## Comprehensive GCSE-Level Mathematical Terms and Definitions

This glossary contains a comprehensive list of mathematical terms and definitions used in GCSE Maths. This is a useful resource for students to bookmark and refer to when revising for exams or preparing for assessments.

#### A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z

## A

**Absolute Value:**The distance of a number from zero on the number line, always positive.**Acute Angle:**An angle that measures less than 90 degrees.**Addition:**The process of combining two or more numbers to get a total or sum.**Algebra:**The branch of mathematics that uses letters and other symbols to represent unknown numbers.**Algebraic Expression:**A mathematical phrase that can contain numbers, variables, and operators but doesn’t have an equals sign.**Algebraic Fraction:**A fraction that contains algebraic expressions in the numerator, denominator, or both.**Algebraic Term:**A number, variable, or product of numbers and variables.**Alternate Angles:**Angles that are on opposite sides of a transversal and are outside the two lines.**Angle:**The measure of the amount of rotation needed to bring one line or plane into coincidence with another.**Area:**The measure of the extent of a surface, usually expressed in square units.**Arithmetic Mean:**Another term for the average, calculated by adding up a set of values and dividing by the number of values.**Asymptote:**A line that a curve approaches but never touches, especially as it extends towards infinity.**Average:**The sum of a set of values divided by the number of values.**Axis:**A reference line from which distances or angles are measured in a coordinate grid.**Axis of Symmetry:**A line that divides a figure into two halves that are mirror images of each other.

## B

**Base:**The bottom side of a two-dimensional shape or the bottom face of a three-dimensional object.**Binomial Theorem:**A formula for expanding a binomial raised to any positive integer power.**Bisect:**To divide into two equal parts.**Box Plot:**A diagram that shows the five-number summary of a data set.**Brackets:**A pair of symbols used in mathematics to group together parts of an expression.**Braces:**A pair of symbols used in mathematics to group together parts of an expression.

## C

**Circumference:**The distance around the outer boundary of a circle.**Circle:**A two-dimensional geometric shape with all points the same distance from the center.**Coefficient:**A numerical or constant factor in an algebraic expression, often multiplied by a variable.**Completing the Square:**A method used to solve quadratic equations by manipulating the equation to create a perfect square trinomial.**Coordinate Plane:**A two-dimensional plane formed by the intersection of a horizontal line (x-axis) and a vertical line (y-axis).**Cosecant (csc), Secant (sec), Cotangent (cot):**Reciprocal trigonometric functions, where cosecant is the reciprocal of sine, secant is the reciprocal of cosine, and cotangent is the reciprocal of tangent.**Cuboid:**A three-dimensional geometric shape with six rectangular faces, twelve edges, and eight vertices.**Cylinder:**A three-dimensional geometric shape with two parallel circular bases and a curved surface connecting the bases.**Cylindrical:**A three-dimensional geometric shape with two parallel circular bases and a curved surface connecting the bases.**Cylindrical Coordinates:**A three-dimensional coordinate system that uses two angles and a distance from a central point to define a point in space.

## D

**Derivative:**The rate at which a function is changing at any given point, representing the slope of the tangent line to the graph.**Diameter:**The distance across a circle through its center, or any straight line passing through the center of a sphere.**Difference:**The result of subtracting one number from another.**Dilation:**A transformation that changes the size of a figure, but not the shape.**Direct Proportion:**A relationship between two variables in which one is a constant multiple of the other.**Direct Variation:**A relationship between two variables in which one is a constant multiple of the other.**Discriminant:**A function of the coefficients of a polynomial equation whose value gives information about the roots of the polynomial.**Distributive Property:**A property of multiplication that states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.**Dividend:**The number that is being divided in a division problem.**Divisor:**The number by which another number is divided in a division problem.**Domain:**The set of all possible input values for a function.**Dot Product:**A scalar product of two vectors that is equal to the product of their magnitudes and the cosine of the angle between them.**Double Bar Graph:**A graph that uses bars to compare two sets of data.**Double Number Line:**A diagram that shows how two related numeric quantities change in relation to each other.**Double Root:**A root of a polynomial equation that has a multiplicity of two.

