labs

Multiplication Explorer

Interactive multiplication explorer: build a deep understanding of multiplication through visual arrays and pattern discovery.

reference

Square Roots 1-100 Reference Chart

Quick-reference chart of perfect square roots from 1 to 100, with visual number lines.

labs

Associative Property Lab

Interactive manipulative demonstrating the associative property of addition and multiplication.

labs

Commutative Property Lab

Interactive manipulative demonstrating the commutative property of addition and multiplication.

labs

Place Value Odometer

Interactive base-10 odometer for young learners. Spin the digit wheels and watch carrying cascade left through each place value column.

labs

Fraction Lab

Interactive fraction explorer. Adjust the numerator and denominator to see the fraction as a bar model, number line, decimal, percentage, and equivalent fractions.

labs

Operations Explorer

Interactive explorer for addition, subtraction, multiplication, and division. Pick two numbers and an operation to see the equation with its vocabulary, counter and array models, number line jumps, fact families, and properties like commutativity.

labs

Making Math Fun

A Grades 4-7 lesson on why math can be fun: the difference between passive scrolling and active play, the top online math game sites, an interactive roll-and-solve dice widget, and nine unplugged card, dice, and board games to play at home.

labs

Distributive Property Lab

Interactive manipulative demonstrating the distributive property of multiplication over addition.

labs

Plug-It-In: Substituting Values for Variables

Interactive algebra lab for grades 5-8. Substitute values into geometric formulas for area and volume across 12 shapes, with a step-by-step substitution machine, formula browser, and practice challenge.

labs

Beating the Odds

A Grades 4-7 interactive probability lesson. Explore the likelihood scale, calculate favorable-over-total, play coin and dice experiments to see the Law of Large Numbers, scratch a simulated lottery ticket, and master a 5-question quiz.

labs

Weights & Measures

Explore Imperial and metric measurement systems through interactive conversion tools. Covers length, weight, volume, speed, and temperature for grades 5-8.

labs

Scale & Magnitude

Explore scale and magnitude from atoms to galaxies. Interactive labs cover the cosmic zoom, powers of ten, scale factors, and order-of-magnitude estimation for grades 4-7.

labs

The Infinite & the Infinitesimal

A wonder-driven lab exploring infinity and the infinitesimal for grades 4-7. Features the Endless Counter, Hilbert's Hotel, Zeno's Walk, the Planck length ladder, and an 8-question quiz.

labs

The Going Rate

A Charlotte-edition interactive lab on rates for grades 4-7. Explore 30 rates across 6 domains, from stock markets to the drifting Moon. Features a live ticker, rate builder, spectrum slider, and 10-question quiz.

labs

Mirror Mirror

An advanced symmetry lab for grades 6-8. Explore reflections on the number line, absolute value as distance, additive inverses (opposites), multiplicative inverses (reciprocals), and even vs odd function symmetry, with a reflect-a-point tool, a distance meter, an opposite finder, a reciprocal flip tool, a symmetry grapher, and a challenge quiz.

labs

Functional

A complete interactive reference for the NC Scientific Calculator: trig and inverse trig, mean/stdev/stdevp, nPr/nCr/factorial, exponents and roots, e^x, abs, round, ln, log, and the constants e and pi, each with a live try-it demo and a 6-question quiz.

games

Product Blast

Blast the correct multiplication product before the meteors reach your base! Practice times tables 1-12 in this fast-paced space shooter.

games

Function Construction

Build a mathematical expression from number and operator tiles to hit a target value. Practice order of operations and algebraic thinking.

games

Code Cracker

A 100-level logic deduction game. Crack the hidden code using written clues alone, every board is guaranteed solvable by pure logic, so it never comes down to luck.

worksheets

Right Triangle Trigonometry Worksheet

18 right-triangle trigonometry practice problems (sin, cos, tan, sin-1, cos-1, tan-1) with scaled diagrams and a Reveal Answer button on every problem.

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Linear Equation - Math Glossary

A linear equation is an algebraic equation whose graph is a straight line, containing variables raised only to the first power.

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Slope - Math Glossary

Slope measures the steepness and direction of a line as the ratio of vertical change to horizontal change between any two points.

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Y-Intercept - Math Glossary

The y-intercept is the point where a line or curve crosses the y-axis, found by setting x equal to zero in the equation.

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X-Intercept - Math Glossary

The x-intercept is the point where a line or curve crosses the x-axis, found by setting y equal to zero in the equation.

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Slope-Intercept Form - Math Glossary

Slope-intercept form is the equation of a line written as y = mx + b, where m is the slope and b is the y-intercept.

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Point-Slope Form - Math Glossary

Point-slope form is a way to write a linear equation using a known point on the line and the slope: y - y1 = m(x - x1).

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Standard Form (Linear) - Math Glossary

Standard form of a linear equation is Ax + By = C, where A, B, and C are integers and A is non-negative.

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Rise Over Run - Math Glossary

Rise over run is a way to describe slope: the vertical change (rise) divided by the horizontal change (run) between two points on a line.

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Positive Slope - Math Glossary

A positive slope means a line rises from left to right on a graph, indicating that as x increases, y also increases.

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Negative Slope - Math Glossary

A negative slope means a line falls from left to right on a graph, indicating that as x increases, y decreases.

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Zero Slope - Math Glossary

Zero slope describes a horizontal line where y does not change as x increases; the line is perfectly flat.

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Undefined Slope - Math Glossary

Undefined slope describes a vertical line where the horizontal change is zero, making the slope calculation a division by zero.

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Parallel Lines (Algebra) - Math Glossary

Parallel lines are lines in the same plane that never intersect, and in algebra they are identified by having equal slopes but different y-intercepts.

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Perpendicular Lines (Algebra) - Math Glossary

Perpendicular lines intersect at a 90-degree angle, and in algebra their slopes are negative reciprocals of each other.

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System of Equations - Math Glossary

A system of equations is a set of two or more equations with the same variables, solved simultaneously to find values that satisfy all equations at once.

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Elimination Method - Math Glossary

The elimination method solves a system of equations by adding or subtracting equations to cancel out one variable, then solving for the remaining variable.

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Substitution Method - Math Glossary

The substitution method solves a system of equations by solving one equation for a variable and substituting that expression into the other equation.

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Graphing Method - Math Glossary

The graphing method solves a system of equations by plotting each equation on the same coordinate plane and identifying the point of intersection.

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Consistent System - Math Glossary

A consistent system of equations has at least one solution, meaning the equations are satisfied by some set of variable values.

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Inconsistent System - Math Glossary

An inconsistent system of equations has no solution because the equations contradict each other, corresponding to parallel lines on a graph.

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Dependent System - Math Glossary

A dependent system of equations has infinitely many solutions because the equations represent the same line and every point on that line is a solution.

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Independent System - Math Glossary

An independent system of equations has exactly one solution, corresponding to two lines that intersect at precisely one point.

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Polynomial - Math Glossary

A polynomial is an algebraic expression consisting of variables and coefficients combined using addition, subtraction, and multiplication, with non-negative integer exponents.

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Monomial - Math Glossary

A monomial is a polynomial with exactly one term, consisting of a coefficient multiplied by variables raised to non-negative integer powers.

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Binomial - Math Glossary

A binomial is a polynomial with exactly two unlike terms connected by addition or subtraction.

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Trinomial - Math Glossary

A trinomial is a polynomial with exactly three unlike terms connected by addition or subtraction.

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Degree of a Polynomial - Math Glossary

The degree of a polynomial is the value of the largest exponent on the variable in the polynomial, which determines its general shape and behavior.

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Leading Coefficient - Math Glossary

The leading coefficient is the coefficient of the term with the highest degree in a polynomial written in standard form.

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Leading Term - Math Glossary

The leading term is the term with the highest degree in a polynomial, combining the leading coefficient and the variable raised to the highest power.

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Adding Polynomials - Math Glossary

Adding polynomials means combining like terms from two or more polynomials to produce a single simplified polynomial.

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Subtracting Polynomials - Math Glossary

Subtracting polynomials means distributing the negative sign across the second polynomial, then combining like terms.

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Multiplying Polynomials - Math Glossary

Multiplying polynomials means applying the distributive property to multiply every term of one polynomial by every term of the other, then combining like terms.

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FOIL Method - Math Glossary

FOIL is a mnemonic for multiplying two binomials: First, Outside, Inside, Last, standing for the four pairs of terms to multiply.

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Factoring - Math Glossary

Factoring is the process of rewriting a polynomial as a product of simpler expressions (its factors), reversing the process of multiplication.

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Factoring by GCF - Math Glossary

Factoring by GCF means pulling out the greatest common factor from all terms of a polynomial as the first step in factoring.

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Factoring Trinomials - Math Glossary

Factoring trinomials means expressing a three-term polynomial, usually in the form ax^2 + bx + c, as a product of two binomials.

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Difference of Squares - Math Glossary

The difference of squares pattern states that a^2 - b^2 factors as (a + b)(a - b), applicable whenever a polynomial is a perfect square minus a perfect square.

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Perfect Square Trinomial - Math Glossary

A perfect square trinomial is a trinomial that equals the square of a binomial, following the patterns a^2 + 2ab + b^2 or a^2 - 2ab + b^2.

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Quadratic Equation - Math Glossary

A quadratic equation is a polynomial equation of degree 2, generally written as ax^2 + bx + c = 0, solvable by factoring, completing the square, or the quadratic formula.

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Standard Form (Quadratic) - Math Glossary

Standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants and a is not zero.

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Quadratic Formula - Math Glossary

The quadratic formula gives the solutions to any quadratic equation ax^2 + bx + c = 0 as x = (-b +/- sqrt(b^2 - 4ac)) / (2a).

