Abacus – A counting tool with beads used to perform basic arithmetic calculations.Example: An abacus can be used to add 145 + 276 by moving beads representing hundreds, tens, and ones
Absolute Value – The distance of a number from zero on the number line, always a non-negative number Example: |–8| = 8
Acute Angle – An angle that measures more than 0° but less than 90°.Example: An angle measuring 45° is an acute angle.
Acute Triangle – A triangle in which all three angles are less than 90°.Example: A triangle with angles of 40°, 60°, and 80° is acute.
Addend – A number that is added to another in an addition problem.Example: In 7 + 5 = 12, both 7 and 5 are addends.
Addition – The process of combining two or more numbers to get their total.Example: 14 + 6 = 20
Additive Identity – The number 0, which doesn’t change a number when added to it.Example: 12 + 0 = 12
Additive Inverse – A number that, when added to a given number, gives zero.Example: The additive inverse of 8 is –8.
Adjacent Angles – Two angles that share a common side and a common vertex.Example: If one angle is 30° and the adjacent one is 60°, together they form a 90° angle.
Algebra – A branch of mathematics that uses letters and symbols to represent numbers and expressions.Example: In x + 3 = 9, x represents an unknown number.
Algebraic Expression – A mathematical phrase using numbers, variables, and operations but no equal sign.Example: 4x + 5 is an algebraic expression.
Algorithm – A step-by-step method used to solve a mathematical problem.Example: The steps for long division are part of a division algorithm.
Alternate Angles – Angles on opposite sides of a transversal that intersect two parallel lines and are equal in measure.Example: If one alternate angle is 70°, the other is also 70°.
Altitude (of Triangle) – A line segment from a vertex perpendicular to the opposite side.Example: If a triangle has a base of 10 cm and a height of 5 cm, its area is ½ × 10 × 5 = 25 cm².
Amplitude – The height from the middle to the peak of a wave or periodic function.Example: In y = 2 sin x, the amplitude is 2.
Angle Bisector – A ray that divides an angle into two equal angles.Example: A 60° angle bisected creates two 30° angles.
Angle of Rotation – The degree of turn about a fixed point Example: A 180° rotation turns a figure upside down B
Angle – The space between two intersecting lines or surfaces measured in degrees Example: A right angle measures exactly 90°
Annual Rate – A percentage used to express how much something grows or earns in one year Example: A 10% annual interest on ₱1,000 adds ₱100 after one year
Annulus – A ring-shaped area between two concentric circles Example: A washer has the shape of an annulus
Anticlockwise – A direction of rotation opposite to the hands of a clock Example: A 90° turn to the left is an anticlockwise rotation
Apex – The top or highest point of a shape, often a cone or pyramid Example: The pointed top of a cone is its apex
Apothem – A perpendicular line from the center of a regular polygon to the midpoint of one of its sides Example: The area of a regular hexagon can be found using its apothem
Approximation – A value close to but not exactly the true number Example: 3 14 is an approximation of π
Arc Length – The distance along a curved line forming part of a circle Example: A 60° arc on a circle with radius 6 cm has length (60/360) × 2π × 6 = 2π cm.
Arc – A part of the circumference of a circle Example: A quarter of a circle includes a 90° arc
Area Model – A method of solving multiplication problems by breaking them into parts.Example: To multiply 23 × 15, split into (20 + 3)(10 + 5) and calculate partial products
Area – The amount of space inside a two-dimensional shape, measured in square units.Example: The area of a rectangle with length 6 cm and width 4 cm is 24 cm².
Arithmetic Mean – Another name for the average of a set of numbers.Example: The arithmetic mean of 10 and 20 is (10 + 20) ÷ 2 = 15.
Arithmetic Sequence – A number sequence with a constant difference between terms.Example: 3, 6, 9, 12 is an arithmetic sequence with a common difference of 3.
Arithmetic – The branch of mathematics that deals with numbers and basic operations.Example: 9 × 7 = 63 is an arithmetic calculation.
Array – A group of items arranged in rows and columns.Example: A 3 by 4 array shows 3 rows of 4 objects, or 12 in total.
Ascending Order – A sequence of numbers arranged from smallest to largest.Example: 1, 3, 5, 8, 10 are in ascending order.
Association (Statistics) – A relationship between two variables.Example: As the number of study hours increases, test scores also increase, showing a positive association.
Associative Property – Changing the grouping of numbers does not change their sum or product.Example: (2 + 3) + 4 = 2 + (3 + 4)
Asymptote – A line that a graph approaches but never touches.Example: The graph of y = 1/x has a vertical asymptote at x = 0.
Autocorrelation – A measure of how similar a data point is to previous data poin ts in a time series.Example: In daily temperature records, a hot day today likely follows a hot day yesterday due to autocorrelation.
Average (Mean) – The total sum of values divided by how many values there are Example: The average of 5, 10, and 15 is (5 + 10 + 15) ÷ 3 = 10.
Axis of Symmetry – A line that divides a shape into two equal halves Example: A regular triangle has 3 axes of symmetry.
Axis – A reference line used in graphs to locate points, usually horizontal (x-axis) or vertical (y-axis) Example: In the point (4, 2), 4 is on the x-axis and 2 is on the y-axis.
B
Back-to-Back Stem-and-Leaf Plot – A tool for comparing two data sets by showing their values side by side Example: A teacher compares test scores from two different classes using a back-to-back stem-and-leaf plot
Balance Scale – A tool used to model equality between two sides, often used to explain equations Example: If both sides of the scale show equal weight, then the equation is balanced
Balance – To keep two sides of an equation equal Example: To balance the equation x + 4 = 10, subtract 4 from both sides to get x = 6
Bar Graph – A chart that uses rectangular bars to show the size of different values Example: A bar graph can show the number of books read by students in each grade level
Bar Notation – A horizontal line used to show repeating digits in a decimal Example: 0 333 is written as 0 3
Base (in exponents) – The number that is multiplied by itself in an exponential expression Example: In 3⁴, the base is 3
Base (of a shape) – The bottom side of a geometric figure, often used to calculate area or volume Example: The area of a triangle is ½ × base × height
Base Angle – One of the two equal angles in an isosceles triangle Example: In an isosceles triangle, if the vertex angle is 40°, each base angle is 70°.
Base of a Logarithm – The number that is raised to a power to get another number Example: In log₂ 8 = 3, the base is 2.
Base Ten Blocks – A visual tool that represents units, tens, hundreds, and thousands to model numbers.Example: To show 243, use 2 hundreds blocks, 4 tens blocks, and 3 unit blocks.
Base-10 System – The number system we commonly use, based on powers of 10.Example: The number 472 means 4 hundreds, 7 tens, and 2 ones.
Basic Fact – A simple, commonly memorized math operation.Example: 6 × 7 = 42 is a multiplication basic fact.
Basic Operations – The four main operations in arithmetic: addition, subtraction, multiplication, and division.Example: 12 ÷ 4 is a basic operation (division).
Benchmark Angle – A common angle used for estimating, like 30°, 45°, 60°, and 90°.Example: An angle close to 47° is estimated using the benchmark angle 45°.
Benchmark – A known value used for estimation or comparison.Example: 0.5 is a benchmark fraction close to 47% when estimating.
Bias (Sampling) – A flaw in the sampling method that results in unfair or unbalanced results.Example: Surveying only athletes in a school creates sampling bias when asking about sports interest.
Bias (Statistics) – A systematic error that affects the accuracy of data.Example: Surveying only morning shoppers creates bias if the goal is to learn about all customers.
Bimodal – A data set that has two modes, or values that occur most often.Example: In the set 2, 3, 3, 5, 7, 7, both 3 and 7 are modes, so it’s bimodal.
Bin – A category or interval used in organizing data in a histogram.Example: If test scores are grouped by 10s, the bin 70–79 includes all scores from 70 to 79.
Binary System – A number system using only 0 and 1, common in computing.Example: The binary number 1011 equals 11 in decimal.
Binomial – An algebraic expression with two terms Example: x + 5 is a binomial
Bisect – To divide something into two equal parts.Example: A line bisects a 90° angle into two 45° angles.
Bisection Method – A technique for finding the root of an equation by repeatedly halving intervals.Example: Used in algebra or calculus to approximate solutions.
Bivariate Data – Data that involves two different variables.Example: A study comparing students’ height and weight uses bivariate data.
Borrowing – A method used in subtraction when the top digit is smaller than the bottom digit Example: In 402 – 185, you borrow from the tens or hundreds to subtract
Boundary Line – A line on a graph that divides solutions from non-solutions in an inequality Example: In the inequality y > 2x + 1, the boundary line is y = 2x +
Boundary – The edge or border of a geometric figure or graph region Example: In a shaded graph of an inequality, the boundary line shows where the solution region begins
Bounded Region – A region enclosed within boundaries, often in graphs or geometry Example: A triangle drawn on a coordinate plane creates a bounded region
Box Method – A strategy for multiplying two-digit numbers using area models Example: To multiply 23 × 14, use the box method to separate the digits and add the partial products
Box – The rectangle portion of a box-and-whisker plot showing the interquartile range Example: In a data set, the box shows where the middle 50% of values lie
Box-and-Whisker Plot – A graph that shows the median, quartiles, and extremes of a data set Example: A box-and-whisker plot can show the spread of students' test scores
Braces – Curly symbols used in math to list elements of a set Example: {2, 4, 6} uses braces to show a set of even numbers.
Bracket (in matrices) – A symbol used to enclose the elements of a matrix Example: A 2×2 matrix is written as [ [1, 2], [3, 4] ].
Bracket Notation (in intervals) – A symbol that shows whether endpoints are included in an interval Example: [2, 5) includes 2 but not 5.
Bracket – A symbol used to group parts of a mathematical expression.Example: In [3 + (4 × 2)], the operations inside the brackets are done first.
Break-even Point – The point where income and expenses are equal.Example: A business reaches breakeven when its sales equal its total costs.
Broken Calculator Problem – A math challenge where some keys are missing, and you must find another way to get the answer.Example: If the 5 key is broken, how can you make 25 using other keys? C
Broken Line Graph – A graph that connects data points with straight lines and may show changes over time.Example: A broken line graph shows temperature changes across several hours.
Budget Line – A graph that shows all possible combinations of goods a consumer can afford.Example: A budget line might show combinations of books and pens one can buy with ₱100.
Budget – A financial plan that estimates income and expenses over a period.Example: A student plans a weekly budget to spend ₱500 on food and ₱300 on transportation.
CCategorical Data – Data that can be sorted into categories.Example: Eye colors like brown, blue, and green are categorical data.
Center of a Circle – The point that is equally distant from all points on the circle.Example: The point (0, 0) is the center of a circle with radius 5.
Cents – A unit of money equal to 1/100 of a dollar or peso.Example: 50 cents is equal to half a peso or half a dollar.
Check – A method to verify the correctness of an answer Example: After solving 6 × 7 = 42, check by dividing 42 ÷ 6 = 7.
Circle Sector – A part of a circle bounded by two radii and an arc Example: A 90° slice of a pizza is a sector of the circle.
Circle Segment – A region of a circle bounded by a chord and the arc it subtends Example: The area between a chord and its arc in a circle forms a segment D
Circumscribed – A shape drawn around another so that it touches at certain points Example: A circle circumscribed around a triangle touches all three vertices
Clockwise Rotation – A turn to the right, in the same direction as a clock’s hands Example: Rotating a shape 90° clockwise changes its position
Closed Figure – A shape that starts and ends at the same point and encloses an area Example: A triangle is a closed figure
Closed Interval – An interval that includes its endpoints Example: The interval [2, 5] includes both 2 and 5
Coin – A small flat round piece of metal used as money Example: A 5-peso coin is a common currency in the Philippines
Column – A vertical arrangement of numbers or data Example: In a table, the height values may be listed in one column
Common Denominator – A common multiple of the denominators of two or more fractions Example: The common denominator of 1/4 and 1/6 is 12
Common Factor – A number that is a factor of two or more numbers Example: 4 is a common factor of 8 and 12
Complementary Angles – Two angles whose measures add up to 90 degrees Example: Angles of 40° and 50° are complementary.
Complex Number – A number made of a real and imaginary part, written as a + bi Example: 2 + 3i is a complex number.
Composite Number – A whole number with more than two factors Example: 6 is a composite number because its factors are 1, 2, 3, and 6.
Compound Interest – Interest calculated on both the principal and accumulated interest.Example: ₱1,000 at 10% annual compound interest becomes ₱1,210 after two years.
Concentric Circles – Circles with a common center but different radii.Example: A dartboard has concentric circles.
Cone – A 3D shape with a circular base and a point (apex) opposite the base.Example: An ice cream cone is shaped like a cone.
Congruent Angles – Angles that have the same measure.Example: Two angles measuring 45° are congruent.
Congruent – Having exactly the same shape and size.Example: Two squares of side 5 cm are congruent.
Constant of Proportionality – The ratio between two directly proportional quantities.Example: If y = 4x, the constant of proportionality is 4.
Constant – A value that does not change.Example: In the equation y = 2x + 4, the number 4 is a constant.
Construct – To draw a shape using only a ruler and compass following precise steps.Example: Constructing an equilateral triangle with all sides equal to 6 cm.
Consumer Mathematics – The use of math in real-life financial decisions.Example: Calculating a 20% discount on a ₱500 item means the price is ₱400.
Coordinate Plane – A grid formed by a horizontal x-axis and a vertical y-axis.Example: The point (3, –2) lies in the fourth quadrant of the coordinate plane.
