Mathematics GCSE

Mathematics GCSE glossary

988 key terms for Mathematics GCSE, A to Z, each linked to the topic pages that use it.

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A

Acceleration: Rate of change of velocity with respect to time; in a same-direction speed-time context, the gradient measures change in speed per unit time.Pearson Edexcel
Accumulated total: The amount built up over an interval by a varying rate, represented by area under a rate graph.AQA
accurate drawing: A drawing made to stated measurements using appropriate instruments.Pearson Edexcel
Accurate substitution and rearrangement: Substituting values accurately into the chosen rule, including correct use of the included angle and correct order of operations, and rearranging to make cos…AQA
Addition of path probabilities: The probability of an event made up of several paths is the sum of the probabilities of those paths.AQA
adjacent: The side next to the chosen angle that is not the hypotenuse.AQA
Adjacent side: The side touching the chosen angle that is not the hypotenuse.Pearson Edexcel
algebraic equivalence: Each step must preserve this, so check by substituting a value such as x = 2 into the original and simplified forms.AQA, Pearson Edexcel
Algebraic fraction: A quotient of algebraic expressions whose denominator must be nonzero.Pearson Edexcel
Algebraic manipulation and rearrangement: Rearranging a quadratic equation to the form ax² + bx + c = 0 before factorising.AQA
Algebraic modelling of real-world situations: Writing other quantities in terms of a defined unknown, such as an expression for the cost of pens or a formula for a taxi fare.Pearson Edexcel
algebraic notation: A compact language in which juxtaposition means multiplication, indices record repeated multiplication, a fraction bar means division and brackets group terms.AQA, Pearson Edexcel
algebraic proof: An argument in algebra that covers every case, not a check on a few numbers, starting from letters that carry the conditions and ending with a sentence saying…Pearson Edexcel
Algebraic rearrangement of compound-unit formulae: Rearranging the density and pressure formulae to find the missing quantity, such as mass = density × volume or force = pressure × area.AQA
algebraic subtraction method: A method that removes the repeat by subtraction, multiplying by ten when a single digit repeats and by a hundred when two do.Pearson Edexcel
algebraic term: A part of an expression separated from other parts by addition or subtraction, with its sign retained.Pearson Edexcel
Alternate and corresponding angles on parallel lines: On parallel lines, alternate angles are equal and corresponding angles are equal, which supports reasoning about figures containing a transversal.AQA
Alternate segment: For a tangent-chord angle, the circle segment containing the circumference vertex that subtends the chord and gives the matching angle.Pearson Edexcel
Ambiguous case: A side-side-angle situation in which the same given measurements may permit two different triangles.Pearson Edexcel
analysis: Asking whether results are consistent with a fair model by comparing observed counts with expected counts, not merely reading numbers off the table.AQA
Angle: A measure of the turn between two rays with a common endpoint, usually expressed in degrees.AQA
angle at the centre: The angle θ at the centre of the circle that determines the fraction of the circle a sector represents.AQA
Angle bisection: Bisecting an angle requires an arc across both arms from the vertex, then equal arcs from the two crossing points, joining the vertex to their intersection.AQA
Angle properties: Facts such as angles at a point summing to 360°, angles on a straight line summing to 180°, and vertically opposite angles being equal.Pearson Edexcel
Angle properties in circles: Standard theorems concerning angles, including that the angle at the centre is double the angle at the circumference and that angles in the same segment are…Pearson Edexcel
Angle sums in triangles, polygons and regular polygons: The sum of angles in a triangle is 180°, any polygon with n sides has an interior angle sum of (n − 2) × 180°, and exterior angles sum to 360°.AQA
Angles at a point and on a straight line: Angles at a point sum to 360°, while angles at a point on a straight line sum to 180°.AQA
Application of index laws: The standard index laws still apply, which explains why x^½ is the square root of x.Pearson Edexcel
Application to multiple-choice assessment: In an MCQ, you may be asked to identify a correct value or match an expression to its exact value.AQA
Applications of ratio in context: Applying ratio to real contexts and problems such as those involving conversion, comparison, scaling, mixing and concentrations.Pearson Edexcel
apply: Using properties to find missing angles.AQA
Applying bounds to real-life measurement problems: Combining bounds of positive quantities to find the maximum or minimum possible result, keeping units consistent and using correct inequality signs.AQA
Applying estimation to any positive number: Using this Higher tier skill on any given positive number, including decimals and numbers that are not perfect powers.AQA
appropriate language: Includes terms like parallel, perpendicular, bisect, and adjacent.AQA
Approximate solution: A value or pair close to the exact solution, stated at a precision justified by the method or instruction.Pearson Edexcel
Approximation: A value sufficiently close to another value for the stated purpose, but not necessarily exactly equal to it.Pearson Edexcel
Approximation by rounding: Rounding numbers to convenient values to form an estimate, such as rounding to one significant figure for a quick check.AQA
Arc: A connected part of the circumference between two points on a circle.AQA, Pearson Edexcel
arc length: The length along the curved edge of a sector, found as (θ/360) × 2πr where θ is the angle at the centre in degrees.AQA, Pearson Edexcel
area: The amount of two-dimensional space inside a boundary, measured in square units.Pearson Edexcel
Area = ½ab sin C: A formula where a and b are the two sides meeting at angle C, used to calculate the area, sides or angles of any triangle.AQA
area and volume units: Length is a single step, but area squares that factor and volume cubes it, so 1 m² = 10 000 cm² and 1 m³ = 1 000 000 cm³.Pearson Edexcel
Area of a circle: The space inside a circle, found using the formula πr², squaring the radius before multiplying by π.AQA
area of a segment: Found by subtracting this triangle from a sector, or by working out the sector area and the triangle area separately before subtracting.Pearson Edexcel
area scale factor: When the length scale factor is k, every area is multiplied by k², because area is built from two lengths.Pearson Edexcel
area under a graph: A region split into strips of equal width, each treated as a trapezium, and totalled; under a velocity-time graph it is the distance travelled.Pearson Edexcel
Area under a graph as an accumulated total: Estimated by splitting the region into strips, often trapezia, and adding their areas, and in financial contexts can represent total accumulated value.AQA
arithmetic progression: A sequence with a constant first difference between terms, such as 7, 11, 15, which adds 4.Pearson Edexcel
Arithmetic progressions: A sequence where the difference between consecutive terms is constant, for example 5, 9, 13, 17, ...AQA
Arithmetic sequence: A sequence with a constant difference between consecutive terms.AQA
ASA: Two angles and the included side of one triangle are equal to two angles and the included side of another, so the triangles are congruent.AQA
ascending order: An arrangement from the smallest value to the largest value.Pearson Edexcel
Asymptote: A line such as the x-axis or y-axis that the curve approaches but never touches.AQA, Pearson Edexcel
Asymptotes: Lines at x = 0 and y = 0 that the two separate branches of a reciprocal graph approach but never join across.AQA, Pearson Edexcel
Asymptotes and domain restrictions: The x-axis is a horizontal asymptote for y = kˣ, and y = tan x is undefined at 90°, 270°, etc., where it has vertical asymptotes.AQA
average rate of change: The rate of change between two points, found as the gradient of the chord connecting them.AQA, Pearson Edexcel
Average speed: Total distance travelled divided by the total time taken over the specified journey.Pearson Edexcel
average with spread: Pairing the average with a measure of spread, because two groups can share a mean and still look nothing alike.Pearson Edexcel
axis of symmetry: The vertical line that divides a parabola into two matching halves and passes through the turning point.Pearson Edexcel
Axis-aligned: Having relevant sides or directions parallel to the coordinate axes.AQA

B

Balancing equations: Applying the same balance principle so that whatever operation you perform on one side must be performed on the other.AQA
Base: The number or algebraic expression raised to a power.Pearson Edexcel
Bearing: A direction measured clockwise from north at the reference point and written as a three-figure angle.AQA
bias: A feature of a sample, such as being taken at one time of day, that may make it not representative and the estimate unreliable.Pearson Edexcel
Biased: Not fair; the outcomes are not equally likely.AQA
Biased object: An object whose outcomes do not follow the probabilities of the proposed fair model.Pearson Edexcel
binomial: An algebraic expression containing two terms.Pearson Edexcel
Binomial expansion: Multiplying every term in the first bracket by every term in the second, often remembered as FOIL, then collecting like terms.AQA
Bisect: To divide a line segment or angle into two equal parts.Pearson Edexcel
Bivariate Data: Data for two variables (e.g., height and weight for the same person).Pearson Edexcel
bounding by known powers: Naming the two known powers the value sits between, such as 49 and 64 for a square root near 50.Pearson Edexcel
box plot: A diagram used to visualise the five-figure summary: minimum, lower quartile (Q₁), median (Q₂), upper quartile (Q₃), and maximum.AQA, Pearson Edexcel
Brackets: Grouping symbols indicating that the enclosed expression is treated as one unit for an operation.Pearson Edexcel
brackets in algebra: Brackets show what an operation acts on, so 2(x + 5) doubles the whole of x + 5 while 2x + 5 doubles only x.Pearson Edexcel
Branches: The two separate parts of the graph, which are disconnected because x cannot be zero.AQA