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Discriminant - Math Glossary

The discriminant (b^2 - 4ac) of a quadratic equation determines whether it has two real solutions, one real solution, or no real solutions.

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Vertex of a Parabola - Math Glossary

The vertex of a parabola is its highest or lowest point, located at the coordinates (-b/(2a), f(-b/(2a))) for a quadratic in standard form.

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Axis of Symmetry - Math Glossary

The axis of symmetry of a parabola is the vertical line that passes through the vertex, dividing the parabola into two mirror-image halves.

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Parabola - Math Glossary

A parabola is the U-shaped graph of a quadratic function, characterized by a vertex, axis of symmetry, and opening either upward or downward.

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Roots / Zeros - Math Glossary

The roots (or zeros) of a polynomial are the values of x that make the polynomial equal to zero, corresponding to x-intercepts on the graph.

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Completing the Square - Math Glossary

Completing the square is a method of rewriting a quadratic expression into vertex form by adding and subtracting a carefully chosen constant to create a perfect square trinomial.

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Rational Expression - Math Glossary

A rational expression is a fraction where both the numerator and denominator are polynomials, defined for all values that do not make the denominator zero.

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Radical Expression - Math Glossary

A radical expression contains a root symbol (square root, cube root, etc.) applied to a variable or polynomial expression.

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Radical Equation - Math Glossary

A radical equation contains a variable inside a radical (such as a square root), solved by isolating the radical and raising both sides to the appropriate power.

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Direct Variation - Math Glossary

Direct variation describes a relationship where two variables are proportional: y = kx, where k is the constant of variation and the graph always passes through the origin.

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Proportionality Constant - Math Glossary

The proportionality constant (k) is the fixed ratio between two directly proportional variables, appearing as the slope in the direct variation equation y = kx.

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Function - Math Glossary

A function is a rule that assigns exactly one output value to each input value.

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Domain of a Function - Math Glossary

The domain of a function is the complete set of all possible input values for which the function is defined.

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Range of a Function - Math Glossary

The range of a function is the set of all possible output values produced by the function.

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Function Notation - Math Glossary

Function notation uses symbols like f(x) to represent the output of a function f when the input is x.

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Evaluating Functions - Math Glossary

Evaluating a function means substituting a specific input value into the function to find the corresponding output.

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Vertical Line Test - Math Glossary

The vertical line test determines whether a graph represents a function by checking that no vertical line crosses the graph more than once.

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One-to-One Function - Math Glossary

A one-to-one function is a function in which every output value corresponds to exactly one input value.

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Linear Function - Math Glossary

A linear function is a function whose graph is a straight line, described by an equation of the form f(x) = mx + b.

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Quadratic Function - Math Glossary

A quadratic function is a polynomial function of degree 2 whose graph forms a U-shaped curve called a parabola.

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Exponential Function - Math Glossary

An exponential function has the form f(x) = a * b^x, where the variable appears as the exponent and the base b is a positive constant not equal to 1.

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Logarithmic Function - Math Glossary

A logarithmic function is the inverse of an exponential function, written as f(x) = log_b(x), and tells you what exponent is needed to produce x from base b.

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Parent Function - Math Glossary

A parent function is the simplest, most basic form of a family of functions, before any transformations are applied.

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Horizontal Shift - Math Glossary

A horizontal shift is a transformation that moves the graph of a function left or right along the x-axis.

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Vertical Shift - Math Glossary

A vertical shift is a transformation that moves the graph of a function up or down along the y-axis.

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Reflection of a Function - Math Glossary

A reflection of a function flips its graph across an axis, creating a mirror image across the x-axis or y-axis.

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Stretch and Shrink - Math Glossary

Stretching or shrinking a function scales its graph vertically or horizontally, making it taller, shorter, wider, or narrower.

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Composition of Functions - Math Glossary

Composition of functions combines two functions by applying one function to the output of another, written as (f o g)(x) = f(g(x)).

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Inverse Function - Math Glossary

An inverse function reverses the effect of the original function, swapping inputs and outputs so that f(f^-1(x)) = x.

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Arithmetic Sequence - Math Glossary

An arithmetic sequence is a list of numbers where the difference between consecutive terms is always the same constant.

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Common Difference

The common difference is the constant value added to each term in an arithmetic sequence to obtain the next term.

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Geometric Sequence - Math Glossary

A geometric sequence is a list of numbers where each term is found by multiplying the previous term by a fixed constant called the common ratio.

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Common Ratio - Math Glossary

The common ratio is the constant multiplier between consecutive terms in a geometric sequence.

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Recursive Formula - Math Glossary

A recursive formula defines each term of a sequence using one or more previous terms, along with a starting value.

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Explicit Formula - Math Glossary

An explicit formula directly calculates any term of a sequence using its position number, without needing previous terms.

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Arithmetic Series - Math Glossary

An arithmetic series is the sum of the terms of an arithmetic sequence.

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Geometric Series - Math Glossary

A geometric series is the sum of the terms of a geometric sequence, with a finite or infinite number of terms.

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Sigma Notation - Math Glossary

Sigma notation uses the Greek letter sigma to compactly represent a sum of many terms according to a pattern.

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Partial Sum - Math Glossary

A partial sum is the sum of a finite number of terms from the beginning of a sequence, used to study infinite series.

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Infinite Series - Math Glossary

An infinite series is the sum of infinitely many terms of a sequence, which may converge to a finite value or diverge.

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Converge - Math Glossary

A sequence or series converges when its terms or partial sums approach a specific finite value as the number of terms increases without bound.

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Diverge - Math Glossary

A sequence or series diverges when its terms or partial sums do not approach a finite limit.

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Exponential Growth - Math Glossary

Exponential growth occurs when a quantity increases by a constant percentage rate over equal time intervals, causing it to grow faster and faster.

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Exponential Decay - Math Glossary

Exponential decay occurs when a quantity decreases by a constant percentage rate over equal time intervals, shrinking rapidly at first then more slowly.

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Half-Life - Math Glossary

Half-life is the time required for an exponentially decaying quantity to decrease to half of its original value.

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Doubling Time - Math Glossary

Doubling time is the length of time required for an exponentially growing quantity to double in size.

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Logarithm - Math Glossary

A logarithm answers the question "to what power must the base be raised to get this number?" and is written as log_b(x) = y meaning b^y = x.

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Natural Logarithm - Math Glossary

The natural logarithm, written ln(x), is the logarithm with base e (approximately 2.718) and is the inverse of the natural exponential function.

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Common Logarithm - Math Glossary

The common logarithm, written log(x) or log_10(x), is the logarithm with base 10 and represents the power of 10 needed to equal x.

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Change of Base Formula - Math Glossary

The change of base formula converts a logarithm in any base to a ratio of logarithms in a more convenient base, such as base 10 or base e.

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Properties of Logarithms - Math Glossary

The properties of logarithms are rules that govern how logarithms interact with multiplication, division, and exponents.

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Product Rule for Logarithms - Math Glossary

The product rule for logarithms states that the logarithm of a product equals the sum of the logarithms of the factors.

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Quotient Rule for Logarithms - Math Glossary

The quotient rule for logarithms states that the logarithm of a quotient equals the logarithm of the numerator minus the logarithm of the denominator.

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Power Rule for Logarithms - Math Glossary

The power rule for logarithms states that the logarithm of a number raised to an exponent equals the exponent times the logarithm of the number.

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Complex Number - Math Glossary

A complex number is a number of the form a + bi, where a and b are real numbers and i is the imaginary unit satisfying i^2 = -1.

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Imaginary Unit - Math Glossary

The imaginary unit i is defined as the square root of negative one, satisfying i^2 = -1, and is the foundation of complex numbers.

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Real Part - Math Glossary

The real part of a complex number a + bi is the real number a, written Re(z) = a.

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Imaginary Part - Math Glossary

The imaginary part of a complex number a + bi is the real number b (the coefficient of i), written Im(z) = b.

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Complex Conjugate - Math Glossary

The complex conjugate of a + bi is a - bi, formed by negating the imaginary part while keeping the real part unchanged.

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Matrix - Math Glossary

A matrix is a rectangular array of numbers arranged in rows and columns, used to organize data and perform transformations.

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Matrix Dimensions - Math Glossary

Matrix dimensions describe the size of a matrix as the number of rows by the number of columns, written as m x n.

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Matrix Addition - Math Glossary

Matrix addition is performed by adding the corresponding entries of two matrices that have the same dimensions.

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Scalar Multiplication of a Matrix - Math Glossary

Scalar multiplication of a matrix multiplies every entry of the matrix by a single number called a scalar.

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Matrix Multiplication - Math Glossary

Matrix multiplication combines two matrices by taking dot products of rows and columns, producing a new matrix that represents a composition of transformations.

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Determinant - Math Glossary

The determinant is a scalar value computed from a square matrix that encodes information about the matrix's invertibility and the scaling factor of the transformation it represents.

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Identity Matrix - Math Glossary

The identity matrix is a square matrix with 1s on the main diagonal and 0s everywhere else, acting as the multiplicative identity for matrix multiplication.

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Inverse Matrix - Math Glossary

The inverse of a square matrix A, written A^-1, is the unique matrix such that A times A^-1 equals the identity matrix.

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Integer - Math Glossary

An integer is any whole number, its negative counterpart, or zero, with no fractional or decimal part.

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Whole Number - Math Glossary

A whole number is any non-negative integer: 0, 1, 2, 3, and so on, with no fractions or decimals.

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Natural Number - Math Glossary

A natural number is a positive counting number (1, 2, 3, ...) used to count and order objects.

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Rational Number - Math Glossary

A rational number is any number that can be expressed as a fraction p/q where p and q are integers and q is not zero.

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Irrational Number - Math Glossary

An irrational number is a real number that cannot be expressed as a fraction of two integers; its decimal form never terminates or repeats.