Coordinate – A number (or pair of numbers) that shows the position of a point.Example: The point (0, 0) is at the origin of the coordinate plane.
Counting Numbers – The set of numbers beginning with 1, 2, 3, and so on.Example: 1, 2, 3, 4, and 5 are counting numbers.
Counting Principle – A rule to determine the total number of outcomes by multiplying choices.Example: If you have 3 shirts and 2 pants, you can make 3 × 2 = 6 outfits.
Cross Product – The product of the means and the extremes in a proportion.Example: If 2/3 = 4/6, then cross products 2×6 = 3×4 = 12.
Cube Root – A number that when multiplied by itself three times gives the original number Example: The cube root of 8 is 2 because 2 × 2 × 2 = 8
Cube – A 3D shape with 6 equal square faces Example: A dice is shaped like a cube
Cumulative Frequency – A running total of frequencies in a data set Example: If the frequencies are 3, 5, and 7, the cumulative frequencies are 3, 8, and 15
Currency – A system of money used in a country Example: In the Philippines, the currency is the peso (₱)
Curve – A continuous and smooth-flowing line without sharp angles Example: The path of a thrown ball follows a curve
Customary System – A system of measurement used mainly in the U S , including inches, feet, and pounds Example: 12 inches make 1 foot in the customary system
Cyclic Quadrilateral – A quadrilateral whose vertices lie on the same circle Example: If all corners of a rectangle touch the circle, it is a cyclic quadrilateral
Cylinder – A 3D shape with two parallel circular bases connected by a curved surface Example: A soda can is shaped like a cylinder
Data – A collection of facts, numbers, or measurements used for analysis.Example: Test scores like 85, 90, 78, and 92 are data
Decagon – A polygon with ten sides and ten angles.Example: A regular decagon has all angles equal to 144°.
Decimal Fraction – A fraction written with a decimal point Example: 0 75 is a decimal fraction equal to ¾
Decimal Number System – A base-10 number system using digits 0–9.Example: 245 is written in the decimal system
Decimal Point – The dot used to separate the whole number from the fractional part.Example: In 5.6, the decimal point separates 5 and 6
Decimal – A number that uses a dot to show values less than one.Example: 3.14 is a decimal number.
Decompose – To break a number or shape into parts Example: Decomposing 10 into 6 and 4
Defined Term – A term with a clear meaning in math.Example: A triangle is a defined term with three sides and three angles
Degree of a Polynomial – The highest exponent of a term in a polynomial.Example: The degree of 4x³ + x² 7 is 3
Degree – A unit used to measure angles.Example: A right angle measures 90 degrees.
Denary – Another name for the decimal system (base-10) Example: The number 50 is written in denary as 50
Denominator – The bottom number in a fraction that shows how many parts make a whole.Example: In ¾, the denominator is 4
Dependent Variable – A variable whose value depends on another.Example: In y = 2x, y is the dependent variable
Descending Order – Arranging numbers from largest to smallest.Example: 9, 6, 4, 2 is in descending order.
Diagonal of a Polygon – A segment connecting two non-adjacent vertices Example: A pentagon has 5 diagonals.
Diagonal – A straight line connecting opposite corners of a polygon Example: A square has two diagonals
Diagonally Opposite – Two corners that are across from each other.Example: In a rectangle, opposite corners are diagonally opposite
Diameter – A straight line passing through the center of a circle from one side to the other.Example: A circle with radius 4 has a diameter of 8.
Difference of Squares – A pattern where a² b² = (a b)(a + b).Example: 9 4 = (3 2)(3 + 2) = 1 × 5 = 5.
Difference Table – A table used to find patterns by subtracting terms Example: Subtracting consecutive terms in a sequence: 2, 5, 8 → differences: 3, 3.
Difference – The result of subtracting one number from another Example: The difference between 10 and 6 is 4
Digit – Any of the numerals from 0 to 9 Example: The number 372 has three digits: 3, 7, and 2
Dilation – A transformation that changes the size of a shape but not its shape Example: Enlarging a triangle while keeping its angles the same is dilation
Dimensions – The measurements of length, width, and height Example: A box with dimensions 3 cm × 4 cm × 5 cm
Direct Proportion – A relationship where one quantity increases as another increases Example: If x = 2 and y = 4, and doubling x makes y = 8, they are directly proportional
Directed Number – A number with direction, like positive or negative Example: 7 is a directed number showing a value below zero.
Discrete Data – Data that can only take specific values Example: The number of students in a class is discrete data.
Disjoint Sets – Sets that have no elements in common Example: {1, 2} and {3, 4} are disjoint sets
Displacement Vector – A vector that shows the direction and distance of movement.Example: 10 meters north is a displacement vector
Displacement – A vector showing change in position.Example: Moving from point A to B, 5 meters east, is a displacement.
Distance – The amount of space between two points.Example: The distance between (0, 0) and (3, 4) is 5 units.
Distributive Property – A rule that lets you multiply a number by a sum or difference.Example: 3 × (4 + 2) = 3 × 4 + 3 × 2 = 12 + 6 = 18.
Dividend – The number being divided in a division problem.Example: In 12 ÷ 3, the dividend is 12.
Divisibility Rule – A shortcut to check if a number can be divided by another.Example: A number ending in 0 or 5 is divisible by 5.
Division – Splitting a number into equal parts or groups.Example: Dividing 18 by 6 gives 3.
Divisor – The number you divide by in a division problem.Example: In 20 ÷ 5, the divisor is 5.
Domain – The set of input values for a function.Example: For f(x) = √x, the domain is x ≥ 0.
Double Bar Graph – A graph that compares two sets of data using bars.Example: A graph showing test scores of boys and girls side by side.
Double Line Graph – A graph that uses two lines to compare changes over time.Example: A graph showing temperature in two cities across a week.
Doubling – Multiplying a number by 2.Example: Doubling 6 gives 12.
Draw – To create a shape, figure, or graph accurately using tools.Example: Using a ruler to draw a triangle with sides 5 cm, 5 cm, and 8 cm.
EEccentricity – A measure of how much a conic section deviates from being circular.Example: A circle has eccentricity 0.
Edge of a Graph – A connection between two vertices in graph theory.Example: A triangle has three edges in its graph.
Edge – The line segment where two faces of a solid figure meet.Example: A cube has 12 edges. E
Eigenvalue – A scalar indicating how a linear transformation changes a vector.Example: In matrix A, if Av = λv, then λ is an eigenvalue.
Eigenvector – A vector that only changes by a scalar factor under a transformation Example: If A·v = 3v, then v is an eigenvector of A.
Eighth – One part of something divided into 8 equal parts Example: ⅛ of 32 is 4
Elapsed Time – The amount of time that has passed between two events.Example: From 3:00 PM to 4:30 PM, the elapsed time is 1 hour and 30 minutes
Element – A member of a set.Example: In the set {2, 4, 6}, the number 4 is an element.
Ellipse – An oval shape; the set of all points such that the sum of distances from two points (foci) is constant.Example: The orbit of a planet is often an ellipse.
Empty Set – A set with no elements Example: The set of even prime numbers greater than 2 is an empty set
End Behavior – Describes how the graph of a function behaves as x → ∞ or ∞.Example: For f(x) = x², the end behavior is upward in both directions. F
Endpoint – A point that marks the end of a line segment or ray Example: A segment from A to B has endpoints A and B.
Equal Sign – A symbol showing two expressions are the same Example: In 7 = 3 + 4, the equal sign shows both sides are equal.
Equal – Having the same value or amount Example: 8 + 2 is equal to 10
Equality Property – A rule that keeps an equation balanced.Example: If a = b, then a + c = b + c.
Equation – A mathematical statement that shows two expressions are equal Example: 3x + 2 = 11 is an equation.
Equiangular Triangle – A triangle where all angles are equal Example: A triangle with all angles 60° is equiangular.
Equidistant – The same distance from two or more points Example: A point on the perpendicular bisector is equidistant from both endpoints.
Equilateral Triangle – A triangle with all three sides the same length.Example: A triangle with sides 5 cm each is equilateral.
Equivalence Class – A set of elements related under an equivalence relation.Example: Mod 3 equivalence classes are {..., 3, 0, 3, ...}, {..., 2, 1, 4, ...}, etc.
Equivalence Relation – A relation that is reflexive, symmetric, and transitive.Example: "Is equal to" is an equivalence relation.
Equivalence – The condition of being equal in value, function, or meaning.Example: ½ and 2⁄4 are equivalent fractions.
Error Bound – The maximum possible error in a calculation.Example: If a measurement is 15 cm ± 0.1 cm, then 0.1 is the error bound.
Error Margin – A range that expresses the uncertainty of a measurement.Example: 75 ± 3 means the value could be between 72 and 78.
Error – The difference between an exact value and an estimate.Example: If the actual weight is 20 kg and you estimate 18 kg, the error is 2 kg
Estimate – An approximate value or answer.Example: Estimating 49 × 21 as about 50 × 20 = 1000.
Euclidean Geometry – The study of geometry based on Euclid’s postulates.Example: The sum of angles in a triangle is 180° in Euclidean geometry.
Evaluate – To find the value of a mathematical expression.Example: Evaluate 6 + 2 × 3 = 12.
Evaluation – Finding the value of an expression.Example: Evaluate 5x when x = 2: 5 × 2 = 10.
Even Number – A whole number divisible by 2.Example: 4, 8, and 10 are even numbers.
Event – An outcome or group of outcomes in probability Example: Getting a 6 when rolling a die is an event
Exact Value – A value expressed without rounding or estimating.Example: The exact value of √25 is 5.
Expanded Form – A number written to show the value of each digit Example: 345 = 300 + 40 + 5
Expected Outcome – The most likely result based on probability.Example: Rolling a die, the expected outcome is between 1 and 6
Expected Value – The average result if an experiment is repeated many times.Example: The expected value of flipping a coin is 0 5 heads
Experimental Probability – Probability based on actual results.Example: Rolling a die 60 times and getting 6 on 10 rolls gives a probability of 10/60
Exponent – A number that tells how many times to multiply the base by itself.Example: 2³ = 2 × 2 × 2 = 8.
Exponential Function – A function where the variable is in the exponent Example: f(x) = 2ˣ is an exponential function.
Exponentiation – Repeated multiplication of a number by itself Example: 3⁴ = 3 × 3 × 3 × 3 = 81
Expression – A mathematical phrase without an equal sign.Example: 4x + 7 is an expression.
Extremum – The maximum or minimum value of a function Example: The vertex of a parabola is an extremum
Face Diagonal – A diagonal across a face of a 3D shape Example: A square face of a cube has a face diagonal across it.
Face – A flat surface on a 3D shape Example: A cube has 6 faces
Factor Pair – Two numbers multiplied together to get another number.Example: (2, 6) is a factor pair of 12. G
Factor Tree – A diagram showing the prime factors of a number Example: A factor tree for 60 shows 2 × 2 × 3 × 5.
Factor – A number that divides another exactly Example: 3 is a factor of 12 because 3 × 4 = 12
Factorial – The product of all positive integers up to a given number Example: 4! = 4 × 3 × 2 × 1 = 24
Factoring – The process of breaking an expression into a product of factors Example: x² 9 factors to (x 3) (x + 3).
Fahrenheit – A temperature scale Example: 32°F is the freezing point of water
Feasible Region – The area of all possible solutions in a system of inequalities Example: The shaded region that satisfies all constraints in linear programming
Fibonacci Sequence – A sequence where each term is the sum of the two before it Example: 0, 1, 1, 2, 3, 5, 8,
Field – A set where you can add, subtract, multiply, and divide (except by 0).Example: Rational numbers form a field
Finite Decimal – A decimal with a limited number of digits.Example: 0.75 is a finite decimal.
Finite Set – A set with a countable number of elements Example: The set {apple, banana, cherry} is finite
Finite – Having an end or limit.Example: A set {1, 2, 3} is finite.
First Derivative – The derivative of a function, showing its rate of change Example: The first derivative of f(x) = x² is f '(x) = 2x.
First Quartile – The value separating the lowest 25% of data Example: In the list {2, 4, 6, 8, 10}, the first quartile is 4.
Fixed Point – A point that doesn’t change under a transformation Example: The center of rotation is a fixed point.
Flat Angle – An angle that measures exactly 180 degrees Example: A straight line forms a flat angle
Flat – A level surface in geometry.Example: A plane is a flat surface extending in all directions.
Flip – Another term for reflection over a line.Example: Flipping a shape over the y-axis.
Floating Point – A way of representing real numbers in computing Example: 0 000567 written in floating point as 5.67 × 10 ⁴ .
Flow Chart – A diagram showing steps in a process.Example: A flow chart for solving a quadratic equation.
Fluctuation – A variation or change in data values.Example: Temperature changes daily, showing fluctuation.
Focal Point – The point where rays meet after reflection or refraction Example: Light rays passing through a lens meet at the focal point.
Focus – A point used to define conic sections like parabolas Example: A parabola is the set of all points equidistant from a focus and a directrix.
Foot – A unit of length in the U.S. customary system.Example: One foot equals 12 inches.
Formula – A mathematical rule written using symbols Example: The formula for area of a rectangle is A = l × w
Fractal – A pattern that repeats at different scales.Example: The Mandelbrot set is a famous fractal.
Fraction Bar – The line separating the numerator and denominator Example: In ½, the bar is the fraction bar
Fraction – A part of a whole expressed with a numerator and a denominator.Example: ¾ represents three parts out of four
Fractional Part – The non-whole part of a number.Example: In 5.75, the fractional part is 0.75.
