the definition, redo the example by hand, then solve a problem: that is the best way to remember a word for good.
Math Made Easy glossary: every key math term from 6th to 12th grade, defined in one sentence, explained with a worked example and linked to the lesson where it is taught.
A B C D E F G H I K L M N O P Q R S T U V Y Z A Geometry AA Similarity The AA criterion states that if two angles of one triangle are congruent to two angles… Geometry AAS Congruence The AAS criterion states that if two angles and a non-included side of one triangle match… Functions Absolute Value Function The absolute value function f(x) = |x| returns the distance of x from zero, and its… Numbers Absolute Value The absolute value of a number is its distance from zero on the number line, so… Geometry Adjacent Angles Adjacent angles are two angles that share a common vertex and a common side, but do… Algebra Algebraic Expression An algebraic expression is a mathematical phrase that combines numbers, variables, and operation symbols, but has… Geometry Alternate Interior Angles Alternate interior angles lie between two lines on opposite sides of a transversal; when the lines… Functions Amplitude The amplitude of a sine or cosine graph is half the distance between its maximum and… Geometry Angle Bisector An angle bisector is a ray from the vertex of an angle that splits it into… Geometry Angle of Elevation The angle of elevation is the angle between the horizontal line of sight and the line… Calculus Antiderivative An antiderivative of f is a function F whose derivative is f; every function has a… Geometry Arc Length Arc length is the distance along a circle between two points, equal to the fraction (angle… Measurement Area of a Circle The area of a circle is pi times the square of its radius, A = pi… Measurement Area of a Triangle The area of a triangle equals one half times its base times its height, A =… Algebra Arithmetic Sequence An arithmetic sequence is an ordered list of numbers in which each term is found by… Algebra Arithmetic series An arithmetic series is the sum of the terms of an arithmetic sequence, whose consecutive terms… Geometry ASA Congruence The ASA criterion states that if two angles and the included side of one triangle match… Functions Asymptote An asymptote is a line that a graph gets closer and closer to without ever settling… Functions Average Rate of Change The average rate of change of a function over an interval is the change in output… Functions Axis of Symmetry The axis of symmetry of a parabola is the vertical line through its vertex that divides… C Geometry Cavalieri's Principle Cavalieri's principle says that two solids of equal height have equal volume if every parallel cross-section… Geometry Central Angle A central angle has its vertex at the center of a circle, and its measure equals… Statistics Central limit theorem The central limit theorem says the distribution of sample means becomes approximately normal as the sample… Geometry Centroid The centroid of a triangle is the point where its three medians meet, the triangle center… Calculus Chain rule The chain rule differentiates a composite function: the derivative of f of g of x is… Functions Change of base formula The change of base formula rewrites a logarithm in any base as a quotient of logarithms… Statistics Chi-square test A chi-square test compares observed counts with expected counts in categorical data to judge whether a… Geometry Chord A chord is a segment whose endpoints both lie on a circle; the longest chord is… Geometry Circumcenter The circumcenter of a triangle is the point where the three perpendicular bisectors of its sides… Measurement Circumference Circumference is the distance around a circle, equal to pi times the diameter, or C =… Algebra Coefficient A coefficient is the number multiplied by a variable in a term, such as the 9… Algebra Common Difference The common difference is the constant amount added to each term of an arithmetic sequence to… Algebra Common Ratio The common ratio is the constant multiplier that takes each term of a geometric sequence to… Geometry Complementary Angles Complementary angles are two angles whose measures add up to 90 degrees, and together they form… Algebra Completing the Square Completing the square rewrites a quadratic expression as a squared binomial plus a constant by adding… Numbers Complex conjugate The conjugate of the complex number a + bi is a - bi, the same number… Numbers Complex number A complex number is a number of the form a + bi, where a and b… Functions Composition of functions Composition of functions means feeding the output of one function into another, written (f o g)(x)… Probability Compound Event A compound event is an event made of two or more simple events, such as flipping… Algebra Compound Inequality A compound inequality joins two inequalities with and or or; an and statement describes an overlap… Functions Compound Interest Compound interest is interest earned on both the original principal and the interest already added, giving… Calculus Concavity Concavity describes how a graph bends: concave up when the slope is increasing, which means the… Conditional Statement A conditional statement has the form if p, then q; it is false only when p… Statistics Confidence interval A confidence interval is a range of plausible values for a population parameter, built from sample… Geometry Congruent Figures Congruent figures have exactly the same