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Real Number - Math Glossary

A real number is any value on the continuous number line, including all rational and irrational numbers.

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Zero - Math Glossary

Zero is the integer that represents the absence of quantity; it is the additive identity and separates positive from negative numbers.

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Digit - Math Glossary

A digit is any one of the ten symbols (0-9) used to write numbers in the base-10 number system.

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Numeral - Math Glossary

A numeral is a symbol or combination of symbols used to represent a number, such as "7," "VII," or "seven."

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Place Value - Math Glossary

Place value is the value of a digit based on its position within a number, such as ones, tens, hundreds, and thousands.

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Expanded Form - Math Glossary

Expanded form is a way of writing a number as the sum of the values of each of its digits according to place value.

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Period - Math Glossary

In place value, a period is a group of three digits separated by commas, such as the ones period, thousands period, and millions period.

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Addition - Math Glossary

Addition is the arithmetic operation of combining two or more numbers to find their total, or sum.

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Subtraction - Math Glossary

Subtraction is the arithmetic operation of finding the difference between two numbers by taking one away from the other.

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Multiplication - Math Glossary

Multiplication is the arithmetic operation of repeated addition, combining equal groups to find a product.

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Division - Math Glossary

Division is the arithmetic operation of splitting a quantity into equal groups or finding how many times one number goes into another.

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Sum - Math Glossary

The sum is the result of adding two or more numbers together.

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Difference - Math Glossary

The difference is the result of subtracting one number from another.

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Product - Math Glossary

The product is the result of multiplying two or more numbers together.

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Quotient - Math Glossary

The quotient is the result of dividing one number by another.

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Remainder - Math Glossary

The remainder is the amount left over after dividing one integer by another when the division is not exact.

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Divisor - Math Glossary

A divisor is the number by which another number (the dividend) is divided.

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Dividend - Math Glossary

The dividend is the number being divided in a division problem.

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Factor - Math Glossary

A factor is a number that divides evenly into another number, leaving no remainder.

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Multiple - Math Glossary

A multiple of a number is the product of that number and any positive integer.

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Prime Number - Math Glossary

A prime number is a whole number greater than 1 that can only be divided evenly by 1 and itself.

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Composite Number - Math Glossary

A composite number is a whole number greater than 1 that has more than two factors, meaning it can be divided by numbers other than 1 and itself.

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Prime Factorization - Math Glossary

Prime factorization is the process of expressing a composite number as a product of its prime factors.

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Greatest Common Factor - Math Glossary

The greatest common factor (GCF) is the largest number that divides evenly into two or more numbers.

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Least Common Multiple - Math Glossary

The least common multiple (LCM) is the smallest positive number that is a multiple of two or more given numbers.

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Divisibility - Math Glossary

Divisibility is the property of one integer being divided by another with no remainder; divisibility rules provide shortcuts for checking this.

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Even Number - Math Glossary

An even number is any integer that is exactly divisible by 2, such as 0, 2, 4, 6, and 8.

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Odd Number - Math Glossary

An odd number is any integer that is not divisible by 2, such as 1, 3, 5, 7, and 9.

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Rounding - Math Glossary

Rounding is replacing a number with a nearby value that is simpler or less precise, based on a specified place value.

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Estimation - Math Glossary

Estimation is the process of finding an approximate value that is close enough to the exact answer for a given purpose.

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Absolute Value - Math Glossary

The absolute value of a number is its distance from zero on the number line, always a non-negative result.

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Opposite Number - Math Glossary

The opposite of a number is the number the same distance from zero on the number line but on the other side; it is the additive inverse.

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Addend - Math Glossary

An addend is any one of the numbers being added together in an addition problem.

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Minuend - Math Glossary

The minuend is the number from which another number (the subtrahend) is subtracted in a subtraction problem.

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Subtrahend - Math Glossary

The subtrahend is the number being subtracted from the minuend in a subtraction problem.

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Number Line - Math Glossary

A number line is a straight line on which numbers are represented as points, with positive numbers to the right of zero and negative numbers to the left.

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Consecutive Numbers - Math Glossary

Consecutive numbers are integers that follow each other in order without any gaps, such as 4, 5, 6, 7.

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Ascending Order - Math Glossary

Ascending order means arranging numbers from smallest to largest.

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Descending Order - Math Glossary

Descending order means arranging numbers from largest to smallest.

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Exponent - Math Glossary

An exponent is a number that tells how many times a base is multiplied by itself.

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Base - Math Glossary

In a power expression, the base is the number that is multiplied by itself the number of times indicated by the exponent.

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Power - Math Glossary

A power is the result of multiplying a base by itself a specified number of times, written as base^exponent.

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Perfect Square - Math Glossary

A perfect square is an integer that is the product of some integer multiplied by itself.

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Perfect Cube - Math Glossary

A perfect cube is an integer that is the product of some integer multiplied by itself three times.

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Square Root - Math Glossary

The square root of a number is the value that, when multiplied by itself, gives that number.

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Cube Root - Math Glossary

The cube root of a number is the value that, when multiplied by itself three times, gives that number.

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Order of Operations - Math Glossary

The order of operations is the standard set of rules that determines the sequence in which calculations are performed in a mathematical expression.

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Additive Identity - Math Glossary

The additive identity is zero: adding zero to any number leaves that number unchanged.

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Multiplicative Identity - Math Glossary

The multiplicative identity is one: multiplying any number by one leaves that number unchanged.

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Additive Inverse - Math Glossary

The additive inverse of a number is the number that, when added to it, gives zero; it is the opposite or negation of the number.

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Multiplicative Inverse - Math Glossary

The multiplicative inverse (reciprocal) of a number is the value that, when multiplied by the original number, gives a product of one.

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Undefined - Math Glossary

In mathematics, an expression is undefined when there is no valid value it can take, most commonly seen in division by zero.

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Infinity - Math Glossary

Infinity is the concept of a quantity without bound or end; it is not a real number but is used to describe values that grow without limit.

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Number Sentence - Math Glossary

A number sentence is a mathematical statement that uses numbers and symbols (such as =, <, or >) to show a relationship, similar to a sentence in language.

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Numerical Expression - Math Glossary

A numerical expression is a mathematical phrase made of numbers and operation symbols that represents a single value but does not contain an equality or inequality sign.

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Limit - Math Glossary

A limit describes the value a function approaches as its input gets closer and closer to a specific number.

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One-Sided Limit - Math Glossary

A one-sided limit looks at what value a function approaches from only one direction, either from the left or from the right.

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Limit at Infinity - Math Glossary

A limit at infinity describes what value a function approaches as its input grows without bound in the positive or negative direction.

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Continuity - Math Glossary

Continuity means a function has no breaks, holes, or jumps and can be drawn without lifting your pencil.

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Discontinuity - Math Glossary

A discontinuity is a point where a function breaks, jumps, or has a hole, making it impossible to draw without lifting your pencil.

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Derivative - Math Glossary

The derivative measures the instantaneous rate of change of a function, telling you how steeply the graph rises or falls at any point.

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Differentiation - Math Glossary

Differentiation is the process of finding the derivative of a function using rules and formulas.

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Instantaneous Rate of Change - Math Glossary

The instantaneous rate of change is the rate at which a quantity is changing at one specific moment, equal to the derivative at that point.

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Average Rate of Change - Math Glossary

The average rate of change measures how much a function changes per unit of input over an interval, equal to the slope of the secant line.

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Tangent Line - Math Glossary

A tangent line just touches a curve at one point and has the same slope as the curve at that exact point.

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Power Rule - Math Glossary

The power rule is the differentiation rule that says d/dx[x^n] = nx^(n-1), making it easy to differentiate polynomial terms.

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Product Rule - Math Glossary

The product rule gives the derivative of a product of two functions: (fg)' = f'g + fg'.

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Quotient Rule - Math Glossary

The quotient rule gives the derivative of one function divided by another: (f/g)' = (f'g - fg') / g^2.

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Chain Rule - Math Glossary

The chain rule differentiates composite functions by multiplying the derivative of the outer function by the derivative of the inner function.

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Implicit Differentiation - Math Glossary

Implicit differentiation finds dy/dx for equations where y is not isolated, by differentiating both sides with respect to x.

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Higher-Order Derivative - Math Glossary

A higher-order derivative is the result of differentiating a function more than once, such as the second or third derivative.

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Critical Point - Math Glossary

A critical point is a location on a function where the derivative equals zero or is undefined, often corresponding to a peak, valley, or plateau.

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Local Maximum - Math Glossary

A local maximum is a point on a function that is higher than all nearby points, like the top of a hill.

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Local Minimum - Math Glossary

A local minimum is a point on a function that is lower than all nearby points, like the bottom of a valley.

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Global Extrema - Math Glossary

Global extrema are the absolute highest (global maximum) and absolute lowest (global minimum) values a function achieves over its entire domain or a closed interval.

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Inflection Point - Math Glossary

An inflection point is where a curve changes from concave up to concave down (or vice versa), marking a shift in bending direction.

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Concavity - Math Glossary

Concavity describes whether a curve bends upward like a bowl (concave up) or downward like a dome (concave down), determined by the sign of the second derivative.

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Increasing and Decreasing Functions - Math Glossary

A function is increasing where its graph rises from left to right and decreasing where it falls, determined by the sign of the first derivative.

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First Derivative Test - Math Glossary

The first derivative test classifies a critical point as a local maximum, local minimum, or neither by checking whether the derivative changes sign there.

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Second Derivative Test - Math Glossary

The second derivative test classifies a critical point using the sign of the second derivative: positive means local min, negative means local max.

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Antiderivative - Math Glossary

An antiderivative of a function f is any function F whose derivative equals f, representing the reverse process of differentiation.