Free Body Diagram – A diagram showing forces acting on an object Example: A box with arrows showing gravity and friction.
Frequency Distribution – How values are spread over categories or intervals Example: A table showing test score ranges and how many students fell into each.
Frequency Histogram – A bar graph showing frequency of data intervals Example: A histogram showing scores of students grouped into ranges.
Frequency Polygon – A graph made by joining the midpoints of histogram bars Example: A line graph connecting frequency midpoints of test scores.
Frequency Table – A table showing how often values occur Example: A table listing test scores and how many students received each.
Frequency – The number of times an event occurs.Example: If 4 students got 90%, the frequency of 90 is 4.
Frustum – A portion of a solid (like a cone) cut by parallel planes.Example: A cone with the top sliced off forms a frustum.
Full Angle – An angle that measures 360 degrees.Example: A complete turn around a point is a full angle.
Function – A relation where each input has one output Example: f(x) = 2x + 1 is a function
Gallon – A unit of liquid measurement in the U S customary system Example: There are 4 quarts in a gallon
Game Theory – A study of strategies in competitive situations.Example: Rock-paper-scissors can be analyzed using game theory
Gaussian Curve – Another name for the bell-shaped normal distribution graph.Example: Test scores often form a Gaussian curve
Gaussian Elimination – A method for solving systems of linear equations.Example: Solving 2x + y = 5 and x y = 1 using Gaussian steps.
GCF (Greatest Common Factor) – The largest factor shared by two or more numbers.Example: The GCF of 12 and 18 is 6.
Generating Function – A formal power series used in combinatorics.Example: For sequence 1, 1, 1…, the generating function is 1/(1 − x)
Generic Point – A typical point in a space used in mathematical reasoning.Example: “Let (x, y) be a generic point in the plane ”
Geocentric Coordinates – A 3D coordinate system centered at Earth's center.Example: Satellites' positions can be described using geocentric coordinates
Geodesic – The shortest path between two points on a curved surface.Example: A great circle route on Earth is a geodesic
Geodesy – The science of measuring Earth's shape and features using math.Example: Calculating Earth's curvature is part of geodesy
Geometric Figure – Any shape formed in geometry.Example: Triangles, squares, and circles are geometric figures
Geometric Mean – The square root of the product of two numbers Example: The geometric mean of 4 and 16 is √(4 × 16) = √64 = 8.
Geometric Probability – Probability based on measurements like length or area Example: Probability that a randomly chosen point falls within a shaded region.
Geometric Sequence – A sequence where each term is multiplied by the same number Example: 2, 4, 8, 16 is a geometric sequence with a ratio of 2.
Geometric Solid – A three-dimensional geometric figure.Example: A sphere is a geometric solid.
Geometric Transformation – Changing a figure’s position or size.Example: Rotating a triangle 90° is a geometric transformation.
Geometry – The branch of mathematics that studies shapes, sizes, and properties of space.Example: Studying the angles of a triangle is part of geometry.
Geopositioning – Using coordinates to determine a specific place on Earth.Example: GPS uses geopositioning to find locations.
Geospatial Data – Data that includes geographical components.Example: A map showing rainfall in different regions uses geospatial data.
Girth – The distance around an object, often used for 3D shapes.Example: The girth of a box is 2 × (height + width).
Glide Reflection – A transformation combining a reflection and translation.Example: Sliding and flipping a footprint creates a glide reflection.
Gnomon – A shape formed by removing a similar smaller shape from a larger one.Example: An L-shape formed by cutting a square from a corner of another square.
Golden Ratio – A special number approximately equal to 1.618, often found in nature and art.Example: If a/b = (a + b)/a, then the ratio is golden.
Golden Rectangle – A rectangle whose side lengths are in the golden ratio.Example: A rectangle with sides 1 and 1.618 is a golden rectangle.
Gradient Vector – A vector pointing in the direction of greatest increase Example: In f(x, y) = x² + y², the gradient at (1,1) is (2,2).
Gradient – The measure of the steepness of a line (slope) Example: A line with a rise of 2 and run of 4 has a gradient of ½.
Gram – A metric unit for measuring mass Example: A paperclip weighs about 1 gram
Graph of a Function – A visual representation of all ordered pairs of a function.Example: The graph of y = x² is a parabola
Graph Theory – The study of graphs and networks of points and connections Example: Social networks are analyzed using graph theory
Graph – A diagram showing the relationship between two variables Example: A line graph showing distance over time
Graphical Solution – Solving equations by interpreting a graph Example: Finding where y = 2x 1 and y = x + 2 intersect on a graph
Graphing Calculator – A calculator capable of displaying graphs Example: A TI-84 calculator is used to graph functions like y = sin(x) H
Great Circle – The largest possible circle that can be drawn on a sphere Example: The equator is a great circle on Earth
Greatest Integer Function – A function that rounds a number down to the nearest integer Example: The greatest integer less than 4 7 is 4
Grid – A network of evenly spaced lines used to locate points Example: A coordinate plane is a grid with x and y axes
Gridlines – The horizontal and vertical lines on a graph Example: Gridlines help read points on a coordinate plane.
Gross – A group of 144 items Example: A gross of pencils means 144 pencils
Group – A set with a binary operation that satisfies certain conditions (algebra).Example: Integers under addition form a group
Growth Rate – A measure of how fast a quantity increases.Example: A bank account growing at 5% per year has a 5% growth rate.
Guess and Check – A strategy of trying different solutions and checking results.Example: Trying x = 2 in an equation and adjusting based on the result.
HHalf – One of two equal parts of a whole Example: Half of 10 is 5
Half-Life – The time it takes for a quantity to reduce to half its original amount.Example: A substance with a half-life of 5 years will reduce to 50% in 5 years.
Half-Open Interval – An interval including one endpoint but not the other.Example: [3, 7) includes 3 but not 7.
Half-Plane – One side of a line in a two-dimensional space Example: The inequality y > 2x divides the plane into two half-planes.
Hamiltonian Cycle – A path in a graph that visits every vertex exactly once and returns.Example: In a triangle, a cycle that goes A → B → C → A is Hamiltonian.
Harmonic Mean – A type of average calculated using reciprocals Example: The harmonic mean of 2 and 4 is 2(2×4)/(2+4) = 2 67
Harmonic Oscillator – A model for systems like springs and waves Example: y'' + y = 0 models a harmonic oscillator
Harmonic Series – The sum of the reciprocals of the natural numbers Example: 1 + ½ + ⅓ + ¼ +
Height of a Prism – The perpendicular distance between its bases Example: A rectangular prism with height 10 cm
Height – The perpendicular distance from the base to the top Example: The height of a triangle is measured from the base to the top vertex
Heptagon – A polygon with seven sides Example: A shape with 7 equal sides is a regular heptagon
Hessian Matrix – A square matrix of second-order partial derivatives Example: Used in calculus to find local maxima and minima of functions
Heterogeneous Data – Data composed of different kinds or sources Example: Mixing heights, ages, and test scores is heterogeneous data
Hexadecimal – A base-16 number system using digits 0–9 and letters A–F.Example: The decimal 255 is FF in hexadecimal
Hexagon – A polygon with six sides.Example: A honeycomb cell is a hexagon.
Hexahedron – A 3D shape with six faces Example: A cube is a regular hexahedron
Hierarchical Clustering – Grouping data in a nested tree-like structure Example: Used in data science to cluster customer behavior I
Hilbert Space – An infinite-dimensional space used in quantum mechanics.Example: Functions can be analyzed in a Hilbert space
Hinge Theorem – Compares two triangles with two sides the same length.Example: If one included angle is larger, the opposite side is longer
Histogram Bin – Another name for a group or interval in a histogram.Example: A bin for 50–60 holds scores between 50 and 60
Histogram Interval – The range of values in each bar of a histogram Example: 70–80, 80–90 are intervals in a histogram.
Histogram – A bar graph representing the frequency of data intervals Example: A histogram showing how many students scored in certain grade ranges.
Hollow Cylinder – A 3D shape like a pipe with an inner and outer radius Example: A pipe is a hollow cylinder
Hollow Sphere – A spherical shell with an empty interior.Example: A basketball is a hollow sphere.
Homogeneous Coordinates – A system using extra dimensions in geometry Example: (x, y, 1) is a point in homogeneous coordinates for 2D geometry.
Homogeneous Equation – An equation where all terms are of the same degree Example: 3x² + 4xy + y² = 0 is homogeneous.
Hook Length – A number assigned to a cell in a Young diagram Example: Used in combinatorics and partition theory.
Horizontal Asymptote – A horizontal line that a graph approaches.Example: y = 0 is a horizontal asymptote of y = 1/x.
Horizontal Line Test – A way to check if a function is one-to-one.Example: y = x² fails the horizontal line test.
Horizontal Shift – Moving a graph left or right.Example: y = (x 2)² is a parabola shifted right by 2 units.
Horizontal – Parallel to the horizon or x-axis.Example: The line y = 3 is horizontal.
Householder Matrix – A matrix used to reflect vectors.Example: Used in numerical linear algebra to simplify matrices.
Hyperbola – A type of curve with two branches.Example: The graph of x² y² = 1 is a hyperbola.
Hyperbolic Function – Functions like sinh, cosh related to exponential functions Example: sinh(x) = (e^x e^ x)/2.
Hypergeometric Distribution – A probability distribution without replacement.Example: Probability of drawing 2 red balls from a bag without putting them back.
Hypotenuse Formula – c² = a² + b² in a right triangle.Example: If a = 5 and b = 12, then c = 13.
Hypotenuse – The longest side of a right triangle, opposite the right angle.Example: In a right triangle with legs 3 and 4, the hypotenuse is 5.
Hypotenuse-Leg Theorem – A rule for triangle congruence in right triangles.Example: If hypotenuse and one leg are equal, triangles are congruent.
Hypothesis Testing – A method for making decisions using data.Example: Testing if a new drug is more effective than the current one.
Hypothesis – A statement to be tested in statistics.Example: "The mean score is 80" is a hypothesis in a test.
IIdentity Element – A number that doesn’t change another number when used in an operation.Example: 0 is the identity for addition because 5 + 0 = 5
Identity Matrix – A square matrix with 1’s on the diagonal and 0’s elsewhere.
Identity – An equation that is true for all values of the variable.Example: (a + b)² = a² + 2ab + b² is an algebraic identity.
Imaginary Number – A number that is a multiple of √ 1 Example: 3i is an imaginary number
Implicit Equation – An equation not solved for one variable.Example: x² + y² = 1 is an implicit equation.
Improper Fraction – A fraction where the numerator is greater than or equal to the denominator.Example: 7/4 is an improper fraction.
Improper Integral – An integral with an infinite limit or an unbounded function.Example: ∫₁^∞ 1/x² dx is an improper integral.
Incircle – A circle inside a triangle that touches all three sides Example: A triangle's incircle is tangent to its sides.
Increasing Function – A function where the output increases as the input increases Example: f(x) = 2x is increasing.
Independent Events – Events where the outcome of one doesn’t affect the other Example: Tossing a coin and rolling a die are independent events.
Independent Variable – The variable that is changed or controlled.Example: In y = 3x, x is the independent variable.
Inductive Reasoning – Making general conclusions from specific cases.Example: Observing patterns like 2, 4, 6… and guessing the next number is 8.
Inequality – A mathematical sentence that shows a relationship of greater or less than.Example: 5 < 9 is an inequality.
Inequation – Another term for inequality.Example: x + 2 > 7 is an inequation.
Infinity – A value that goes on without end.Example: There are infinitely many numbers.
Infix Notation – Mathematical notation where the operator is between operands.Example: 5 + 2 uses infix notation.
Inflation Rate – The percentage increase in prices over time.Example: If a price rises from $100 to $105, the inflation rate is 5%.
Inflection Point – Where a curve changes concavity.Example: f(x) = x³ has an inflection point at x = 0.
Influence – A value’s effect on a statistical outcome.Example: An outlier can have a strong influence on the mean.
Input – The value substituted into a function.Example: For f(x) = x + 4, the input x = 3 gives 7.
Integer – Whole numbers and their negatives.Example: 3, 0, and 5 are integers.
Integral – The area under a curve, used in calculus.Example: ∫₀ ² x dx = 2.
Integration – The process of finding an integral.Example: Integration of 2x gives x² + C.
Intercept Form – A linear equation written as y = mx + b.Example: y = 2x + 5 is in intercept form.
Intercept – The point where a graph crosses the axis Example: The y-intercept of y = 2x + 3 is 3
Interior Angle – The angle inside a polygon.Example: A square has four 90° interior angles.
Interior Point – A point within a set, not on the boundary Example: Point (2, 2) is interior to the circle x² + y² = 25.
Interpolation – Estimating values within a known range Example: Estimating a missing value between two data points on a line.
Interval – A set of numbers between two endpoints.Example: [2, 5] includes 2 and 5 and all numbers between.
Inverse Function – A function that reverses another function.Example: If f(x) = 2x, then f ¹(x) = x/2.
Inverse Matrix – A matrix that, when multiplied by the original, gives the identity matrix.Example: For a 2x2 matrix A, A × A ¹ = I.
Inverse Operation – An operation that undoes another.Example: Division is the inverse of multiplication.
Inverse Square Law – A principle that a quantity is inversely proportional to the square of the distance.Example: Gravity follows the inverse square law. J
Inverse – The opposite or reverse of a function or operation.Example: The inverse of addition is subtraction.