shape and size, so one can be moved onto the… Geometry Conic section A conic section is a curve formed by slicing a double cone with a plane; the… Algebra Constant of Proportionality The constant of proportionality is the constant ratio y/x in a proportional relationship, the number k… Calculus Continuity A function is continuous at a point when the limit exists there, the function is defined… Geometry Coordinate Plane The coordinate plane is a flat grid formed by a horizontal x-axis and a vertical y-axis… Statistics Correlation coefficient The correlation coefficient r measures the strength and direction of a linear relationship between two quantitative… Statistics Correlation vs. Causation Correlation means two variables move together; causation means a change in one produces a change in… Geometry Corresponding Angles Corresponding angles occupy the same relative position at two intersections of a transversal; when the lines… Geometry Cosine Ratio In a right triangle, the cosine of an acute angle is the length of the side… Counterexample A counterexample is a single specific case that satisfies the hypothesis of a statement but fails… Geometry CPCTC CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent; once triangles are proven congruent, all… Calculus Critical point A critical point of a function is an input where the derivative equals zero or fails… Geometry Cross Section A cross section is the two-dimensional shape you see when a plane slices through a three-dimensional… Numbers Cube Root The cube root of a number is the value that, when used as a factor three… E Algebra Elimination Method The elimination method solves a system by adding or subtracting the equations, after scaling them if… Geometry Ellipse An ellipse is the set of points whose distances to two fixed points, the foci, add… Functions End behavior End behavior describes what happens to the values of a function as x grows very large… Geometry Equation of a Circle The equation of a circle with center (h, k) and radius r is (x - h)^2… Algebra Equation An equation is a mathematical statement that two expressions are equal, joined by an equal sign,… Algebra Equivalent Expressions Equivalent expressions are expressions that have the same value for every value of their variables, even… Numbers Equivalent Ratios Equivalent ratios are ratios that express the same relationship, found by multiplying or dividing both quantities… Algebra Evaluate an Expression To evaluate an expression means to replace each variable with a given number and then calculate… Algebra Explicit Formula An explicit formula gives the nth term of a sequence directly from its position n, so… Operations Exponent An exponent tells how many times a base is used as a factor in repeated multiplication,… Functions Exponential Decay Exponential decay occurs when a quantity is multiplied by the same factor between 0 and 1… Algebra Exponential equation An exponential equation has the unknown in an exponent, such as 4 to the x equals… Functions Exponential Growth Exponential growth occurs when a quantity is multiplied by the same factor greater than 1 in… I Numbers Imaginary unit The imaginary unit, written i, is the number whose square is negative 1, so i equals… Calculus Implicit differentiation Implicit differentiation finds dy/dx for a relation where y is not isolated, by differentiating both sides… Geometry Incenter The incenter of a triangle is the point where its three angle bisectors meet; it is… Algebra Independent and Dependent Variables The independent variable is the input that you choose or change, and the dependent variable is… Algebra Inequality An inequality is a mathematical statement that compares two expressions using less than, greater than, at… Calculus Inflection point An inflection point is a point on a continuous graph where the concavity changes, so the… Geometry Inscribed Angle An inscribed angle has its vertex on a circle and its sides are chords; its measure… Numbers Integer An integer is any whole number or its opposite, including positive whole numbers, negative whole numbers,… Statistics Interquartile Range The interquartile range, or IQR, is the difference between the third quartile and the first quartile,… Functions Inverse function An inverse function reverses another function: if f sends x to y, then f inverse sends… Algebra Inverse matrix The inverse of a square matrix A is the matrix that multiplies with A to give… Functions Inverse sine function The inverse sine function, written arcsin or sin inverse, returns the angle between negative pi over… Geometry Inverse Trigonometric Functions Inverse trigonometric functions take a ratio of sides and return the acute angle that produces it;… Numbers Irrational Number An irrational number is a real number that cannot be written as a fraction of two… M Geometry Magnitude of a vector The magnitude of a vector is its length, found with the Pythagorean theorem: for the vector… Statistics Margin of error The margin of error is the amount added and subtracted from a sample estimate to form… Algebra Matrix multiplication Matrix multiplication builds each entry of the product by taking the dot product of a row… Algebra Matrix A matrix is a rectangular array of numbers arranged in rows and columns, used to organize… Statistics Mean Absolute Deviation Mean absolute deviation, or MAD, is the average distance of the data values from their mean,… Calculus Mean value theorem The mean value theorem