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Indefinite Integral - Math Glossary

The indefinite integral of a function is the family of all its antiderivatives, written with a constant C to represent all possibilities.

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Definite Integral - Math Glossary

A definite integral computes the exact net area between a function and the x-axis over a specific interval [a, b].

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Area Under a Curve - Math Glossary

The area under a curve is the region between the graph of a function and the x-axis over an interval, calculated using a definite integral.

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Riemann Sum - Math Glossary

A Riemann sum approximates the area under a curve by adding up the areas of many thin rectangles placed under the graph.

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Fundamental Theorem of Calculus - Math Glossary

The Fundamental Theorem of Calculus links differentiation and integration, showing they are inverse operations and providing a way to evaluate definite integrals.

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U-Substitution - Math Glossary

U-substitution is an integration technique that simplifies a complex integral by replacing an inner expression with the variable u.

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Integration by Parts - Math Glossary

Integration by parts is a technique that transforms the integral of a product of two functions using the formula ∫u dv = uv - ∫v du.

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Set - Math Glossary

A set is a well-defined collection of distinct objects called elements, and is one of the most fundamental building blocks of mathematics.

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Element of a Set - Math Glossary

An element is an individual object that belongs to a set, written using the membership symbol ∈.

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Subset - Math Glossary

A subset is a set whose every element is also contained in another set, written A ⊆ B.

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Proper Subset - Math Glossary

A proper subset is a subset that is strictly smaller than the original set, meaning it is missing at least one element.

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Union of Sets - Math Glossary

The union of two sets is the set of all elements that belong to either set (or both), written A ∪ B.

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Intersection of Sets - Math Glossary

The intersection of two sets is the set of all elements that belong to both sets simultaneously, written A ∩ B.

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Complement of a Set - Math Glossary

The complement of a set A contains all elements in the universal set that are NOT in A, written A' or A^c.

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Empty Set - Math Glossary

The empty set is the unique set that contains no elements, written as {} or ∅.

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Universal Set - Math Glossary

The universal set is the set that contains all objects under consideration in a given context, often written as U.

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Venn Diagram - Math Glossary

A Venn diagram is a visual representation of sets using overlapping circles inside a rectangle to show unions, intersections, and complements.

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Cardinality - Math Glossary

Cardinality is the measure of the number of elements in a set, extending the concept of "size" to infinite sets.

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Theorem - Math Glossary

A theorem is a mathematical statement that has been rigorously proved to be true from axioms and previously established results.

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Axiom - Math Glossary

An axiom is a foundational statement accepted as true without proof, serving as the starting point from which theorems are derived.

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Conjecture - Math Glossary

A conjecture is a mathematical statement believed to be true based on evidence or intuition but not yet rigorously proven.

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Counterexample - Math Glossary

A counterexample is a specific case that disproves a general statement by showing it fails for at least one instance.

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Mathematical Induction - Math Glossary

Mathematical induction is a proof technique for statements about all natural numbers, working by proving a base case and an inductive step.

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Deductive Reasoning - Math Glossary

Deductive reasoning draws certain conclusions from general principles, moving from accepted truths to specific results with logical necessity.

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Inductive Reasoning - Math Glossary

Inductive reasoning forms general conclusions from specific observed examples, producing likely but not certain results.

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Conditional Statement - Math Glossary

A conditional statement is an "if-then" statement of the form "If P, then Q," which asserts that P being true forces Q to be true.

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Converse - Math Glossary

The converse of "If P, then Q" is "If Q, then P," which swaps the hypothesis and conclusion and is not always true when the original is true.

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Contrapositive - Math Glossary

The contrapositive of "If P, then Q" is "If not Q, then not P," which is logically equivalent to the original statement.

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Biconditional - Math Glossary

A biconditional statement "P if and only if Q" is true when both P and Q have the same truth value, meaning each implies the other.

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Graph Theory - Math Glossary

Graph theory is the mathematical study of graphs, which are structures made of vertices (dots) connected by edges (lines), used to model networks and relationships.

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Vertex (Graph Theory) - Math Glossary

In graph theory, a vertex is a fundamental node or point in a graph, connected to other vertices by edges.

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Edge (Graph Theory) - Math Glossary

In graph theory, an edge is a connection between two vertices, representing a relationship or link between them.

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Path (Graph Theory) - Math Glossary

A path in a graph is a sequence of vertices connected by edges where no vertex is repeated, representing a route through the graph.

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Tree (Graph Theory) - Math Glossary

A tree is a connected graph with no cycles, where any two vertices are connected by exactly one path.

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Binomial Theorem - Math Glossary

The Binomial Theorem gives a formula for expanding (a + b)^n as a sum of terms involving binomial coefficients.

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Pascal's Triangle - Math Glossary

Pascal's Triangle is a triangular array where each number is the sum of the two numbers above it, generating the binomial coefficients.

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Modular Arithmetic - Math Glossary

Modular arithmetic is a system of arithmetic for integers where numbers "wrap around" after reaching a modulus, like hours on a clock.

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Congruence (Modular) - Math Glossary

Two integers are congruent modulo n if they have the same remainder when divided by n, written a ≡ b (mod n).

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Vector - Math Glossary

A vector is a mathematical object with both magnitude (size) and direction, represented by an arrow or as a list of components.

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Scalar - Math Glossary

A scalar is a single real number with magnitude but no direction, used to scale vectors or represent undirected quantities.

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Dot Product - Math Glossary

The dot product of two vectors multiplies their corresponding components and adds the results, producing a scalar that encodes the angle between them.

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Cross Product - Math Glossary

The cross product of two 3D vectors produces a new vector perpendicular to both, with magnitude equal to the area of the parallelogram they form.

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Magnitude of a Vector - Math Glossary

The magnitude of a vector is its length, calculated as the square root of the sum of the squares of its components.

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Fraction - Math Glossary

A fraction represents a part of a whole, written as one number over another separated by a line.

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Numerator - Math Glossary

The numerator is the top number in a fraction, indicating how many parts of the whole are being counted.

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Denominator - Math Glossary

The denominator is the bottom number in a fraction, showing how many equal parts the whole is divided into.

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Unit Fraction - Math Glossary

A unit fraction is a fraction with a numerator of 1, representing exactly one equal part of a whole.

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Proper Fraction - Math Glossary

A proper fraction is a fraction where the numerator is less than the denominator, representing a quantity less than one whole.

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Improper Fraction - Math Glossary

An improper fraction is a fraction where the numerator is greater than or equal to the denominator, representing a value of one or more wholes.

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Mixed Number - Math Glossary

A mixed number combines a whole number and a proper fraction to represent a quantity greater than one.

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Equivalent Fractions - Math Glossary

Equivalent fractions are different fractions that name the same value or represent the same portion of a whole.

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Simplest Form - Math Glossary

A fraction is in simplest form when the numerator and denominator share no common factor other than 1.

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Common Denominator - Math Glossary

A common denominator is a shared multiple of the denominators of two or more fractions, allowing them to be added or compared.

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Least Common Denominator - Math Glossary

The least common denominator (LCD) is the smallest number that is a multiple of two or more denominators, used to add or compare fractions efficiently.

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Benchmark Fraction - Math Glossary

Benchmark fractions are common reference fractions like 0, 1/4, 1/2, 3/4, and 1 used to estimate and compare other fractions.

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Reciprocal - Math Glossary

The reciprocal of a number is 1 divided by that number; for a fraction a/b, the reciprocal is b/a.

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Adding Fractions - Math Glossary

Adding fractions requires a common denominator; then the numerators are added while the denominator stays the same.

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Subtracting Fractions - Math Glossary

Subtracting fractions follows the same rules as adding: find a common denominator, then subtract the numerators.

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Multiplying Fractions - Math Glossary

To multiply fractions, multiply the numerators together and the denominators together, then simplify the result.

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Dividing Fractions - Math Glossary

To divide fractions, multiply the first fraction by the reciprocal of the second fraction.

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Decimal - Math Glossary

A decimal is a number that uses a decimal point to show values that are parts of a whole, based on powers of ten.

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Decimal Point - Math Glossary

The decimal point is the dot in a decimal number that separates the whole number part from the fractional part.

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Repeating Decimal - Math Glossary

A repeating decimal is a decimal in which one or more digits after the decimal point repeat infinitely in a regular pattern.

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Terminating Decimal - Math Glossary

A terminating decimal is a decimal that ends after a finite number of digits, such as 0.25 or 3.125.

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Tenths - Math Glossary

Tenths is the decimal place value immediately after the decimal point, representing one part out of ten equal parts.

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Hundredths - Math Glossary

Hundredths is the second decimal place value, representing one part out of one hundred equal parts.

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Thousandths - Math Glossary

Thousandths is the third decimal place value, representing one part out of one thousand equal parts.

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Comparing Decimals - Math Glossary

Comparing decimals means determining which of two decimal numbers is greater, less, or equal by examining place values from left to right.

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Percent - Math Glossary

Percent means "per hundred" and is a way to express a ratio or fraction as a number out of 100, written with the % symbol.

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Percentage - Math Glossary

A percentage is a specific amount or portion expressed as a rate per hundred, often used to describe how much of a whole a part represents.

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Converting Percent - Math Glossary

Converting percent means changing a percent to a decimal or fraction, or changing a decimal or fraction to a percent.

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Percentage Increase - Math Glossary

Percentage increase measures how much a quantity has grown relative to its original value, expressed as a percent.

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Percentage Decrease - Math Glossary

Percentage decrease measures how much a quantity has fallen relative to its original value, expressed as a percent.

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Ratio - Math Glossary

A ratio is a comparison of two quantities showing how many times one value contains or is contained within the other.

