If a quantity has true value $T$ and an estimate (or measured value) $A$, the absolute error is $|A-T|$.

For a real number $x$, the absolute value $|x|$ is its distance from $0$ on the number line.

If you add (or subtract) the same quantity to both sides of an equation, the resulting equation is equivalent to the original.

For any events $A$ and $B$,
$$P(A\cup B)=P(A)+P(B)-P(A\cap B).$$

For any events $A$ and $B$,
$$P(A\cup B)=P(A)+P(B)-P(A\cap B).$$

The angle between a **tangent** and a **chord** at the point of contact equals the angle subtended by that chord in the alternate segment of the circle.

An angle formed when two lines from a point meet two points on a circle. For example, chord $AC$ subtends an angle at the center $\angle AOC$ and an angle at the circumference $\angle ABC$.

The point where the triangular faces of a pyramid (or the curved surface of a cone) meet.

A part of the circumference of a circle between two points.

The measure of the size of a two-dimensional surface, expressed in square units.

The vertical line that divides the parabola into two mirror-image halves. Its equation is $x=x_v$.

A chart that displays frequencies for qualitative categories using separated, equal-width bars where bar height represents frequency.

The number being raised to a power in an exponential expression.

Data consisting of pairs of values $(x, y)$ where two quantitative variables are measured for each case.

A diagram that displays the five-number summary using a box from $Q_1$ to $Q_3$, a median line, and whiskers extending to the minimum and maximum (or to the most extreme non-outlier values, depending on convention).

The amount of space available to hold something, often measured in liters (L) or milliliters (ml).

The cardinality of a set $A$, written $n(A)$, is the number of elements in $A$.

A grid formed by two perpendicular number lines, the x-axis (horizontal) and y-axis (vertical), used to locate points with ordered pairs $(x,y)$.

Data grouped into categories or labels (for example, eye color, type of transport). Arithmetic operations like averaging are not meaningful.

The point inside a circle that is the same distance from every point on the circumference.

A line segment joining two points on the circumference of a circle.

The curved boundary (perimeter) of a circle.

A range of values (such as $20.0 < x \le 20.5$) used to group quantitative data in a frequency table.

The set of elements not in a set. The complement of $A$ (relative to $U$) is $A'$.

A method of rewriting a quadratic into a perfect-square form (plus or minus a constant), allowing solutions by taking square roots.

A unit formed by combining other units through multiplication or division, such as km/h or m/s.

The conditional probability of $B$ given $A$ is
$$P(B\mid A)=\frac{P(A\cap B)}{P(A)}, \quad P(A)>0.$$

The conditional probability of $B$ given $A$ is
$$P(B\mid A)=\frac{P(A\cap B)}{P(A)}, \quad P(A)>0.$$

A 3D solid with a circular base and an apex (vertex). It is not a polyhedron because it has a curved surface.

Two figures are congruent if they have the same shape and the same size.

A statement that appears to be true based on observed examples, but has not yet been proven.

Quantitative data that is measured and can take any value within a range (for example, height, mass, temperature).

A statement formed by switching the “if” part and the “then” part of a conditional statement.

A measure of the association between two variables, describing whether they tend to increase together, decrease together, or show no consistent pattern.

For an acute angle $A$ in a right triangle, $\cos A=\dfrac{\text{adjacent}}{\text{hypotenuse}}$.

A measure of how two variables vary together, based on the products of their deviations from their means.

The running total of frequencies up to a given value or class boundary.

A quadrilateral whose vertices all lie on the circumference of the same circle.

For any sets $A$ and $B$ in a universal set $U$,
$$(A \cup B)' = A' \cap B' \quad\text{and}\quad (A \cap B)' = A' \cup B'.$$

A chord that passes through the center of the circle, its length is twice the radius.

A pattern where $a^2-b^2=(a-b)(a+b)$.

A pattern where $a^2-b^2=(a-b)(a+b)$.

A transformation that multiplies all distances from a center point by the same scale factor, producing a similar image.

A relationship where $y$ is proportional to a positive power of $x$: $y\propto x^n$ with $n>0$, so $y=kx^n$.

A relationship where $y$ is proportional to a positive power of $x$: $y\propto x^n$ with $n>0$, so $y=kx^n$.

A relationship of the form $y=kx$, where $k$ is a constant. If $x$ is multiplied by a factor, $y$ is multiplied by the same factor.

Quantitative data that can be counted or can only take specific separated values (for example, number of goals scored, number of people, shoe size).

The value $\Delta=b^2-4ac$ for $ax^2+bx+c=0$, which determines the number of real solutions.

