Mathematics A-Level

Mathematics A-Level glossary

1309 key terms for Mathematics A-Level, A to Z, each linked to the topic pages that use it.

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A

Abstraction: Representing the situation with variables, equations, diagrams or functions.AQA
Acceleration: The rate of change of velocity, a vector, so an object can accelerate by changing direction even at constant speed.AQA, Pearson Edexcel, WJEC
Acceptance region: The set of values of the test statistic that do not lead to rejection of H₀ at the stated significance level.AQA
Accumulation functions and their derivatives: An integral with a variable limit can be differentiated; when the upper limit is a function of x, the chain rule must be used.AQA
accuracy and rounding: Rounding solutions to a degree of precision justified by the input data, avoiding inappropriate precision such as giving money to four decimal places.WJEC
Accurate recording: Recording inputs and outputs clearly, with units, for example in a table or graph, and being prepared to explain what the outputs mean.Pearson Edexcel
action-reaction pairs: Pairs that are equal in magnitude, opposite in direction, of the identical physical nature, and act on two different bodies.WJEC
actual significance level: For discrete distributions, the value equal to P(X in critical region | H₀ is true), which may be strictly less than the nominal α.WJEC
Adaptive problem solving: Adjusting the chosen route when an intermediate result shows the original plan needs revision, rather than expecting a single remembered procedure to finish…Pearson Edexcel
addition and subtraction identities: Formulas where cos has minus for addition and plus for subtraction, and tan has (tan A ± tan B) / (1 ∓ tan A tan B).WJEC
addition rule: For mutually exclusive events, the probability of A or B is found by adding their probabilities.AQA, WJEC
algebraic division: A method required for improper algebraic fractions, dividing a polynomial P(x) by a linear divisor (ax + b) to produce a quotient Q(x) and a constant…WJEC
Algebraic division by linear expressions: Dividing a polynomial by a linear expression by long division or by comparing coefficients, stating the quotient and remainder correctly.Pearson Edexcel
algebraic limit evaluation: Applying these approximations to rational expressions enables the evaluation of limits as θ → 0.WJEC
Algebraic manipulation: Using the laws to simplify expressions, expand or condense logarithmic forms, and combine multiple laws, for example writing 2 log_a(x) − log_a(y) as…AQA
algebraic modelling: Setting up suitable variables and defining the algebraic relationships representing the scenario, transforming the contextual problem into an abstract…WJEC
algebraic preparation: Prior to differentiating, expressions must be rewritten as sums of individual power terms Axⁿ, splitting algebraic fractions and expanding products.WJEC
algebraic probability: Solving algebraic probability equations to find unknown intersections or conditional terms, without requiring diagrams.WJEC
Algebraic rearrangement and factorisation: Looking for common factors and factorising first where necessary to enable separation, and rearranging the solution to the required form.AQA
algebraic simplification: Applying logarithm laws before differentiating can simplify complex arguments, such as splitting a quotient into a difference of logarithms.WJEC
algebraic splitting: Splitting fractions over a single monomial denominator into individual power terms Axⁿ before integrating.WJEC
Alternative hypothesis: Written H₁, it states the direction or difference being tested against the null hypothesis.Pearson Edexcel
Alternative hypothesis (H₁): The statement that contradicts H₀ and specifies the direction or difference being investigated.AQA
ambient temperature baseline: The room temperature θ_room ignored by a decay prediction that approaches zero, giving the baseline refinement θ(t) = θ_room + (θ₀ − θ_room)e^(−kt).WJEC
ambiguous case: May yield two valid angle solutions since sin θ = sin(180° − θ), arising when given two sides and a non-included angle.WJEC
Amplitude: Sin and cos have amplitude 1, while tan has no amplitude.AQA, Pearson Edexcel
analytical methods: Methods that seek exact closed-form solutions through algebraic manipulation and standard integration techniques.WJEC
Analytical solution: Expressing the answer exactly in terms of known functions, which some equations cannot be rearranged into.Pearson Edexcel
Analytical vs numerical solutions: Many mathematical problems cannot be solved analytically, but numerical methods permit solution to a required level of accuracy.AQA
angle in a semicircle: A right angle, so a triangle with a diameter as one side has a right angle at the circumference.Pearson Edexcel, WJEC