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Rate - Math Glossary

A rate is a ratio that compares two quantities with different units, such as miles per hour or dollars per pound.

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Unit Rate - Math Glossary

A unit rate is a rate with a denominator of 1, expressing how much of one quantity exists per single unit of another.

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Proportion - Math Glossary

A proportion is an equation stating that two ratios are equal, used to solve problems where one quantity scales with another.

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Proportional Relationship - Math Glossary

A proportional relationship exists when two quantities always have a constant ratio, represented by the equation y = kx.

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Cross-Multiplication - Math Glossary

Cross-multiplication is a method for solving proportions by multiplying the numerator of each fraction by the denominator of the other and setting the products equal.

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Scale Factor - Math Glossary

A scale factor is the ratio between corresponding measurements of a scaled figure and an original figure, indicating how much the figure has been enlarged or reduced.

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Direct Variation - Math Glossary

Direct variation describes a relationship where two quantities increase or decrease together at a constant rate, expressed as y = kx.

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Inverse Variation - Math Glossary

Inverse variation describes a relationship where one quantity increases as the other decreases, with their product always remaining constant.

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Simple Interest - Math Glossary

Simple interest is interest calculated only on the original principal amount, not on previously earned interest.

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Compound Interest - Math Glossary

Compound interest is interest calculated on both the original principal and the accumulated interest, causing exponential growth over time.

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Tax - Math Glossary

In math, tax is a percentage of a purchase price or income added to or subtracted from a base amount, calculated using percent concepts.

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Discount - Math Glossary

A discount is a reduction in price, usually expressed as a percentage of the original price.

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Markup - Math Glossary

Markup is the amount added to the cost price of a product to determine its selling price, usually expressed as a percentage of the cost.

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Commission - Math Glossary

A commission is a fee or payment calculated as a percentage of a sale or transaction, earned by a salesperson or agent.

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Part-to-Whole Ratio - Math Glossary

A part-to-whole ratio compares one part of a group to the total number of items in the entire group.

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Part-to-Part Ratio - Math Glossary

A part-to-part ratio compares one part of a group directly to another part of the same group, not to the total.

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Equivalent Ratios - Math Glossary

Equivalent ratios are ratios that express the same relationship between quantities, obtained by multiplying or dividing both terms by the same nonzero number.

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Tape Diagram - Math Glossary

A tape diagram is a rectangular bar model that uses length to represent and compare quantities, especially useful for visualizing ratios and fractions.

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Double Number Line - Math Glossary

A double number line is a diagram with two parallel number lines used to represent and find equivalent ratios or rates.

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Perimeter - Math Glossary

Perimeter is the total distance around the outside of a two-dimensional shape, found by adding the lengths of all its sides.

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Area - Math Glossary

Area is the measure of the amount of space inside a two-dimensional shape, expressed in square units.

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Base (of a Shape) - Math Glossary

The base of a shape is the side or face used as the reference bottom for measuring height and computing area or volume.

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Height / Altitude - Math Glossary

The height or altitude of a shape is the perpendicular distance from a base to the opposite vertex or parallel side.

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Area of a Rectangle - Math Glossary

The area of a rectangle is found by multiplying its length by its width, giving the number of square units it covers.

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Area of a Triangle - Math Glossary

The area of a triangle equals one-half times its base times its height, representing the region enclosed by its three sides.

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Area of a Parallelogram - Math Glossary

The area of a parallelogram equals its base times its perpendicular height, derived by rearranging the shape into a rectangle.

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Area of a Trapezoid - Math Glossary

The area of a trapezoid is one-half the sum of its two parallel sides multiplied by the height between them.

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Area of a Circle - Math Glossary

The area of a circle is pi times the square of its radius, representing the total space enclosed within the circle.

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Circumference - Math Glossary

Circumference is the distance around the outside of a circle, calculated as pi times the diameter or two times pi times the radius.

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Pi - Math Glossary

Pi is the mathematical constant equal to the ratio of any circle's circumference to its diameter, approximately 3.14159.

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Arc Length - Math Glossary

Arc length is the distance along a curved portion of a circle, proportional to the central angle and the radius.

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Sector Area - Math Glossary

The area of a sector is the region bounded by two radii and an arc, equal to a fractional part of the full circle's area.

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Coordinate Plane - Math Glossary

The coordinate plane is a two-dimensional surface formed by a horizontal x-axis and vertical y-axis intersecting at the origin, used to locate points.

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X-Axis - Math Glossary

The x-axis is the horizontal number line on the coordinate plane, used to measure left and right position.

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Y-Axis - Math Glossary

The y-axis is the vertical number line on the coordinate plane, used to measure up and down position.

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Origin - Math Glossary

The origin is the point (0, 0) where the x-axis and y-axis intersect on the coordinate plane.

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Ordered Pair - Math Glossary

An ordered pair is a set of two numbers written in the form (x, y) that gives the exact location of a point on the coordinate plane.

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Quadrant - Math Glossary

A quadrant is one of the four regions of the coordinate plane divided by the x-axis and y-axis, numbered I through IV counterclockwise.

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X-Coordinate - Math Glossary

The x-coordinate is the first number in an ordered pair, indicating a point's horizontal distance and direction from the origin.

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Y-Coordinate - Math Glossary

The y-coordinate is the second number in an ordered pair, indicating a point's vertical distance and direction from the origin.

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Plotting Points - Math Glossary

Plotting points means locating and marking ordered pairs on the coordinate plane using the x- and y-coordinates.

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Distance Formula - Math Glossary

The distance formula calculates the straight-line distance between two points in the coordinate plane using the Pythagorean theorem.

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Midpoint Formula - Math Glossary

The midpoint formula finds the exact center point between two given points on the coordinate plane by averaging their coordinates.

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Volume - Math Glossary

Volume is the measure of the three-dimensional space enclosed within a solid figure, expressed in cubic units.

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Surface Area - Math Glossary

Surface area is the total area of all the outer faces of a three-dimensional solid, measured in square units.

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Lateral Surface Area - Math Glossary

Lateral surface area is the total area of all the side faces of a solid, excluding the bases.

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Prism - Math Glossary

A prism is a 3-D solid with two parallel, congruent polygon bases connected by rectangular side faces.

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Rectangular Prism - Math Glossary

A rectangular prism is a 3-D solid with six rectangular faces, including a box or cuboid shape.

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Triangular Prism - Math Glossary

A triangular prism is a 3-D solid with two parallel triangular bases and three rectangular side faces.

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Cylinder - Math Glossary

A cylinder is a 3-D solid with two parallel circular bases connected by a curved lateral surface.

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Cone - Math Glossary

A cone is a 3-D solid with a circular base tapering to a single point called the apex.

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Sphere - Math Glossary

A sphere is a perfectly round 3-D solid where every point on the surface is the same distance from the center.

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Pyramid - Math Glossary

A pyramid is a 3-D solid with a polygon base and triangular faces that meet at a single apex point.

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Face - Math Glossary

A face is any flat surface of a 3-D solid; polyhedra are made entirely of polygonal faces.

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Edge - Math Glossary

An edge is a line segment where two faces of a 3-D solid meet.

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Vertex (3-D) - Math Glossary

A vertex of a 3-D solid is a corner point where three or more edges meet.

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Net of a Solid - Math Glossary

A net of a solid is a flat 2-D pattern that can be folded along its edges to form the 3-D solid.

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Cross-Section - Math Glossary

A cross-section is the 2-D shape obtained by cutting through a 3-D solid with a plane.

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Volume of a Prism - Math Glossary

The volume of a prism equals the area of its base multiplied by its height.

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Volume of a Cylinder - Math Glossary

The volume of a cylinder equals pi times the radius squared times the height.

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Volume of a Cone - Math Glossary

The volume of a cone is one-third times pi times the radius squared times the height.

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Volume of a Sphere - Math Glossary

The volume of a sphere is four-thirds times pi times the radius cubed.

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Volume of a Pyramid - Math Glossary

The volume of a pyramid is one-third times the base area times the height.

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Congruent - Math Glossary

Two figures are congruent if they have the same shape and size, meaning one can be mapped onto the other by a rigid motion.

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Similar Figures - Math Glossary

Similar figures have the same shape but not necessarily the same size; corresponding angles are equal and corresponding sides are proportional.

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Similarity Ratio - Math Glossary

The similarity ratio is the constant ratio of corresponding side lengths between two similar figures.

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Scale Factor (Geometry) - Math Glossary

A scale factor in geometry is the ratio by which all dimensions of a figure are multiplied in a dilation or scale drawing.

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Transformation - Math Glossary

A transformation is a rule that moves, flips, turns, or resizes every point of a figure to a new position.

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Translation - Math Glossary

A translation slides every point of a figure the same distance in the same direction without rotating or reflecting it.

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Reflection - Math Glossary

A reflection flips a figure across a line of reflection, producing a mirror image that is congruent to the original.

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Rotation - Math Glossary

A rotation turns a figure by a specified angle about a fixed center point, producing a congruent image.

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Dilation - Math Glossary

A dilation resizes a figure by a scale factor from a center point, producing a similar figure that is larger or smaller.

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Center of Dilation - Math Glossary

The center of dilation is the fixed point from which all points of a figure are scaled outward or inward during a dilation.

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Image (Transformation) - Math Glossary

The image is the resulting figure after a transformation has been applied to the original figure (preimage).

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Preimage - Math Glossary

The preimage is the original figure before a transformation is applied.

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Rigid Motion - Math Glossary

A rigid motion is a transformation that preserves distances and angle measures, so the image is always congruent to the preimage.

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Line of Symmetry - Math Glossary

A line of symmetry divides a figure into two mirror-image halves that are identical when folded along the line.

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Rotational Symmetry - Math Glossary

A figure has rotational symmetry if it looks identical to itself after being rotated by some angle less than 360 degrees about its center.