IQR (Interquartile Range) – The range between the 1st and 3rd quartiles.Example: If Q1 = 25 and Q3 = 75, then IQR = 50.
Irrational Number – A number that cannot be written as a fraction.Example: π and √2 are irrational numbers.
Isoceles Triangle – A triangle with two equal sides Example: A triangle with sides 5, 5, and 8 is isosceles
Isometry – A transformation that preserves distance.Example: A rotation or reflection is an isometry.
Isomorphic – Having the same structure or form in mathematics Example: Two graphs are isomorphic if their connections match.
Iteration – Repeating a process to get a result Example: Successive approximation methods use iteration
JJ-invariant of a Curve – A numerical invariant used to classify elliptic curves Example: The j-invariant determines whether two curves are isomorphic.
J-Invariant – A number used in classifying elliptic curves Example: The J-invariant remains constant under isomorphism of elliptic curves.
Jaccard Distance – Measures dissimilarity between two sets Example: 1 (Intersection / Union)
Jaccard Index – A statistic used for comparing the similarity of sets.Example: If A = {1, 2}, B = {2, 3}, Jaccard Index = 1/3
Jacobi Elliptic Functions – Functions used to describe motion in elliptical orbits.Example: sn(u, k) is one Jacobi elliptic function
Jacobi Field – A vector field along a geodesic in differential geometry.Example: Describes how geodesics diverge or converge.
Jacobi Identity – A condition satisfied in Lie algebras and vector cross products.Example: Used in abstract algebra and advanced physics.
Jacobi Integral – A conserved quantity in mechanics.Example: Appears in the restricted three-body problem.
Jacobi Method – An iterative method used to solve systems of linear equations Example: Useful for large matrix systems in numerical computation.
Jacobi Symbol – A generalization of the Legendre symbol in number theory.Example: (a/n) helps determine quadratic residues modulo n.
Jacobi Theta Function – A special function used in number theory.Example: Related to modular forms and elliptic functions.
Jacobian Coordinates – A coordinate system used in physics and geometry.Example: Often used for simplifying celestial mechanics problems. K
Jacobian Determinant – The determinant of the Jacobian matrix, used in multivariable calculus.Example: For f(x, y) = (x², y²), the Jacobian determinant is 4xy.
Jacobian – A matrix of all first-order partial derivatives of a vector-valued function.Example: The Jacobian of f(x, y) = (x², y²)
Jensen Inequality for Expectations – Applied in probability and economics Example: Used to compare riskaverse behaviors.
Jensen Measure – A concept in probability theory and potential theory Example: Used to define subharmonic functions.
Jensen's Formula – In complex analysis, connects mean values of logarithmic functions Example: Involves the average of log|f| on a circle
Jensen's Inequality – A result in convex analysis regarding expectations Example: For a convex function f,f(E[x]) ≤ E[f(x)]
Jitter – Small, rapid variations in a waveform from an ideal signal Example: In digital communication, jitter affects signal clarity
Jittering – Adding small random noise to data points to reduce overplotting in graphs Example: Jittering a scatterplot helps visualize overlapping points
Joint Cumulative Distribution Function – A function that describes the probability a pair of variables fall below specific values.Example: F(x, y) = P(X ≤ x and Y ≤ y).
Joint Distribution – The distribution of two or more random variables considered at once Example: A table showing the probability of age and income combinations.
Joint Frequency – The number of times two categories occur together in a two-way table Example: 15 students who are both left-handed and wear glasses is a joint frequency.
Joint Probability – The probability of two events occurring together.Example: P(A and B) = 0.2 means both A and B happen with 20% chance.
Joint Variation – When a variable varies directly as the product of two or more variables.Example: z varies jointly with x and y → z = kxy.
Jordan Algebra – A type of algebra used in quantum mechanics Example: Elements follow a special commutative multiplication rule
Jordan Canonical Form – A simplified version of a matrix showing its structure Example: Shows eigenvalues and geometric multiplicities clearly
Jordan Curve – A simple closed curve in the plane Example: A circle is a Jordan curve
Jordan Decomposition – Breaking a function or matrix into simple components Example: Decomposing a signed measure into positive and negative parts
Jordan Form – A type of matrix form used in linear algebra for simplification Example: A matrix similar to a diagonal matrix but includes 1’s on the superdiagonal
Jordan Matrix – A block matrix used in linear algebra simplification
Jordan Measurable – A set whose boundary has zero measure Example: Any rectangle is Jordan measurable
Jordan – Hölder Theorem – A theorem in group theory about composition series Example: Any two composition series of a finite group have isomorphic factor groups
Joule – A unit of energy in physics that is often calculated using math Example: Work = Force × Distance = 10 N × 2 m = 20 Joules
Jump Discontinuity – A sudden break in a graph where the limit from the left does not equal the limit from the right Example: The function f(x) = 1 when x < 0, f(x) = 2 when x ≥ 0 has a jump discontinuity at x = 0
Jump Function – Describes sudden changes in a function’s value Example: Used in signal processing
Jump Matrix – In applied math, used to describe discontinuous changes Example: In inverse scattering methods
Jump Process – A stochastic process with discontinuities Example: The Poisson process is a jump process
Just-Noticeable Difference – A concept in psychophysics that can be modeled mathematically.Example: The smallest change in sound level detectable by humans
Justify – To provide a logical explanation or proof in mathematics.Example: "Justify your answer" means explain why 2x = 6 gives x = 3.
K
K-Fold Cross Validation – A method for evaluating predictive models Example: In 5-fold validation, data is split into 5 parts and tested 5 times.
K-Mean Clustering – A method to group data into k distinct clusters Example: Grouping students into 3 clusters based on test scores using the k-means algorithm.
K-Nearest Neighbors (KNN) – A classification method in machine learning.Example: Classifying a data point by the majority label of its 5 closest neighbors.
K-Sample Test – A statistical test comparing more than two samples.Example: Kruskal-Wallis test is a nonparametric k-sample test.
K-Statistic – A measure used in estimating higher moments in statistics Example: Used to estimate skewness or kurtosis from a sample.
K-Statistics – Unbiased estimators of cumulants in statistics Example: Used for calculating measures like variance and skewness. L
K-Value – A constant or coefficient used in equations Example: In f(x) = kx, k is the constant rate of change
Kakutani's Theorem – A fixed-point theorem used in game theory and economics.Example: Applied to prove the existence of Nash equilibrium.
Kalman Filter – An algorithm for estimating unknown variables over time.Example: Used in GPS systems to estimate location.
Kaprekar Number – A number where a specific manipulation of its square gives the original number.Example: 45² = 2025 → 20 + 25 = 45.
Kaprekar’s Constant – A number (6174) reached through a repeated process on 4-digit numbers Example: 5432 → 5432 2345 = 3087 → continue → reach 6174
Karnaugh Map – A diagram used in logic to simplify Boolean expressions.Example: Used to simplify logic circuits in digital electronics.
Keller’s Conjecture – A mathematical conjecture about tiling hypercubes.Example: In dimensions up to 6, hypercubes can tile space without gaps or overlaps.
Kelley’s Theorem – A result in topology related to compactness.Example: Every compact Hausdorff space is normal.
Kepler’s Laws – Laws of planetary motion describing orbital paths.Example: Planets move in elliptical orbits with the Sun at one focus.
Kernel (Calculus) – A function used under an integral sign, especially in convolution.Example: e^( x²) as a kernel in Gaussian integrals.
Kernel (Linear Algebra) – The set of all inputs that map to zero.Example: For matrix A, the kernel is the solution to Ax = 0.
Kernel Density Estimation (KDE) – A method to estimate a probability distribution.Example: A smooth curve that approximates a histogram.
Kinematic Equation – An equation describing motion using velocity, acceleration, time, and displacement.Example: s = ut + ½at² is a kinematic equation.
Kinematics Graph – A graph showing motion (displacement, velocity, or acceleration vs time) Example: A velocity-time graph with a constant slope indicates constant acceleration.
Kinematics – The study of motion without considering forces Example: Using equations to find the distance a car travels in 5 seconds
Kinetic Energy – Energy due to motion, often calculated using math Example: KE = ½mv² for an object of mass m and velocity v
Kinetic Theory – Describes gas behavior using molecular motion Example: Relates temperature to average kinetic energy of particles
Kite – A quadrilateral with two pairs of adjacent sides equal Example: A kite with sides 5 cm, 5 cm, 3 cm, and 3 cm
Klein Bottle – A non-orientable surface with no distinct "inside" or "outside" Example: Similar to a Möbius strip, but in 4D
Klein Four-Group – A group of four elements where every element is its own inverse Example: Used in group theory and symmetry
Kneser Graph – A type of graph used in combinatorics Example: K(5,2) is a Kneser graph with vertices as 2element subsets of {1,2,3,4,5}
Knot Theory – A branch of topology studying knots and their properties Example: Used in DNA modeling and molecular biology.
Knot – In topology, a closed, non-self-intersecting curve embedded in 3D space Example: The trefoil knot is the simplest nontrivial knot.
Kolmogorov Axioms – The foundational rules of probability Example: One axiom says the probability of the whole sample space is 1.
Kolmogorov Complexity – The length of the shortest possible program that outputs a string.Example: The string “abababab” has lower complexity than a random string.
Kriging – A method of interpolation for spatial data.Example: Used in geostatistics to predict unknown terrain heights.
Kronecker Delta – A function that equals 1 if indices are equal, 0 otherwise.Example: δ₍ᵢⱼ₎ = 1 if i = j; else 0.
Kronecker Product – A matrix operation producing a block matrix.Example: If A is 2×2 and B is 2×2, A ⊗ B is 4×4.
Kruskal’s Algorithm – A method for finding a minimum spanning tree in a graph.Example: Connecting all cities with the shortest possible total road length.
Kullback-Leibler Divergence – A measure of difference between two probability distributions.Example: Used in information theory and machine learning.
Kuratowski's Theorem – Describes non-planar graphs.Example: A graph is non-planar if it contains K₅ or K₃,₃ as a subgraph.
Kuratowski’s Closure Axioms – A set of rules defining closure operators in topology.Example: Describes how to extend a set to its closure.
Kurtosis – A measure of the "tailedness" of a probability distribution.Example: A normal distribution has a kurtosis of 3.
König’s Theorem – A result in graph theory about matchings and covers.Example: In bipartite graphs, the size of the max matching equals the size of the min vertex cover.
L
Lagrange Interpolation – A method to find a polynomial that fits a given set of points.Example: Used to estimate values between known data points
Lagrange Multiplier – A technique to find local maxima and minima with constraints.Example: Maximize f(x, y) = xy subject to x² + y² = 1
Laplacian – A differential operator used in calculus and physics.Example: ∇²f = ∂²f/∂x² + ∂²f/∂y².
Lateral Area – The surface area of the sides of a 3D solid, excluding the base(s) Example: The lateral area of a cylinder is 2πrh
Lattice – A regular arrangement of points in space Example: A grid of points at (m, n) where m and n are integers
Law of Cosines – A formula to find a side or angle in any triangle Example: c² = a² + b² 2ab cos(C)
Law of Sines – Relates the ratios of sides and their opposite angles in a triangle Example: a/sin(A) = b/sin(B) = c/sin(C) M
Least Common Denominator – The smallest common multiple of denominators in a set of fractions Example: LCD of 1/4 and 1/6 is 12
Least Common Multiple (LCM) – The smallest multiple shared by two or more numbers Example: LCM of 3 and 5 is 15
Least Squares Method – A technique to minimize the sum of squared differences between observed and predicted values Example: Used in linear regression to find the best-fit line
Least Upper Bound – The smallest number that is greater than or equal to every number in a set Example: For set {1, 2, 3}, the least upper bound is 3
Left-Hand Limit – The value a function approaches as the input approaches a number from the left Example: limₓ→3 f(x) = 5 means the function approaches 5 from the left.
Leg – One of the two shorter sides of a right triangle.Example: In a triangle with sides 3, 4, and 5, the legs are 3 and 4
Length – The measurement of the extent of something from end to end Example: The length of a line segment from (1,2) to (4,6) is 5
Level Curve – A curve on a surface where the function has a constant value Example: Contour lines on a map are level curves of elevation
Leverage Point – In statistics, a data point far from the mean of the predictor variable Example: In regression, a leverage point can significantly affect the slope
Limit – The value that a function approaches as the input approaches a certain value Example: limₓ→2 (x² 4)/(x 2) = 4.
Line Graph – A graph that uses points connected by lines to show trends over time.Example: Showing the change in temperature over a week.
Line Integral – An integral where the function is evaluated along a curve.Example: ∫₍C₎ x² ds, where C is a curve in the plane.
Line of Best Fit – A straight line that best represents the data on a scatter plot.Example: y = 2x + 5 might be a line of best fit for plotted points.
Line of Symmetry – A line that divides a shape into two identical parts.Example: A square has 4 lines of symmetry.
Line Segment – A part of a line with two endpoints.Example: The segment from A(0,0) to B(3,4) has a length of 5.
Line – A straight one-dimensional figure with no thickness that extends infinitely in both directions.Example: The graph of y = 2x + 1 is a line
Linear Equation – An equation that forms a straight line when graphed.Example: y = 3x 7 is a linear equation
Linear Function – A function whose graph is a straight line.Example: f(x) = 2x + 4.
Linear Inequality – An inequality involving a linear expression.Example: 2x + 3 < 7.