## E

**Equation:**A mathematical statement that asserts the equality of two expressions, indicated by the equals sign.**Equilateral Triangle:**A triangle with all three sides of equal length and all three angles equal to 60 degrees.**Exponential Function:**A mathematical function in the form (f(x) = a^x), where (a) is a positive constant.**Expression:**A mathematical phrase that can contain numbers, variables, and operators but doesn’t have an equals sign.**Exterior Angle:**The angle between a side of a rectilinear figure and an adjacent side extended outward.**Extrapolation:**The process of estimating a value outside a known range by extending a curve.**Extraneous Solution:**A solution that does not satisfy the original equation.**Extrude:**To push or thrust outwards.**Extrusion:**The process of pushing or thrusting outwards.

## F

**Factorization:**Expressing a number or algebraic expression as the product of its factors.**Frequency Distribution:**A table that displays the frequency of various outcomes in a sample.**Frequency Polygon:**A graph that uses line segments connected to points located directly above class midpoint values.**Function:**A relation between a set of inputs and a set of outputs in which each input is related to exactly one output.**Function Notation:**A way to name a function that is defined by an equation.**Function Rule:**An equation that describes a functional relationship between two quantities.**Fundamental Theorem of Algebra:**A theorem that states that every polynomial equation of degree (n) has (n) roots, or solutions.**Fundamental Trigonometric Identities:**A set of trigonometric identities that are true for all values of the variables.

## G

**Geometry:**The branch of mathematics involving points, lines, planes, and figures, and their properties, measurement, and mutual relations in space.**Greatest Common Divisor (GCD):**The largest positive integer that divides two or more numbers without leaving a remainder.**Greatest Common Factor (GCF):**The largest positive integer that divides two or more numbers without leaving a remainder.**Grid:**A network of horizontal and vertical lines that form squares, rectangles, or other shapes.**Grouped Frequency Distribution:**A table that displays the frequency of various outcomes in a sample that has been organized into groups or classes.**Grouped Frequency Table:**A table that displays the frequency of various outcomes in a sample that has been organized into groups or classes.

## H

**Hexagon:**A six-sided polygon.**Highest Common Factor (HCF):**The largest positive integer that divides two or more numbers without leaving a remainder.**Histogram:**A graph that uses bars to display the frequency of data in equal intervals.**Hypotenuse:**The longest side in a right-angled triangle, opposite the right angle.**Hypothesis:**A proposed explanation for an observable phenomenon.

## I

**Identity:**An equation that is true for all values of the variable.**Imaginary Number:**A complex number that can be written as a real number multiplied by the imaginary unit (i), which is defined by its property \(i^2 = -1\).**Inequality:**A mathematical statement that asserts that one quantity is greater than, less than, or equal to another.**Integral:**The reverse process of differentiation, representing the accumulation of quantities.**Integer:**A whole number that can be positive, negative, or zero, without any fractional part.**Isosceles Triangle:**A triangle with at least two sides of equal length and two angles of equal measure.**Iteration:**The process of repeating a set of instructions a specified number of times or until a condition is met.

## J

**Joint Probability:**The probability of the intersection of two or more events happening simultaneously.**Joint Probability Distribution:**A probability distribution that gives the probability of each possible combination of values for two or more random variables.**Joint Variation:**A relationship between two variables in which one is a constant multiple of the other.

## K

**Kilogram:**The base unit of mass in the International System of Units (SI).**Kilometer:**A unit of length equal to 1,000 meters.**Kite:**A quadrilateral with two pairs of adjacent sides that are equal in length.

## L

**Least Common Denominator (LCD):**The smallest multiple of the denominators of two or more fractions.**Least Common Multiple (LCM):**The smallest multiple that is exactly divisible by two or more numbers.**Length:**The measurement or extent of something from end to end.**Line Graph:**A graph that uses line segments to show changes in data over time.**Linear Equation:**An equation between two variables that gives a straight line when plotted on a graph.**Linear Function:**A function whose graph is a straight line.**Linear Relationship:**A relationship between two variables in which one is a constant multiple of the other.**Logarithm:**The exponent to which a base must be raised to produce a given number.