C

Calculating gradient from two points on a straight line: Choosing two points on the line and dividing the vertical difference by the horizontal difference.AQA
calculating with bounds: Choosing the pair of bounds that drives the answer to the extreme you want, such as the upper bound of the first quantity and the lower bound of the second…Pearson Edexcel
Calculating with powers of 10: Adjusting coefficients and powers separately, multiplying coefficients and adding indices, or dividing coefficients and subtracting indices.AQA
Calculations involving multiples of π: π is treated as an exact symbol rather than a decimal, so an answer is left as a multiple of π unless told otherwise.Pearson Edexcel
Cancellation: Simplifying a calculation or expression by dividing numerator and denominator by a common factor.AQA
cancelling common factors: Simplifying calculations and expressions by dividing by a common factor, for example 36/48 simplifies to 3/4 by cancelling the common factor of 12.Pearson Edexcel
Categorical data: Labels or groups, such as eye colour or favourite subject, for which you can use a frequency table, a bar chart with gaps between bars, a pie chart or a…AQA
Central angle: The angle between two radii, measured at the centre; it determines the sector fraction θ/360 when measured in degrees.Pearson Edexcel
centre: The fixed point from which every point on the circle is at a fixed distance.AQA, Pearson Edexcel
changing the subject: Rewriting a formula so that a different letter stands alone on one side.Pearson Edexcel
checking a term: Substituting a position back into the expression to justify an answer when asked to show that a number is or is not a term.Pearson Edexcel
Checking answers by substitution: Substituting each option back into the power or root to test it, which is faster and safer than estimating when the numbers are small.AQA
Checking for repeats and omissions: Checking the list for repeats and omissions before stating the final answer, finishing by counting or checking the list against the structure.AQA
Checking reasonableness of shares: Always verify that the fractions sum to 1 and that the shares are in the stated ratio.AQA
Checking solutions by substitution: Substitute a test value from your solution set back into the original inequality to confirm the direction is correct.AQA
Checking technology-obtained answers: Comparing the display with a mental or written approximation and considering whether the size and unit of the answer make sense in context.AQA
Checking the reasonableness: Using estimation to check an answer, since a speed in m/s will have a smaller numerical value than the same speed in km/h.AQA
choosing an average: Picking the mode for categories, the median where very large or very small values would distort things, and the mean where every value should count.Pearson Edexcel
Choosing an efficient method: Recognising the multiplier form makes percentage change, reverse percentage and fraction-of-amount questions a single consistent method.AQA
Choosing appropriate diagrams: Selecting the diagram that suits the data type, for example a bar chart for categorical data and a vertical line chart for ungrouped discrete numerical data.AQA
Chord: A straight line segment joining two points on the circumference; the diameter is the special chord that passes through the centre.AQA, Pearson Edexcel
Chord versus tangent: A chord joins two points on a curve, while a tangent is a straight line that touches the curve at the required point and extends clearly on both sides.AQA
Circle: The set of points in a plane at a fixed distance from a fixed point, the centre.AQA
Circle equation centred at the origin: A circle with centre at the origin and radius r has equation x² + y² = r², so a point lies on the circle exactly when its coordinates satisfy that equation.AQA
Circle formulae: The circumference of a circle is 2πr = πd and the area of a circle is πr².Pearson Edexcel
circle formulas: The circumference is 2πr = πd, and the area of a circle is πr², so the formula chosen must match the part named.Pearson Edexcel
Circular segment: A region bounded by a chord and one of its corresponding arcs.Pearson Edexcel
Circumference: The distance around a circle, found using the formula 2πr, which equals πd because the diameter is twice the radius.AQA, Pearson Edexcel
Classification and vocabulary of solids: Solids are classified using precise vocabulary: face, edge, vertex, curved surface, cross-section and apex.AQA
Coefficient: The numerical multiplier of an algebraic term, including its sign.AQA, Eduqas, Pearson Edexcel
coefficient of n²: The second difference equals 2a, so halve it to find a, the coefficient of n².AQA, Pearson Edexcel
coefficients as fractions: Coefficients are kept as fractions, so three quarters of x is written (3/4)x rather than 0.75x.Pearson Edexcel
Coincident lines: Two equations representing exactly the same straight line.AQA
collecting like terms: Adding the coefficients of terms with exactly the same letters and powers, so 5a + 3b − 2a is 3a + 3b.AQA, Pearson Edexcel
column vector arithmetic: Adding two vectors means adding the tops and adding the bottoms, and subtracting means adding the reverse.Pearson Edexcel
column vector notation: A way of recording a slide where the top number is the movement right, negative for left, and the bottom number is the movement up, negative for down.Pearson Edexcel
Column vectors: A translation is given as a column vector, with the top number for horizontal movement.Pearson Edexcel
Combinations of transformations: Performing two or more transformations in sequence on a shape.AQA
Combined experiments: A tree diagram is a branching possibility space for these, represented as successive stages with each branch showing one outcome at that stage.AQA
Combined transformation: An ordered sequence of transformations, each acting on the image produced by the preceding transformation.Pearson Edexcel
combined transformations: When one transformation is followed by another, the pair together often has the same effect as a single transformation.Pearson Edexcel
Combining like terms: When adding or subtracting, combining the coefficients of like terms, such as 3π + 5π = 8π.AQA
common denominator: Fractions are compared by rewriting them over this, so 3/5 and 4/7 become 21/35 and 20/35, which puts 3/5 ahead.Pearson Edexcel
common difference: The same amount by which a linear sequence changes at every step, and it is the coefficient of n.Pearson Edexcel
Common factors: Taking these out reverses multiplying a single term over a bracket, so 6x² + 9x = 3x(2x + 3).AQA
Common ratio: The constant multiplier r between successive terms of a geometric sequence; for a non-zero preceding term, r = next term ÷ preceding term.AQA, Pearson Edexcel
comparing quantities: The comparison is often hidden in wording such as "what fraction of the class", so decide which quantity is the whole before writing anything.Pearson Edexcel
Comparing quantities of the same kind: The denominator must be the quantity being compared with, so read the wording carefully to decide which quantity goes on the bottom.AQA
Complement: All outcomes in the sample space for which the named event does not occur.Pearson Edexcel
Complement, A': Elements of the universal set that do not belong to A.Pearson Edexcel
Complementary Event: The event that something does not happen.AQA
completing missing frequencies: Finding missing values by subtraction, ensuring all parts add up correctly.Pearson Edexcel
completing the square: Rewriting a quadratic from expanded form into vertex form, halving the coefficient of x inside the bracket and subtracting the square of that half from the…AQA, Pearson Edexcel
Component-wise addition and subtraction: To add vectors, add corresponding components; to subtract, subtract corresponding components.AQA
Composite function: A function formed by applying one function and then applying another to its output.Pearson Edexcel
composite functions: A composite applies two rules in succession: fg(x) means work out g(x) first, then put that result into f.AQA, Pearson Edexcel
composite shapes: Shapes made of more than one part, where you identify which fraction of the circle is required and add any straight edges to find the total perimeter.AQA
Composite shapes and solids: Shapes and solids made of standard parts, where areas are added or subtracted and only external lengths or faces are counted.Pearson Edexcel
Composite solid: A three-dimensional object made by joining or removing simpler solids.AQA
composite solids: Solids that are split into simpler parts, calculating each part and adding or subtracting as appropriate.AQA
compound growth and decay: Problems using a multiplier above 1 for growth or below 1 for decay, such as 0.85 for a 15% fall.Pearson Edexcel
compound interest: Interest found by applying a repeated percentage change to an initial amount, unlike simple interest which adds the same amount each period.AQA, Pearson Edexcel
Compound Measure: A measure made up of two or more other measurements, such as speed (distance and time) or density (mass and volume).AQA, Eduqas, Pearson Edexcel
compound measures: A measure that divides one quantity by another, such as speed = distance ÷ time, density = mass ÷ volume, and pressure = force ÷ area, each rearranging to…Pearson Edexcel
compound unit: A unit that combines two measures, such as miles per hour, pounds per hour or pounds per kilogram.AQA, Pearson Edexcel
Compound unit changes: Changing compound units such as speed, rates of pay and prices by changing the numerator and denominator separately.AQA
compound units: A unit built from two others, where the name gives the operation, such as kilometres divided by hours or grams divided by cubic centimetres.Pearson Edexcel
Concentration as a percentage of a mixture: For the stated mixture model, the ingredient amount divided by total mixture amount, multiplied by 100, using compatible quantities.Pearson Edexcel
Conditional probability: The probability of event A happening, given that B has already occurred, written P(A | B), which restricts the sample space to outcomes where B is true.Pearson Edexcel
Conditional probability, Higher-only: The probability of an event when the selection or information is restricted by another event.Pearson Edexcel
Congruence: A relationship between shapes that are identical in shape and size, where one can be transformed onto the other by rotation, reflection or translation.AQA, Pearson Edexcel
Congruence and similarity: Translation, reflection and rotation produce a congruent image, identical in size and shape, while enlargement produces a similar image with the same angles…AQA, Pearson Edexcel
congruence criteria: The standard tests SSS, SAS, ASA and RHS, used to show that shapes identical in shape and size have all corresponding sides and angles equal.Pearson Edexcel
congruence under transformation: Rotations, reflections and translations keep every length and every angle, so the final shape is congruent to the first.Pearson Edexcel
Congruent: Having the same shape and size, with equal corresponding lengths and angles.Eduqas, Pearson Edexcel
Congruent figures: Figures that are identical in shape and size, meaning corresponding lengths and angles are equal.AQA
Congruent triangles: Triangles with matching corresponding side lengths and angles, having the same size and shape.AQA
Conjecture: A statement believed to be true but not yet proven.Pearson Edexcel
Conjugate: For a two-term expression u + v, the matching expression u − v, or vice versa.AQA, Pearson Edexcel
consecutive integers: Written as n and n + 1, where n stands for any integer, so the letters carry the condition rather than forcing a special case.Pearson Edexcel
consistency of totals: The requirement that rows and columns sum to their respective totals and that the grand total must be consistent.Pearson Edexcel
consistent units: Both quantities must be put into the same unit before the fraction is written and cancelled.Pearson Edexcel
constant: A fixed value that does not change with n; in dn + c, c is the additive adjustment.Pearson Edexcel
constant of proportionality: The constant k in the form X = kY or X = k/Y, found from a given pair of values and used to calculate an unknown value.AQA, Eduqas, Pearson Edexcel
Constant of proportionality k: Found by substituting a known pair of values into the correct equation before calculating the unknown quantity.AQA
constant product: In a table of values, this points to an inverse relationship, and in an inverse relationship the two quantities multiply to a fixed number.Pearson Edexcel
constant second difference: A quadratic sequence features this, found by calculating the first differences between consecutive terms and then the second differences.AQA
Constant sequence: A sequence whose terms all have the same value, possibly zero.Pearson Edexcel
Constant term: A term whose value does not depend on the variables in the expression.Pearson Edexcel
Constructing images: Transforming each vertex and joining them in order, joining corresponding vertices in the correct order.AQA
construction: A precise geometric drawing created with specified construction methods and instruments.Pearson Edexcel
Continuous Data: Data that can take any value within a range (e.g., height, time, weight).AQA, Eduqas, Pearson Edexcel
Converge: What values do when an iteration is continued until they reach a required degree of accuracy, giving an approximate solution to an equation.AQA
Convergence: Successive values settling to a required accuracy, which a good starting value and a convergent rearrangement are essential for.AQA
converging sequences: Successive terms that close in on a value, such as the positive solution of x² = 3x + 4.Pearson Edexcel
Conversion factor: A multiplier relating the numerical values of the same quantity in two specified units.Pearson Edexcel
Conversion factors: The multiplicative factors used to convert correctly between related metric units, for example 3.5 m = 350 cm.AQA
Converting between ordinary and standard form: Evaluating the power of 10 and multiplying to convert from standard form, with the decimal point moving left for large numbers and right for small numbers.AQA
Coordinate: A numerical value giving a point's position relative to an axis and the origin; two coordinates locate a point in this plane.AQA
Coordinate pair: An ordered pair (x, y) giving a point's horizontal and vertical positions relative to the origin.AQA
coordinate plane: The plane is cut by the two axes into four quadrants, and a coordinate pair gives across first, then up.AQA, Pearson Edexcel
Coordinates: An ordered pair (x, y) locating a point by horizontal position followed by vertical position.AQA
Correlation: Describes how closely the points follow a pattern, but does not indicate causation, because a strong link between two variables does not prove one causes the…AQA
correlation and causation: Points rising from left to right show positive correlation and points falling show negative correlation, but correlation alone never shows that one quantity…Pearson Edexcel
Corresponding: Matching the same geometric position or role in two figures.Pearson Edexcel
Corresponding lengths: Lengths occupying matching positions in similar shapes or in a drawing and the real object.AQA
Corresponding sides and angles: Matching sides are paired with the side opposite the same angle, and corresponding angles are equal in similar figures.AQA
Corresponding vertices: The vertices written in the correct matching order in a concluding statement of congruence, e.g.Pearson Edexcel
Corresponding vertices and sides: The matching parts of congruent or similar figures, which must be identified and matched correctly before calculating an unknown length.AQA
cosine rule: Use a² = b² + c² – 2bc cos A when you know two sides and the angle between them, or when you know all three sides.Pearson Edexcel
Cosine rule for non-right-angled triangles: States a² = b² + c² − 2bc cos A, and can be rearranged to find an angle as cos A = (b² + c² − a²)/(2bc).AQA
Counterexample: One permitted example for which a general claim is false, sufficient to disprove that claim.Pearson Edexcel
Counting outcomes in context: The total count or a missing number of options is found by identifying the stages and whether repetition is permitted before multiplying.AQA
Counting without replacement: When items are selected without replacement, each choice reduces the available pool, so the number of choices at subsequent stages is smaller by one.Pearson Edexcel
Cube number: A number formed by multiplying three equal integer factors.Pearson Edexcel
Cube numbers: A sequence such as 1, 8, 27, 64, 125, ...AQA
cube root of ratio: Taking the cube root of a volume ratio gets back to lengths, so volumes 8 : 125 come from lengths 2 : 5.Pearson Edexcel
Cumulative frequency graph: A plot of a running total of frequencies against the upper class boundary of each interval, with the points joined by a smooth curve and used to estimate the…AQA, Pearson Edexcel
Cumulative frequency in an experiment: A running total of the event occurrences up to a stated number of trials.Pearson Edexcel
Cyclic quadrilateral: A four-sided shape where all four vertices lie on the circumference of a circle.AQA, Eduqas, Pearson Edexcel
cylinder volume: The cross-section is a circle, so the volume of this right prism is πr²h.Pearson Edexcel

D

Decimal multipliers for increase and decrease: A single multiplier is used for increase or decrease, for example multiplying by 1.2 for a 20% increase and by 0.8 for a 20% decrease.AQA
Decimal place: A position to the right of the decimal point, counted from the tenths position.Pearson Edexcel
decimal place value: The value of a digit determined by its position, including tenths, hundredths and thousandths after the decimal point.Pearson Edexcel
decimal places: Counted after the point, with money written to two decimal places.Pearson Edexcel
Deduction: Reading the coordinates from the completed-square form, not plotting points.AQA
Defining variables and interpreting solutions: Stating what your unknown stands for and its units, then rereading the question and stating units clearly so the answer makes sense in context.Pearson Edexcel
denominator: The bottom non-zero number of a fraction; for a positive denominator, it identifies how many equal parts make one whole.AQA, Pearson Edexcel
Density: Mass per unit volume, calculated as mass divided by volume, using units such as g/cm³ or kg/m³.AQA, Pearson Edexcel
density and pressure: Density is mass ÷ volume and pressure is force ÷ area, and a compound measure carries a compound unit such as g/cm³.Pearson Edexcel
Dependent combined events: Events where the first outcome changes the second-stage probabilities, so you adjust the denominator and numerator.AQA
Dependent Events: Events where the outcome of the first event changes the probability of the second event.Pearson Edexcel
derive: Reasoning from facts, like showing a rhombus has opposite angles equal using parallel lines.AQA
descending order: An arrangement from the largest value to the smallest value.Pearson Edexcel
describing a population: Turning a data set into a few figures and then saying what those figures mean about the group.Pearson Edexcel
Describing transformations fully: To describe fully, give all required data: for rotation, centre, angle and direction; for enlargement, centre and scale factor.Pearson Edexcel
Describing transformations precisely: Stating all required details so the mapping is unambiguous, such as the centre, angle and direction for a rotation.AQA
Diagonal: A line segment joining two non-adjacent vertices of a polygon.Pearson Edexcel
Diagrammatic and column representations: Column vectors and diagrams represent the same displacement; diagrammatically, draw vectors end-to-end for addition and reverse the second vector for…AQA
diagrammatic representation: A vector can be drawn as an arrow, because a vector has size and direction.Pearson Edexcel
Diameter: A straight-line distance across a circle or sphere through its centre; equal to twice its radius.AQA, Pearson Edexcel
Difference between shares: The larger amount minus the smaller amount, represented by the corresponding difference in ratio parts.Pearson Edexcel
difference of two squares: A form a² − b² that factorises as (a + b)(a − b), for example x² − 49 = (x + 7)(x − 7).AQA, Pearson Edexcel
Dimensional consistency: Using compatible units so that an equation or calculation describes the same physical quantities throughout.Pearson Edexcel
Dimensionless ratio: A ratio with no units because the same units cancel.Pearson Edexcel
direct proportion: A relationship of the form X = kY for a constant k, so X increases as Y increases and the graph is a straight line through the origin.AQA, Pearson Edexcel
Direct proportion and the constant of proportionality: If y is proportional to x with y : x = 3 : 5, then y = (3/5)x, where the constant of proportionality is the gradient of the line.AQA
direct proportion graph: A straight line through the origin, whose gradient is the constant multiplier.Pearson Edexcel
Discrete Data: Data that can only take specific, exact values (e.g., shoe size, number of siblings).Eduqas, Pearson Edexcel
Discriminant: D = b² − 4ac.Pearson Edexcel
Displacement: The signed area under a velocity-time graph, so negative velocity means motion in the opposite direction.AQA, Pearson Edexcel
disproof by counter-example: Showing a statement is false with one counter-example, given with the numbers that break it.Pearson Edexcel
distance time graphs: Graphs showing a journey, where the gradient (steepness) represents speed and a horizontal line means stationary.Pearson Edexcel
Distance travelled: The total area under a velocity-time graph ignoring sign, found by adding the absolute areas of each section separately.AQA, Pearson Edexcel
Distributive law: Multiplying a single term over a bracket uses this law, for example 4(2a - 3) = 8a - 12.AQA
Divergence: What happens when some rearrangements do not settle, so the rearrangement or starting value must be adjusted.AQA
Dividing in a ratio: Adding the parts of a part : part ratio to find the total number of shares, dividing the quantity by that total to find one share, then multiplying by each…AQA
Division by reciprocal: Multiplying the first fraction by the reciprocal of the second fraction.AQA
domain: The set of values the function is defined for; for y = 1/x it excludes x = 0.AQA, Pearson Edexcel
Drawing from a description: A diagram drawn from a written description shows every fact in the description, with each stated length and angle in the right place.Pearson Edexcel
drawing on squared paper: Keeping the lengths as they are on the solid and drawing a line wherever there is an edge or a change in height.Pearson Edexcel
Duplicate: A second listing of an outcome already counted as the same result in the context.Pearson Edexcel