Two sets $A$ and $B$ are disjoint if they have no elements in common, so $A \cap B = \varnothing$.

For points $A(x_1,y_1)$ and $B(x_2,y_2)$, the distance between them is
$$AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$

The overall pattern of a data set, including its center, spread, and shape (for example, symmetry, skewness, clusters, and gaps).

The set of all input values $x$ used in a relation or function.

Written $\emptyset$, is the set with no elements.

An operation applied to an equation (or system) that produces a new equation (or system) with the same solution set, such as adding the same value to both sides or multiplying both sides by a non-zero constant.

Equations that have exactly the same solutions.

Equations that have exactly the same solutions.

A set of outcomes from a random experiment (for example, “rolling an odd number”).

To multiply out all terms in brackets and rewrite the expression without brackets.

To multiply out all terms in brackets and rewrite the expression without brackets.

A rule that gives the value of $u_n$ directly from the term number $n$.

The small raised number in a power, for example the $n$ in $10^{n}$, which tells how many times the base is multiplied by itself. Negative exponents represent reciprocals.

Estimating a value outside the range of the collected data.

To rewrite an expression as a product of factors (multiplication). For a quadratic, this often means writing it as a product of two brackets.

The **first difference** is the difference between consecutive terms, computed as $u_{n+1}-u_n$.

A set of five values that describe a distribution: minimum, $Q_1$, median ($Q_2$), $Q_3$, and maximum.

A set of five values that summarizes a distribution: minimum, $Q_1$, median ($Q_2$), $Q_3$, maximum.

A set of five values that describe a distribution: minimum, $Q_1$, median ($Q_2$), $Q_3$, and maximum.

An equation that describes an algebraic relationship between two or more variables, where each variable can take different values depending on the others.

Frequency divided by class width, used on the vertical axis of a histogram when class widths are unequal.

A relation in which every input value in the domain is mapped to one and only one output value in the range.

A general statement or rule made on the basis of specific examples.

A rule that maps every point of a figure to a new point, producing an image of the figure.

For two distinct points $A(x_1,y_1)$ and $B(x_2,y_2)$ on a line, the gradient is
$$m=\frac{y_2-y_1}{x_2-x_1},\quad x_2\neq x_1$$

A frequency table where values are combined into class intervals, and each interval has a frequency.

A graph for quantitative data where values are grouped into class intervals on the horizontal axis, the bars touch, and the bar area represents frequency (or relative frequency).

The side opposite the right angle in a right triangle, always the longest side.

A statement that is true for all values of the variable(s), often written using $\equiv$.

The new figure produced after a transformation is applied to an original figure.

Events $A$ and $B$ are independent if knowing that $A$ happened does not change the probability of $B$. Formally, $P(B\mid A)=P(B)$.

Its subscript (for example, the index of $u_5$ is 5), which indicates the term’s position in the sequence.

Infinitely many ordered pairs satisfy both equations. Graphically, the lines are coincident (the same line written in two forms).

Infinitely many ordered pairs satisfy both equations. Graphically, the lines are coincident (the same line written in two forms).

The **integers** are $\mathbb{Z}=\{\ldots,-2,-1,0,1,2,\ldots\}$.

The integers $\mathbb{Z}$ are the whole numbers and their negatives: $\{\dots,-3,-2,-1,0,1,2,3,\dots\}$.

Estimating a value within the range of the collected data.

The spread of the middle 50% of the data: $\text{IQR}=Q_3-Q_1$.

A relationship of the form $y=\frac{k}{x}$, where $k$ is a constant. If $x$ is multiplied by a factor, $y$ is divided by the same factor.

An **irrational number** cannot be written as a fraction $\frac{p}{q}$. Its decimal representation is non-terminating and non-repeating.

An irrational number is a real number that cannot be written in the form $\frac{a}{b}$ with integers $a$ and $b\neq 0$. The set of irrationals is often written $\mathbb{Q}'$.

A transformation that preserves distances (and therefore preserves shape and size). Translations, rotations, and reflections are isometries.

A one-dimensional measure of size, describing how long something is.

A straight line drawn through the middle of a scatter plot so that points are (roughly) evenly distributed above and below it, used to model and predict relationships.

A mathematical relationship in which the change in the output variable is constant for equal changes in the input variable, typically written as $y=mx+c$.

A relation where at least one input maps to multiple outputs and at least one output is shared by multiple inputs.

A relation where at least one input maps to multiple outputs and at least one output is shared by multiple inputs.

A relation where two or more different inputs are mapped to the same output.

The arithmetic average of a data set, found by adding all values and dividing by the number of values.