says that for a function continuous on [a, b] and differentiable inside,… Statistics Mean The mean is the average of a data set, found by adding all the values and… Geometry Median of a Triangle A median of a triangle is a segment from a vertex to the midpoint of the… Statistics Median The median is the middle value of a data set when the numbers are listed in… Geometry Midpoint The midpoint of a segment is the point exactly halfway between its endpoints, dividing the segment… Geometry Midsegment of a Triangle A midsegment of a triangle joins the midpoints of two sides; it is parallel to the… Statistics Mode The mode is the value that appears most often in a data set, and a set… Algebra Monomial A monomial is a polynomial with exactly one term: a number, a variable, or a product… P Statistics P-value The p-value is the probability, assuming the null hypothesis is true, of getting a result at… Functions Parabola A parabola is the U-shaped curve that is the graph of a quadratic function; it is… Geometry Parallelogram A parallelogram is a quadrilateral with two pairs of parallel sides; its opposite sides are congruent,… Functions Parametric equations Parametric equations describe a curve by giving x and y each as a function of a… Operations PEMDAS PEMDAS is a memory aid for the order of operations: Parentheses, Exponents, Multiplication and Division, then… Numbers Percent Change Percent change is the amount of increase or decrease in a quantity, written as a percent… Numbers Percent Increase and Discount A markup or discount is a percent of the original price that is added to or… Numbers Percent A percent is a ratio that compares a number to 100, written with the symbol %,… Algebra Perfect Square Trinomial A perfect square trinomial is a trinomial that equals a binomial squared: a^2 + 2ab +… Numbers Perfect Square A perfect square is a number that equals an integer multiplied by itself, such as 49… Functions Period of a function The period of a repeating function is the length of the shortest interval after which its… Geometry Perpendicular Bisector A perpendicular bisector of a segment is a line that passes through its midpoint at a… Functions Phase shift A phase shift is the horizontal translation of a trigonometric graph; for y = A sin(B(x… Geometry Pi Pi is the constant ratio of any circle's circumference to its diameter, an irrational number approximately… Functions Piecewise Function A piecewise function uses different rules on different parts of its domain, so its graph is… Functions Point-Slope Form Point-slope form writes a line as y - y1 = m(x - x1), using the slope… Geometry Polar coordinates Polar coordinates locate a point by its distance r from the origin and its angle theta… Numbers Polar form of a complex number The polar form of a complex number writes it as r(cos theta + i sin theta),… Geometry Polygon A polygon is a closed flat figure made of three or more straight line segments that… Algebra Polynomial A polynomial is an expression made of terms that are numbers times variables raised to whole-number… Statistics Population and Sample A population is the entire group you want to learn about, and a sample is the… Probability Probability Probability is a number from 0 to 1 that measures how likely an event is to… Calculus Product rule The product rule gives the derivative of two functions multiplied together: the derivative of f times… Algebra Proportional Relationship A proportional relationship is a relationship between two quantities in which the ratio of one to… Geometry Pythagorean Theorem The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the… R Measurement Radian A radian is the angle at the center of a circle that cuts off an arc… Algebra Radical Expression A radical expression contains a root symbol, such as the square root or cube root of… Functions Range of a Function The range of a function is the set of all output values, usually y-values, that the… Statistics Range The range of a data set is the difference between its greatest value and its least… Functions Rate of Change The rate of change describes how fast one quantity changes compared with another, found by dividing… Numbers Rate A rate is a ratio that compares two quantities measured in different units, such as miles… Numbers Ratio A ratio is a comparison of two quantities by division, written a:b, a to b, or… Algebra Rational Exponent A rational exponent is a fractional power: a^(m/n) means the nth root of a, raised to… Functions Rational function A rational function is a ratio of two polynomials, f(x) = p(x)/q(x) with q(x) not zero,… Numbers Rational Number A rational number is any number that can be written as a fraction of two integers… Geometry Ray A ray is a part of a line that starts at one endpoint and extends forever… Numbers Reciprocal The reciprocal of a nonzero number is the number you multiply it by to get 1,… Algebra Recursive Formula A recursive formula defines each term of a sequence from the term or terms before it,… Geometry Reflection A reflection is a transformation that flips a figure over a line, called the line of… Calculus Related rates Related rates problems connect how fast several changing quantities move over time, using an equation that… Statistics Relative Frequency Relative frequency is the fraction or percent of the total that falls in a category, found… Algebra Remainder theorem The remainder theorem states that when a polynomial f(x) is divided by x - c, the… Statistics