E

edge: Where two faces meet; a cylinder has two circular edges and a cone has one circular edge.AQA, Pearson Edexcel
effect of extreme values: A few very large or very small values can distort the mean, so the median may describe a typical value better.Pearson Edexcel
Elevation: A view from the front or side of a 3D shape, showing the face seen from that direction.AQA
Elimination: Combining equations by addition or subtraction, after any necessary scaling, to remove one variable.Pearson Edexcel
elimination method: Matching the coefficients of one letter, then adding or subtracting the equations so that letter disappears.Pearson Edexcel
Empirical result: An outcome obtained by carrying out an experiment and recording what happens.AQA
endpoint: A boundary value in an inequality condition, such as 5 in x ≤ 5.Pearson Edexcel
Enlargement: A transformation that changes size from a centre of enlargement by a scale factor, including fractional and negative scale factors.AQA, Pearson Edexcel
Enumerate: List every allowed outcome exactly once.Pearson Edexcel
equality of ratios: Two ratios are in proportion when they reduce to the same simplified ratio, so 3 : 4 and 9 : 12 are in proportion because both reduce to 3 : 4.AQA, Pearson Edexcel
equally likely: Describes events where each outcome has the same probability.Pearson Edexcel
Equally likely events: Events that have the same probability, which lets you calculate expected outcomes by multiplying the probability of an outcome by the number of trials.AQA
Equally likely outcomes: Outcomes that each have the same chance, which the method requires before counting alone gives theoretical probability.AQA, Pearson Edexcel
equation: A statement that holds for particular values of the letter, such as 3x + 6 = 12, which is true only when x = 2.AQA, Eduqas, Pearson Edexcel
equation of a circle: A circle of radius r drawn about the origin has equation x² + y² = r², which is Pythagoras' theorem applied to the right-angled triangle under any point on…Pearson Edexcel
Equations and solutions: An equation such as 2x + 6 = 10 has a single solution, whereas an identity holds for every value.AQA
Equilateral triangle: A triangle with three equal sides and three angles of 60°.Pearson Edexcel
Equivalent expressions: Expressions that have the same value for every permitted value of their variables.Pearson Edexcel
equivalent fractions: Fractions that represent the same value; multiplying or dividing numerator and denominator by the same non-zero number preserves equivalence.AQA, Pearson Edexcel
Equivalent fractions and comparison: Rewriting fractions with a common denominator or converting them to decimals in order to compare them.AQA
Equivalent fractions and ratio notation: A share given as a fraction of the total becomes a ratio using a common denominator, and a ratio becomes fractions by dividing each part by the total parts.AQA
Equivalent ratios: Ratios representing the same multiplicative relationship, obtained by multiplying or dividing every entry by the same non-zero factor.Pearson Edexcel
equivalent single transformation: The one transformation that has the same effect as a pair of transformations carried out in order.Pearson Edexcel
Equivalent single transformations: The overall single transformation that maps the original object to the final image; two parallel reflections give a translation and two intersecting…AQA
Equivalent transformation: A transformation with the same effect as the given combination on every relevant point.Pearson Edexcel
Error interval: An inequality specifying the possible true values consistent with a stated rounded or truncated value.Pearson Edexcel
error intervals: Names every true value a rounded figure could have come from, with the upper end strict because that value would round up instead.Pearson Edexcel
Error intervals and inequality notation: The range formed by the lower and upper bounds, written with correct inequality signs as lower bound ≤ value < upper bound.AQA
Estimate: An approximate value found using simpler numbers or a suitable numerical comparison.Pearson Edexcel
Estimated line of best fit: A straight line placed through the middle of the points, with roughly equal numbers above and below and the same overall slope.AQA
Estimating powers using known values: Finding a value close enough to the true answer without calculating it exactly by relating it to a nearby known value.AQA
estimating probability: Using relative frequency as the best estimate of the probability where equally likely outcomes cannot be counted.Pearson Edexcel
estimating roots: Placing an inexact root between two values you already know, by trapping it between neighbouring powers and reading the answer off.Pearson Edexcel
Estimating roots by bracketing between known powers: Finding a value close enough to the true answer without calculating it exactly by placing the number between two known powers.AQA
Estimation to check calculations: Using an estimate to check whether an exact or technology-obtained answer is reasonable, identifying errors such as a misplaced decimal point.AQA
Even integer: An integer divisible by 2, expressible as 2n for some integer n.Pearson Edexcel
Event: A specified outcome or set of outcomes of an experiment.Pearson Edexcel
Exact answer: A value expressed without rounding, such as 24π or 608π/3.AQA
Exact answer in terms of π: A value retaining π symbolically rather than replacing it with a rounded decimal approximation.Pearson Edexcel
Exact answers in geometry: Using exact values in geometry problems involving circles, cylinders, and spheres to avoid premature rounding errors.AQA
Exact evaluation and checking by expansion: Work out the exact value or simplified power before looking at the options, and check index-law answers by expanding small cases.AQA
Exact form: A representation with no rounding error, such as 6√3 or the integer 18.AQA
Exact form (non-decimal answers): An exact calculation gives an answer that is not rounded, so it is left as a simplified fraction or as a multiple of π rather than a decimal.Pearson Edexcel
exact form answers: A term left in exact surd form rather than rounded to a decimal, such as 8√3 rather than a rounded 13.9.Pearson Edexcel
exact surd answers: An answer that keeps the root in place rather than rounding, as the wording of the question on accuracy wanted.Pearson Edexcel
Exact surd solutions: Both methods may produce surd solutions; leave them exact unless asked for decimals, with the answer left with a square root and simplified fully.AQA
Exact value: A value represented without rounding or approximation.AQA, Pearson Edexcel
exact values: Values kept in fraction, surd or π form instead of being rounded, so the answer stays exact the whole way through.Pearson Edexcel
Exhaustive: Covering every possible outcome, so at least one of the listed categories must occur.Pearson Edexcel
Exhaustive Events: A set of events that covers all possible outcomes, meaning their probabilities must sum to 1.Pearson Edexcel
Exhaustive sets of outcomes: A set of outcomes that covers every possible result of an experiment, so their probabilities sum to 1.AQA
expanding brackets: Multiplying each term in the first bracket by each term in the second, so (x + 2)(x + 5) is x² + 7x + 10.AQA, Pearson Edexcel
expanding three brackets: Multiplying two of the brackets first, writing the quadratic down, then multiplying it by the remaining bracket term by term.Pearson Edexcel
Expected frequencies: Theoretical counts calculated from probabilities, for example if P(X) = 0.1, the expected frequency in 50 trials is 0.1 × 50 = 5.Pearson Edexcel
Expected frequency: The mean number of occurrences of an event across repetitions of the experiment; for n trials each with event probability p, it is np.Eduqas, Pearson Edexcel
expected outcomes: Calculated as P(event) × number of trials, giving a theoretical average that the actual number may differ from.AQA, Pearson Edexcel
exponential graphs: A curve y = kˣ, with k positive, always passes through (0, 1) and stays above the x axis, approaching it without touching.Pearson Edexcel
Exponential growth and decay: For y = kˣ with k > 1 the graph rises, and for 0 < k < 1 the graph falls, but both pass through (0, 1) and have the x-axis as a horizontal asymptote.AQA
Expressing division as a ratio: Comparing the two part amounts in simplest form.AQA
Expression: A collection of terms with operations but no equals or inequality sign, like 3x² + 5y.AQA, Eduqas, Pearson Edexcel
expressions as rules: A simple expression can be read as a rule, so 3x − 4 is multiply by 3, then subtract 4.Pearson Edexcel
Exterior angle: For a convex polygon, the angle between one side and the extension of an adjacent side, supplementary to the interior angle at that vertex.Pearson Edexcel
Extrapolation: Predicting outside the plotted data range, which is risky because the apparent trend may not continue.AQA, Eduqas, Pearson Edexcel

F

face: A flat surface of a solid; the curved surface of a cylinder is not one.Pearson Edexcel
Face height of a pyramid: The perpendicular height within one triangular face, measured from its apex to that face's base edge.AQA
Faces, edges, vertices and curved surfaces: A face is a flat surface, a curved surface is distinct, an edge is where surfaces meet, and a vertex is a corner.AQA
Factor: A quantity that multiplies another quantity to give the quantity under consideration.Pearson Edexcel
factorise: Rewrite an expression as a product of factors.Pearson Edexcel
factorise fully: Write an expression as a product, removing all common factors and factorising any remaining eligible expressions.Pearson Edexcel
Factorising quadratic expressions: Rearranging a quadratic expression into two brackets, such as finding two numbers that multiply to the constant and add to the coefficient of x.AQA
factorising quadratics: Reversing expansion of the form ax² + bx + c by finding two numbers that multiply to ac and sum to b, splitting the middle term, then factorising in pairs.AQA, Pearson Edexcel
factorising to isolate: When the new subject appears twice, gather those terms on one side, factorise it out, then divide by the bracket.Pearson Edexcel
Factors (divisors): A factor of a number divides it exactly.AQA
fair: Usually implies equally likely outcomes, as with a fair dice or coin.Pearson Edexcel
Fair game: In an equal-stakes, equal-reward two-player game, a game giving the players equal probabilities of winning.Pearson Edexcel
Fair randomising device: A device whose relevant outcomes have the equal probabilities specified by the fair model, such as each face of a fair six-sided die having probability 1/6.Pearson Edexcel
Fairness: No outcome is favoured, so a fair six-sided die gives each face probability 1/6.AQA
Fibonacci-type sequence: A sequence where each term is formed by adding the two previous terms, and the starting terms need not be 1 and 1.AQA, Pearson Edexcel
Finding missing angles: Use the inverse trigonometric function on the ratio of the two relevant sides.AQA
Finding missing lengths: Substitute two known lengths into the appropriate formula and solve.AQA
finding the hypotenuse: Square the two shorter sides, add, then take the square root, so 5 cm and 12 cm give 25 + 144 = 169, and the hypotenuse is 13 cm.Pearson Edexcel
First difference: The next term minus the current term: u_(n+1) − u_n for consecutive positions.AQA, Pearson Edexcel
First differences: The changes obtained by subtracting each term from the next.Pearson Edexcel
Footprint: The set of ground positions occupied by a solid; for the gap-free vertical stacks here, it equals the occupied plan cells.Pearson Edexcel
Formal written methods: These include column addition and subtraction, long multiplication, and short or long division, and should be shown with clear layout.AQA, Pearson Edexcel
Forming and simplifying ratios: Writing two quantities as a ratio and simplifying it to its lowest terms by dividing both by a common factor.Pearson Edexcel
Forming expressions, equations and formulae: Translating simple situations or procedures into algebraic expressions or formulae, or deriving an equation or two simultaneous equations from the facts given.Pearson Edexcel
Formula: A rule connecting quantities, like A = πr², used for substitution.AQA, Eduqas, Pearson Edexcel
Four operations with integers and decimals: Applying the four operations to integers and decimals, including both positive and negative values.AQA
four quadrants: Top right has both coordinates positive, top left has x negative and y positive, bottom left has both negative, and bottom right has x positive and y negative.Pearson Edexcel
fraction: A number written as a numerator over a non-zero denominator, representing division or a number of equal parts.AQA, Pearson Edexcel
Fraction arithmetic: Adding or subtracting needs a common denominator, multiplying means multiplying numerators and denominators, and dividing means inverting the second fraction…Pearson Edexcel
Fraction notation and simplification: Writing the first quantity as the numerator and the second as the denominator, then dividing numerator and denominator by their highest common factor.AQA
Fraction notation: part-to-part and part-to-whole: Writing the relationship as a fraction, choosing correctly between a part-to-part fraction and a part-to-whole fraction according to what the question asks.AQA
fraction of a quantity: Writing one quantity as a fraction of another means putting the quantity named after the word "of" on the bottom.Pearson Edexcel
fraction of circle: The angle at the centre over 360, written down first so the working stays exact.Pearson Edexcel
Fraction to decimal conversion: Either divide the numerator by the denominator or, if possible, scale the fraction to have a denominator of 10, 100, or 1000.Pearson Edexcel
Fractional index: A rational exponent $m/n$ which, for a positive base, represents an nth root and an mth power: $a^{m/n}=(\sqrt[n]{a})^m$.Pearson Edexcel
Fractional indices as roots and powers: The denominator of the fraction represents the root, and the numerator represents the power.Pearson Edexcel
Fractions and mixed numbers: Calculating with simple fractions (proper and improper) and mixed numbers, converting mixed numbers to improper fractions before multiplying or dividing.AQA
Fractions and percentages as multiplicative operators: A fraction or percentage acts as an operator when applied to a quantity to produce a new quantity, equivalent to multiplying by the fraction or by the decimal.AQA
fractions as operators: Used as an operator, a fraction acts on a number, and the word 'of' means multiply, so 3/4 of 20 is 3/4 × 20, which is 15.Pearson Edexcel
Fractions greater than 1 as improper fractions: The fraction may be less than 1 or greater than 1, so allow fractions greater than 1 when the first quantity is larger than the second.AQA
Fractions of a total: The ratio a : b gives the first part as a/(a + b) of the total and the second part as b/(a + b).AQA
Frequency: The number of times an event occurs in the recorded trials.Pearson Edexcel
Frequency density: The vertical axis value for a histogram with unequal class intervals, calculated as frequency ÷ class width, so that the area of each bar equals the frequency.AQA, Eduqas, Pearson Edexcel
frequency table: A structured table in which each outcome is recorded and tallied as it occurs, with a clearly labelled outcome column and a running total.AQA, Pearson Edexcel
Frequency tables: A table used to record counts for categorical data, read by reading the frequencies for each category or value.AQA
frequency tree: An organisational tool that records the same information across successive stages, where each branch records a count and the branch counts at each stage sum…AQA
frequency trees: A diagram starting with the total population on the left, whose branches split this total by one category and then split each group by the second category.Pearson Edexcel
front and side elevations: The views from the front and from the side, both looking horizontally, drawn flat with no perspective.Pearson Edexcel
Front elevation: The view from the front of the shape, showing the face seen from the front.AQA, Pearson Edexcel
Frustum: The part of a cone or pyramid remaining after a smaller similar cone or pyramid is cut off by a plane parallel to the base.AQA, Pearson Edexcel
Function: A rule assigning exactly one output to each permitted input.Pearson Edexcel
function machines: A drawing of the same rule as boxes in a row, read from left to right.Pearson Edexcel
function notation: The rule is written f(x), so if f(x) = 3x − 4 then f(5) = 11.Pearson Edexcel