angle of friction: An angle from which the coefficient of friction can be calculated under limiting equilibrium conditions.WJEC
Antiderivative: A function F(x) such that F'(x) = f(x), used to evaluate the definite integral of f(x).AQA, Pearson Edexcel, WJEC
Antilogarithm: The inverse operation of taking a logarithm: $10^c$ reverses $\log_{10}$ and $e^c$ reverses $\ln$.Pearson Edexcel
Application of initial conditions: Substituting the given x and y values into the integrated equation to solve for C and obtain the particular solution.AQA
Application of mathematical models to explore scenarios: Using the model to generate predictions or explore 'what if' scenarios by varying inputs, such as a range of values or extreme cases.AQA
Applications of calculus: The result is applied to contextual problems, such as finding the rate of change from a given exponential model or the gradient at a specific point.AQA
Applications of trigonometry to vectors: Resolving vectors into components using sine and cosine, or finding angles using the cosine rule on a vector triangle.Pearson Edexcel
applied numerical methods: Methods used to solve problems in context where governing equations lack exact analytical solutions.WJEC
Appropriate precision: Rounding or presenting results at a level of precision appropriate to the context, rather than quoting an excessive number of significant figures.Pearson Edexcel
Appropriateness evaluation: Checking whether outputs are realistic and assumptions reasonable, relative to the model's intended purpose and required accuracy.AQA
Approximate solution of equations: If the sequence converges, its limit is a root of the original equation, so the iteration approximates that root.Pearson Edexcel
Approximation and convergence: Iterations are carried out until a required degree of accuracy is reached, with convergence shown by the behaviour of successive iterates.AQA
Approximation and error: Numerical methods approximate solutions when exact algebra is impractical, continuing until the required accuracy is reached.AQA
Approximation sign, ≈: A symbol meaning ‘is approximately equal to’; it does not state an exact equality.Pearson Edexcel
Approximation using series expansions: Substitute a small value of x and truncate the series, ensuring the validity condition holds.AQA
arc length: Of a circle of radius r subtending angle θ, given by s = rθ.WJEC
Arc length and sector area: For θ in radians, arc length is l = rθ and sector area is A = ½r²θ.Pearson Edexcel
Arcsin, arccos and arctan: Inverse trigonometric functions that return an angle for a given ratio, restricted to principal ranges because sine and cosine are periodic.Pearson Edexcel
Area between curves: Found by integrating the difference between the upper curve and the lower curve, ensuring the integrand is always (upper curve) − (lower curve).AQA, Pearson Edexcel, WJEC
Area between two curves: Found by integrating the upper curve minus the lower curve over the interval between their intersection points.Pearson Edexcel
area of a triangle: Given by Area = ½ab sin C, which requires two sides and the sine of their included angle.Pearson Edexcel, WJEC
Area of a triangle using ½ab sin C: A formula giving the area of a triangle as ½ab sin C, applied when two sides and the included angle are known.AQA
area proportional to frequency: The property that the area of each bar is directly proportional to class frequency, with frequency = k × area.WJEC
Area under a curve: The area enclosed between a curve y = f(x), the x-axis, and the vertical boundary lines x = a and x = b, calculated using definite integration.AQA, Pearson Edexcel, WJEC
Area under a curve as accumulation: The area between a velocity–time graph and the time axis gives displacement, with areas below the time axis counting as negative displacement.AQA
Area under a rate graph: The area between a velocity–time graph and the time axis gives displacement, with areas above the axis counted positive and areas below counted negative.Pearson Edexcel
area under the graph: On a velocity-time graph, area above the time axis represents positive displacement, whereas area below represents negative displacement.WJEC
Argument: The complete input of a function.Pearson Edexcel
Arithmetic: Describes a pattern with a constant difference between terms.Pearson Edexcel
arithmetic progression: A sequence with a constant common difference d between consecutive terms, so that uₙ₊₁ − uₙ = d.WJEC
Arithmetic sequence: A sequence that increases or decreases by a fixed common difference, d.AQA, WJEC
ascending powers of x: The order in which the expansion is expressed, with coefficients evaluated accurately.WJEC
Assumption: A condition or fact that is given and may be used as the starting point of an argument.WJEC