Statistics that describe where most data values lie (location), answering the question “What is a typical (average) value?”

Statistics that describe how spread out the data is (spread), answering the question “How much variation is there between the values?”

The middle value when the data set is ordered. If there are two middle values, the median is their average.

For endpoints $A(x_1,y_1)$ and $B(x_2,y_2)$, the midpoint is
$$M\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$$

The **minor arc** between two points on a circle is the shorter path along the circumference; the **major arc** is the longer path. A major arc is often named using three points (for example, arc $ADB$).

If you multiply (or divide) both sides of an equation by the same non-zero quantity, the resulting equation is equivalent to the original.

Two events are mutually exclusive if they cannot happen at the same time. In set notation, $A\cap B=\varnothing$, so $\mathrm{P}(A\cap B)=0$.

Two events are mutually exclusive if they cannot occur at the same time, so $A\cap B=\varnothing$.

The **natural numbers** are $\mathbb{N}=\{0,1,2,3,\ldots\}$.

The natural numbers $\mathbb{N}$ are the counting numbers. Depending on convention, $0$ may or may not be included.

For any non-zero real number $a$ and positive integer $n$, $a^{-n}=\frac{1}{a^{n}}$.

A linear proportional relationship with a negative constant of variation: $y=-kx$ where $k>0$.

No ordered pair satisfies both equations. Graphically, the lines are parallel (same gradient, different intercepts).

Data measured or counted as numbers (for example, height, time, number of siblings). Numerical data can be summarized using measures such as mean and quartiles.

A relation where at least one input is mapped to more than one output.

A relation where each input is mapped to a unique output, and no two different inputs share the same output.

A data value that lies an unusually large distance from the rest of the data set.

Two non-vertical lines are parallel if they have the same gradient.

Two non-vertical, non-horizontal lines are perpendicular if their gradients multiply to $-1$. If one line has gradient $m\,(m\neq 0)$, then a perpendicular line has gradient $-\frac{1}{m}$.

A line through $(x_1,y_1)$ with gradient $m$ can be written as $$y-y_1=m(x-x_1)$$

A 3D solid that has only plane (flat) faces.

The whole group you want information about (for example, all students in your year group).

The **positive integers** are $\mathbb{Z}^+=\{1,2,3,\ldots\}$.

A number being multiplied by itself a specific number of times. Power is the whole expression including the base and the exponent.

The original figure before a transformation is applied.

For a positive number $x$, the **principal square root** is the positive square root, written $\sqrt{x}$.

A process of understanding a task, choosing and applying strategies to reach a solution, and checking that the result makes sense.

A non-zero constant, usually called $k$, that links two proportional variables (also called the constant of variation).

In any right triangle, the squares of the two shorter sides add to the square of the hypotenuse: $a^2+b^2=c^2$.

An equation that can be written in the form $ax^2+bx+c=0$ where $a\neq 0$.

An algebraic expression in one variable whose highest exponent is 2 (and with a non-zero $x^2$ term). It can be written in the form $ax^2+bx+c$ where $a\neq 0$.

A formula giving the solutions of $ax^2+bx+c=0$ (with $a\neq 0$): $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$.

A function whose graph is a parabola and can be written in the form $y=ax^2+bx+c$ where $a\neq 0$.

Non-numerical information that reveals people's thoughts, feelings, and perceptions, often gathered through interviews or observations.

Numerical information that can be measured and recorded, such as height, weight, shoe size, or the depth of a kitchen counter.

Values that split an ordered data set into four equal parts: $Q_1$ (lower quartile), $Q_2$ (the median), and $Q_3$ (upper quartile).

An irrational number written in radical form, such as $\sqrt{2}$ or $2\sqrt{3}$.

The symbol $\sqrt{\;}$ used to indicate a root.

The number or expression inside the radical sign, for example the $5$ in $\sqrt{5}$.

A line segment from the center of a circle to a point on the circumference.

The set of all possible output values (often $y$-values) that the function can produce from its set of input values (the domain).

A **rational number** is a number that can be written as $\frac{p}{q}$ where $p,q\in\mathbb{Z}$ and $q\neq 0$.

The **rational numbers** are $\mathbb{Q}=\left\{\frac{p}{q}\mid p,q\in\mathbb{Z},\ q\ne 0\right\}$.

A rational number $q$ is any number that can be written as a fraction $q=\frac{a}{b}$ where $a,b\in\mathbb{Z}$ and $b\neq 0$.

To **rationalize the denominator** means to rewrite a fraction so that the denominator is a rational number (no roots remain in the denominator).

The **real numbers**, $\mathbb{R}$, are the set of all rational and irrational numbers.