G

general fractional index: A general fractional index combines a root and a power: a^(m/n) means the nth root of a raised to the power m, equivalently the mth power of the nth root.AQA
generalising with letters: Writing an even number as 2n, where n is a whole number, so that algebra can support arguments about numbers in general.Pearson Edexcel
generate terms: To produce terms from a term-to-term rule by starting with the given first term and applying the rule repeatedly, or from a position-to-term rule by…AQA
Generating coordinate pairs from a linear equation: Choosing several x-values, substituting each into the equation to find the matching y-value, and recording the results as coordinate pairs.AQA
geometric progression: A sequence with a common ratio found by dividing each term by the one before it, where the nth term is a × r^(n−1).Pearson Edexcel
geometric progressions: Sequences with a constant ratio, such as 16, 8, 4, 2 with ratio ½, and at Higher tier with surd ratios such as 1, √2, 2, 2√2, 4 with ratio √2 and rule (√2)ⁿ⁻¹.Pearson Edexcel
Geometric proof: A logical argument constructing a proof of a standard circle theorem, often by adding radii to form isosceles triangles, or proving a related result.Pearson Edexcel
Geometric proof structure: Listing three matching facts with reasons, then stating the criterion, then writing a concluding statement of congruence.Pearson Edexcel
Geometric proofs: Arguments and proofs constructed using vectors, such as showing one vector is a scalar multiple of another.Pearson Edexcel
Geometric reasoning and hierarchy of shapes: A square is also a rectangle, a rhombus and a parallelogram, and a property can be derived from a definition, for example using parallel lines to show…Pearson Edexcel
Geometric reasoning and proof: Calculating angles and giving a named geometric reason for each step, with a complete chain of reasoning for multi-step problems.Pearson Edexcel
Geometric sequence: A sequence in which each term is obtained by multiplying the previous term by a fixed ratio.AQA
Geometric sequence or progression: A sequence in which each term is obtained by multiplying the preceding term by the same constant.AQA
Geometric vocabulary and notation: The conventional terms include point, line, plane, edge, vertex, parallel lines, perpendicular lines, right angles, polygons and regular polygons.Pearson Edexcel
Gradient: On a distance-time graph it gives speed, and on a velocity-time graph it gives acceleration, found using change in y divided by change in x.AQA, Pearson Edexcel
gradient and intercept: In the form y = mx + c, the number in front of x is the gradient and the number on its own is where the line crosses the y axis.Pearson Edexcel
Gradient and intercepts: In y = mx + c, m is the gradient and c is the y-intercept.AQA
Gradient and y-intercept: In the form y = mx + c, m is the gradient and c is the y-intercept.AQA
gradient as a rate: The multiplier between the two quantities, read from a graph as a change in y divided by the matching change in x.Pearson Edexcel
Gradient as a rate of change: On a straight-line graph, it measures how steeply the line rises or falls and represents the change in the vertical quantity divided by the change in the…AQA
gradient as rate: The gradient of a straight line graph measures how fast one quantity changes as the other changes, with units of the vertical axis per unit on the horizontal…Pearson Edexcel
gradient of a chord: The change in y divided by the change in x between two points on a curve, giving the average rate of change.Pearson Edexcel
gradient of a line: How steep a straight line is: the change in y for every increase of 1 in x, and negative when the line falls from left to right.Pearson Edexcel
gradient of a tangent: The change in y divided by the change in x between two points far apart on a tangent line that just touches the curve and follows its direction.Pearson Edexcel
Gradient triangle: A right-angled triangle whose horizontal and vertical sides measure coordinate changes along a straight line.Pearson Edexcel
graph sketching: Drawing a changed version of a given curve so that the shape stays identical, only moved or flipped, working with key points.Pearson Edexcel
graphical approximate solutions: The intersection of the two graphs gives the solution; read approximate coordinates from the grid, or draw the line and curve to estimate them.Pearson Edexcel
Graphical representation: Direct proportion passes through (0, 0), while inverse proportion has a decreasing curve.AQA
Graphical representation of inequalities: Showing the solution set as a region on a graph, using a dashed boundary line for strict inequalities and a solid line for ≤ or ≥.AQA
Graphical solutions: Plotting each side as a straight line and reading the x-coordinate of their intersection.AQA
graphs through the origin: A straight line for a relationship where zero of one quantity means zero of the other, such as a conversion graph with pounds across and euros up.Pearson Edexcel
Grouped discrete data: Data that take exact values such as counts, summarised in classes, using suitable class boundaries when constructing the diagram so adjacent classes are…AQA
Grouping with brackets: Using brackets to group terms so the whole group is treated as one quantity.AQA
growth and decay: Problems using the same method, with a multiplier above 1 for growth and a multiplier between 0 and 1 for decay.Pearson Edexcel
Growth and decay multipliers: For growth the multiplier is 1 + r, where r is the decimal rate; for decay it is 1 − r.AQA

H

half equilateral triangle: Cutting an equilateral triangle of side 2 in half gives a right-angled triangle with sides 1, √3 and 2.Pearson Edexcel
Handedness: The clockwise or anticlockwise order of corresponding labelled vertices around a shape.Pearson Edexcel
Height plan: A plan supplemented by a label giving the height of each occupied stack.Pearson Edexcel
Hemisphere: Half a sphere formed by cutting through the sphere's centre with a plane.AQA
higher tier estimation: A Higher tier skill of estimating powers and roots of any given positive number, showing the pair of known values or the rounded base rather than a calculator…Pearson Edexcel
Higher tier only: This work on sketching translations and reflections of a given function is Higher tier only.Pearson Edexcel
Highest common factor: Common factors are shared by two or more numbers, and the highest common factor is the largest of these.AQA, Pearson Edexcel
highest common factor (HCF): The largest number that is a factor of two or more numbers.Pearson Edexcel
Histogram: Represents grouped continuous data with bars whose area is proportional to frequency, so frequency density equals frequency divided by class width.AQA, Pearson Edexcel
horizontal and vertical components: The two numbers of a column vector, with the horizontal component on top and the vertical component below.Pearson Edexcel
Hypotenuse: The side opposite the right angle, which is the longest side in a right-angled triangle.AQA, Eduqas, Pearson Edexcel

I

Identities: An equation that is true for every value of the variable, so it cannot be solved to give a single value.AQA
identity: A statement that holds for every value of the letter, written with the sign ≡ in place of an equals sign.Eduqas, Pearson Edexcel
Identity function: The function that leaves every permitted input unchanged: I(x) = x.Pearson Edexcel
Identity symbol: The symbol ≡, used to show that a statement is true whatever number replaces the variable.AQA
Identity transformation: A transformation that maps every point to itself.Pearson Edexcel
image: The result of the translation, whose coordinates minus the object coordinates give the vector.AQA, Pearson Edexcel
improper fraction: A fraction whose numerator has magnitude at least as large as its positive denominator, so its magnitude is at least 1.AQA, Pearson Edexcel
improper fractions: An answer greater than 1 is left as an improper fraction unless the question asks for a mixed number.Pearson Edexcel
included angle: The angle that sits between the two sides named in the formula, which has to be the one used.AQA, Pearson Edexcel
Included angle and side: The angle between two sides, or the side between two angles, used in the SAS and ASA criteria.Pearson Edexcel
inclusive inequality: A comparison using ≤ or ≥ that allows equality as well as the stated direction of difference.Pearson Edexcel
increase and decrease: 15% more than an amount is that amount × 1.15, and 15% less is the amount × 0.85, because a fall of 15% keeps 85% of the value.Pearson Edexcel
Independent: Events for which one occurring does not change the probability of the other.Pearson Edexcel
Independent and dependent events: For independent stages the probability on a second-stage branch is unchanged by the first-stage outcome; for dependent stages second-stage probabilities must…AQA, Pearson Edexcel
Independent combined events: Events where the outcome of one stage does not change the probabilities at the next stage, so you multiply along branches.AQA
Independent Events: Events where the outcome of one does not affect the probability of the other.AQA, Eduqas, Pearson Edexcel
Independent successive choices: A task has successive independent choices, and the number of options at each stage is multiplied.AQA
Independent trials: Trials for which knowing the outcome of one does not change the probabilities of outcomes in the others.Pearson Edexcel
index: An exponent written above and to the right of its base.Pearson Edexcel
Index / exponent: The raised number specifying a power; a positive integer index counts repeated factors of the base.Pearson Edexcel
index laws: Rules that let you handle powers without writing them out in full, adding the indices for a product and subtracting them for a quotient.Pearson Edexcel
Index laws for multiplication, division and brackets: These let you combine powers with the same base: the indices add for multiplication, subtract for division, and multiply for brackets.AQA
index notation: Recording repeated multiplication so that a² means a × a, a³ means a × a × a and a²b means a × a × b.AQA, Pearson Edexcel
Index notation and repeated multiplication: A positive integer power records repeated multiplication, where the base is the number multiplied and the index is the number of times it is used.AQA
Index or exponent: The value specifying the power of the base.Pearson Edexcel
Index/exponent: The power n applied to a base; in standard form the base is 10 and n is an integer.AQA
inequality: A statement, such as x > 4, that is satisfied by a range of values.AQA, Pearson Edexcel
Inequality notation and direction: A linear inequality in one variable compares expressions using <, >, ≤ or ≥, and multiplying or dividing both sides by a negative number reverses the…AQA
inequality symbols: The strict signs < and > say one side is definitely bigger, while ≤ and ≥ also allow the two sides to match, and ≠ says only that two values differ.Pearson Edexcel
Inequality symbols and their meanings: The symbols =, ≠, <, >, ≤, ≥, which let you state exact relationships, where ≤ and ≥ include equality.AQA
inference: A conclusion about properties of a population or distribution drawn from a sample, which is an estimate rather than proof.Pearson Edexcel
Input: The value or expression to which a function rule is applied.Pearson Edexcel
inputs and outputs: A rule takes an input, does something to it, and gives one output, though two inputs can share an output.Pearson Edexcel
instantaneous rate of change: The rate of change at a single point, found as the gradient of the tangent to the curve at that point.AQA, Pearson Edexcel
Integer: A whole number that can be positive, negative, or zero.AQA, Eduqas, Pearson Edexcel
Integer indices including zero and negative indices: An integer index tells you how many times the base multiplies itself, a negative integer index gives a reciprocal, and any non-zero base to the power zero…AQA
integer solutions: The integers in the range, listed with none missing and none extra, such as the integers satisfying −2 < n ≤ 3.Pearson Edexcel
Inter-quartile range: A measure of spread calculated as Q₃ - Q₁, measuring the spread of the middle half.Pearson Edexcel
Interior angle: An angle inside a polygon between two adjacent sides at a vertex.AQA
Interpolation: Predicting inside the plotted data range, which is usually reliable.AQA
interpolation and extrapolation: A reading taken inside the range of the plotted data is interpolation and is fairly safe, while going beyond that range is extrapolation, where the trend may…Pearson Edexcel
Interpretation in context with units: The numerical gradient is interpreted with correct units, such as m/s or £/year, and in the context of the problem, distinguishing average from instantaneous.AQA
Interpretation in financial and real contexts: Interpreting the result in context, including whether it is a growth or decay situation and what the final value means.AQA
Interpreting an equation: Using the equation to predict a value, such as finding y when x = 5, or rearranging to find x when y is known.AQA
interpreting equations: To read an equation, substitute a value and watch what happens, which tells you which kind of proportion you are looking at.Pearson Edexcel
Interpreting standard form in context: Recognising what a value written as A × 10ⁿ means in a real situation, for example that 5 × 10⁻³ metres is 5 millimetres.AQA
interquartile range: Upper quartile minus lower quartile, measuring the spread of the middle half, so it is less affected by outliers than the range.AQA
Interquartile Range (IQR): The difference between the upper quartile and the lower quartile, representing the spread of the middle 50% of the data.AQA
Intersection: A point common to two graphs, whose coordinates satisfy both graph equations.Eduqas, Pearson Edexcel
Interval notation and inequality statements: Writing the interval with the lower limit included and the upper limit excluded, for example 6.5 ≤ x < 7.5.AQA
Invariance of length, angle and area: Properties unchanged by the combination; lengths, angles and area are invariant under any combination of rotations, reflections and translations.AQA
Invariant: A quantity or expression that stays unchanged as other values change.Pearson Edexcel
Invariant point: A point whose final position under the specified transformation or combination is exactly its original position.Pearson Edexcel
invariant points: A point that stays exactly where it is, such as a point on the mirror line.Pearson Edexcel
Invariant property: A property unchanged by a transformation, such as length or angle under an isometry.Pearson Edexcel
Inverse function: A function that reverses the input/output mapping of the original function, where such a reverse is a function on the relevant inputs.Pearson Edexcel
inverse functions: The reverse process that reverses the original function, so applying a function then its inverse returns the original input.AQA, Pearson Edexcel
Inverse operation: An operation that reverses another operation under the relevant conditions, such as multiplication reversing division by a non-zero value.Pearson Edexcel
inverse operations: Operations that undo each other, such as addition and subtraction, or multiplication and division; they are used to check answers and solve equations.AQA, Pearson Edexcel
Inverse probability: A problem like P(A | B) solved by finding P(A and B) by multiplying along branches, then dividing by P(B), which may require summing multiple path…Pearson Edexcel
inverse proportion: A relationship in which the product of the two quantities stays fixed, so y = k/x, and with k positive the graph is a curve that falls as x grows for positive…AQA, Pearson Edexcel
inverse proportion graph: With both quantities positive, a curve that drops steeply and then flattens, moving closer to the axes without ever meeting them.Pearson Edexcel
Inverse proportion graphs as curves that never meet the axes: A curve that falls as the horizontal value increases, never touching either axis, because the product of the two quantities stays constant.AQA
Inverse sine: Used after rearranging to sin C = 2 × Area ÷ (ab) in order to find an angle.AQA
inverse square proportion: A relationship such as y = k/x², where y is inversely proportional to the square of x.Pearson Edexcel
Inverse trigonometric function: A function used to obtain an angle from a trigonometric ratio, such as sin⁻¹ or cos⁻¹.Pearson Edexcel
inverse trigonometric functions: Used to find an angle from two known sides: if opposite = 3 cm and hypotenuse = 6 cm, then sin θ = 3/6 = 0.5, so θ = sin⁻¹(0.5) = 30°.Pearson Edexcel
Irrational number: A real number that cannot be expressed as a fraction p/q of integers with q ≠ 0.AQA, Eduqas, Pearson Edexcel
Isometry: A transformation preserving the distance between every pair of points.Pearson Edexcel
Isosceles triangle: A triangle with at least two equal sides; the angles opposite equal sides are equal.OCR, Pearson Edexcel
Iteration: A method that finds approximate solutions to equations that cannot be solved exactly by repeatedly applying a formula.AQA
iteration formula: A rearrangement with a single x on the left, such as xₙ₊₁ = √(5 − xₙ), into which each answer is fed back.Pearson Edexcel
iterative methods: Ways of finding approximate solutions to equations numerically, closing in on a root by improving a guess over and over.Pearson Edexcel

J

Joint probability: The probability that both events occur, P(A ∩ B).Pearson Edexcel