Linear Pair – A pair of adjacent angles whose non-common sides form a straight line.Example: Angles measuring 120° and 60° form a linear pair
Linear Programming – A method to achieve the best outcome in a mathematical model with linear relationships Example: Maximizing profit based on cost and resource constraints
Linear Relationship – A relationship with a constant rate of change between variables Example: A car traveling at 60 km/h shows a linear relationship between time and distance
Linear Transformation – A function between vector spaces that preserves vector addition and scalar multiplication Example: f(x, y) = (2x, 3y)
Linearity – A property where a function satisfies additivity and homogeneity Example: f(x + y) = f(x) + f(y) and f(cx) = c f(x)
Locus – A set of points satisfying a certain condition Example: The set of all points equidistant from a point is a circle
Logarithm – The inverse of exponentiation; logₐb is the power to which a must be raised to get b Example: log₂8 = 3
Logarithmic Function – A function involving a logarithm Example: f(x) = log₁₀x
Logarithmic Scale – A scale that increases by powers of 10 Example: The Richter scale for earthquake magnitude
Logic – The study of valid reasoning using rules and symbols Example: If A is true and A implies B, then B must be true.
Logical AND – A Boolean operation that is true only if both operands are true Example: True AND False = False.
Logical NOT – A Boolean operation that inverts the truth value Example: NOT(True) = False
Logical OR – A Boolean operation that is true if at least one operand is true.Example: False OR True = True.
Logistic Function – A function used to model population growth that levels off at a maximum Example: f(x) = 1 / (1 + e^( x)).
Lognormal Distribution – A distribution of a variable whose logarithm is normally distributed Example: Stock prices often follow a lognormal distribution.
MMagnitude of a Complex Number – The distance from the origin to the complex number on the complex plane.Example: |3 + 4i| = √(3² + 4²) = 5.
Magnitude of Displacement – The length of the shortest path between two points.Example: From (0,0) to (3,4), displacement magnitude is 5.
Magnitude – The size or length of a vector.Example: The magnitude of vector (3, 4) is √(3² + 4²) = 5.
Margin of Error – A range that estimates the accuracy of survey results.Example: A poll with ±3% margin of error.
Marginal Cost – The cost of producing one more unit.Example: If total cost rises from $100 to $120 when producing one more item, marginal cost = $20.
Marginal Revenue – The revenue from selling one more unit.Example: If revenue increases from $200 to $230 after selling one more unit, marginal revenue = $30.
Markov Chain – A sequence of events where the next state depends only on the current state.Example: Predicting weather based only on today’s condition.
Markup – An amount added to the cost price to determine selling price.Example: If cost is $50 and markup is 20%, price = $60.
Mathematical Expression – A combination of numbers, variables, and operations without an equals sign.Example: 3x + 2 is a mathematical expression.
Mathematical Induction – A method of proof for natural numbers.Example: Proving that 1 + 2 + ... + n = n(n+1)/2.
Mathematical Model – A representation of a real-world situation using math.Example: Using y = 3x + 2 to model a car's distance over time
Mathematical Notation – Symbols used to represent mathematical concepts Example: ∑ represents summation
Mathematical Operation – An action like addition, subtraction, multiplication, or division Example: Subtraction is a basic operation
Mathematical Reasoning – The process of thinking logically about math problems Example: Using deduction to solve an equation
Mathematical Sentence – A statement that includes numbers and symbols and expresses a complete thought Example: 5 + 2 = 7
Matrix Determinant – A value that can be computed from a square matrix Example: For
Matrix Equation – An equation involving matrices Example: AX = B
Matrix Inverse – A matrix that, when multiplied by the original, gives the identity matrix Example: A × A ¹ = I
Matrix Multiplication – Combining two matrices to produce a third matrix Example:
Matrix – A rectangular array of numbers arranged in rows and columns Example:
Maximum – The largest value in a set or function.Example: The maximum of {2, 4, 7, 1} is 7.
Mean Absolute Deviation – The average distance between each data value and the mean Example: For data {2, 4, 4, 4, 6, 8}, the MAD is 1.33.
Mean – The average of a set of numbers Example: Mean of 2, 4, 6 is (2+4+6)/3 = 4
Measure of Central Tendency – A value that describes a set of data by identifying the central position Example: Mean, median, and mode are all measures of central tendency
Median – The middle number in a sorted list.Example: Median of {1, 3, 5} is 3.
Midpoint – The point exactly halfway between two others Example: Midpoint of (2, 4) and (6, 8) is (4, 6)
Minimum – The smallest value in a set or function.Example: The minimum of {3, 5, 1, 9} is 1.
Mixed Number – A number made up of a whole number and a fraction Example: 2½ is a mixed number
Mode – The value that appears most frequently in a set Example: In {1, 2, 2, 3}, the mode is 2
Modulo Operation – Finding the remainder when one number is divided by another Example: 17 mod 5 = 2
Modulus – The absolute value of a number or the remainder in division (mod) Example: | 5| = 5; 10 mod 3 = 1
Moment – A quantitative measure related to the shape of a function's graph Example: The second moment about the mean is the variance
Monomial – An algebraic expression with only one term Example: 5x² is a monomial
Monotonic Function – A function that is always increasing or always decreasing Example: f(x) = 2x is monotonic increasing.
Multiples – The result of multiplying a number by an integer Example: Multiples of 3 are 3, 6, 9, 12
Multiplication – A basic arithmetic operation showing repeated addition Example: 4 × 3 = 12
Multiplicative Comparison – Comparing numbers using multiplication Example: 12 is 3 times as much as 4 N
Multiplicative Identity – The number that doesn't change another number when multiplied Example: 1 is the multiplicative identity since 1 × a = a.
Multiplicative Inverse – A number that when multiplied by a given number results in 1 Example: The inverse of 5 is 1/5.
Multivariable Calculus – Calculus with functions of more than one variable Example: f(x, y) = x² + y²
Naperian Logarithm – Another name for the natural logarithm (log base e) Example: ln(e) = 1
Natural Number – A positive whole number used for counting Example: 1, 2, 3,
Negative Angle – An angle measured clockwise.Example: 90° turns clockwise from the positive x-axis.
Negative Correlation – A relationship where one variable increases as the other decreases Example: More exercise, less weight.
Negative Exponent – Indicates reciprocal of a number Example: 2 ³ = 1/8
Negative Integer – An integer less than zero.Example: 4 is a negative integer.
Negative Number – A number less than zero Example: 7 is a negative number
Negative Slope – A slope that goes down from left to right.Example: In y = 2x + 3, the slope is 2.
Nested Parentheses – Parentheses placed inside other parentheses Example: 2 × (3 + (4 1))
Nested Radical – A radical inside another radical Example: √(1 + √2)
Net Change – The difference between the final and initial value Example: If a stock rises from $40 to $55, the net change is $15.
Net – A two-dimensional shape that can be folded into a 3D object Example: A net for a cube has six squares
Neutral Element – An element that leaves another unchanged in an operation.Example: 0 is the neutral element for addition
Newton’s Binomial Theorem – A formula to expand powers of binomials.Example: (a + b)³ = a³ + 3a²b + 3ab² + b³.
Newton’s Method – A technique to approximate roots of a real-valued function.Example: Used to solve f(x) = 0.
Nominal Data – Data classified into categories without order.Example: Hair color: black, brown, blonde.
Non-Euclidean Geometry – Geometry that doesn't follow Euclid’s parallel postulate Example: Geometry on a curved surface like a sphere.
Nonagon – A polygon with nine sides.Example: A stop sign with nine edges is a nonagon.
Nonassociative Property – When grouping affects the result.Example: (a ÷ b) ÷ c ≠ a ÷ (b ÷ c).
Noncommutative Property – When order of operation affects the result Example: a b ≠ b a
Nonlinear Equation – An equation that does not form a straight line when graphed.Example: y = x² + 3 is nonlinear.
Nonlinear Function – A function whose graph is not a straight line.Example: f(x) = x³ 2x is nonlinear.
Nonstandard Unit – A unit of measure not part of a formal system Example: Measuring length in hand spans or paper clips. O
Nonzero Number – Any number that is not zero Example: 5 and 3 are nonzero numbers
Norm – A function that assigns a non-negative length or size to vectors.Example: The norm of (3, 4) is √(3² + 4²) = 5.
Normal Curve – The graph of a normal distribution.Example: A bell-shaped curve for standardized test scores.
Normal Distribution – A symmetric, bell-shaped distribution of data Example: Heights of people often follow a normal distribution.
Normal Line – A line perpendicular to a curve at a given point Example: The normal to the curve y = x² at (1,1) has a slope of ½.
Normal Vector – A vector perpendicular to a surface or curve.Example: For a plane, the normal vector is (A, B, C) in Ax + By + Cz = D.
Notation – A system of symbols used in mathematics.Example: π is notation for the ratio of a circle’s circumference to diameter.
Null Hypothesis – A statistical assumption that there is no effect or difference Example: H₀: μ = 100
Null Set – A set with no elements.Example: ∅ = {} is a null set.
Number Line – A line with numbers placed in order at equal intervals.Example: The point 2 is to the left of 0 on a number line.
Number Property – A rule that numbers follow.Example: Even + even = even.
Number System – A way to represent numbers using digits or symbols.Example: The decimal system uses digits 0–9
Numeral – A symbol or group of symbols representing a number.Example: "7" is a numeral for seven.
Numerator – The top number in a fraction that shows how many parts are taken.Example: In 3/4, the numerator is 3.
Numerical Coefficient – The number multiplying a variable.Example: In 5x, the coefficient is 5.
Numerical Data – Data that consists of numbers Example: The test scores 75, 80, and 95 are numerical data
Numerical Expression – A math expression using only numbers and operations.Example: 8 + 3 × 2.
Objective Function – The function to be maximized or minimized in linear programming.Example: Maximize P = 5x + 3y
Oblique Lines – Lines that are neither perpendicular nor parallel.Example: Two diagonal lines crossing at an angle other than 90°
Oblique Triangle – A triangle with no right angle.Example: A triangle with angles 70°, 60°, and 50°.
Observation – A data value collected during a survey or experiment Example: Recording the temperature each hour for a day.
Observed Frequency – The actual number of times an outcome occurs Example: Rolling a die 60 times and getting 6 exactly 12 times.
Obtuse Angle – An angle greater than 90° but less than 180° Example: An angle measuring 120° is obtuse
Obtuse Triangle – A triangle with one obtuse angle.Example: A triangle with angles 120°, 30°, and 30°.
Octagon – A polygon with eight sides and eight angles Example: A stop sign is shaped like a regular octagon
Odd Function – A function symmetric about the origin.Example: f(x) = x³ is an odd function.
Odd Number – An integer not divisible by 2 Example: 3, 5, and 7 are odd numbers
One-to-One Function – A function where each input has a unique output Example: f(x) = x + 2 is one-to-one
Open Interval – An interval that does not include its endpoints Example: (2, 5) includes all values between 2 and 5 but not 2 or 5.
Open Sentence – A mathematical sentence containing a variable Example: x + 2 = 5 is open until x is known
Open Set – A set that does not contain its boundary points Example: The set of all points (x, y) such that x² + y² < 1
Operation – A mathematical process such as addition, subtraction, multiplication, or division.Example: 6 ÷ 2 is a division operation
Operational Definition – A definition based on measurable actions.Example: Defining distance as the number of meters between two points
Opposite Angles – Angles opposite each other when two lines cross.Example: If two lines intersect and one angle is 40°, the opposite angle is also 40°
Opposite Numbers – Two numbers the same distance from zero, but on different sides.Example: 7 and 7 are opposites
Opposite Rays – Two rays that share an endpoint and go in opposite directions.Example: Ray AB and ray AC where B and C are on opposite sides of A.
Optimal Solution – The best possible answer in a math problem.Example: In linear programming, the optimal solution maximizes or minimizes the objective function.
Order of a Matrix – The number of rows and columns in a matrix.Example: A 2×3 matrix has 2 rows and 3 columns.
Order of Magnitude – A rough measure of size based on powers of 10.Example: 1,000 has an order of magnitude of 3 (10³) P
Order of Operations – The rules for the correct sequence to evaluate expressions.Example: In 3 + 4 × 2, multiplication comes first, so the result is 11
Order of Rotation – The number of times a figure maps onto itself during a full rotation.Example: An equilateral triangle has an order of rotation of 3
Ordered Pair – A pair of numbers used to locate a point on a plane.Example: (3, 2) is an ordered pair.
Ordinal Data – Data that shows order but not exact values Example: Rankings like 1st, 2nd, and 3rd in a race
Ordinal Number – A number that indicates position or order.Example: First, second, and third are ordinal numbers
Origin – The point (0, 0) on a coordinate plane.Example: The graph of y = x² passes through the origin.
Orthant – A region in space defined by signs of coordinates Example: In 3D space, the first orthant has all positive coordinates.
Orthocenter – The point where the altitudes of a triangle intersect Example: In an acute triangle, the orthocenter lies inside the triangle.
Orthogonal Lines – Lines that intersect at right angles Example: The x- and y-axes are orthogonal
Orthogonal Vectors – Vectors with a dot product of zero.Example: Vectors (1, 0) and (0, 1) are orthogonal.
Orthographic Projection – A way to show 3D objects in 2D Example: A cube shown with front, top, and side views.
Oscillation – A regular back-and-forth motion Example: The sine function oscillates between 1 and 1
Outcome – A possible result of a probability experiment.Example: Rolling a die and getting a 4.