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Point Symmetry - Math Glossary

A figure has point symmetry if it looks identical after a 180-degree rotation about a central point.

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Point - Math Glossary

A point is an exact location in space with no size, length, width, or depth, represented by a dot and named with a capital letter.

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Line - Math Glossary

A line is a straight, one-dimensional figure that extends infinitely in both directions, with no endpoints.

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Line Segment - Math Glossary

A line segment is a part of a line with two definite endpoints, having a measurable length.

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Ray - Math Glossary

A ray is a part of a line that has one endpoint and extends infinitely in one direction.

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Plane - Math Glossary

A plane is a flat, two-dimensional surface that extends infinitely in all directions, with no thickness.

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Collinear - Math Glossary

Collinear points are three or more points that all lie on the same straight line.

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Coplanar - Math Glossary

Coplanar points or lines are those that all lie within the same flat plane.

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Angle - Math Glossary

An angle is the figure formed by two rays that share a common endpoint, measured in degrees or radians.

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Vertex of an Angle - Math Glossary

The vertex of an angle is the common endpoint shared by the two rays that form the angle.

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Acute Angle - Math Glossary

An acute angle is an angle that measures greater than 0 degrees and less than 90 degrees.

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Right Angle - Math Glossary

A right angle measures exactly 90 degrees and is formed when two lines or rays are perpendicular to each other.

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Obtuse Angle - Math Glossary

An obtuse angle is an angle that measures greater than 90 degrees and less than 180 degrees.

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Straight Angle - Math Glossary

A straight angle measures exactly 180 degrees and looks like a straight line.

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Reflex Angle - Math Glossary

A reflex angle measures greater than 180 degrees and less than 360 degrees.

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Complementary Angles - Math Glossary

Complementary angles are two angles whose measures add up to exactly 90 degrees.

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Supplementary Angles - Math Glossary

Supplementary angles are two angles whose measures add up to exactly 180 degrees.

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Vertical Angles - Math Glossary

Vertical angles are the pairs of opposite angles formed when two lines intersect, and they are always equal in measure.

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Adjacent Angles - Math Glossary

Adjacent angles are two angles that share a common vertex and a common side but do not overlap.

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Linear Pair - Math Glossary

A linear pair is a pair of adjacent angles formed when two lines intersect, with their outer sides forming a straight line and their measures summing to 180 degrees.

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Perpendicular - Math Glossary

Perpendicular lines or segments intersect at exactly 90 degrees, forming right angles at their point of intersection.

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Transversal - Math Glossary

A transversal is a line that intersects two or more other lines at distinct points, creating pairs of angles with special relationships.

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Corresponding Angles - Math Glossary

Corresponding angles are pairs of angles in matching positions when a transversal crosses two lines, and they are equal when the lines are parallel.

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Alternate Interior Angles - Math Glossary

Alternate interior angles are pairs of angles on opposite sides of a transversal between two lines, equal in measure when the lines are parallel.

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Alternate Exterior Angles - Math Glossary

Alternate exterior angles are pairs of angles outside two lines on opposite sides of a transversal, equal in measure when the lines are parallel.

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Co-interior Angles - Math Glossary

Co-interior angles (also called same-side interior or consecutive interior angles) are between two lines on the same side of a transversal, summing to 180 degrees when the lines are parallel.

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Angle Bisector - Math Glossary

An angle bisector is a ray that divides an angle into two congruent angles of equal measure.

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Perpendicular Bisector - Math Glossary

A perpendicular bisector is a line that crosses a segment at its midpoint at a right angle, and every point on it is equidistant from the segment's endpoints.

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Triangle - Math Glossary

A triangle is a polygon with three sides, three vertices, and three interior angles that always sum to 180 degrees.

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Equilateral Triangle - Math Glossary

An equilateral triangle has all three sides equal in length and all three angles equal to 60 degrees.

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Isosceles Triangle - Math Glossary

An isosceles triangle has at least two sides of equal length, and the angles opposite those equal sides are also equal.

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Scalene Triangle - Math Glossary

A scalene triangle has all three sides of different lengths and all three angles of different measures.

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Right Triangle - Math Glossary

A right triangle has one angle measuring exactly 90 degrees, and its sides satisfy the Pythagorean theorem: a^2 + b^2 = c^2.

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Acute Triangle - Math Glossary

An acute triangle has all three interior angles measuring less than 90 degrees.

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Obtuse Triangle - Math Glossary

An obtuse triangle has one interior angle measuring greater than 90 degrees.

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Exterior Angle of a Triangle - Math Glossary

An exterior angle of a triangle is formed by one side and the extension of an adjacent side, and it equals the sum of the two non-adjacent interior angles.

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Triangle Angle Sum - Math Glossary

The triangle angle sum theorem states that the three interior angles of any triangle always add up to exactly 180 degrees.

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Quadrilateral - Math Glossary

A quadrilateral is a polygon with four sides, four vertices, and four interior angles summing to 360 degrees.

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Rectangle - Math Glossary

A rectangle is a quadrilateral with four right angles and opposite sides that are equal and parallel.

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Square - Math Glossary

A square is a regular quadrilateral with all four sides equal and all four angles equal to 90 degrees.

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Parallelogram - Math Glossary

A parallelogram is a quadrilateral with two pairs of parallel sides, with opposite sides equal and opposite angles equal.

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Rhombus - Math Glossary

A rhombus is a parallelogram with all four sides of equal length, with perpendicular diagonals that bisect each other.

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Trapezoid - Math Glossary

A trapezoid is a quadrilateral with exactly one pair of parallel sides, called the bases.

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Isosceles Trapezoid - Math Glossary

An isosceles trapezoid is a trapezoid with equal legs, equal base angles, and congruent diagonals.

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Kite - Math Glossary

A kite is a quadrilateral with two pairs of consecutive equal sides, with perpendicular diagonals where one diagonal bisects the other.

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Polygon - Math Glossary

A polygon is a closed, flat figure made of three or more straight sides and angles, with the interior angle sum equal to (n-2) * 180 degrees.

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Regular Polygon - Math Glossary

A regular polygon has all sides equal in length and all interior angles equal in measure.

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Diagonal - Math Glossary

A diagonal is a line segment connecting two non-adjacent vertices of a polygon.

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Convex Polygon - Math Glossary

A convex polygon has all interior angles less than 180 degrees, with every diagonal lying entirely inside the figure.

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Concave Polygon - Math Glossary

A concave polygon has at least one interior angle greater than 180 degrees, creating an inward-pointing "dent."

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Pentagon - Math Glossary

A pentagon is a polygon with five sides and five interior angles summing to 540 degrees.

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Hexagon - Math Glossary

A hexagon is a polygon with six sides and six interior angles summing to 720 degrees.

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Octagon - Math Glossary

An octagon is a polygon with eight sides and eight interior angles summing to 1080 degrees.

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Circle - Math Glossary

A circle is the set of all points in a plane that are the same distance (the radius) from a fixed center point.

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Center (of a Circle) - Math Glossary

The center of a circle is the fixed interior point that is equidistant from every point on the circle.

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Radius - Math Glossary

The radius is the distance from the center of a circle to any point on the circle, equal to half the diameter.

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Diameter - Math Glossary

The diameter is a chord that passes through the center of a circle, equal to twice the radius and the longest chord in the circle.

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Chord - Math Glossary

A chord is a line segment with both endpoints on a circle, with the diameter being the longest possible chord.

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Arc - Math Glossary

An arc is a portion of the circumference of a circle, defined by two endpoints and measured in degrees or in length.

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Semicircle - Math Glossary

A semicircle is exactly half of a circle, formed by a diameter and the arc it subtends, with any inscribed angle on the arc being 90 degrees.

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Tangent to a Circle - Math Glossary

A tangent to a circle is a line that touches the circle at exactly one point (the point of tangency) and is perpendicular to the radius at that point.

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Secant - Math Glossary

A secant is a line that intersects a circle at exactly two points, passing through the interior of the circle.

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Central Angle - Math Glossary

A central angle is an angle whose vertex is at the center of a circle, with sides that are radii, and whose measure equals the arc it intercepts.

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Inscribed Angle - Math Glossary

An inscribed angle has its vertex on a circle with sides that are chords, measuring exactly half the central angle that intercepts the same arc.

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Sector - Math Glossary

A sector is the region of a circle bounded by two radii and the arc between them, shaped like a pie slice.

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Variable - Math Glossary

A variable is a letter or symbol used in algebra to represent an unknown or changing quantity.

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Constant - Math Glossary

A constant is a fixed value in a mathematical expression that does not change, such as the number 7 in 3x + 7.

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Coefficient - Math Glossary

A coefficient is the numerical factor multiplied by the variable in an algebraic term, such as 5 in the term 5x.

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Algebraic Expression - Math Glossary

An algebraic expression is a mathematical phrase that combines numbers, variables, and operations but contains no equals sign.

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Term (Algebra) - Math Glossary

A term in algebra is a single number, variable, or product of numbers and variables separated from other terms by addition or subtraction.

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Like Terms - Math Glossary

Like terms are terms in an algebraic expression that have the same variable(s) raised to the same exponent(s) and can be combined by adding or subtracting their coefficients.

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Unlike Terms - Math Glossary

Unlike terms are algebraic terms that have different variable parts or different exponents, and therefore cannot be combined by addition or subtraction.

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Simplify an Expression - Math Glossary

Simplifying an expression means rewriting it in its most compact form by combining like terms, applying properties, and removing unnecessary operations.

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Evaluate an Expression - Math Glossary

Evaluating an expression means substituting specific values for variables and calculating the resulting numerical value.

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Substitute - Math Glossary

To substitute in algebra means to replace a variable with a specific number or expression in order to evaluate or simplify.