K

Kite: A quadrilateral with two pairs of adjacent equal sides.Pearson Edexcel

L

Laws of indices: These are applied to simplify sums, products and powers of algebraic terms, for example aᵐ × aⁿ = aᵐ⁺ⁿ.AQA
length: Comes from the horizontal and vertical steps of a segment with a² + b² = c².Pearson Edexcel
length area volume ratios: Lengths in a ratio give areas in the square of that ratio and volumes in its cube, so lengths 2 : 3 give areas 4 : 9 and volumes 8 : 27.Pearson Edexcel
Length scale factor: The constant ratio of corresponding side lengths, found by dividing a side length on the new shape by the corresponding side length on the old shape.Pearson Edexcel
Length, area and volume relationships: If the length scale factor is k, then every length is multiplied by k, every area by k squared, and every volume by k cubed.AQA
Like surds: Surd terms with the same radicand once the roots have been fully simplified.AQA
Like terms: Terms with exactly the same variable part, including the same powers, which can be combined by adding their coefficients.Pearson Edexcel
Limits of accuracy: The range of possible true values that a rounded measurement represents, also called bounds.AQA, Pearson Edexcel
line: A straight one-dimensional object with no width, extending indefinitely in both directions.AQA, Pearson Edexcel
line graph: Plots time series data to show trends over time.Pearson Edexcel
line meeting a curve: Two pairs mean the line cuts the curve twice; one repeated root means it is a tangent.Pearson Edexcel
line of best fit: One straight line following the trend with roughly as many points above it as below, which need not pass through the origin.Pearson Edexcel
Line of reflection symmetry: A line in which reflection maps the whole shape exactly onto itself.AQA
line of symmetry: A line that runs vertically through the turning point.Pearson Edexcel
Line segment: The finite straight part of a line between two endpoints.AQA, Pearson Edexcel
Linear / arithmetic sequence: A sequence with constant first differences, expressible as dn + c.Pearson Edexcel
Linear equation: An equation whose graph is a straight line, with variables appearing only to the first power, for example ax + by = d with a and b not both zero.AQA, Pearson Edexcel
Linear equation in two variables: An equation expressible as ax + by = c, with constant coefficients a and b not both zero; its graph is a straight line.Pearson Edexcel
Linear equation in x and y: An equation that can be written ax + by = d, with constant coefficients a and b not both zero, whose graph is a straight line.AQA
Linear function: In GCSE straight-line graph work, a function written in the form y = mx + c.Pearson Edexcel
linear functions: A relationship such as y = 3x, where every matching pair of values lies on a straight line through the origin.Pearson Edexcel
Linear functions and gradient: A ratio describes a linear function y = kx, a straight-line graph through the origin whose gradient is the constant of proportionality.AQA
Linear graphs: Graphs of linear functions, which have the form y = mx + c and graph as straight lines.AQA
linear inequalities: A statement describing a range of values rather than a single one, handled the way an equation is handled by doing the same thing to both sides.Pearson Edexcel
Linear inequalities in one and two variables: Inequalities solved by rearranging correctly, and where necessary reversing the inequality sign when multiplying or dividing by a negative number.AQA
Linear remainder: The sequence bn + c remaining after an² is subtracted from a quadratic sequence.AQA
linear remainder sequence: Subtracting the an² component from each original term generates this, whose nth term is bn + c.AQA
Linear sequence / arithmetic sequence: A sequence with a constant difference between consecutive terms; its nth term can be written dn + c.Pearson Edexcel
linear sequences: A sequence that changes by the same amount at every step, so the common difference is the coefficient of n.Pearson Edexcel
linear/linear elimination: A method for two linear equations in which one letter is removed by adding or subtracting the equations.Pearson Edexcel
linear/quadratic substitution: The method for a linear/quadratic pair: make one letter the subject of the linear equation and substitute it into the quadratic.Pearson Edexcel
Loci and shortest distance: The perpendicular distance from a point to a line is the shortest distance, so a locus at a fixed distance from a line is a pair of parallel lines.AQA
Lower limit: The smallest value that would round up to the stated value.AQA, Pearson Edexcel
lower quartile: The value one quarter of the way through the ordered data.AQA
lowest common multiple (LCM): The smallest number that is a multiple of two or more numbers.Pearson Edexcel
lowest terms: A fraction form in which numerator and denominator have no common factor greater than 1.AQA

M

Maximising and minimising sums and differences: For a sum, add the upper bounds for the maximum and the lower bounds for the minimum; for a difference, choose bounds for the required extreme.AQA
maximum: The highest y-value on a downward-opening quadratic graph, occurring at the turning point.Pearson Edexcel
mean: The total divided by the count, and an outlier distorts it so the median can be a more representative average.Pearson Edexcel
measuring angles: Using a protractor and reading the scale that starts at zero on one arm of the angle.Pearson Edexcel
measuring lines: Using a ruler to measure a line segment to the nearest millimetre.Pearson Edexcel
median: The middle of an ordered list, and it can be a more representative average when outliers distort the mean and range.Pearson Edexcel
Membership: Whether a proposed value is a term of the specified sequence.Pearson Edexcel
Mensuration: The calculation or measurement of lengths, areas and volumes.AQA
Mensuration formulae: Formulae for the circumference and area of a circle and for the volume and surface area of spheres, pyramids, cones and composite solids.Pearson Edexcel
metric unit conversion: A multiplication in which you decide first whether the answer should be a larger or a smaller number, then multiply or divide to match.Pearson Edexcel
midpoint: Found by averaging the two x coordinates and averaging the two y coordinates of a segment.Pearson Edexcel
midpoint of a line segment: Averaging each coordinate of two points gives the point halfway between them, such as (−1, 5) for (−4, 3) and (2, 7).Pearson Edexcel
minimum: The lowest y-value on an upward-opening quadratic graph, occurring at the turning point.Pearson Edexcel
Minor and major sector: A minor sector has central angle below 180°; the corresponding major sector has the reflex angle above 180°.Pearson Edexcel
mixed number: A whole number written together with a proper fraction, for example 2 1/3.AQA, Pearson Edexcel
Modal class: A measure of central tendency: the class interval with the highest frequency.Pearson Edexcel
monic quadratic: A quadratic expression whose x² coefficient is 1, such as x² + 2x − 15.Pearson Edexcel
Multiples: A multiple is the result of multiplying a number by an integer.AQA
multiples of π: Answers left in the form of a number times π, such as 6π for the circumference of a circle of radius 3 cm, rather than a decimal.Pearson Edexcel
Multiplication along branches: The probability of a path is found by multiplying the probabilities along its branches.AQA
Multiplication and cancellation: Multiplying the numerators together and the denominators together, then simplifying the result by cancelling common factors.AQA
Multiplication and division: Operating on the numerical coefficients while keeping π as a factor, for example, 2π × 3 = 6π and 6π ÷ 2 = 3π.AQA
Multiplication by juxtaposition: Writing letters or numbers together so that ab means a × b and 3y means y + y + y and 3 × y.AQA
Multiplication of choices across stages: The total number of outcomes is found by multiplying the number of options at each stage.AQA
Multiplicative comparison of two quantities: A comparison of two quantities by multiplication or division, where one quantity may be a multiple of the other.AQA
Multiplicative reasoning with percentages: Percentage changes are interpreted multiplicatively: an increase of 20% multiplies by 1.20, and a decrease of 20% multiplies by 0.80.AQA
multiplicative relationship: A link where one quantity is always a fixed multiple of the other, which can be recorded as a ratio, a fraction or an equation.Pearson Edexcel
Multiplier: A factor that multiplies an original quantity to produce another quantity.AQA, Eduqas, Pearson Edexcel
multiplier between quantities: The fixed multiple found by dividing one quantity by the other.Pearson Edexcel
Mutually Exclusive: Events that cannot happen at the same time (e.g., rolling a 2 and rolling a 5 on a single die).AQA, Eduqas, Pearson Edexcel
Mutually exclusive and exhaustive outcomes: Mutually exclusive outcomes cannot occur together in one trial; exhaustive outcomes include every possible outcome.Pearson Edexcel
Mutually exclusive events: Events that cannot happen at the same time, so their probabilities add without overlap.AQA, Pearson Edexcel

N

negative index: An index indicating a reciprocal power: 10^-k = 1/10^k for positive integer k.AQA, Pearson Edexcel
negative indices: For a non-zero base, a negative index means the reciprocal of the matching positive power, so 2⁻³ = 1/2³ = 1/8.Pearson Edexcel
Negative indices as reciprocals: A negative index signifies a reciprocal, so a negative fractional index combines this with the root and power.Pearson Edexcel
negative numbers: On a number line the negatives run the other way, so −9 sits to the left of −2 and is the smaller of the two.Pearson Edexcel
Negative reciprocal gradients: The tangent gradient is the negative reciprocal of the radius gradient, so a radius gradient of 2 gives a tangent gradient of −1/2.AQA
Negative reciprocals: If one line has gradient m, a perpendicular line has gradient −1/m, the negative reciprocal.AQA
no real roots: What a quadratic has when its minimum sits above the x axis on a curve opening upwards, so the curve never reaches the x axis.Pearson Edexcel
Non-repeating prefix: The decimal digits before the recurring block begins; leading zeros count as digit positions.Pearson Edexcel
Normalisation: Rewriting an equivalent coefficient-times-power expression so its positive coefficient lies in the interval 1 ≤ A < 10.AQA
nth root: A value which, when raised to the positive integer power n, gives the original number; for a non-negative input, an even-root symbol denotes the principal…Pearson Edexcel
nth term: Another name for a position-to-term rule, which tells you what to do to the position number to land on any term.Pearson Edexcel
nth term / position-to-term rule: An expression giving the value u_n directly from position n.Pearson Edexcel
nth term expression: The complete rule in n, such as 3n + 2, found by starting with the difference times n and then finding the constant.Pearson Edexcel
number line: A scaled line on which each point represents a number and values increase from left to right.Pearson Edexcel
Number line and ordering: Placing numbers on a number line from least to greatest, with negative numbers to the left of zero and positive numbers to the right.AQA
number line representation: Marking the boundary with an open circle when that value is not included and a filled circle when it is, then drawing an arrow along the values that work.Pearson Edexcel
numerator: The number above the fraction bar; in a positive part-of-a-whole fraction, it counts the equal parts being considered.AQA, Pearson Edexcel
Numerator and denominator: The numerator is the quantity above a fraction bar; the denominator is the non-zero quantity below it.Pearson Edexcel
Numerical map scale: A ratio comparing map length with real length expressed in the same unit, usually written 1 : n.AQA
Numerical substitution and calculation with compound units: Substituting values into the density and pressure formulae and evaluating the result, keeping units consistent and converting them before substituting.AQA
Numerical, algebraic and graphical representation: Rates of change are worked numerically, algebraically using equations to find coordinates, and graphically by drawing a tangent and reading its gradient.AQA

O

Obtuse angle: An angle greater than 90° and less than 180°.Pearson Edexcel
Obtuse at C: A case where the calculator's acute answer is subtracted from 180°, because sin(180° - θ) = sin θ.AQA
odd and even forms: An even number is written as 2n and an odd number as 2n + 1, with n standing for any integer.Pearson Edexcel
Odd integer: An integer expressible as 2n + 1 for some integer n.Pearson Edexcel
one part value: When the question supplies a single share or a difference, find the value of one part first and build everything else from it.Pearson Edexcel
Operations with negative numbers: The rules for negative numbers, such as negative × negative = positive, apply to all number types.Pearson Edexcel
opposite: The side across from the chosen angle in a right-angled triangle.AQA
Opposite side: The side joining the two vertices other than the vertex of the specified angle.Pearson Edexcel
order of composition: With f(x) = 3x − 4 and g(x) = x + 2, fg(x) = 3x + 2 while gf(x) = 3x − 2, so the order changes the answer.Pearson Edexcel
order of operations: A strict order of priority for calculations: brackets, then indices (powers, roots), then division and multiplication left to right, and finally addition and…Pearson Edexcel
order of rotational symmetry: The number of matching positions in one full turn, counting the completed 360° position but not counting the start again.AQA, Pearson Edexcel
Ordered outcome: An outcome in which the positions or roles matter, so reversing different entries changes the result.Pearson Edexcel
ordered pair: Coordinates locate a point using an ordered pair (x, y), and reversing the order changes the point.AQA
ordering numbers: Putting values in size order, starting with reading the direction the question wants, smallest first or largest first.Pearson Edexcel
Ordinary form: Writing a number as a usual integer or decimal rather than as a coefficient multiplied by a power of ten.AQA
Orientation and congruence: Orientation describes the order of vertices (clockwise or anticlockwise), while position is where the shape sits on the grid; rotations, reflections and…AQA
Origin: The coordinate (0, 0), through which every direct-proportion graph y = kx passes.AQA, Pearson Edexcel
Original value: The quantity before a stated change, representing the 100% baseline for that change.Pearson Edexcel
Orthographic projection: A representation formed by parallel lines of sight perpendicular to a viewing plane.Pearson Edexcel
other plane figures: Includes polygons, which may be regular or irregular.AQA
Outcome: One possible result of an experiment or sequence of choices.Pearson Edexcel
Outlier: An extreme value that lies outside the main data distribution, identifiable using rules like being more than 1.5 × IQR below Q₁ or above Q₃.AQA, Eduqas, Pearson Edexcel
Outlier (Anomaly): A data point that differs significantly from other observations in the same dataset.Pearson Edexcel
outliers: Extreme values that distort the mean and range, so the median can be a more representative average.Pearson Edexcel
Outliers and causation: Outliers do not fit the pattern, and correlation does not prove that one variable causes the other.AQA
Output: The result obtained by applying the function to its input.Pearson Edexcel
Overestimate: An estimated value greater than the true value.AQA, Pearson Edexcel