## M

**Magnitude:**The size or extent of something.**Mass:**A measure of the amount of matter in an object.**Matrix:**A rectangular array of numbers, symbols, or expressions arranged in rows and columns.**Mathematics:**The abstract science of number, quantity, and space, either as abstract concepts (pure mathematics) or as applied to other disciplines such as physics and engineering (applied mathematics).**Mean:**The average of a set of numbers, calculated by adding all values and dividing by the number of values.**Median:**The middle value in a set of numbers when they are ordered.

## N

**Natural Number:**A positive integer.**Negative Exponent:**An exponent less than zero, indicating the reciprocal of the base raised to the positive exponent.**Negative Number:**A number less than zero.**Net:**A two-dimensional pattern that can be folded to form a three-dimensional figure.**Nonagon:**A nine-sided polygon.**Nonlinear Equation:**An equation that is not a linear equation.**Nonlinear Function:**A function that is not a linear function.**Nonlinear Relationship:**A relationship between two variables that is not a linear relationship.**Non-Right-Angled Triangle:**A triangle that does not have a right angle.**Normal Distribution:**A probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.**Number:**A mathematical object used to count, measure, and label.**Number Line:**A line on which numbers are marked at intervals, used to illustrate simple numerical operations.**Number Plane:**A two-dimensional plane formed by the intersection of a horizontal line (x-axis) and a vertical line (y-axis).**Numerical Expression:**A mathematical phrase that contains only numbers and operators.**Numerator:**The top number in a fraction, showing how many parts of a whole are being considered.**Nth Root:**A value that, when raised to the power of n, gives the original number.**Null Set:**A set that contains no elements.**Null Vector:**A vector with a magnitude of zero, represented by a point.

## O

**Obtuse Angle:**An angle that measures greater than 90 degrees and less than 180 degrees.**Octagon:**An eight-sided polygon.**Odd Number:**A number that cannot be divided by two without leaving a remainder.**Opposite Angles:**Angles that are on opposite sides of a transversal and are outside the two lines.**Orthogonal:**Perpendicular, often used in the context of vectors or lines in geometry.**Origin:**The point at which the x-axis and y-axis intersect in a coordinate plane.**Outcome:**A possible result of an experiment.**Outlier:**A value that is much greater or much less than the other values in a data set.

## P

**Parabola:**A U-shaped curve formed by the graph of a quadratic function.**Pentagon:**A five-sided polygon.**Perimeter:**The total length of the boundary of a two-dimensional figure.**Perpendicular:**At an angle of 90 degrees to a given line, plane, or surface. opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.**Pi (π):**The ratio of the circumference of a circle to its diameter, approximately equal to 3.14159.**Plane:**A flat surface that extends infinitely in all directions.**Point:**An exact location in space, represented by a dot.**Polygon:**A closed figure with straight sides. Common polygons include triangles, quadrilaterals, and pentagons.**Polynomial:**An expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents.**Positive Exponent:**An exponent greater than zero, indicating repeated multiplication of the base.**Positive Number:**A number greater than zero.**Power:**The number of times a number is multiplied by itself.**Prime Number:**A natural number greater than 1 that has no positive divisors other than 1 and itself.**Probability:**The likelihood of an event occurring, expressed as a value between 0 (impossible) and 1 (certain**Product:**The result of multiplying two or more numbers.**Proportion:**A relationship between two variables in which one is a constant multiple of the other.**Pyramid:**A three-dimensional geometric shape with a polygonal base and triangular faces that meet at a common point.**Pythagorean Theorem:**In a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

## Q

**Quadrant:**One of the four regions of the coordinate plane formed by the intersection of the x-axis and y-axis.**Quadrilateral:**A four-sided polygon.**Quadratic Equation:**An equation of the form ax^2 + bx + c = 0, where x represents an unknown variable and a, b, and c are coefficients.**Quadratic Formula:**A formula used to solve quadratic equations: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).**Quotient:**The result of dividing one quantity by another.