Residual plot A residual plot graphs the differences between observed and predicted values against the predictor, showing whether… Statistics Residual A residual is the difference between an observed y-value and the y-value predicted by a model,… Geometry Rhombus A rhombus is a parallelogram with four congruent sides; its diagonals are perpendicular and bisect the… Calculus Riemann sum A Riemann sum approximates the area under a curve by adding the areas of thin rectangles… Geometry Rigid Motion A rigid motion is a transformation that preserves distance and angle measure, so the image is… Geometry Rotation A rotation is a transformation that turns every point of a figure by a given angle… S Probability Sample Space The sample space of an experiment is the set of all possible outcomes, which can be… Statistics Sampling distribution A sampling distribution shows how a statistic, such as a sample proportion or mean, varies across… Geometry SAS Congruence The SAS criterion states that if two sides and the included angle of one triangle match… Geometry Scale Drawing A scale drawing is a smaller or larger picture of a real object in which all… Geometry Scale Factor A scale factor is the number by which every length of a figure is multiplied to… Statistics Scatter Plot A scatter plot is a graph of ordered pairs that shows the relationship between two numerical… Numbers Scientific Notation Scientific notation writes a number as a product of a value from 1 up to 10… Geometry Sector of a Circle A sector is the region of a circle bounded by two radii and the arc between… Algebra Sigma notation Sigma notation uses the Greek letter sigma to write a sum compactly, showing a formula, an… Geometry Similar Figures Similar figures have the same shape but not necessarily the same size, with equal corresponding angles… Numbers Simple Interest Simple interest is money earned or owed on only the original amount, calculated with the formula… Statistics Simple Random Sample A simple random sample is a sample chosen so that every member of the population has… Geometry Sine Ratio In a right triangle, the sine of an acute angle is the length of the side… Calculus Slope field A slope field is a grid of short line segments showing the slope that a differential… Functions Slope-Intercept Form Slope-intercept form is the equation y = mx + b of a line, where m is… Functions Slope Slope is a number that measures how steep a line is, found by dividing the vertical… Geometry SOH CAH TOA SOH CAH TOA is a mnemonic for the three right-triangle ratios: sine is opposite over hypotenuse,… Numbers Square Root The square root of a number is a value that, when multiplied by itself, gives that… Geometry SSS Congruence The SSS criterion states that if three sides of one triangle are congruent to three sides… Statistics Standard deviation The standard deviation measures how far data values typically fall from the mean; a small value… Functions Standard Form of a Line Standard form writes a linear equation as Ax + By = C, with A, B, and… Statistics Statistical Question A statistical question is a question that expects different answers from different individuals, so the answer… Algebra Substitution Method The substitution method solves a system of equations by solving one equation for a variable and… Geometry Supplementary Angles Supplementary angles are two angles whose measures add up to 180 degrees, and together they form… Measurement Surface Area Surface area is the total area of all the faces of a three-dimensional figure, measured in… Algebra Synthetic division Synthetic division is a shortcut for dividing a polynomial by a linear factor x - c,… Algebra System of Equations A system of equations is a set of two or more equations with the same variables,… T Statistics T-distribution The t-distribution is a bell-shaped model with heavier tails than the normal, used for inference about… Geometry Tangent Ratio In a right triangle, the tangent of an acute angle is the length of the opposite… Geometry Tangent to a Circle A tangent to a circle is a line that touches the circle at exactly one point… Probability Theoretical and Experimental Probability Theoretical probability is what should happen based on equally likely outcomes, while experimental probability is what… Geometry Transformation A transformation is a rule that moves or resizes a figure on the plane, such as… Geometry Translation A translation is a transformation that slides every point of a figure the same distance in… Geometry Transversal and Parallel Lines A transversal is a line that crosses two or more other lines, and when those lines… Geometry Trapezoid A trapezoid is a quadrilateral with at least one pair of parallel sides, called bases; its… Functions Trigonometric identity A trigonometric identity is an equation involving trig functions that is true for every angle where… Algebra Trinomial A trinomial is a polynomial with exactly three unlike terms, for example x^2 + 5x +… Algebra Two-Step Equation A two-step equation is an equation that needs two inverse operations to solve, such as 3x… Algebra Two-Step Inequality A two-step inequality is solved like a two-step equation, but you must reverse the inequality symbol… Statistics Two-Way Table A two-way table shows how often each combination of two categorical variables occurs, with rows for… Statistics Type I error A Type I error happens when a test rejects a true null hypothesis; its probability equals…