Outlier – A data point much higher or lower than the rest Example: In {1, 2, 2, 3, 20}, 20 is an outlier
Overestimate – A guess or calculation that is more than the actual value.Example: Estimating 8.7 × 3 as 9 × 3 = 27 (actual is 26 1)
Overhead – Fixed costs in a math or business problem.Example: Monthly rent or electricity in a production cost calculation
Overlapping Events – Events that can happen at the same time.Example: Drawing a red card and a king from a deck of cards
Overlapping Sets – Sets that share common elements.Example: Set A = {1, 2, 3}, Set B = {3, 4, 5}; they overlap at 3.
P
Parabola – A U-shaped curve defined by a quadratic equation Example: The graph of y = x² is a parabola
Parallel Lines – Lines in a plane that never meet.Example: The lines y = 2x + 1 and y = 2x 3 are parallel.
Parallel Planes – Planes that never intersect Example: The top and bottom faces of a box are parallel planes
Parallelogram – A quadrilateral with opposite sides parallel.Example: A rhombus is a parallelogram.
Parameter – A constant in an equation that defines a family of curves Example: In y = mx + b, m and b are parameters.
Parentheses – Symbols used to group parts of an expression Example: (2 + 3) × 4 = 20
Partial Product – The result of multiplying part of one factor by another.Example: In 23 × 5, 20 × 5 = 100 is a partial product.
Partial Quotient – A part of the answer in division.Example: In 100 ÷ 4, the partial quotient 25 helps build the answer.
Partition – To divide into parts or sections.Example: Partitioning a set of 12 marbles into 3 groups of 4.
Percent Decrease – The amount a value drops as a percentage.Example: From $80 to $60 is a 25% decrease.
Percent Increase – The amount a value grows as a percentage.Example: If a price rises from $50 to $60, the percent increase is 20%.
Percent – A ratio out of 100.Example: 25% means 25 out of 100.
Perfect Cube – A number that is the cube of an integer.Example: 27 is a perfect cube because 3³ = 27.
Perfect Square – A number that is the square of an integer Example: 49 is a perfect square because 7 × 7 = 49.
Perimeter – The distance around a shape Example: A rectangle with sides 4 and 6 has a perimeter of 20
Permutation – An arrangement of objects in a specific order.Example: The permutations of ABC are ABC, ACB, BAC, BCA, CAB, CBA
Pi (π) – The ratio of a circle’s circumference to its diameter.Example: π ≈ 3.14.
Place Value – The value of a digit based on its position Example: In 345, the 4 has a place value of 40
Plane Geometry – Geometry dealing with flat shapes.Example: Studying triangles and circles is plane geometry
Plane – A flat, two-dimensional surface that extends forever.Example: A piece of paper represents part of a plane
Point of Intersection – The point where two graphs meet.Example: y = x and y = x + 4 intersect at (2, 2). Q
Point – A location in space with no size Example: (2, 3) is a point on a graph
Point-Slope Form – A way to write linear equations using a point and slope.Example: y y₁ = m(x x₁).
Polar Coordinates – A system using distance and angle from the origin Example: (5, 60°) in polar form
Polygon – A closed figure with straight sides.Example: A hexagon has six sides and is a polygon.
Polynomial – An expression with one or more terms using variables and coefficients Example: 3x² + 2x 5 is a polynomial.
Population – The entire group being studied in statistics Example: All students in a school form the population
Positive Number – A number greater than zero.Example: 5 is positive.
Power – The product of multiplying a number by itself a certain number of times Example: 2⁴ = 2 × 2 × 2 × 2 = 16.
Prime Number – A whole number with exactly two factors: 1 and itself Example: 7 is prime
Principal Axis – The main axis of symmetry in geometry.Example: In an ellipse, the longest diameter is the principal axis
Principal – The original amount of money before interest.Example: If you deposit $100, that is the principal.
Prism – A solid shape with two parallel, congruent bases Example: A rectangular prism looks like a box
Probability – The chance of an event happening Example: The probability of rolling a 6 on a die is 1/6
Product – The result of multiplication Example: 6 × 7 = 42, so 42 is the product
Proof – A logical argument showing a statement is true Example: A proof can show why the sum of angles in a triangle is 180°
Proportion – An equation that shows two ratios are equal Example: 3/4 = 6/8 is a proportion
Protractor – A tool used to measure angles.Example: A protractor measures a 45° angle.
Pyramid – A solid object with a polygon base and triangular sides Example: The Great Pyramid of Giza is a square pyramid.
Pythagorean Theorem – A formula relating the sides of a right triangle Example: a² + b² = c²
Quadrangle – Another name for a quadrilateral Example: A trapezoid is a quadrangle
Quadrant – One of the four regions of the coordinate plane.Example: The point (3, 2) is in the first quadrant.
Quadratic Equation – An equation of the form ax² + bx + c = 0 Example: x² 4x + 3 = 0 is a quadratic equation.
Quadratic Expression – An expression in the form ax² + bx + c Example: 2x² + 3x 1
Quadratic Formula – The solution to ax² + bx + c = 0.Example: x = ( b ± √(b² 4ac)) / 2a.
Quadratic Function – A function where the highest power of the variable is 2 Example: f(x) = x² + 2x + 1
Quadratic Graph – The graph of a quadratic function.Example: The graph of y = x² + 3 is a parabola.
Quadratic Inequality – An inequality involving a quadratic expression Example: x² 4 > 0
Quadratic Model – A model using a quadratic function to represent data Example: A ball’s height over time follows a quadratic model
Quadratic Sequence – A sequence where the second differences are constant.Example: 1, 4, 9, 16, 25.
Quadratic Term – The term involving x² in a quadratic expression Example: In 3x² + 2x + 1, 3x² is the quadratic term.
Quadrature – The process of finding area Example: Using integrals to find the area under a curve is quadrature.
Quadrilateral Angle Sum – The sum of interior angles in a quadrilateral is 360° Example: A rectangle’s angles add to 360°.
Quadrilateral Family – The group of all four-sided polygons Example: Parallelograms, trapezoids, rectangles, and squares. R
Quadrilateral – A polygon with four sides and four angles Example: A square is a quadrilateral
Quadrinomial – An algebraic expression with four terms.Example: x³ + 2x² x + 5 is a quadrinomial.
Qualitative Data – Data that describes qualities or characteristics Example: Colors of cars in a parking lot
Quantifier – A word like “for all” or “there exists” used in logic.Example: ∀x ∈ R, x² ≥ 0.
Quantile – A cut point dividing a range of data into equal parts Example: A median is a type of quantile
Quantitative Data – Data that can be measured or counted Example: The heights of students in centimeters
Quantity – An amount or number Example: The quantity of apples is 12
Quantum – A fixed unit of measure in physics and math Example: A quantum leap in energy levels
Quarter Circle – One-fourth of a circle Example: A slice of pie that is 90°
Quarter – One-fourth or 25% of a whole Example: A quarter of 100 is 25
Quartic Equation – An equation of degree 4 Example: x⁴ 5x² + 4 = 0 is quartic
Quartile – One of three values dividing data into four equal parts Example: The lower quartile (Q1) of {1, 2, 3, 4, 5} is 2
Queue Theory – The study of waiting lines using mathematics Example: Calculating wait times at a service desk
Quick Estimate – A fast approximation Example: Estimating 49 × 21 as 50 × 20 = 1000
Quick Ratio – In finance, a measure of a company’s short-term liquidity.Example: (Current Assets Inventory) ÷ Current Liabilities
Quinary System – A base-5 number system.Example: 132 in base-5 is 42 in decimal.
Quincunx – An arrangement of five points in a cross, often used in probability models Example: Galton's board uses a quincunx pattern.
Quintic Equation – An equation of degree 5 Example: x⁵ x + 1 = 0 is a quintic equation
Quintile – A value that divides data into five equal parts.Example: The top 20% of scores form the highest quintile
Quotient Field – The field of fractions formed from an integral domain.Example: The quotient field of integers is the rational numbers
Quotient Group – A concept in abstract algebra involving cosets Example: Z/2Z is the group of integers mod 2.
Quotient Identity – A trigonometric identity: tan(x) = sin(x)/cos(x) Example: tan(π/4) = sin(π/4) / cos(π/4)
Quotient Property of Exponents – Rule: aᵐ ÷ aⁿ = aᵐ ⁿ.Example: x⁵ ÷ x² = x³.
Quotient Rule – A rule for differentiating a quotient of two functions Example: If f(x) = u(x)/v(x), then f′(x) = [v u′ u·v′]/v².
Quotient Space – A space formed by partitioning a space into equivalence classes Example: The unit circle as a quotient of the real line mod 2π.
Quotient – The result of division Example: 12 ÷ 4 = 3, so 3 is the quotient
Radians – A unit for measuring angles Example: π radians = 180°
Radical – A symbol used to indicate a root.Example: √16 = 4.
Radicand – The number inside the radical symbol Example: In √25, the radicand is 25
Radius – The distance from the center of a circle to any point on its edge.Example: A circle with a radius of 5 cm has a diameter of 10 cm
Random Sample – A sample in which every member has an equal chance of being selected.Example: Drawing names from a hat
Range (Data) – The difference between the highest and lowest values.Example: For data {2, 5, 9}, the range is 7
Range (Function) – The set of all possible output values.Example: For f(x) = x², the range is all non-negative numbers
Range (Statistics) – Another term for the spread of data.Example: In {2, 4, 7, 9}, range = 7.
Range Rule of Thumb – A rule for estimating standard deviation Example: SD ≈ (Range)/4
Rate of Change – Describes how one quantity changes in relation to another.Example: In y = 3x, the rate of change is 3
Rate – A ratio comparing two different units.Example: 60 miles per hour.
Ratio Table – A table that shows equivalent ratios
Ratio – A comparison of two quantities by division.Example: A 2:3 ratio means 2 parts to 3 parts.
Rational Expression – A fraction with polynomials in numerator and denominator Example: (x² + 1)/(x 2)
Rational Number – A number that can be expressed as a fraction.Example: 3/4 and 2 are rational numbers.
Rationalize – To eliminate the radical from the denominator Example: Rationalize 1/√2 to √2/2
Ray – A part of a line with one endpoint that extends infinitely in one direction Example: A ray starting at point A and passing through B.
Real Number – Any number on the number line Example: 1, 0, 2 5, and √2 are real numbers
Reciprocal – The inverse of a number.Example: The reciprocal of 4 is 1/4.
Rectangle – A quadrilateral with four right angles Example: A shape with sides 6 cm and 3 cm is a rectangle
Rectangular Prism – A solid with 6 rectangular faces.Example: A cereal box is a rectangular prism.
Rectilinear Figure – A shape with only straight sides and right angles Example: A rectangular floor plan
Reflection – A mirror image of a shape over a line.Example: Reflecting a triangle over the y-axis.
Reflex Angle – An angle greater than 180° and less than 360° Example: An angle measuring 270° is a reflex angle.
Regression Line – A line that best fits the data Example: y = 2x + 1 fits the trend of data points
Regression – A statistical method to model relationships between variables.Example: Linear regression finds the best line through data points
Regular Polygon – A polygon with all sides and angles equal.Example: An equilateral triangle is a regular polygon
Relative Frequency – The ratio of a frequency to the total number.Example: 5 red balls out of 20 = 0.25.
Remainder – The amount left over after division Example: 10 ÷ 3 = 3 with a remainder of 1
Repeating Decimal – A decimal that has a repeating pattern.Example: 1/3 = 0.333...
Resultant Vector – The combined effect of two or more vectors Example: Adding vectors (3, 4) and (1, 2) gives (4, 6). S
Rhombus – A quadrilateral with all sides equal in length Example: A square is a special type of rhombus
Right Angle – An angle of exactly 90 degrees.Example: The corner of a square is a right angle.
Right Triangle – A triangle with one 90° angle Example: A triangle with sides 3, 4, and 5
Root – A value that satisfies an equation when substituted.Example: A root of x² 4 = 0 is x = 2.
Rotation – A turn of a shape around a point Example: Rotating a triangle 90° clockwise
Rounding – Approximating a number to a nearby value Example: Rounding 3 76 to 3 8
Row (Matrix) – A horizontal line of entries in a matrix Example: In a 2×3 matrix, each row has 3 numbers
Row Vector – A 1×n matrix Example: [2 4 6] is a row vector
Sample – A subset of a population Example: Surveying 50 students out of 500
Scalar – A quantity with only magnitude, not direction Example: Speed = 60 km/h is a scalar
Scale – The ratio between the size on a model and real size Example: 1 cm : 1 km on a map
Scalene Triangle – A triangle with all sides of different lengths Example: A triangle with sides 3 cm, 4 cm, and 5 cm
Scatter Plot – A graph showing data points to observe relationships Example: Plotting students' height vs weight
Scientific Notation – A method of writing large or small numbers using powers of ten Example: 3,000 = 3 × 10³
Sector – A part of a circle enclosed by two radii and an arc Example: A pizza slice is a sector
Segment – A part of a line with two endpoints Example: Line segment AB has endpoints A and B
Sequence – An ordered list of numbers Example: 2, 4, 6, 8 is a sequence
Set – A collection of distinct objects Example: Set A = {2, 4, 6}
Side – A line segment that forms part of a polygon Example: A square has four equal sides
Significant Figures – Digits that carry meaning in a number Example: 3 450 has four significant figures
Simplify – To make an expression shorter or easier to understand Example: 2x + 3x simplifies to 5x
Sine – In a right triangle, the ratio of opposite side to hypotenuse Example: sin(30°) = 1/2
Slope – The steepness of a line Example: A line with slope 2 rises 2 units for every 1 unit run
Slope-Intercept Form – An equation of the form y = mx + b Example: y = 2x + 5
Solid – A 3D object with length, width, and height Example: A cube is a solid
Solution – A value that makes an equation true Example: x = 2 is the solution to x + 3 = 5
Sphere – A 3D object where every point is the same distance from the center Example: A basketball is a sphere.