Assumption review: Examining the simplifying assumptions of a model and identifying specific ones that could be refined or removed.Pearson Edexcel
Assumptions: Things a probability model takes as given, such as independence, equal likelihood, or constant probability.AQA
Assumptions and limitations: Explaining the assumptions or limitations that affect the interpretation of the output, stating how they affect its validity.AQA
Assumptions and validity: Specific assumptions such as constant acceleration or no air resistance, whose failure limits how valid the model is.Pearson Edexcel
Asymptote: A line that the curve approaches but does not cross, such as the axes for y = a/x.AQA, OCR, Pearson Edexcel
Asymptotes: For y = a/x and y = a/x², the axes act as vertical and horizontal asymptotes, so the curve approaches but never touches them.AQA, Pearson Edexcel, WJEC
asymptotes of tan: Vertical asymptotes occur at odd multiples of 90° (or π/2) because cos x = 0, where the tangent function is undefined.WJEC
Asymptotic behaviour and intercepts: When a>1 the graph increases and y=0 is a horizontal asymptote as x→-∞; when 0<a<1 it decreases and y=0 is an asymptote as x→+∞.AQA
asymptotic limits: The long-term behaviour of the solution as t → ∞ in context, where exponential decay terms e^(−kt) approach 0, revealing steady-state or terminal values.WJEC
axis intercepts: The y-intercept occurs at (0, c), while the x-intercepts, or roots, are determined by setting f(x) = 0.WJEC

B

Base: The large number or letter that is being multiplied by itself.Pearson Edexcel
baseline intercept: The regression parameter a, interpreted within the practical context of the scenario.WJEC
Bearing: A direction measured clockwise from North, conventionally written as a three-figure angle.Pearson Edexcel
binomial approximation: Choosing a suitable small value of x and computing more terms to get closer to the true value, with error controlled by the discarded higher-order terms.WJEC
binomial approximations: Calculated for decimal powers by substituting small values of x into the expansion.WJEC
Binomial coefficient: ${n\choose r}=n!/[r!(n-r)!]$, the coefficient used in the rth choice of a binomial expansion.AQA
binomial coefficients: Quantities that quantify combinations and generate the entries of Pascal's triangle.WJEC
Binomial coefficients and powers: In P(X = r) = C(n, r) pʳ (1 − p)ⁿ⁻ʳ, C(n, r) is the binomial coefficient, with pʳ and (1 − p)ⁿ⁻ʳ as the powers.Pearson Edexcel
Binomial conditions: A fixed number of trials, two outcomes, independence and constant success probability must all be checked.AQA
Binomial distribution: The model used for a binomial test, in which the test statistic is the number of successes and is compared with critical values or a p-value.AQA, Pearson Edexcel
binomial distribution model: Applies when there is a fixed number of trials n, two mutually exclusive outcomes, a constant probability of success p, and independent trials.WJEC
binomial expansion in limits: For small positive integer powers f(x) = xⁿ, expand (x + h)ⁿ using the Binomial Theorem.WJEC
binomial hypothesis testing: Conducting a statistical hypothesis test for the proportion in the binomial distribution and interpreting the results in context.AQA, WJEC
Binomial hypothesis tests for a proportion: A test of a claim about a proportion p that takes a random sample of size n and counts successes X, with X ~ B(n, p₀) under H₀.Pearson Edexcel
Binomial model: Models the number of successes in n independent trials, each with the same success probability p, written X ~ B(n, p).Pearson Edexcel
binomial probability calculations: For X ~ B(n, p), P(X = r) = ⁿC_r p^r (1 − p)ⁿ⁻ʳ for r = 0, 1, ..., n, with mean np.WJEC
binomial theorem: For a positive integer n, expands (a + bx)ⁿ into a finite series of n + 1 terms.WJEC
binomial to Normal approximation: By the Central Limit Theorem, the discrete binomial distribution B(n, p) converges to N(np, np(1 − p)) when n is large and p is not close to 0 or 1.WJEC
binomial versus Poisson: The binomial model fits when trials are fixed and dichotomous, while the Poisson model suits counts of rare events occurring in continuous time or space.WJEC
Bisection and interval narrowing: Narrowing the interval by repeated bisection, evaluating the midpoint and keeping the half with the sign change, until it is as small as required.Pearson Edexcel
Bisection method: Repeatedly bisect the interval, testing the midpoint, to narrow down the root.AQA
Bivariate data: Data involving two variables, shown on a scatter diagram and described using given regression lines without calculating the line yourself.AQA
bivariate interpretation: Analysis of the relationship between two quantitative variables, including interpreting the gradient b as the change in y per unit increase in x in context.WJEC