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Equation - Math Glossary

An equation is a mathematical statement that two expressions are equal, indicated by an equals sign.

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Inequality - Math Glossary

An inequality is a mathematical statement comparing two expressions using symbols such as less than, greater than, or not equal to.

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Solution - Math Glossary

A solution is a value (or set of values) for the variable(s) that makes an equation or inequality true.

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Solving Equations - Math Glossary

Solving an equation means finding the value(s) of the variable that make the equation true, using inverse operations to isolate the variable.

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Inverse Operations - Math Glossary

Inverse operations are pairs of mathematical operations that undo each other, such as addition and subtraction, or multiplication and division.

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Two-Step Equation - Math Glossary

A two-step equation requires exactly two inverse operations to isolate the variable and find the solution.

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Multi-Step Equation - Math Glossary

A multi-step equation requires three or more operations to solve, often involving the distributive property or combining like terms before isolating the variable.

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Distributive Property - Math Glossary

The distributive property states that a(b + c) = ab + ac, allowing multiplication to be distributed over addition or subtraction.

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Commutative Property - Math Glossary

The commutative property states that the order of numbers in addition or multiplication does not change the result: a + b = b + a and a x b = b x a.

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Associative Property - Math Glossary

The associative property states that the way numbers are grouped in addition or multiplication does not affect the result: (a + b) + c = a + (b + c).

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Identity Property - Math Glossary

The identity property states that adding 0 or multiplying by 1 leaves a number unchanged: a + 0 = a and a x 1 = a.

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Zero Product Property - Math Glossary

The zero product property states that if a product of factors equals zero, then at least one of the factors must equal zero.

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Open Sentence - Math Glossary

An open sentence is a mathematical statement containing one or more variables that is neither true nor false until specific values are substituted for the variables.

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Translating Expressions - Math Glossary

Translating expressions means converting a verbal (word) description into an algebraic expression using the appropriate operations and variables.

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Verbal Expression - Math Glossary

A verbal expression is a mathematical relationship described in words rather than symbols, such as "five more than twice a number."

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One-Variable Equation - Math Glossary

A one-variable equation contains a single unknown quantity and can be solved to find one specific value (or a finite set of values) for that variable.

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Two-Variable Equation - Math Glossary

A two-variable equation contains two unknowns and describes a relationship between them, typically graphed as a line or curve in the coordinate plane.

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Literal Equation - Math Glossary

A literal equation is an equation that contains two or more variables (letters), such as a formula that can be rearranged to solve for any one variable.

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Inequality Symbols - Math Glossary

Inequality symbols are the mathematical notation used to compare two quantities: less than (<), greater than (>), less than or equal to (<=), greater than or equal to (>=), and not equal to (not equal).

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Strict Inequality - Math Glossary

A strict inequality uses < or > to show that one quantity is strictly less than or strictly greater than another, not allowing equality.

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Non-Strict Inequality - Math Glossary

A non-strict inequality uses <= or >= to show that one quantity is less than or equal to, or greater than or equal to another, including the possibility of equality.

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Compound Inequality - Math Glossary

A compound inequality joins two inequalities with "and" or "or," representing either an intersection or a union of solution sets.

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Absolute Value Equation - Math Glossary

An absolute value equation contains an absolute value expression and is solved by considering both positive and negative cases of the expression inside the absolute value.

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Interval Notation - Math Glossary

Interval notation is a way to describe a set of numbers on the number line using brackets and parentheses to indicate whether endpoints are included or excluded.

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Number Line Graph - Math Glossary

A number line graph is a visual representation of the solution set of an equation or inequality, plotted as points or rays on a number line.

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Set-Builder Notation - Math Glossary

Set-builder notation describes a set by stating the property or condition its elements must satisfy, written as {x | condition} or {x : condition}.

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Coordinate Pair - Math Glossary

A coordinate pair (also called an ordered pair) is a pair of numbers (x, y) that specifies a unique location in the coordinate plane.

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Table of Values - Math Glossary

A table of values is an organized chart of input (x) and output (y) pairs generated from an equation or rule, used to analyze relationships and create graphs.

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Input-Output Table - Math Glossary

An input-output table shows how a rule or function transforms input values into output values, with each input paired with exactly one output.

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Pattern - Math Glossary

A pattern is a sequence of numbers, shapes, or events that follow a consistent rule, allowing the next term to be predicted.

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Arithmetic Pattern - Math Glossary

An arithmetic pattern is a sequence in which each term is obtained from the previous one by adding or subtracting a fixed constant, called the common difference.

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Formula (Algebra) - Math Glossary

An algebraic formula is a rule expressed as an equation that shows how variables are related, allowing you to calculate one quantity when others are known.

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Combining Like Terms - Math Glossary

Combining like terms is the process of adding or subtracting terms that have the same variable part to simplify an algebraic expression.

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Expression vs. Equation - Math Glossary

An expression is a mathematical phrase with no equals sign that can be evaluated; an equation is a statement that two expressions are equal and can be solved.

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Balance Method - Math Glossary

The balance method is a strategy for solving equations by performing the same operation on both sides to keep the equation balanced, like a scale, until the variable is isolated.

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Statistics - Math Glossary

Statistics is the branch of mathematics concerned with collecting, organizing, analyzing, interpreting, and presenting data.

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Data - Math Glossary

Data is a collection of facts, measurements, or observations gathered for analysis.

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Population (Statistics) - Math Glossary

In statistics, a population is the complete set of all individuals or items that a study aims to describe.

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Sample (Statistics) - Math Glossary

A sample is a subset of a population selected for study in order to draw conclusions about the whole population.

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Parameter (Statistics) - Math Glossary

A parameter is a numerical value that describes a characteristic of an entire population.

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Statistic (Value) - Math Glossary

A statistic is a numerical value calculated from a sample that is used to estimate a population parameter.

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Bias (Statistics) - Math Glossary

Bias in statistics is a systematic error that causes results to consistently deviate from the true population value.

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Random Sample - Math Glossary

A random sample is a subset of a population in which every member has an equal chance of being selected.

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Census - Math Glossary

A census is a study that collects data from every member of an entire population rather than a sample.

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Observational Study - Math Glossary

An observational study collects data by watching or measuring subjects without any manipulation or intervention.

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Quantitative Data - Math Glossary

Quantitative data consists of numerical values that represent measurable quantities, such as height, weight, or temperature.

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Qualitative Data - Math Glossary

Qualitative data consists of categories or labels that describe characteristics rather than numerical measurements.

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Discrete Data - Math Glossary

Discrete data consists of countable values with no values possible in between, such as the number of students in a class.

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Continuous Data - Math Glossary

Continuous data can take any value within a range, including decimals and fractions, such as height or temperature.

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Frequency - Math Glossary

Frequency is the number of times a particular value or category appears in a dataset.

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Relative Frequency - Math Glossary

Relative frequency is the proportion of times a value occurs in a dataset, expressed as a fraction or percentage of the total.

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Frequency Table - Math Glossary

A frequency table is a chart that lists values or categories alongside how often each one appears in a dataset.

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Histogram - Math Glossary

A histogram is a bar graph that displays the distribution of numerical data by grouping values into intervals called bins.

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Bar Graph - Math Glossary

A bar graph uses rectangular bars to compare the frequencies or values of different categories.

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Pie Chart - Math Glossary

A pie chart is a circular graph divided into slices, each representing a category's share of the whole.

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Line Graph - Math Glossary

A line graph displays data points connected by lines, showing how a quantity changes over time or another continuous variable.

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Scatter Plot - Math Glossary

A scatter plot displays pairs of values as individual points on a coordinate plane to reveal relationships between two variables.

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Dot Plot - Math Glossary

A dot plot displays each data value as a dot above a number line, making it easy to see the distribution of a small dataset.

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Box Plot - Math Glossary

A box plot summarizes a dataset using five key values: minimum, Q1, median, Q3, and maximum, displayed as a box with whiskers.

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Stem-and-Leaf Plot - Math Glossary

A stem-and-leaf plot organizes data by splitting each value into a stem (leading digits) and leaf (final digit), preserving the original data.

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Mean - Math Glossary

The mean is the arithmetic average of a dataset, found by adding all values and dividing by the count.

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Median - Math Glossary

The median is the middle value of a dataset when arranged in order, splitting the data into two equal halves.

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Mode - Math Glossary

The mode is the value that appears most frequently in a dataset.

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Range (Statistics) - Math Glossary

The range is the difference between the maximum and minimum values in a dataset, measuring overall spread.

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Outlier - Math Glossary

An outlier is a data value that is significantly different from the rest of the dataset, appearing far from the other values.

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Weighted Mean - Math Glossary

A weighted mean is an average that gives more importance to certain values by multiplying each value by its assigned weight before averaging.

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Standard Deviation - Math Glossary

Standard deviation measures how spread out the values in a dataset are from the mean, expressed in the same units as the data.

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Variance - Math Glossary

Variance measures the average squared distance of data values from the mean, indicating how spread out the data is.

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Interquartile Range - Math Glossary

The interquartile range (IQR) is the difference between the third and first quartiles, measuring the spread of the middle 50% of a dataset.

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Quartile - Math Glossary

Quartiles divide a dataset into four equal parts, with Q1, Q2 (median), and Q3 marking the boundaries.

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Percentile - Math Glossary

A percentile indicates the value below which a given percentage of data falls, placing an observation in context of the full dataset.

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Z-Score - Math Glossary

A z-score measures how many standard deviations a data value is from the mean, allowing comparison across different distributions.

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Normal Distribution - Math Glossary

The normal distribution is a symmetric, bell-shaped probability distribution that describes many natural phenomena.