Square (Shape) – A quadrilateral with all sides equal and all angles 90° Example: A tile with four equal sides and right angles.
Square Number – A number multiplied by itself Example: 5² = 25
Square Root – A number that when multiplied by itself gives the original number.Example: √49 = 7.
Standard Deviation Rule (Empirical Rule) – Describes how data falls within standard deviations Example: About 68% of values lie within 1 SD of the mean in normal distribution.
Standard Deviation – A measure of how spread out numbers are Example: A small standard deviation means the data is close to the mean.
Standard Form (Equation) – A common way of writing linear equations: Ax + By = C Example: 2x + 3y = 6
Statistics – The study of collecting and analyzing data.Example: Mean, median, and mode are part of statistics.
Straight Angle – An angle of exactly 180 degrees.Example: A straight line forms a straight angle.
Strategy – A plan or method to solve a math problem Example: Using factoring to solve a quadratic equation
Substitute – Replacing a variable with a number.Example: If x = 3, then 2x = 6. T
Subtraction – Taking one number away from another Example: 10 4 = 6
Subtrahend – The number being subtracted.Example: In 9 3, 3 is the subtrahend.
Sum – The result of adding two or more numbers Example: 5 + 7 = 12
Supplementary Angles – Two angles whose sum is 180°.Example: 120° and 60° are supplementary.
Surface Area – The total area of the surface of a 3D object Example: The surface area of a cube with side 2 is 24.
Symmetry – A figure has symmetry if it can be folded or reflected into itself Example: A circle has infinite lines of symmetry.
System of Equations – A set of equations with the same variables Example:x + y = 5x y = 1
T-score – A type of standardized score in statistics Example: A T-score of 2 5 may indicate significance in a test.
Table of Values – A table showing input and output pairs
Table – A way to organize data using rows and columns.Example: A multiplication table shows products of numbers
Tally Chart – A chart using tally marks to record data counts.Example: |||| = 4 items.
Tangent (Geometry) – A line that touches a curve at one point without crossing it.Example: A tangent touches a circle at exactly one point.
Tangent (Trigonometry) – Ratio of the opposite side to the adjacent side in a right triangle.Example: tan(45°) = 1.
Tangent Line – A line that touches a curve at just one point.Example: The line touching a circle at point A.
Tens Place – The second digit from the right in a number.Example: In 47, the 4 is in the tens place.
Tenths – One part of ten equal parts.Example: 0.3 is three tenths.
Term – A single number, variable, or a product of both in an expression Example: In 3x + 5, the terms are 3x and 5.
Tessellation – A pattern of shapes that fit together perfectly.Example: Hexagons tessellate without gaps.
Tetrahedron – A solid with four triangular faces Example: A triangular pyramid is a tetrahedron
Theorem – A statement that can be proven true using logic and other theorems.Example: Pythagorean Theorem
Theta (θ) – A common variable used to represent an unknown angle.Example: sin(θ) = 0.5.
Three-Dimensional (3D) – Having length, width, and height Example: A cube is a 3D shape
Tick Mark – Small marks used on graphs or rulers to show units.Example: Each tick on a ruler shows 1 cm.
Tiling Pattern – A repetitive arrangement of shapes covering a surface Example: Bathroom tiles in a repeating square design.
Tiling – Covering a surface with shapes without gaps or overlaps Example: Tiling a floor with square tiles
Time Interval – The difference between two time values.Example: From 3:00 PM to 5:00 PM is a 2-hour interval
Time – A measure of the duration between events.Example: 60 minutes equals 1 hour.
Timeline – A line representing events in chronological order Example: A timeline from year 2000 to 2020
Total Surface Area – The area covering the outside of a 3D shape.Example: The total surface area of a cube is 6 × (side²)
Total – The sum of all values.Example: The total of 4, 5, and 6 is 15.
Transformation – Changing a shape’s position, size, or orientation Example: Reflecting or rotating a triangle
Translation – Moving a shape without rotating or flipping it Example: Sliding a square 3 units to the right
Transversal – A line that crosses two or more other lines Example: A transversal cutting across two parallel lines.
Trapezoid – A quadrilateral with one pair of parallel sides Example: A bridge support shaped like a trapezoid
Tree Diagram – A diagram showing all possible outcomes Example: Flipping a coin twice can be shown in a tree diagram
Tree Map – A graphic organizer showing categories and subcategories.Example: Breaking down types of triangles into scalene, isosceles, and equilateral U
Trend – A general direction in data over time.Example: Sales increasing each month show an upward trend.
Trial – A single performance of an experiment Example: One roll of a die is a trial
Triangle – A three-sided polygon Example: A shape with sides 3 cm, 4 cm, and 5 cm
Triangular Prism – A solid with two triangular bases and three rectangular faces Example: A tent with triangle ends.
Trigonometry – The study of the relationships between angles and sides in triangles Example: sin, cos, and tan are basic trigonometric functions.
Trinomial – A polynomial with three terms.Example: x² + 2x + 1 is a trinomial.
True Equation – An equation that is mathematically correct Example: 2 + 3 = 5
Turn – Another word for rotation in geometry.Example: A 90° turn rotates a shape one-quarter around a point.
Unbalanced Equation – An equation where the values on both sides are not equal.Example: 3 + 2 ≠ 10.
Unbiased Sample – A sample that fairly represents the population Example: Randomly selecting 50 people from a city.
Unbounded – A graph or region that goes on infinitely Example: A line that continues without end
Uncertainty – The doubt in a measured or estimated value.Example: Measurement = 3.0 ± 0.1 cm.
Uncountable Set – A set with infinitely many elements that can’t be listed Example: Real numbers between 0 and 1.
Undefined – A value that has no meaning in math, like dividing by zero Example: 5 ÷ 0 is undefined
Underestimate – An estimate that is lower than the actual value.Example: Estimating 4.8 as 4.
Unidirectional – Going in one direction only Example: A function that always increases
Uniform – Consistent in form or character throughout.Example: A uniform scale increases by the same amount each time
Union – The set containing all elements from two or more sets.Example: A = {1,2}, B = {2,3}, A ∪ B = {1,2,3}.
Unit Circle – A circle with radius 1, centered at the origin Example: On the unit circle, cos(0°) = 1
Unit Fraction – A fraction with numerator 1.Example: 1/5 is a unit fraction.
Unit Price – The cost for one unit of an item Example: $4 for 2 cans is $2 per can
Unit Rate – A rate with a denominator of 1 Example: 60 miles per hour means 60 miles in 1 hour
Unit Vector – A vector with a magnitude of 1 Example: (1/√2, 1/√2) is a unit vector
Unit – A standard quantity used for measurement Example: 1 inch, 1 kilogram, or 1 hour
Univariate Data – Data involving one variable Example: A list of student ages
Univariate Function – A function with only one variable Example: f(x) = x² is univariate
Universal Set – The set of all possible elements under consideration Example: If discussing numbers under 10, the universal set is {0–9}
Unknown – A value in an equation that needs to be found Example: In x + 5 = 9, x is the unknown
Unlike Terms – Terms that have different variables or powers Example: 3x and 4y are unlike terms
Unlikely Event – An event that has a low probability of happening Example: Rolling a 1 on a 20-sided die
Unordered Pair – A pair where the order of elements doesn’t matter Example: {a, b} is the same as {b, a}
Unpaired Data – Data sets that are not linked together Example: Heights of girls and weights of boys
Unroll – Flattening a 3D shape into 2D Example: Unrolling a cylinder into a rectangle
Upper Bound – The greatest value that a variable or function can reach Example: If x < 10, then 10 is the upper bound
Upper Limit – The highest value allowed in a range Example: Ages 5 to 12 have an upper limit of 12
Upper Quartile (Q3) – The median of the upper half of a data set Example: In {1, 3, 5, 7, 9}, Q3 = 7
Uppercase Letters – Often used to name sets or angles Example: Set A = {2, 4, 6}
Upright Prism – A prism with sides perpendicular to the base Example: A rectangular box standing upright
Upscaling – Increasing a shape’s size using a scale factor Example: Enlarging a triangle by a factor of 2
Upside Down Fraction – Also called reciprocal Example: The reciprocal of 3/4 is 4/3
Upward Curve – A graph that increases in steepness Example: y = x² is an upward curve V
Upward Trend – When data values increase over time Example: A graph showing sales going up
Usage – The way math tools or concepts are applied Example: Using Pythagorean Theorem to find a missing side
Used Value – A value that has been substituted or selected Example: Plugging in x = 4
V-shaped Graph – The graph of an absolute value function Example: y = |x| forms a V shape
Value – The result or worth of a number or expression Example: The value of 4 + 5 is 9
Variable Equation – An equation that contains variables.Example: x + 4 = 10.
Variable Expression – An expression that includes variables Example: 3x + 2 is a variable expression
Variable Table – A table showing values for variables W
Variable Term – A term that includes a variable Example: In 5x + 7, 5x is a variable term
Variable – A symbol that represents an unknown value Example: In 2x + 3 = 7, x is the variable
Variance – A measure of how spread out numbers are Example: A low variance means values are close to the mean.
Variation – How values differ from each other Example: A data set with high variation has values far apart
Vary – To change or differ in amount or value Example: As x increases, y may vary
Vector Addition – Combining two vectors to get a result Example: ⟨2, 3⟩ + ⟨1, 1⟩ = ⟨3, 4⟩
Vector Notation – A way to write vectors using symbols Example: v = ⟨3, 4⟩ represents a 2D vector
Vector Quantity – A quantity with direction and magnitude Example: Velocity is a vector quantity
Vector Subtraction – Subtracting one vector from another Example: ⟨5, 4⟩ ⟨2, 1⟩ = ⟨3, 3⟩
Vector – A quantity with both magnitude and direction Example: Moving 5 units right and 2 units up
Venn Diagram – A diagram showing relationships between sets using overlapping circles Example: One circle for people who like apples, another for people who like bananas
Verbal Expression – A math problem written in words Example: "Five more than twice a number" means 2x + 5
Verbal Model – Describing a math problem using words Example: “Distance equals rate times time ”
Verify – To prove or confirm that something is correct Example: Verify a solution by plugging it back into the equation
Vertex of a Parabola – The highest or lowest point on a parabola Example: The vertex of y = (x 2)² is (2, 0)
Vertex – A point where two or more lines or edges meet Example: A triangle has three vertices
Vertical Angles – Angles opposite each other when two lines cross Example: Vertical angles are always equal
Vertical Asymptote – A vertical line a graph approaches but never touches Example: y = 1/x has a vertical asymptote at x = 0
Vertical Line Test – A test to determine if a graph is a function Example: If a vertical line touches more than one point, it's not a function
Vertical Shrink – Compressing a graph toward the x-axis Example: y = 0 5f(x) shrinks the graph vertically
Vertical Stretch – Pulling a graph away from the x-axis Example: y = 2f(x) stretches the graph vertically
Vertical – A line or direction that goes up and down Example: A vertical line is parallel to the y-axis
Vinculum – A horizontal line used in fractions or repeating decimals Example: In �� ��, the vinculum shows the digit 5 repeats
Visual Estimate – An approximate value based on a visual Example: Guessing a bar on a graph is about 30
Visual Representation – A picture, graph, or diagram that shows data Example: A pie chart is a visual representation.
Volume of Cone – The space inside a cone Example: V = 1/3πr²h
Volume of Cylinder – The space inside a cylinder Example: V = πr²h
Volume of Sphere – The space inside a sphere Example: V = 4/3πr³
Volume Unit – A unit used to measure volume Example: Cubic centimeters (cm³) or liters (L)
Volume – The amount of space a 3D object occupies.Example: Volume of a cube = side³.
Vulgar Fraction – A common fraction written with numerator and denominator Example: ¾ is a vulgar fraction W
W-coordinate – A fourth dimension in advanced math, often beyond x, y, and z Example: In 4D space, a point is (x, y, z, w).
Wall Clock Math – Using clock hands and times for math problems Example: What angle forms between 3 and 6?
Wave – A repeating pattern like a sine curve Example: y = sin(x) creates a wave
Wavy Line – Used in math to show approximation.Example: 3.14 ≈ π, shown with a wavy equals sign.
Way – A possible method or path to a solution Example: One way to find area is multiplying length by width
Wedge – A shape like a triangle or slice Example: A slice of pizza is shaped like a wedge
Weight – A measure of how heavy something is Example: A book weighing 1 5 kg
Weighted Average – An average where some values count more than others Example: If a test counts for 70% and homework 30%
Weighted Graph – A graph with numbers (weights) on its edges Example: A map showing distances between cities
Well-Defined – A rule or function that works the same every time Example: “Add 5” is well-defined; “choose your favorite” is not
Well-Ordered Set – A set where every subset has a least element.Example: Natural numbers are wellordered
Whole Number – A number without fractions or decimals; non-negative integers.Example: 0, 1, 2, 3 are whole numbers
Whole-Part Model – A way to show how parts combine into a whole.Example: 3 + 2 = 5, where 3 and 2 are parts
Whole-to-Part Ratio – Compares the whole quantity to one part.Example: In 10 apples, 3 are green: 10:3.