P

Parabola: A symmetrical U-shaped curve created by a quadratic function, opening upwards if 'a' is positive and downwards if 'a' is negative.Pearson Edexcel
parallel: Coplanar lines that never meet, however far they are extended.Pearson Edexcel
Parallel and collinear vectors: Lines are parallel when one vector is a scalar multiple of the other; points are collinear when one vector between them is a scalar multiple of another and…Pearson Edexcel
Parallel distinct lines: Different straight lines with the same direction that never meet; non-vertical examples have equal gradients and different intercepts.Pearson Edexcel
Parallel lines: When a transversal line crosses them, alternate and corresponding angles are equal, while co-interior angles sum to 180°.AQA, OCR, Pearson Edexcel
Parallelogram: A quadrilateral with two pairs of parallel opposite sides.Pearson Edexcel
part to part comparison: A fraction comparing one share with another rather than with the whole, such as red being 3/5 of the number of blue.Pearson Edexcel
Part-to-part and part-to-whole comparison: Ratio compares quantities part-to-part or part-to-whole, while a fraction expresses a part relative to a whole.AQA
Part-to-part fraction: One quantity divided by another separate quantity.Pearson Edexcel
Part-to-whole fraction: A part divided by the complete total.Pearson Edexcel
part:part ratio: A ratio comparing one component with another component, rather than with their combined total.Pearson Edexcel
part:whole fraction: A fraction comparing one category with the total of all categories, for example 2/7 red in a 2:5 ratio.Pearson Edexcel
Part:whole ratio: A ratio comparing a component with the complete quantity that includes that component.Pearson Edexcel
parts of a circle: The centre, radius, chord, diameter, circumference, tangent, arc, sector and segment, each known by where it sits on a circle.Pearson Edexcel
parts of a whole: A ratio splits an amount into parts, and a fraction of the whole is the number of parts you want out of the total number of parts.Pearson Edexcel
percentage: A number of parts per hundred, which can be written as a fraction or a decimal.Pearson Edexcel
Percentage as parts per hundred: A number of parts per hundred, so 35% means 35/100 = 0.35.AQA
Percentage change and original value problems: Problems include finding a new value after an increase or decrease, and finding the original value when the new value and percentage change are known, using…AQA
Percentage decrease: The decrease divided by the original value, expressed as a percentage.Pearson Edexcel
Percentage increase: The increase divided by the original value, expressed as a percentage.Pearson Edexcel
percentage multipliers: A single multiplier used instead of finding the change and adding it on, such as 1.15 for a 15% increase or 0.85 for a 15% decrease.Pearson Edexcel
Percentage operator: A percentage used as a multiplication instruction: p% of x means (p/100) × x.Pearson Edexcel
Percentage point: A unit for the direct difference between two percentages, found by subtracting their percentage numbers.Pearson Edexcel
Perimeter: The total length of the boundary of a two-dimensional shape.Pearson Edexcel
Perimeter of a composite shape: Found by adding every outer edge, using the circumference formula for any circular arc and summing only the boundary edges, not internal dividing lines.AQA
period of a curve: The repeat length of a trigonometric graph: 360° for sine and cosine, and 180° for tangent.Pearson Edexcel
Periodic functions and their properties: y = sin x and y = cos x have a period of 360° and range from −1 to 1, while y = tan x has a period of 180°.AQA
Permitted inputs: The values for which a function is defined and which satisfy any stated restrictions.Pearson Edexcel
perpendicular: Lines that meet at a right angle of 90°.Pearson Edexcel
Perpendicular bisector: A line that passes through a segment’s midpoint at 90° to that segment.Pearson Edexcel
Perpendicular bisector and perpendiculars: The perpendicular bisector of a line segment is the set of points equidistant from the two endpoints, found by equal arcs from each endpoint.AQA
perpendicular height: The height that is at right angles to the base, never the slanted edge read off the diagram.AQA, Pearson Edexcel
perpendicular lines: Lines whose gradients multiply to −1, so each is the negative reciprocal of the other.AQA, Pearson Edexcel
perpendicular radius: The radius drawn to the point of contact is at right angles to the tangent there, so the tangent's gradient is the negative reciprocal of the radius gradient.Pearson Edexcel
pie chart: A display in which the whole circle of 360° is the total, and a category's angle is (frequency ÷ total) × 360°.Pearson Edexcel
Place value: This is key when working with very large or very small numbers and when calculating with decimals, for example the '4' in 3,400,000 is 4 hundred thousand.Pearson Edexcel
Place value in decimals: Comparing decimals column by column by aligning place value, so that 0.30 is greater than 0.25.AQA
Place value with very large or small numbers: Understanding and using place value when working with very large or very small numbers, using powers of ten, and when calculating with decimals.AQA
Plan: The view from directly above a 3D shape, showing the footprint.AQA, Pearson Edexcel
plan view: The view looking straight down from above, drawn flat with no perspective and no extra lines added to show depth.Pearson Edexcel
plane: A flat two-dimensional surface extending indefinitely.AQA, Pearson Edexcel
Plotting and reading from graphs: Plotting points accurately from a table of values and reading a value correctly from a graph, with clear construction lines shown.Pearson Edexcel
plotting points: Start at the origin (0, 0), move along the x axis, then move parallel to the y axis, reading the numbers on each axis first.Pearson Edexcel
Plotting points accurately on a scaled coordinate grid: Marking the coordinate pairs on axes with a suitable scale, with the x-value first and the y-value second.AQA
point: An exact position with no size, usually named by a capital letter.Pearson Edexcel
Point-gradient and y = mx + c forms: Substitute the point's coordinates into y = mx + c, or use the point-gradient form, to obtain the tangent's equation.AQA
Polygon: A closed two-dimensional shape with three or more straight sides.AQA, OCR, Pearson Edexcel
Polygon angle sums: For an n-sided polygon the interior angle sum is (n-2) × 180°, and the exterior angles of any convex polygon always sum to 360°.Pearson Edexcel
pooling results: Combining stages by taking total successes over total trials, rather than averaging the separate fractions.Pearson Edexcel
population: The entire group of interest, such as all shoppers at a supermarket, from which a sample is taken.Pearson Edexcel
Position n: The index identifying a term's place in the sequence; here n is a positive whole number starting at 1.Pearson Edexcel
position-to-term rule: Usually called the nth term, tells you what to do to the position number, so you can land on any term without the ones before it.AQA, Pearson Edexcel
Positive integer position: A permitted index 1, 2, 3, ...Pearson Edexcel
Power of ten: A number of the form 10^k, such as 10, 100 or 1000 for positive integer k.Pearson Edexcel
Powers and roots in scale-factor problems: To find a length scale factor from an area ratio, take the square root; from a volume ratio, take the cube root.AQA
powers of the same base: Multiplying these adds the indices, dividing them subtracts the indices, and raising one to another power multiplies the indices.Pearson Edexcel
Pressure: A comparison of force with area, calculated as force ÷ area, commonly in N/m² or pascals (Pa).AQA, Pearson Edexcel
prime factorisation: Writing a number as a product of prime factors, which can be found using a factor tree.Pearson Edexcel
Prime Number: A number that has exactly two factors: 1 and itself, for example 2, 3, 5 and 7.AQA, Eduqas, Pearson Edexcel
Prime numbers: A number that has exactly two factors, 1 and itself, so 2, 3, 5, 7, 11 and 13 are prime, while 1 is not prime.AQA
Principal: The original amount invested or borrowed on which interest is calculated.Pearson Edexcel
Principal square root: The non-negative square root denoted by $\sqrt{x}$ for $x\ge0$.Pearson Edexcel
Priority of operations: The agreed order: work inside brackets first, then powers and roots, then multiplication and division left to right, then addition and subtraction left to…AQA
prism: A solid with the same cross-section all along its length, with two identical end faces and rectangles joining them.Pearson Edexcel
prism volume: The area of the cross-section that stays the same all the way along multiplied by the length of the right prism.Pearson Edexcel
Prisms and pyramids: A prism has a constant cross-section with identical polygonal ends and rectangular sides, while a pyramid has a polygonal base and triangular faces meeting at…AQA
Probabilities summing to 1: When a set is both exhaustive and mutually exclusive, the probabilities sum to exactly 1.AQA
Probability: A numerical measure of the likelihood of an event, from 0 to 1 inclusive.Pearson Edexcel
probability scale: A line from 0 to 1 where 0 means impossible and 1 means certain, with words such as unlikely, even chance and likely marking places along it.Pearson Edexcel
Problem solving in context: Using the limits to solve a problem, choosing the upper or lower bound the context requires and writing a conclusion in words.Pearson Edexcel
Problem solving in two and three dimensions: Identifying the relevant triangle before choosing a method, such as a face diagonal or space diagonal, to find the required length or angle.AQA
Product rule for counting: If there are m ways of doing one task and for each of these there are n ways of doing another, the total number of ways is m × n.Pearson Edexcel
proper fraction: A fraction whose numerator has a smaller magnitude than its positive denominator, so its magnitude is less than 1.AQA, Pearson Edexcel
Properties of 3D shapes: These are identified by counting faces, surfaces, edges and vertices for each solid.AQA
Properties of quadrilaterals and triangles: Shapes are defined by a few core properties, from which others can be derived, and special types include square, rectangle, parallelogram, trapezium, kite and…Pearson Edexcel
Proportion: The statement that two ratios are equal, so that the two ratios describe the same multiplicative relationship even though the actual quantities may differ.AQA, Pearson Edexcel
Proportionality symbol, ∝: A symbol meaning 'is proportional to'.Pearson Edexcel
Pythagoras' theorem: A result derived from similarity or area arguments and used to find a missing side in a right-angled triangle, for example a² + b² = c² where c is the…AQA, Pearson Edexcel
Pythagoras’ theorem in three dimensions: Applying a² + b² = c² to a right-angled triangle within a two-dimensional or three-dimensional figure to find a length.AQA

Q

Quadrant: One of the four open regions formed by the coordinate axes, numbered anticlockwise from the top-right region.AQA
quadrants: The regions holding the branches: the first and third for positive k, the second and fourth for negative k.AQA
Quadratic equation: An equation involving a variable squared, reducible in one variable to ax² + bx + c = 0 with a ≠ 0.Pearson Edexcel
quadratic equations: Equations solved by factorising, completing the square or using the quadratic formula, which can have two, one or no real solutions.AQA, Pearson Edexcel
quadratic expression: A polynomial expression of degree two, such as ax² + bx + c with a ≠ 0.Pearson Edexcel
Quadratic factorisation: Reversing expansion by finding two numbers that multiply to c and add to b for expressions of the form x² + bx + c.AQA
quadratic formula: A method that runs off the coefficients alone, written as x = (−b ± √(b² − 4ac)) / (2a), and is the safe choice when nothing factorises neatly.Pearson Edexcel
Quadratic function: A function of the form y = ax² + bx + c whose graph is a parabola.AQA, Pearson Edexcel
quadratic graph: The graph of y = ax² + bx + c, where a ≠ 0; it is a parabola with highest x-power two.Pearson Edexcel
quadratic graphs: A smooth U shape called a parabola, which opens upwards when the x² term is positive and downwards when that term is negative.AQA, Pearson Edexcel
Quadratic inequalities in one variable: Inequalities solved by finding the critical values where the quadratic equals zero, then testing intervals to determine where the inequality holds.AQA
quadratic sequence: A sequence with a constant second difference, for example 2, 5, 10, 17, where first differences 3, 5, 7 have a second difference of 2.AQA, Pearson Edexcel
quadratic sequences: A sequence is quadratic when its second differences are constant.Pearson Edexcel
Qualitative Data: Non-numerical data that is descriptive or categorical.Eduqas

R

Radicand: The number or expression inside a root symbol.AQA
Radius: Any straight line segment from the centre to a point on the circle; all radii of the same circle are equal.AQA, Pearson Edexcel
Radius and tangent perpendicularity: The tangent is perpendicular to the radius, so its gradient is the negative reciprocal of the gradient of the radius joining the origin to that point.AQA
random: Describes a process where the next outcome is unpredictable.Pearson Edexcel
Random outcome: An outcome that is uncertain before the trial, even though its probability may be known.Pearson Edexcel
Random variation: Chance differences between experimental results and the underlying probabilities, including differences between repeated experiments.Pearson Edexcel
Randomness: Each trial is unpredictable, yet over many trials a pattern emerges.AQA
range: The largest value minus the smallest, measuring spread, and outliers stretch it.Pearson Edexcel
Rate: A ratio describing the amount of one quantity per unit of another quantity.Pearson Edexcel
Rate of change: The change in one quantity per unit change in another quantity.Pearson Edexcel
rates of pay: Money per unit time, found using pay rate = total pay ÷ hours worked.AQA
Ratio: An ordered comparison of quantities showing their relative sizes; multiplying all parts by the same non-zero factor gives an equivalent ratio.Eduqas, Pearson Edexcel
ratio and fraction: Two forms of the same relationship, where a phrase such as "two fifths of" signals the fraction form and a question can ask for either form.Pearson Edexcel
ratio notation: A way of writing a comparison of parts of the same kind using a colon, so 12 : 18 means twelve of one thing for every eighteen of another.AQA, Pearson Edexcel
Ratio notation and equivalent ratios: A ratio compares quantities in a fixed order, and two equivalent ratios can be equated to solve a missing-value problem.AQA
Ratio notation and ordering: Writing the relationship as a ratio in the correct order, with the quantity named first in the comparison going first.AQA
Ratio notation for comparison: Ratio notation can compare lengths, areas or volumes directly, so a length ratio 1 : 3 gives an area ratio 1 : 9 and a volume ratio 1 : 27.AQA
Ratio part: One equal-sized unit from which the quantities in a ratio are built.Pearson Edexcel
Ratio scale: A drawing-to-real length ratio expressed using identical units, such as 1:25 000.AQA
Rational Number: Any number that can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$.AQA, Eduqas, Pearson Edexcel
rationalise: Rewrite a fraction so that its denominator contains no surd, without changing its value.AQA, Pearson Edexcel
rationalising denominators: Multiplying numerator and denominator by the same root, or by the conjugate of a two-term denominator, so no root is left in the denominator.AQA, Pearson Edexcel
Rationalising the denominator: Rewriting a fraction as an equivalent fraction whose denominator is rational.AQA
ratios and fractions: A ratio a : b carries the same information as a fraction, where the fraction 2/5 compares one part with the other part while 2/7 compares one part with the…Pearson Edexcel
Ratios on a line: A point dividing a line in a given ratio, where the fractions of the whole line are taken from the total of the ratio, not one part over another.Pearson Edexcel
Ray: A straight part of a line with one endpoint, extending indefinitely in one direction.AQA
Real solution: A solution that is a real number, represented on the number line.Pearson Edexcel
Real-life ratio problems: Applying ratio to real contexts such as those involving conversion, comparison, scaling, mixing and concentrations.AQA
Rearrangement: Using equivalent operations on both sides of an equation to change its subject.Pearson Edexcel
Rearranging quadratic equations: Solving quadratic equations that need rearrangement before solving, by rearranging to ax² + bx + c = 0 and then choosing a method.AQA
rearranging to zero: Tidying up first, so that x(x + 4) = 12 must become x² + 4x − 12 = 0 before any method applies.Pearson Edexcel
Reasonableness check: A comparison of a proposed answer with expected size, sign, units or another valid calculation.Pearson Edexcel
Reasonableness of answers in context: Considering whether the size and unit of the answer make sense in context.AQA
Reasoning about the size of an estimate: Justifying the estimated value by establishing a clear mathematical interval or comparison.AQA
reciprocal: A number that multiplies the original non-zero number to give 1.AQA, Pearson Edexcel
reciprocal function: The function y = 1/x with x ≠ 0, whose graph has two separate branches in opposite quadrants and never touches the axes.AQA, Pearson Edexcel
Reciprocal graph: A graph that comes from an equation y = k/x, where k is a non-zero constant, and which splits into two separate branches.AQA
Reciprocal graphs: Graphs of the form y = k/x, showing that as one quantity increases, the other decreases, like speed and time for a fixed distance.Pearson Edexcel
reciprocals: A reciprocal is 1 divided by the number, so the reciprocal of 4 is 1/4 and of 2/3 is 3/2.Pearson Edexcel
Recognising powers of 2, 3, 4 and 5: Recalling the powers of 2, 3, 4 and 5 and linking each to its root.AQA
Recognition of undefined trigonometric ratios: Tan 90° is undefined and is not required by this statement.AQA
Rectangle: A quadrilateral with four right angles, equivalently a parallelogram with four right angles.Pearson Edexcel
Recurring decimal: A decimal with a digit or block of digits that repeats forever, shown by dots or a bar over the repeating part.AQA, Pearson Edexcel
recurring decimals: Decimals whose digits repeat forever, such as 0.454545..., and which can be changed into their corresponding exact fractions and back again.Pearson Edexcel
Reduction: Uses a scale factor between 0 and 1, which reduces every corresponding length.AQA
reference quantity: The quantity used as the denominator in a multiplicative comparison, such as blue in red/blue.Pearson Edexcel
Reflection: A transformation that flips a shape across a mirror line, such as the x-axis or the line y = x.Pearson Edexcel
reflection symmetry: A property where a line divides a shape into two mirror-image halves.Pearson Edexcel
reflections in axes: A minus sign outside, y = −f(x), reflects the curve in the x axis, while a minus sign inside, y = f(−x), reflects it in the y axis.Pearson Edexcel
Reflections in the x-axis and y-axis: A reflection flips the curve, either in the x-axis or in the y-axis.AQA
Reflex angle: An angle greater than 180° and less than 360°.AQA, Pearson Edexcel
Regular polygon: A polygon with all side lengths equal and all interior angles equal.AQA, Eduqas, OCR, Pearson Edexcel
Relative expected frequency: The expected proportion of times an outcome occurs over many trials, expressed on the 0 to 1 scale, found by dividing the expected frequency count by the…AQA, Pearson Edexcel
relative frequency: A frequency converted into a proportion, for example 18 out of 60 gives 0.3, interpreted in context as an estimate of probability.AQA, Eduqas, Pearson Edexcel
relative frequency estimates: A value from an experiment, written as a fraction, decimal or percentage, that settles closer to the theoretical value as trials increase.Pearson Edexcel
Remainder: The amount left after an integer division step, smaller than the positive divisor.Pearson Edexcel
repeated percentage change: Change handled with a decimal multiplier that is applied for each period, raised to the power n for n periods.AQA, Pearson Edexcel
Repeated root: A root occurring twice in the factorisation, giving one distinct x-value where the parabola touches the x-axis.Pearson Edexcel
repeating block: The block of digits that repeats forever, which appears as soon as a remainder comes round again in short division.AQA, Pearson Edexcel
Repetition: Using the same item more than once within a single outcome.Pearson Edexcel
Repetition allowed versus not allowed: When repetition is allowed the options stay constant, but when it is not allowed the choices reduce at each stage.AQA
Representing solution sets on a number line: Use an open circle for a strict inequality and a filled circle for inclusive inequalities, then draw an arrow or line from the circle indicating all values in…AQA
Residual / leftover sequence: The values obtained by subtracting an² from the original quadratic terms at matching positions.Pearson Edexcel
Restriction: A condition that determines whether a proposed outcome is allowed.Pearson Edexcel
resultant vectors: On a diagram this is the arrow you get by following the first and then the second nose to tail, drawn from the start of the first to the end of the second.Pearson Edexcel
Reverse bearing: The bearing along the same straight route in the opposite direction, differing by 180° with wrap-around at 360°.AQA
Reverse percentage: A calculation recovering an original value from a changed value, usually by dividing by the change multiplier.Pearson Edexcel
Reverse percentage problems: If a value has been increased by 20%, the original is recovered by dividing by 1.2, because 1.2 is the multiplier for a 20% increase.AQA
reverse percentages: Undoing the multiplier to find an original value, so a price of £42 after a 20% rise came from £42 ÷ 1.2 = £35.Pearson Edexcel
reversing the inequality sign: The extra rule that multiplying or dividing both sides by a negative number turns the sign round.Pearson Edexcel
Rhombus: A quadrilateral with four equal sides, equivalently a parallelogram with four equal sides.Pearson Edexcel
RHS: The right angle, hypotenuse and one other side of one right-angled triangle are equal to those of another, so the triangles are congruent.AQA
RHS congruence: Right-angled triangles are congruent when their hypotenuses and one corresponding other side are equal.Pearson Edexcel
right angle: An angle of exactly 90°, formed by perpendicular lines.Pearson Edexcel
Right-angled decomposition in two and three dimensions: Recognising when a general triangle can be decomposed into right-angled triangles and identifying the required construction or information.AQA
root: A value of the unknown that makes a one-variable equation true; for f(x) = 0, a value where the graph meets the x-axis.Pearson Edexcel
root-first evaluation: Take the root first when the numbers are friendly, since the intermediate value stays small.AQA
Roots: The x-values where y = 0, so they are the x-intercepts of the curve.AQA
roots and powers: Roots sit alongside the index laws: when a is zero or greater, √a × √a = a, and the same idea extends to cube roots and higher roots.Pearson Edexcel
Roots as inverse operations of powers: A root reverses a power, so the square root of 49 is 7 because 7 squared is 49.AQA
roots of a function: The solutions to f(x) = 0, which graphically are the x-coordinates where y = f(x) meets the x-axis.Pearson Edexcel
roots of a quadratic: The x values where the curve meets the x axis, so they are the solutions of the equation once y = 0.Pearson Edexcel
Rotation: A transformation that turns a shape about a centre of rotation by a given angle and direction, clockwise or anticlockwise.Pearson Edexcel
rotational symmetry: A shape has non-trivial rotational symmetry if a positive turn smaller than 360° about a centre maps it onto itself; otherwise its order is 1.AQA, Pearson Edexcel
Rounded value: A value expressed to the nearest specified rounding unit.Pearson Edexcel
Rounding unit: The increment to which a value is rounded, such as 1 cm, 10 cm or 0.1 kg.Pearson Edexcel
Ruler and compass constructions: Standard constructions use a ruler and compasses only, keeping arc marks visible.AQA