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Skew (Skewness) - Math Glossary

Skewness describes the asymmetry of a data distribution, indicating whether the tail is longer on the left or right side.

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Bimodal Distribution - Math Glossary

A bimodal distribution has two distinct peaks, indicating that data clusters around two different values.

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Correlation - Math Glossary

Correlation measures the strength and direction of the linear relationship between two quantitative variables.

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Positive Correlation - Math Glossary

Positive correlation means that as one variable increases, the other variable tends to increase as well.

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Negative Correlation - Math Glossary

Negative correlation means that as one variable increases, the other variable tends to decrease.

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Correlation Coefficient - Math Glossary

The correlation coefficient (r) is a number between -1 and 1 that quantifies the strength and direction of the linear relationship between two variables.

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Regression - Math Glossary

Regression is a statistical method that models the relationship between variables, typically to predict the value of one variable from another.

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Line of Best Fit - Math Glossary

The line of best fit is the straight line that most closely follows the pattern of data points on a scatter plot, minimizing overall error.

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Probability - Math Glossary

Probability is a number between 0 and 1 that measures the likelihood that a specific event will occur.

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Event (Probability) - Math Glossary

An event is a specific outcome or set of outcomes from a probability experiment that we are interested in.

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Outcome (Probability) - Math Glossary

An outcome is a single possible result of a probability experiment.

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Sample Space - Math Glossary

The sample space is the complete set of all possible outcomes of a probability experiment.

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Complement of an Event - Math Glossary

The complement of an event is the set of all outcomes in the sample space that are NOT in the event.

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Mutually Exclusive Events - Math Glossary

Mutually exclusive events cannot both occur at the same time; if one happens, the other cannot.

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Independent Events - Math Glossary

Independent events are events where the outcome of one does not affect the probability of the other.

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Dependent Events - Math Glossary

Dependent events are events where the outcome of one affects the probability of the other.

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Conditional Probability - Math Glossary

Conditional probability is the probability of an event occurring given that another event has already occurred.

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Addition Rule (Probability) - Math Glossary

The addition rule gives the probability that at least one of two events occurs, accounting for any overlap between them.

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Multiplication Rule (Probability) - Math Glossary

The multiplication rule gives the probability that two events both occur, using conditional probability for dependent events.

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Permutation - Math Glossary

A permutation is an arrangement of objects in a specific order, where the order matters.

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Combination - Math Glossary

A combination is a selection of items from a group where order does not matter.

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Factorial - Math Glossary

The factorial of a non-negative integer n, written n!, is the product of all positive integers from 1 to n.

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Theoretical Probability - Math Glossary

Theoretical probability is the expected probability of an event calculated from mathematical reasoning before any experiment is conducted.

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Experimental Probability - Math Glossary

Experimental probability is the probability of an event based on the results of an actual experiment or observation.

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Expected Value - Math Glossary

Expected value is the long-run average outcome of a random variable, calculated by weighting each possible value by its probability.

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Law of Large Numbers - Math Glossary

The law of large numbers states that as the number of trials increases, the experimental probability gets closer and closer to the theoretical probability.

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Simulation (Probability) - Math Glossary

A simulation uses random processes to model and estimate the probability of events that are complex to calculate analytically.

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Trigonometry - Math Glossary

Trigonometry is the branch of mathematics that studies the relationships between the angles and sides of triangles.

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Hypotenuse - Math Glossary

The hypotenuse is the longest side of a right triangle, located opposite the right angle.

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Opposite Side - Math Glossary

The opposite side in a right triangle is the side directly across from a given reference angle.

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Adjacent Side - Math Glossary

The adjacent side in a right triangle is the side that forms the reference angle alongside the hypotenuse.

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Sine - Math Glossary

Sine is a trigonometric function defined as the ratio of the opposite side to the hypotenuse in a right triangle.

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Cosine - Math Glossary

Cosine is a trigonometric function defined as the ratio of the adjacent side to the hypotenuse in a right triangle.

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Tangent (Trig) - Math Glossary

Tangent is a trigonometric function defined as the ratio of the opposite side to the adjacent side in a right triangle.

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Cosecant - Math Glossary

Cosecant is the reciprocal of sine, defined as the ratio of the hypotenuse to the opposite side in a right triangle.

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Secant (Trig) - Math Glossary

Secant is the reciprocal of cosine, defined as the ratio of the hypotenuse to the adjacent side in a right triangle.

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Cotangent - Math Glossary

Cotangent is the reciprocal of tangent, defined as the ratio of the adjacent side to the opposite side in a right triangle.

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SOH-CAH-TOA - Math Glossary

SOH-CAH-TOA is a mnemonic for remembering the three basic trigonometric ratios: sine, cosine, and tangent.

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Trigonometric Ratio - Math Glossary

A trigonometric ratio is a ratio of two sides of a right triangle that corresponds to a specific trigonometric function.

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Angle of Elevation - Math Glossary

The angle of elevation is the angle measured upward from a horizontal line to the line of sight toward an object above.

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Angle of Depression - Math Glossary

The angle of depression is the angle measured downward from a horizontal line to the line of sight toward an object below.

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Inverse Sine - Math Glossary

Inverse sine (arcsin) is the function that returns the angle whose sine equals a given value.

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Inverse Cosine - Math Glossary

Inverse cosine (arccos) is the function that returns the angle whose cosine equals a given value.

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Inverse Tangent - Math Glossary

Inverse tangent (arctan) is the function that returns the angle whose tangent equals a given value.

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Unit Circle - Math Glossary

The unit circle is a circle with radius 1 centered at the origin, used to define trigonometric functions for all angles.

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Radian - Math Glossary

A radian is a unit of angle measure equal to the angle subtended at the center of a circle by an arc equal in length to the radius.

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Degree-to-Radian Conversion - Math Glossary

Degree-to-radian conversion is the process of changing an angle measurement from degrees to radians using the ratio pi/180.

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Arc Length (Radian) - Math Glossary

Arc length in radian measure is the distance along a circular arc, calculated as the product of the radius and the central angle in radians.

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Standard Position - Math Glossary

An angle is in standard position when its vertex is at the origin and its initial side lies along the positive x-axis.

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Initial Side - Math Glossary

The initial side of an angle in standard position is the fixed ray along the positive x-axis from which the angle is measured.

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Terminal Side - Math Glossary

The terminal side of an angle in standard position is the rotating ray that ends at the angle's final position after rotation from the initial side.

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Reference Angle - Math Glossary

A reference angle is the acute angle formed between the terminal side of an angle in standard position and the nearest x-axis.

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Coterminal Angles - Math Glossary

Coterminal angles are angles in standard position that share the same terminal side, differing by full rotations of 360 degrees or 2*pi radians.

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45-45-90 Triangle - Math Glossary

A 45-45-90 triangle is a special right triangle with angles of 45, 45, and 90 degrees, where the legs are equal and the hypotenuse is sqrt(2) times a leg.

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30-60-90 Triangle - Math Glossary

A 30-60-90 triangle is a special right triangle where the sides are in the ratio 1 : sqrt(3) : 2.

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Pythagorean Theorem - Math Glossary

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.

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Pythagorean Triple - Math Glossary

A Pythagorean triple is a set of three positive integers that satisfy the equation a^2 + b^2 = c^2.

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Converse of the Pythagorean Theorem - Math Glossary

The converse of the Pythagorean theorem states that if a^2 + b^2 = c^2 for three sides of a triangle, then the triangle is a right triangle.

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Law of Sines - Math Glossary

The law of sines states that in any triangle, the ratio of each side to the sine of its opposite angle is constant.

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Law of Cosines - Math Glossary

The law of cosines generalizes the Pythagorean theorem to any triangle, relating all three sides to the cosine of one of its angles.

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Area Formula (SAS) - Math Glossary

The SAS area formula calculates the area of any triangle given two sides and the included angle: Area = (1/2)*a*b*sin(C).

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Trigonometric Identity - Math Glossary

A trigonometric identity is an equation involving trigonometric functions that is true for all valid values of the variable.

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Pythagorean Identity - Math Glossary

The Pythagorean identity is the fundamental trigonometric equation sin^2(theta) + cos^2(theta) = 1, with two related forms involving tangent and cotangent.

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Reciprocal Identity - Math Glossary

Reciprocal identities express the cosecant, secant, and cotangent functions as reciprocals of sine, cosine, and tangent respectively.

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Quotient Identity - Math Glossary

Quotient identities express tangent as sine divided by cosine, and cotangent as cosine divided by sine.

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Amplitude - Math Glossary

Amplitude is the maximum displacement of a periodic function from its midline, determining the height of peaks and depth of troughs.

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Period (Trig) - Math Glossary

The period of a trigonometric function is the length of one complete cycle of the graph.

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Frequency - Math Glossary

Frequency is the number of complete cycles of a periodic function per unit interval, equal to the reciprocal of the period.

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Phase Shift - Math Glossary

Phase shift is the horizontal translation of a sinusoidal graph, shifting it left or right from its standard position.

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Vertical Shift (Trig) - Math Glossary

Vertical shift in a trigonometric function moves the entire graph up or down by adding or subtracting a constant, setting the midline.

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Graphing Sine - Math Glossary

Graphing sine involves plotting the sinusoidal wave y = A*sin(Bx + C) + D, identifying its amplitude, period, phase shift, and midline.

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Graphing Cosine - Math Glossary

Graphing cosine involves plotting the wave y = A*cos(Bx + C) + D, which starts at its maximum value and follows a smooth oscillating pattern.

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Periodic Function - Math Glossary

A periodic function is a function that repeats its values at regular intervals, called the period.

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Sinusoidal Function - Math Glossary

A sinusoidal function is any function that can be written in the form y = A*sin(Bx + C) + D or y = A*cos(Bx + C) + D, representing a smooth periodic wave.