The real numbers $\mathbb{R}$ are all numbers that can be placed on the number line, including both rational and irrational numbers.

A rule that defines terms using earlier term(s), often together with a starting term (such as $u_1$).

A set of ordered pairs $\{(x,y)\}$ that links elements from one set (inputs) to elements of another set (outputs).

A zero where the factor repeats, for example $(x-h)^2$. The graph touches the x-axis at $x=h$ but does not cross it.

The manner in which information or a relationship is presented (for example, a table, graph, diagram, equation, or written rule).

The percentage of selected individuals who actually provide data.

A triangle with one angle equal to $90^\circ$.

For a point $P(a,b)$:
- $90^\circ$ clockwise: $P'(b,-a)$
- $90^\circ$ counterclockwise: $P'(-b,a)$
- $180^\circ$: $P'(-a,-b)$

A subset of the population from which data are collected.

The set of all possible outcomes, often written $U$ or $S$.

A list (or other complete listing) of all members of the population from which a sample can be selected.

The multiplier that compares corresponding lengths in an image and its pre-image under dilation.

A graph of paired (bivariate) data points plotted on an $x$-$y$ plane to investigate the relationship between two variables.

A way to write very large or very small numbers in the form $A\times 10^n$, where $1\le A<10$ and $n$ is an integer.

A way to write a number as $a\times 10^{n}$ where $1\le a<10$, $a\in\mathbb{R}$, and $n\in\mathbb{Z}$.

A line that intersects a circle at two points.

The region bounded by two radii and the arc between them (a “pizza slice”).

The region bounded by a chord and the arc between the chord’s endpoints.

An ordered list of numbers where each number in the list is called a term.

A collection of objects. Each object in the set is called an element (or member) of the set.

The set of elements that are in both sets. For sets $A$ and $B$, the intersection is $A \cap B$.

A way to describe a set using a variable and a condition, written in the form $\{x\mid \text{condition on }x\}$.

Two figures are similar if corresponding angles are equal and corresponding lengths are in a constant ratio.

For an acute angle $A$ in a right triangle, $\sin A=\dfrac{\text{opposite}}{\text{hypotenuse}}$.

For a pyramid, the distance from the midpoint of a base edge to the apex, measured along a triangular face.

The equation of a non-vertical line can be written as $$y=mx+c$$ where $m$ is the gradient and $c$ is the $y$-intercept.

A value of the variable that makes the equation true when substituted into the equation.

A 3D solid with one curved face; all points on its surface are equidistant from the center. It is not a polyhedron.

A line can be written as $$ax+by+c=0$$ with constants $a,b,c$ (often integers, and sometimes with a required sign convention such as $a>0$).

A display that organizes numerical data by separating each value into a stem and a leaf, allowing the original data values to be reconstructed.

The variable that is isolated on one side of a formula, usually written on the left-hand side.

A set $A$ is a subset of $B$ (written $A\subseteq B$) if every element of $A$ is also an element of $B$.

The total area of all the faces (or curved surfaces) on the outside of a 3-dimensional solid.

A set of two or more linear equations involving the same variables, solved together to find values that satisfy every equation in the system.

A structured set of units based on chosen base units, with rules for creating and converting other (derived) units.

A method where you first find the value for 1 unit (one item, one person, one hour, one trip) and then scale up to the required amount.

For an acute angle $A$ in a right triangle, $\tan A=\dfrac{\text{opposite}}{\text{adjacent}}$.

A straight line that touches the circle's circumference at exactly one point, called the point of tangency, without crossing into the interior

If $AB$ is a **diameter** of a circle and $C$ is any point on the circumference, then $\angle ACB = 90^\circ$.

The set of elements that are in at least one of the sets. For sets $A$ and $B$, the union is $A \cup B$.

Exactly one ordered pair $(x,y)$ satisfies both equations. Graphically, the two lines intersect at one point.

Data consisting of observations of a single variable for each individual or item (for example, one height measurement per student).

The set of all elements being considered in a given situation, usually drawn as a rectangle and often labelled $U$.

The turning point of the parabola, with coordinates $(x_v, y_v)$.

A form of a quadratic function $y=a(x-h)^2+k$ where $(h,k)$ is the vertex.

The perpendicular distance from the apex straight down to the base plane.

The amount of space a 3-dimensional solid occupies, measured in cubic units such as cm$^3$.

The $x$-coordinates where the graph crosses the $x$-axis (where $y=0$). They are also called the zeros (or roots) of the function.

The point where the graph crosses the $y$-axis (where $x=0$).

For any non-zero real number $a$, $a^{0}=1$.