Widen – To increase the width of a shape or graph Example: Stretching a parabola horizontally
Width of Interval – The difference between upper and lower boundaries in a data group.Example: From 10 to 20, the width is 10
Width – The measurement of how wide something is.Example: A rectangle 4 units wide.
Winding Number – In geometry, how many times a curve loops around a point Example: A circle around a point once has winding number 1.
With Replacement – Drawing items where each one is returned before the next draw.Example: Drawing a card and putting it back before the next draw.
Withdrawal – Taking an amount away, often in financial math.Example: Withdrawing $20 from a bank account.
Within – Describes something inside a range or set.Example: Ages within 10 to 20.
Without Replacement – Drawing items and not returning them after each draw.Example: Drawing a marble and keeping it aside.
Word Form of Fractions – Writing fractions in words.Example: ¾ is “three-fourths.”
Word Problem – A math question written in sentence form.Example: “If you have 3 apples and buy 2 more…”
Word Sentence – A complete math statement written in words.Example: “Five plus three is equal to eight.”
Work Rate – How fast a task is done over time.Example: Painting 2 rooms per hour.
Work Shown – Displaying every step used to solve a problem Example: Showing all steps for solving x + 3 = 10. X
Work – In math, often refers to steps taken to solve a problem Example: Showing all your work on a test
Working Backward – A strategy that starts from the end and works in reverse.Example: Solving 3x + 2 = 11 by subtracting 2 first
Working Number – A number used temporarily during calculation.Example: Rounding 398 to 400 to simplify adding.
Worksheet – A sheet with math questions for practice.Example: A worksheet with 10 addition problems.
Worst Case – The most extreme or least favorable outcome Example: The worst case of rolling a die is getting 1.
Worst Value – The least favorable outcome Example: The worst score in a test might be 0
Written Form – Writing numbers in words.Example: 248 is “two hundred forty-eight.”
Written Method – Solving a problem step-by-step on paper Example: Long division is a written method
X – A common variable used to represent an unknown number Example: In x + 3 = 7, x equals 4
X-axis Distance – The horizontal distance between two points.Example: Between (2, 5) and (7, 5), the x-axis distance is 5
X-axis Label – The title or label describing the x-axis.Example: A graph labeled “Time (seconds)” on the x-axis.
X-axis Symmetry – When a graph mirrors across the x-axis Example: The graph of y = f(x) has x-axis symmetry.
X-axis Translation – Shifting a graph left or right Example: f(x 3) moves the graph 3 units right
X-axis – The horizontal axis in a coordinate plane.Example: In point (4, 2), 4 lies on the x-axis.
X-centroid – The x-coordinate of a shape’s center of mass Example: The x-centroid of a rectangle is half its base length.
X-coordinate – The first value in an ordered pair showing horizontal position Example: In (5, 3), the xcoordinate is 5.
X-data – Values or data points placed on the x-axis Example: In a chart, x-data may be years: 2020, 2021, 2022.
X-height – In math typography, the height of lowercase 'x' used in graphs Example: Fonts with larger x-height are easier to read in equations.
X-intercept – The point where a graph crosses the x-axis Example: For y = 2x 4, the x-intercept is (2, 0)
X-measurement – Measuring horizontal values.Example: Measuring distance along the x-axis in geometry.
X-number – A placeholder for an unknown number.Example: Let x-number be 7 if x + 2 = 9.
X-Pattern – A crossing pattern resembling the letter X.Example: Two intersecting lines form an X-pattern.
X-Plane – A plane involving the x-dimension.Example: In 3D, the x-y plane lies flat.
X-range – The span of all possible x-values.Example: For x from 5 to 5, the x-range is 10 units.
X-ray Angle Geometry – Measuring angles formed in X-ray crystal images.Example: The diffraction angle helps identify crystal structure.
X-ray Beam Width – The width of an X-ray beam used in measurements.Example: Beam width affects resolution in CT scans.
X-ray Crystallography – A method using X-rays to study crystal structures.Example: X-ray crystallography helps determine the atomic layout in crystals.
X-ray Diffraction Angle – A measure used in calculating crystal spacing Example: Using Bragg’s law: nλ = 2d sinθ.
X-ray Penetration – The depth X-rays reach, used in measurement calculations Example: Depth depends on X-ray intensity and material type. Y
X-ray Spectrum – The graph showing X-ray intensity over wavelength Example: Used in physics to analyze material properties.
X-rays in Math Models – Using X-ray data in mathematical simulations.Example: Medical imaging models using X-ray inputs.
X-rotation Matrix – A matrix used to rotate objects in 3D around the x-axis.
X-Rotation – Rotating a 3D object around the x-axis.Example: A 90° x-rotation moves a shape up or down.
X-Slice – A horizontal slice or cut in a graph or shape Example: Cutting a cylinder along its length gives an xslice.
X-value Table – A table showing inputs (x) and outputs (y).
X-value – The input value in a function or relation.Example: In the function f(x) = x², 3 is an x-value.
Xenagon – A polygon with ten sides (rarely used variant of decagon) Example: A xenagon has 10 sides and 10 angles.
Xenocentric Coordinate System – A system where origin is at a different reference point.Example: Used in astronomy to observe stars from Earth.
Xenocurrency Calculations – Math involving currencies used outside their home countries.Example: Calculating exchange rates for Japanese yen used in the UK.
Xenographic Function – A rare function used in typography or printing models.Example: Mapping digital font coordinates on the x-axis.
Xenon Decay Math – Using math to track decay of xenon isotopes in physics.Example: Calculating the halflife of xenon-135.
Xenon Gas Volume – Using volume formulas to calculate xenon in containers.Example: V = nRT/P for xenon in a tank.
Xenon Light Math – Calculating brightness or energy output of xenon lamps.Example: Using P = IV to find power output.
Xerographic Scaling – Changing size of a figure or image during copying.Example: Enlarging a triangle by 150% on a copier.
Xerox Area – Area used or copied in scaled diagrams.Example: Enlarging a square of area 4 cm² by 200%.
XOR (Exclusive OR) – A logic gate where the output is true if one input is true, not both.Example: XOR(1, 0) = 1; XOR(1, 1) = 0
Y – A common variable used to represent a dependent value Example: In y = 4x, y changes based on x
Y-axis Distance – Vertical distance between two points.Example: Between (4, 2) and (4, 6), the y-axis distance is 4
Y-axis Label – The title or label describing the y-axis.Example: A graph labeled “Height (cm)” on the y-axis.
Y-axis Reflection – A mirror image across the y-axis Example: The point (3, 4) reflected becomes ( 3, 4)
Y-axis Symmetry – When a graph mirrors across the y-axis.Example: The graph of y = x² has y-axis symmetry
Y-axis – The vertical axis in a coordinate plane.Example: In point (3, 4), 4 lies on the y-axis.
Y-boundary – The edge limit along the y-axis in graphs Example: The graph ends at y = 10
Y-center – The y-coordinate of a shape’s center.Example: A rectangle centered at (0, 5) has y-center 5.
Y-chart Analysis – A technique to compare and contrast concepts Example: Analyzing pros and cons using a Y-chart.
Y-chart – A chart shaped like the letter Y used for comparisons Example: A Y-chart comparing advantages and disadvantages.
Y-component – The vertical part of a vector Example: In a vector at 45°, the y-component equals the xcomponent.
Y-coordinate Graphing – Plotting points using the y-coordinate.Example: To graph (2, 5), go up to 5 on y-axis.
Y-coordinate – The second value in an ordered pair showing vertical position.Example: In (5, 7), the ycoordinate is 7.
Y-curve – A curved graph that extends along the y-axis.Example: The graph of y = √x is a y-curve.
Y-data – Information plotted along the y-axis Example: Test scores on the y-axis over time
Y-equals Form – A way of writing equations starting with y =.Example: y = 2x + 1 is in y-equals form.
Y-error – The difference between expected and actual y-values Example: If predicted y = 5 and actual y = 7, error = 2.
Y-increment – The change in y when x increases Example: In y = 3x, the y-increment is 3 for each unit of x
Y-intercept Form – Linear equations written as y = mx + b.Example: y = 3x + 2 is in y-intercept form.
Y-intercept – The point where a graph crosses the y-axis Example: For y = 2x + 3, the y-intercept is (0, 3)
Y-line Symmetry – Symmetry across a vertical line.Example: y = x² has symmetry across x = 0.
Y-line – Any line parallel to the y-axis Example: x = 4 is a vertical y-line
Y-plane – A plane involving the y-dimension.Example: In 3D, the x-y plane is flat like a table.
Y-point – A point lying directly on the y-axis Example: (0, 6) is a y-point
Y-projection – The projection of a point or shape onto the y-axis Example: Projecting (3, 5) onto the y-axis gives 5
Y-range Table – A table displaying possible y-values.
Y-range – The span of all possible y-values Example: For y = x² and x from 3 to 3, the y-range is 0 to 9
Y-ratio – The vertical ratio in a coordinate relationship Example: Rise over run = y-ratio in slope
Y-rotation – Rotating a 3D object around the y-axis Example: A 90° y-rotation turns a cube sideways
Y-slice – A vertical slice through a shape or graph Example: Cutting a cube straight down gives a y-slice
Y-units – Units of measurement along the y-axis Example: Meters, dollars, or seconds
Y-value Table – A list of inputs and corresponding outputs Example:
Y-value – The output value in a function or relation Example: In f(x) = x², the y-value for x = 2 is 4
Y-variable – A symbol representing a changing output value Example: In y = mx + b, y is the y-variable
Y-zero – The value of x when y equals 0 Example: In y = 2x 4, y = 0 when x = 2 Z
Z – A common variable representing a third dimension or unknown Example: In x + y + z = 12, z is unknown
Z-axis Distance – The space between two points along the z-axis Example: Between (1, 2, 3) and (1, 2, 7), the z-distance is 4
Z-axis Label – The title or label describing the z-axis Example: A 3D graph labeled “Depth (meters)” on the zaxis
Z-axis Rotation – Rotating a 3D object around the z-axis Example: A 90° z-rotation turns a shape on the x-y plane
Z-axis Symmetry – Symmetry around the z-axis in 3D Example: A cylinder has z-axis symmetry when standing upright.
Z-axis – The third axis in 3D coordinate systems, representing depth Example: In (2, 3, 4), 4 lies on the z-axis
Z-bound – A boundary set for z-values in data or space.Example: A function may be defined for z ≤ 10.
Z-centroid – The center of mass in the z-direction Example: For a symmetric shape, the z-centroid lies at half its depth.
Z-column – A column in matrix operations involving z-values or dimensions Example: Matrix column [3, 5, z] includes a variable z.
Z-coordinate Plane – A plane formed using z with x or y axes Example: The y-z plane is vertical and shows height and depth.
Z-coordinate – The third value in an ordered triple showing depth in space Example: In (5, 6, 7), the zcoordinate is 7.
Z-cross Section – A slice of a 3D object perpendicular to the z-axis.Example: Cutting a cylinder horizontally creates a circular z-cross section.
Z-direction – Movement along the z-axis (depth).Example: An object moving away from you follows the positive z-direction.
Z-domain – The set of values used in Z-transforms.Example: Z-domain functions represent digital signals.
Z-form Equation – An equation solved or rewritten in terms of z.Example: In x + y = z, solving for z gives z = x + y.
Z-function – A function involving z as a variable.Example: f(z) = z² + 1 is defined on the complex plane.
Z-graph – A 3D graph including the z-dimension.Example: A surface plot of z = x² + y².
Z-intercept – The point where a 3D graph crosses the z-axis.Example: In z = x + y, the intercept is (0, 0, 0).
Z-matrix – A matrix used in quantum chemistry or special math fields.Example: Z-matrices define molecule geometry in computational models.
Z-measure – A measurement taken in the z-direction.Example: The height of a stack of boxes along z-axis is a z-measure.
Z-pattern – A shape or data trend resembling the letter Z.Example: A Z-pattern shows alternating horizontal and diagonal movement.
Z-plane – A complex plane with real and imaginary axes.Example: The number 3 + 4i lies in the z-plane.
Z-range – The span of possible z-values in a 3D graph.Example: From z = 2 to z = 5, the z-range is 7.
Z-rotation Matrix – A matrix that rotates a point around the z-axis.
Z-row – A row in the simplex method used in linear programming.Example: The Z-row shows the value of the objective function
Z-score – A standardized score indicating how far a value is from the mean.Example: A z-score of 2 means two standard deviations below the mean
Z-section – A cross-section taken along the z-axis.Example: Slicing a cube parallel to the x-y plane shows a zsection
Z-statistic – A value used in hypothesis testing to measure standard deviations.Example: A z-statistic of 2.5 is compared to a critical value
Z-table – A chart showing the area under a standard normal curve.Example: A z-score of 1.96 corresponds to 0 975 in the Z-table
Z-test – A statistical test used to compare means with known variances.Example: A z-test checks if a sample mean differs from the population mean
Z-transform – A method to analyze discrete signals in engineering/math Example: The Z-transform of a sequence helps solve difference equations.
Z-translation – Moving a figure up or down along the z-axis Example: Translating a surface from z = 2 to z = 5
Z-units – Units of measurement along the z-axis.Example: Depth in meters or inches in a 3D model.
Z-value – A number on the z-axis or a standardized score Example: A z-value of 1 5 means 1 5 standard deviations above the mean.
Z-zero – The value of x and y when z = 0 Example: The point (1, 2, 0) lies on the z = 0 plane