## R

**Radius:**The distance from the center to the outer edge of a circle or sphere.**Range:**The difference between the largest and smallest values in a data set.**Ratio:**A relationship between two quantities, often expressed as a fraction.**Rational Number:**A number that can be expressed as a fraction, where the numerator and denominator are integers.**Real Number:**A number that can be represented by a point on the number line.**Reciprocal:**The multiplicative inverse of a number, where the product of a number and its reciprocal is 1.**Rectangle:**A four-sided polygon with opposite sides of equal length and four right angles.**Rectangular Prism:**A three-dimensional geometric shape with six rectangular faces, twelve edges, and eight vertices.**Rectangular Pyramid:**A three-dimensional geometric shape with a polygonal base and triangular faces that meet at a common point.**Reflection:**A transformation that flips a figure over a line of reflection.**Regular Polygon:**A polygon with all sides of equal length and all angles equal to each other.**Relation:**A set of ordered pairs.**Remainder:**The amount left over after division.**Right Angle:**An angle that measures 90 degrees.**Right-Angled Triangle:**A triangle that has a right angle.**Root:**A value that, when multiplied by itself, gives the original number.**Rotation:**A transformation that turns a figure about a fixed point.**Rotational Symmetry:**A figure has rotational symmetry if it can be rotated less than a full turn and still look the same.**Rhombus:**A four-sided polygon with all sides of equal length, opposite angles equal, and diagonals bisect each other at right angles.**Rigid Transformation:**A transformation that preserves the size and shape of a figure.**Rise:**The vertical change between two points on a line.**Rounding:**The process of approximating a number to a certain place value.**Roots:**The solutions to a quadratic equation, representing the values of x that make the equation true.

## S

**Scalene Triangle:**A triangle with all three sides of different lengths and all three angles of different measures.**Scalar:**A quantity that only has magnitude and no direction, as opposed to a vector.**Sine (sin), Cosine (cos), Tangent (tan):**Trigonometric functions used to relate the angles of a right-angled triangle to the ratios of its sides.**Simultaneous Equations:**A set of equations with multiple variables that are solved together to find the values of the variables that satisfy all the equations.**Subtraction:**The process of taking one number away from another.**Sum:**The result of adding two or more numbers.**Surface Area:**The total area of the surface of a three-dimensional object.**Square:**A four-sided polygon with all sides of equal length and all angles equal to 90 degrees.**Square Root:**A value that, when multiplied by itself, gives the original number.**Symmetry:**A figure has symmetry if it can be transformed by a rigid motion and still look the same.

## T

**Tangent (tan):**A trigonometric function that relates the angle of a right-angled triangle to the ratio of the length of the opposite side to the adjacent side.**Total:**The sum of two or more numbers.**Topology:**The mathematical study of shapes and spaces.**Transformation:**A change in the position, size, or shape of a figure.**Transversal:**A line that intersects two or more lines.**Trigonometry:**The branch of mathematics that deals with the relations between the sides and angles of triangles and the calculations based on them.**Trinomial:**A polynomial with three terms.**Trapezium:**A quadrilateral with one pair of parallel sides.**Trapezoid:**A quadrilateral with one pair of parallel sides.**Triangle:**A three-sided polygon.**Translation:**A transformation that slides a figure from one position to another without turning it.

## U

**Unit:**A standard quantity used to express a physical quantity.**Unit Circle:**A circle with a radius of 1, centered at the origin of a coordinate plane.**Unit Vector:**A vector with a magnitude of 1, represented by a point.**Unknown:**A value that is not known.**Uniform Distribution:**A probability distribution where all outcomes are equally likely.

## V

**Variable:**A symbol, usually a letter, used to represent an unknown or unspecified number.**Venn Diagram:**A visual representation of the relationships between different sets, often using overlapping circles.**Vertex (Vertices):**A point where two or more straight lines meet, or where the sides of a polygon meet.**Volume:**The amount of space occupied by a three-dimensional object.

## W

**Width:**The measurement or extent of something from side to side.**Whole Numbers:**Non-negative integers, including zero.

## X

**X-Axis:**The horizontal number line in a coordinate plane.

## Y

**Y-Axis:**The vertical number line in a coordinate plane.

## Z

**Z-Axis:**The third axis in a three-dimensional coordinate system, perpendicular to both the x-axis and y-axis.**Zero:**The integer denoted 0, representing neither a positive nor negative number.

## Study23 GCSE Maths Formula Flash Cards

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