Boundary Condition: Known values of the variables (e.g., $x=0, y=2$) used to find the constant of integration.Pearson Edexcel
boundary condition substitution: Substituting given initial or boundary conditions, such as y = y₀ when x = x₀, to determine the unique numerical value of C.WJEC
boundary conditions: Given initial or boundary conditions, such as s = s₀ and v = v₀ at t = 0, used to determine the constants of integration c₁ and c₂.WJEC
boundary curves: Lines or curves that partition the plane into regions above or below them for two-variable linear and quadratic inequalities.WJEC
bounds for the true integral: An overestimate is an upper bound and an underestimate a lower bound, so the true integral lies on the corresponding side of the estimate.WJEC
box plot conventions: Confirmed outliers are plotted as individual crosses or dots beyond the whiskers, which terminate at the most extreme non-outlier observations.WJEC

C

calculator statistical modes: Modes on a calculator with standard statistical functions used to analyse a subset or features of the data.WJEC
Calculus as the general language of kinematics: This calculus approach handles variable acceleration, where constant-acceleration formulae do not apply.Pearson Edexcel
cancelling factors: Removing common factors after factorising the numerator and denominator fully, rather than cancelling individual terms across a plus or minus sign.WJEC
carrying capacity: A constraint K incorporated into a logistic model so that an unconstrained exponential population model no longer predicts an infinite population as t → ∞.WJEC
Cartesian conversion: Conversion to Cartesian form y = F(x) eliminates the parameter t, algebraically or using trigonometric identities.WJEC
Cartesian decomposition: Writing a force as F = (F cos θ)i + (F sin θ)j in Cartesian coordinate systems.WJEC
Cartesian form: The form obtained by eliminating the parameter, often using substitution or trigonometric identities.AQA
CAST diagram: The four quadrants determining signs: all ratios positive in Quadrant 1, only sine in Quadrant 2, only tan in Quadrant 3, only cos in Quadrant 4.WJEC
causal inference: Claims of causality must not be accepted purely on the basis of observational correlation; plausible confounding factors must be identified and unjustified…WJEC
Causation and confounding variables: Correlation does not imply causation, and clear reasoning about possible confounding variables explains why.AQA
census: A complete enumeration of every population member, providing completely accurate parameters with zero sampling error.WJEC
central tendency: Represented by the mean, median, and mode, where the mean incorporates all numerical values but is sensitive to extreme skewness and outliers, and the median…WJEC
centre and radius: Found by completing the square separately on x and y, giving centre (−g, −f) and radius r = √(g² + f² − c).WJEC
Centre of mass and uniform rods: Include the weight of a uniform rod as acting at its midpoint, and model a non-uniform rod by placing its weight at the centre of mass.AQA
Centre-radius form: The equation of a circle written as (x − a)² + (y − b)² = r², giving centre (a, b) and radius r.Pearson Edexcel
Chain rule: Differentiates composites as dy/dx = (dy/du) × (du/dx), and gives the inverse-function derivative dy/dx = 1/(dx/dy), provided dx/dy ≠ 0.AQA, Pearson Edexcel, WJEC
Chain rule and composite functions: If y = f(g(x)), then dy/dx = f′(g(x))·g′(x), often written as dy/dx = dy/du × du/dx.Pearson Edexcel
Chain rule applied to y terms: Differentiating y terms with respect to x, attaching dy/dx, so d/dx(yⁿ) = n y^(n−1) dy/dx.Pearson Edexcel
Chain rule for y-terms: When differentiating a function of y with respect to x, multiply by dy/dx, since d/dx[f(y)] = f'(y) dy/dx.AQA
chain rule with ln: Applying the chain rule to composite logarithmic functions yields d/dx(ln(f(x))) = f'(x) / f(x).WJEC
change of sign: Opposite signs of f(a) and f(b), expressed by f(a)f(b)<0, indicating at least one root in (a,b) when the function is continuous or sufficiently well-behaved.Pearson Edexcel, WJEC
changing limits: When evaluating definite integrals by substitution, the limits of integration must be converted from x to u.WJEC
circle equation: The locus of all points (x, y) at a fixed radius r from a centre (a, b), written as (x − a)² + (y − b)² = r².WJEC
circular reasoning: Assuming the identity one seeks to prove, which invalidates a geometric or trigonometric proof.WJEC
Cleaning data: Checking for missing entries, impossible values such as negative heights, and outliers, then deciding whether to remove, correct or keep them, and recording…AQA, Pearson Edexcel