S

sample: A smaller part of a population that you collect data from.Pearson Edexcel
sample size: The number of trials run; a larger one makes the relative frequency settle closer to the theoretical probability.Pearson Edexcel
Sample space: The set of all possible outcomes of an experiment.AQA, Eduqas, Pearson Edexcel
Sample space diagrams: A representation that, with a two-way table, can be clearer for simultaneous events such as two dice, with outcomes treated as equally likely only when the…Pearson Edexcel
Sample spaces: Lists every outcome of an experiment, for example the six faces of a fair die for a single experiment.AQA
SAS: Two sides and the included angle of one triangle are equal to two sides and the included angle of another, so the triangles are congruent.AQA
scalar multiplication: Multiplying by a positive scalar changes the length of the arrow without turning it, so both components are multiplied, while a negative scalar reverses it.AQA, Pearson Edexcel
scale: A scale tells you how many real units one drawing unit stands for, such as 1 cm on the map being 25 000 cm on the ground.AQA, Pearson Edexcel
Scale bar: A marked line on a map or drawing labelled with the real distance it represents.AQA
Scale drawing: A drawing in which each represented length has a fixed proportional relationship to its corresponding real length.AQA, Pearson Edexcel
scale drawings: A representation of real distances at a fixed ratio, on a map always a reduction.Pearson Edexcel
Scale factor: The constant ratio between corresponding lengths in similar figures, being the ratio of a length in the image to the corresponding length in the original…AQA, Pearson Edexcel
scale factors: The number every length is multiplied by, with areas multiplied by k² and volumes by k³.Pearson Edexcel
Scale factors and equivalent ratios: In a proportion, both parts of the ratio are multiplied by the same non-zero scale factor, and the scale factor between the ratios can be identified and…AQA
Scaling using a unitary method: One known share is used to find the value of one part, then scaled to find the other share and the total.AQA
scatter graphs: A graph that plots paired bivariate data, one variable on the horizontal axis and the other on the vertical axis, with each point representing one item.AQA, Pearson Edexcel
Scientific calculator E notation: A display format in which E followed by an integer indicates multiplication by ten raised to that integer power.AQA
Seasonality: Regular repeating fluctuations in the values, revealed by a line graph.AQA
Second difference: The difference found after writing the first differences, which is constant for a quadratic sequence.AQA, Pearson Edexcel
second differences: These are set out under the sequence when testing for a quadratic, and all of them must be equal.Pearson Edexcel
Sector: The region bounded by two radii and the arc between them, like a slice of a cake.AQA, Pearson Edexcel
sector and segment: A sector is the region between two radii and an arc, while a segment is the region cut off by a chord.Pearson Edexcel
sector area: The area of a sector, found as (θ/360) × πr², a fraction of the circle's area πr² determined by the angle θ at the centre.AQA, Pearson Edexcel
sector perimeter: The arc plus the two straight radii, rather than the arc alone.Pearson Edexcel
Segment: The region bounded by a chord and the arc cut off by that chord.AQA, Pearson Edexcel
Selecting the appropriate rule for a given triangle: Choosing the correct rule and substituting accurately, paying attention to whether the angle is included between the two known sides.AQA
Sequence: An ordered list of terms generated or described by a rule.AQA, Pearson Edexcel
Sequence membership: Whether a target value occurs at an allowed position in the sequence.Pearson Edexcel
Set notation for solution sets: A way of writing the solution set, for example {x : 2 < x < 3} or {x : x ≤ −1} ∪ {x : x ≥ 4}.AQA
Setting up and solving proportion equations: An equation of the form a/b = c/d is set up, known values are substituted, and the unknown is found by cross-multiplying or by finding the scale factor…AQA
Sharing in a ratio: Dividing a given quantity into two parts in a given part:part or part:whole ratio by finding the total number of parts and the value of one part.Pearson Edexcel
Side elevation: The view from the side of the shape, showing the face seen from the side.AQA, Pearson Edexcel
Signed rate: A rate whose positive or negative sign indicates the direction of change of the quantity.Pearson Edexcel
Significant Figure: A digit counted towards a number’s stated accuracy, beginning with the first non-zero digit; later zeros can be significant.AQA, Eduqas, Pearson Edexcel
Significant figures: Counted from the first non-zero digit, so the zeros at the front never count.AQA, Pearson Edexcel
Silhouette/profile: The outer boundary of the projected shape, without its internal surface-edge detail.Pearson Edexcel
Similar: Two shapes are similar if they have the same angles and their corresponding sides are in proportion.Eduqas, Pearson Edexcel
Similar figures: Figures that have equal corresponding angles and corresponding lengths in a constant ratio called the scale factor.AQA
similar shapes: Shapes where every length is multiplied by the same scale factor k.AQA, Pearson Edexcel
Similarity: A relationship between shapes with the same shape but possibly different sizes, where corresponding angles are equal and the ratio of corresponding side…AQA, Pearson Edexcel
Similarity and scale factors: Similar shapes have equal corresponding angles and corresponding lengths in a fixed ratio, and if the length scale factor is k then every length is multiplied…AQA
similarity criteria: Equal corresponding angles together with corresponding sides in the same ratio, so that one shape is an enlargement of the other.Pearson Edexcel
simple cubic function: A function of the form y = ax³ + bx² + cx + d with a ≠ 0, which has either two or no turning points.AQA
Simple geometric progression: A sequence that multiplies by a fixed rational ratio r greater than 0, written rⁿ for integer n.AQA
simple interest: Interest that adds the same amount each year, so £500 at 4% for 3 years earns £500 × 0.04 × 3 = £60.Pearson Edexcel
Simple interest in financial mathematics: Calculated on the original amount only, using interest = principal × rate × time, and is common in financial mathematics.AQA
Simple proof: Starting from known results, stating each step with a reason, and reaching the required conclusion without gaps.AQA
simplest form: The result of dividing every part of a ratio by the same number until nothing divides again, as 12 : 18 becomes 2 : 3.AQA, Pearson Edexcel
Simplest whole-number form: A ratio whose entries are whole numbers with no common factor greater than 1.Pearson Edexcel
Simplification and equivalent forms: Dividing all parts of a ratio by their highest common factor and cancelling common factors in fractions, since the same relationship can be represented in…AQA
Simplification of expressions: Questions may ask for an expression to be simplified to a single power.Pearson Edexcel
Simplifying fractions: Dividing the numerator and denominator by their highest common factor to reach the simplest form.AQA, Pearson Edexcel
simplifying surds: Splitting a surd at its largest square factor, such as writing √50 as √25 × √2 = 5√2.Pearson Edexcel
Simultaneous equations: Equations solved together where one is linear and the other is quadratic at Higher tier.AQA, Pearson Edexcel
sine rule: Use a/sin A = b/sin B = c/sin C when you know a side together with the angle opposite it, plus one more side or angle.Pearson Edexcel
Single power: An expression with one base and one index, such as $2^3$.Pearson Edexcel
sketch: A clear drawing, not necessarily to scale, that communicates the required facts.Pearson Edexcel
Sketching curves using key features: Moving or flipping the whole curve rather than plotting many individual points, then marking key features such as intercepts, turning points and asymptotes…AQA
slant height: The length denoted by l in the curved surface area of a cone, πrl.AQA
Slant height of a cone: For a right circular cone, the straight-line distance along its curved surface from the apex to the base circumference.AQA
Solution: An allowed value, or set of values, that makes an equation or inequality true.Pearson Edexcel
solution of a quadratic equation: A value of the unknown that makes a quadratic equation true; when the equation is f(x) = 0, its solutions are the function’s roots.Pearson Edexcel
Solution or root: A value of the unknown that makes the equation true.Pearson Edexcel
Solution pair: An ordered pair (x, y) making both original equations true.Pearson Edexcel
Solution pair / ordered pair: A pair (x, y), written in that order, that satisfies both original equations.Pearson Edexcel
Solving trigonometric equations graphically: The graphs are used to solve simple trigonometric equations for angles of any size, including negative angles.AQA
special triangles: The half equilateral triangle and the unit square cut along its diagonal, from which the values come.Pearson Edexcel
speed: Distance per unit time, found using speed = distance ÷ time.AQA, Pearson Edexcel
Speed-time graphs and acceleration: Graphs showing how speed changes, where the gradient represents acceleration and a horizontal line means constant speed.Pearson Edexcel
splitting the middle term: Writing the middle term as two numbers that multiply to ac and add to b, as with 2x² + 7x + 3 where 6 and 1 fit.Pearson Edexcel
Square: A quadrilateral with four equal sides and four right angles.Pearson Edexcel
Square factor: A factor that is the square of an integer.AQA
Square number: A number formed by multiplying an integer by itself.Pearson Edexcel
Square numbers: A sequence such as 1, 4, 9, 16, 25, ...AQA
Square, cube and higher real roots: The associated real root reverses the process of a power, so a square root, cube root or higher root gives the number whose power equals the given value.AQA
Squared and cubed scale factors: Area units use squared scale factors and volume units use cubed factors when changing between units.AQA
Squared and cubed unit notation: Writing units as cm² and m³, and distinguishing area units from volume units.AQA
SSS: Three sides of one triangle are equal to three sides of another, so the triangles are congruent.AQA
Standard Form: A way of writing numbers as $A \times 10^n$, where $1 \leq A < 10$ and $n$ is an integer.AQA, Eduqas
Standard form notation: A way of writing a number as A × 10ⁿ, where A is at least 1 and less than 10, and n is an integer.AQA
standard formulae: Formulae that link quantities by a rule, which you are expected to recall and use as they stand, such as area of a circle = πr² and speed = distance ÷ time.Pearson Edexcel
Standard unit: A recognised unit used to measure a quantity, such as metre for length, kilogram for mass or second for time.Pearson Edexcel
Standard units of measure: Units used for length, area, volume or capacity, mass, time and money, such as mm, cm, m and km for length.AQA
Starting value: The value x₀ chosen before repeatedly applying the formula xₙ₊₁ = g(xₙ).AQA
Stationary: Not moving; on a distance-time graph this is represented by a horizontal section with zero gradient.Pearson Edexcel
Straight-line distance: The length of the direct segment joining two points, not the sum of a multi-leg route between them.AQA
strict inequality: A comparison using < or > that excludes equality.Pearson Edexcel
Subscript notation: A way of labelling terms by position, where x_0 is the starting value and x_{n+1} is the next term after x_n.AQA
Substitution: Rearranging the linear equation to make one variable the subject, then substituting this expression into the quadratic equation.AQA, Pearson Edexcel
substitution method: Making one letter the subject and replacing it in the other equation.Pearson Edexcel
Subtended angle: The angle formed at a specified vertex by lines joining that vertex to the two endpoints of an arc or chord.AQA, Pearson Edexcel
successive approximations: The terms produced by taking the starting value the question supplies and feeding each answer back in, settling towards the root.Pearson Edexcel
Successive terms: Further terms of a sequence generated from a given formula and starting value by applying the rule repeatedly in the correct order.AQA
suitable degree of accuracy: The accuracy worth quoting, found by rounding both bounds to the same accuracy and quoting the most accurate value at which the two agree.Pearson Edexcel
Surd: An irrational root expressed exactly, such as $\sqrt2$ or $\sqrt[3]{5}$.AQA, Pearson Edexcel
surd common ratio: The ratio between successive terms of a geometric progression when that ratio is a surd, found by dividing one term by the term before it, such as dividing…Pearson Edexcel
Surface area: The combined area of the surfaces specified for a three-dimensional object, measured in square units.AQA, Pearson Edexcel
Surface area and volume: For 3D solids, formulae for volume and surface area are required, and for composite solids the volumes are added while only external faces are added.Pearson Edexcel
Symmetry in polygons: Polygons can have reflectional symmetry (lines of symmetry) and rotational symmetry, where the order is how many times it fits onto itself in a full turn.Pearson Edexcel
Systematic list: A list produced using a consistent ordering rule so that all allowed possibilities can be included exactly once.Pearson Edexcel
Systematic listing: A method that ensures all possible outcomes are found without repetition or omission, for example by fixing the first item and cycling through all options for…AQA, Pearson Edexcel
Systematic listing of outcomes: Listing all possible outcomes or members of sets systematically so none are missed or repeated, following a fixed order.AQA

T

table of values: A short table built by choosing three x values and working out y for each, then plotting the points and joining them with a ruler.Pearson Edexcel
Tables and grids for combinations: A table or grid is ideal when two choices combine, such as listing pairs from rolling two dice.AQA
Tables and tree diagrams: Organisational tools that support systematic listing, with a table or tree diagram efficient when there are two or more categories.AQA
tally chart: Used to count items in each category when constructing a frequency table from raw data.Pearson Edexcel
Tangent: A straight line that touches the circle at exactly one point, called the point of contact, and is perpendicular to the radius drawn to that point.AQA, Eduqas, Pearson Edexcel
Tangent and chord methods for curves: A chord gives the gradient between two points on a curve, while a tangent drawn at one point is used to estimate the gradient there.AQA
Tangent and chord properties: A radius is perpendicular to a tangent at the point of contact, tangents from an external point are equal in length, and the perpendicular from the centre to…Pearson Edexcel
tangent and radius: A tangent touches the circle at exactly one point, while a radius joins the centre to the curve.Pearson Edexcel
tangent to a circle: A tangent touches the circle at one point and is at right angles to the radius drawn to that point.Pearson Edexcel
tangent to a curve: A line that touches the curve at a point; it is extended well across the grid, then its rise is divided by its run to find the gradient.Pearson Edexcel
Tens digit: The digit showing the number of tens in a two-digit whole number.Pearson Edexcel
Term: An additive part of an expression at the level being considered, including its attached positive or negative sign.AQA, Eduqas, Pearson Edexcel
Term number: The position of a term, conventionally denoted n.Pearson Edexcel
term-to-term rule: Tells you what to do to one term to reach the next one, so it only works if you are also told where the sequence starts.AQA, Pearson Edexcel
terminating decimal: A decimal representation that ends after finitely many decimal places, equivalently with all later digits zero.Pearson Edexcel
Terminating decimals: A decimal that has a finite number of digits.Pearson Edexcel
The 0 to 1 probability scale: A scale on which 0 is impossible, 1 is certain and 0.5 is an even chance.AQA
Theoretical probability: A probability that assumes equally likely outcomes, stated as a fraction or decimal between 0 and 1 inclusive, or as a percentage between 0% and 100%.AQA, Pearson Edexcel
Theoretical probability distribution: The set of expected probabilities, which can be uniform or non-uniform.AQA
three-figure bearings: An angle measured from north, turning clockwise, and always written with three figures.Pearson Edexcel
time calculations: Working with time, which is not decimal, so 2.5 hours means 2 hours and 30 minutes.Pearson Edexcel
Transformations on a coordinate grid: Rotation, reflection, translation and enlargement change a shape's position or size, often on a coordinate grid.Pearson Edexcel
Transformations on coordinate axes: Rotation, reflection, translation and enlargement applied to shapes while tracking vertex coordinates through each transformation.AQA
Translation: A movement that moves every point of a shape by the same distance and direction, described using a 2D column vector.AQA, Pearson Edexcel
translation on a grid: A slide that moves every point of a shape the same distance in the same direction, so the image is congruent to the object and keeps the same way up.Pearson Edexcel
Translation vector: A column vector whose top entry is the horizontal displacement and bottom entry is the vertical displacement.Pearson Edexcel
translations of curves: A number added outside the function moves the whole curve up or down, while a change inside the bracket moves the curve sideways in the opposite direction to…Pearson Edexcel
Transversal: A line that passes through two or more lines in the same plane at distinct points.OCR
Trapezium: Under this guide's stated inclusive convention, a quadrilateral with at least one pair of parallel opposite sides.AQA, Pearson Edexcel
trapezium area: Half of the sum of the two parallel sides multiplied by the gap between them, where the gap is perpendicular to the parallel sides.Pearson Edexcel
trapezium strips: Strips of equal width with heights read off the curve; they overestimate when the curve bends upwards and underestimate when it bends downwards.Pearson Edexcel
Tree diagram: A branching representation of successive choices or events in which each complete path represents a sequence.Pearson Edexcel
tree diagrams: A representation used for sequential events, where probabilities are multiplied along each path and non-overlapping paths are added when any satisfies the…Pearson Edexcel
Tree diagrams and other representations: Diagrams showing each stage with branches whose probabilities sum to 1, alongside two-way tables, Venn diagrams and outcome grids.AQA
Trend: The overall direction of the values over time, revealed by a line graph.AQA
Trial: One performance of the random experiment being considered.Pearson Edexcel
triangle area formula: Area = ½ab sin C gives the area of any triangle from two sides and the angle between them.Pearson Edexcel
Triangle inequality: In a non-degenerate triangle, the sum of any two side lengths is greater than the third.Pearson Edexcel
Triangle labelling convention: For triangle ABC, vertices are capital letters, and the side opposite is the corresponding lowercase letter, with an angle written as ∠ABC and the vertex B in…Pearson Edexcel
Triangular number: A total formed by adding consecutive positive integers beginning with 1.Pearson Edexcel
Triangular numbers: A sequence such as 1, 3, 6, 10, 15, ...AQA
trigonometric graphs: The graphs of y = sin x and y = cos x wave between −1 and 1, while the tangent graph rises without limit as the angle approaches 90°.Pearson Edexcel
trigonometric ratios: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse and tan θ = opposite/adjacent, where θ is an angle in the triangle.AQA, Pearson Edexcel
Trigonometric ratios in right-angled triangles: For a chosen acute angle, sin = opposite ÷ hypotenuse, cos = adjacent ÷ hypotenuse and tan = opposite ÷ adjacent.AQA
Trigonometry in right-angled triangles: Applying the trigonometric ratios sin, cos or tan to find an angle or length in a right-angled triangle within a two-dimensional or three-dimensional figure.AQA
True value: The actual value of a quantity before the stated rounding or truncation.Pearson Edexcel
Truncation: Removing digits after a stated place without rounding the remaining digits.Pearson Edexcel
truncation versus rounding: Truncation chops the digits rather than rounding them, so a truncated 8.3 cm gives 8.3 ≤ x < 8.4.Pearson Edexcel
Turning point: The lowest point of an upward parabola or the highest point of a downward one, sitting halfway between the two crossings when the curve crosses the x axis…AQA, Pearson Edexcel
Turning point / vertex: The point where the quadratic changes from decreasing to increasing, or increasing to decreasing; it is the minimum or maximum point.Pearson Edexcel
turning point coordinates: Read from the completed square y = (x + p)² + q as (−p, q), because the square can never be negative and its smallest value is 0 when x = −p.Pearson Edexcel
Two-way frequency table: A table classifying a population by two categories and recording their joint frequencies.Pearson Edexcel
two-way tables: A table with rows and columns that lists outcomes by cycling through all second choices before moving to the next first choice.Pearson Edexcel

U

Unbiased sample: A sample in which every outcome has its fair chance and the sample does not favour specific outcomes.AQA
unbiased samples: Results from an experiment with no bias, whose relative frequency tends towards the theoretical probability distribution as the sample size increases.Pearson Edexcel
Undefined: Having no defined numerical value under the stated operation, for example division by zero in real-number arithmetic.AQA, Pearson Edexcel
Undefined expression: An expression with no assigned value under the number system and rules being used; in this topic, $0^{-1}$ is undefined because it requires division by zero.Pearson Edexcel
Undefined gradient: The gradient of a vertical line is undefined because the horizontal change is zero and division by zero is not defined.AQA
Underestimate: An estimated value less than the true value.Pearson Edexcel
Underlying assumptions such as with or without replacement: The assumptions behind a calculation, including independence, fair or biased equipment, and whether selection is with or without replacement.AQA
unfamiliar sequences: Any sequence whose rule you can state, in words or in algebra, such as 1/2, 2/3, 3/4, 4/5 with nth term n/(n + 1), creeping towards 1.Pearson Edexcel
Ungrouped discrete numerical data: Separate values that can be counted, such as the number of pets per student, for which you use a vertical line chart where each value has a vertical line…AQA
Union: The event that at least one of the named events occurs, including the possibility that both occur.Pearson Edexcel
union and intersection: The union is everything in either set, while the intersection is only the overlap.Pearson Edexcel
Union, A ∪ B: The outcomes in A or B or both, with each outcome counted once.Pearson Edexcel
Unit circle: A circle of radius 1 centred at the origin, with a point at angle θ having coordinates (cos θ, sin θ).Pearson Edexcel
Unit consistency: Keeping units consistent, including converting between compatible units such as 1 m³ = 1 000 000 cm³, before comparing or calculating.AQA
unit conversion: Changing a measurement into another unit, such as putting every length into the same unit before calculating, with area and volume factors being the length…Pearson Edexcel
Unit conversion before comparison: Quantities must be in the same unit before forming the fraction; convert first, then simplify.AQA
unit fraction index: A unit fraction index means a root: a^(1/n) is the nth root of a.AQA
Unit price: Cost per unit quantity, found by dividing cost by the mass, volume or number of items.Pearson Edexcel
unit pricing: Cost per unit quantity, found using price per unit = total price ÷ number of units.AQA
Unit rate: The amount of one quantity corresponding to one unit of another, with units stated in the same order as the division.Pearson Edexcel
unitary method: Finding the cost of one item first, so if 4 pens cost £3 then one pen costs £0.75 and 10 pens cost £7.50.Pearson Edexcel
Unitary ratio: A ratio with one part equal to 1, obtained by dividing both parts by the same non-zero quantity.AQA
Universal set: All elements under consideration in a set problem.Pearson Edexcel
Unranked pair: A choice of two distinct items in which neither item has a different position or role.Pearson Edexcel
upper and lower bounds: The limits of accuracy of a rounded measurement, written down for every measurement before any calculation with bounds is started.Pearson Edexcel
Upper and lower bounds in calculations: Used in calculations with rounded values, where the lower bound is the stated value minus half the unit and the upper bound is the stated value plus half the…AQA
Upper limit: The boundary that would round to the next value up.AQA, Pearson Edexcel
upper quartile: The value three quarters of the way through the ordered data.AQA
Use of special triangles to derive values: A reliable method is to sketch the graphs or use the special triangles: a 30°–60°–90° triangle with sides 1, √3 and 2, and a 45°–45°–90° triangle with sides…AQA
Using graphs to find approximate roots: Plotting or reading the curve y = ax² + bx + c and identifying where it crosses the x-axis, as those x-intercepts are the approximate roots.AQA
Using proportion to find unknown lengths and angles: Missing lengths follow from a proportion such as a/A = b/B, and substituting known values finds an unknown side or angle.AQA
Using the quadratic formula: The formula x = (-b ± √(b² - 4ac)) / (2a) solves any quadratic in standard form, substituting the correct values of a, b and c including negative signs.AQA

V

Value of one part: The amount represented by one equal unit of the ratio.Pearson Edexcel
Variable: A symbol representing a number that can vary or whose value is not yet specified.Pearson Edexcel
Vector arithmetic (diagrammatic and column): Addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors.Pearson Edexcel
Vector notation and representation: A vector has both magnitude and direction, and in column form a vector from A to B is written as a column pair.AQA
Venn diagrams for sets and their regions: A diagram useful for showing sets, their intersections and unions, and counting elements in each region.AQA
verify by substitution: Always check the result by substituting at least two values, such as n = 3, to match a term.AQA
Vertex: Where edges meet; a cone has one vertex at the apex and a sphere has none.AQA, Pearson Edexcel
Vertex form: A quadratic rewritten by completing the square from expanded form, which exposes the turning point directly.AQA
Vertical and horizontal translations: A translation shifts the whole curve without turning it over, either vertically by a units or horizontally by −a units.AQA
Vertical asymptote: A vertical line x = a that a graph approaches as its function values become unbounded near x = a.Pearson Edexcel
vertical asymptotes: Lines at 90° and every 180° after that, where the tangent graph is drawn as separate branches because it rises without limit.Pearson Edexcel
Vertical intercept: The value of y when x = 0, equal to c in y = mx + c.Pearson Edexcel
Vertically opposite angles: When two straight lines cross, these angles are equal.AQA, OCR
views of 3D solids: Flat drawings in which an edge lying across your view is drawn its true length, while one sloping away looks shorter than it is.Pearson Edexcel
Visible edge: An edge or surface boundary that can be seen from the specified viewing direction without being completely obscured by a nearer face.Pearson Edexcel
Volume: The amount of three-dimensional space occupied by a solid or contained in a region, measured in cubic units.AQA
Volume and capacity: Related concepts linked by the facts that 1 cm³ = 1 ml and 1 m³ = 1000 litres.AQA
volume scale factor: When the length scale factor is k, every volume is multiplied by k³, because volume is built from three lengths.Pearson Edexcel

W

Without replacement: A selection process in which the chosen item is not returned before the next selection.Pearson Edexcel

X

x-axis: The horizontal axis; every point on it has y = 0.AQA
x-coordinate: Gives horizontal position from the origin: positive values lie to the right, negative values to the left.AQA
x-intercept: The point where the line crosses the x axis, found by setting y = 0.AQA, Pearson Edexcel
x-intercept or root: An x-intercept is a point where the graph meets the x-axis, so y = 0; a root is its x-coordinate.Pearson Edexcel

Y

y = mx + c: The form of a linear function in which m is the gradient and c is the y-intercept.AQA
y-axis: The vertical axis; every point on it has x = 0.AQA
y-coordinate: Gives vertical position: positive values lie above the origin, negative values below.AQA
y-intercept: The value of y where the line meets the y axis, which is the number on its own once the equation has y by itself.AQA, Pearson Edexcel

Z

zero product rule: If a product is zero, at least one factor must be zero, so each bracket is set equal to zero to form separate linear equations.Pearson Edexcel
zero-product property: If a product is zero, at least one factor must be zero.Pearson Edexcel

Other terms

2D column vector: Written as a column with horizontal movement on top and vertical below, where positive top means right and positive bottom means up.AQA
π as an exact symbol: Treating π as an algebraic symbol and retaining it in the final answer rather than converting to a decimal.AQA

Where these terms come from

Each definition is one we publish on a Mathematics GCSE topic page or study guide. Open a term to see how each exam board words it and which topic it belongs to. For the full course, go to Mathematics revision or the glossary for every subject.

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