Clear communication: Presenting the conclusion clearly, with a statement of what it represents, so a non-specialist reader can follow it.Pearson Edexcel
closed formula: A formula for the nth term that allows terms to be generated by substituting consecutive positive integers for n.AQA
Cobweb and staircase diagrams: A cobweb diagram plots the iteration against the line y = x, spiralling inwards for oscillating convergence, while a staircase diagram shows a monotonic…Pearson Edexcel
cobweb diagram: An iterative path where iterations alternate above and below the root, producing an inward spiralling diagram when the gradient is negative (−1 < g'(α) < 0).Pearson Edexcel, WJEC
Codomain: The set the outputs are declared to lie in, distinguished from the range.AQA
Coefficient: The number placed in front of an algebraic term.Pearson Edexcel
coefficient of friction: A dimensionless scalar constant that characterises the microscopic roughness and adhesiveness between two contacting surfaces, being the ratio of limiting…AQA, Pearson Edexcel, WJEC
Collinear: Points that lie on the same straight line.Pearson Edexcel
collinear points: Points A, B, and C lie on a single straight line when AB and BC are parallel and share the common point B.WJEC
Collinearity: Shown by expressing a vector as a scalar multiple of another and identifying a shared point.Pearson Edexcel
column vector: A vertical arrangement of vector components in their defined coordinate order.Pearson Edexcel
column vectors: A representation of a vector written as components such as (3, -2).Pearson Edexcel
combinations: The number of ways to choose r items from n distinct items without regard to order, denoted by nCr or (n choose r).WJEC
combined transformations: Must be applied in a precise order, because order matters, as with y = af(x) + b and y = f(ax + b).WJEC
combining logarithms: Using the product law to combine split logarithmic terms into a single compact argument, enabling direct exponentiation.WJEC
common difference: The constant difference d between consecutive terms of an arithmetic progression, where uₙ₊₁ − uₙ = d.AQA, WJEC
Common difference and linear structure: An arithmetic sequence adds a constant common difference d to each term, so a, a + d, a + 2d, ...; d may be negative or a fraction.Pearson Edexcel
common factors: Common algebraic factors across all terms on the right-hand side, identified as a critical prerequisite step to isolate variables.WJEC
common ratio: The constant value r between consecutive terms of a geometric progression, given by uₙ₊₁ / uₙ = r.WJEC
Communication of results: Writing the interpretation as a clear statement about the real-world situation that a non-mathematician could understand.AQA
comparative analysis: When comparing two distributions, both an average and a spread measure are evaluated, interpreting differences in the practical context.WJEC
Comparing coefficients: A method of solving the identity produced by multiplying through by the original denominator, used for repeated factors or when substitution is awkward.Pearson Edexcel
Complement: Written as ′ or bar notation, it follows from set logic and gives the complement rule P(A′) = 1 − P(A).AQA
Completing the square: Writing ax² + bx + c as a(x + p)² + q, which gives the minimum or maximum value q at x = −p and the line of symmetry x = −p.AQA, Pearson Edexcel, WJEC
completing the square for circles: Applied separately on x and y to an expanded form x² + y² + 2gx + 2fy + c = 0 to reach standard circle form.WJEC
component: One signed coordinate part of a vector in a specified direction.AQA, Pearson Edexcel
component form: A vector written as a column pair (x, y) or as xi + yj, where x and y are the horizontal and vertical components.AQA, Pearson Edexcel
Component form in two and three dimensions: A vector written as a₁i + a₂j in two dimensions, or a₁i + a₂j + a₃k in three dimensions, where i, j and k are unit vectors along the coordinate axes.Pearson Edexcel
component to magnitude-direction conversion: Finding magnitude via Pythagoras' theorem and direction angle via trigonometry, with the angle adjusted to the correct quadrant.WJEC
Componentwise extension of scalar formulae to vectors: In two dimensions each formula applies independently to the x- and y-components, so the formulae become vector equations.Pearson Edexcel
Componentwise treatment of vector motion: In two dimensions the same operations apply to each component, so r = x i + y j, v = ẋ i + ẏ j and a = ẍ i + ÿ j.Pearson Edexcel
Composite function: Applies one function to the output of another, written (f ∘ g)(x) = f(g(x)) and read as 'f of g of x'.AQA, Pearson Edexcel
composite functions: A composite function fg(x) = f(g(x)) applies function g first and then function f to the output of g.WJEC
composite trigonometric arguments: When squaring composite arguments, cos(kθ) becomes 1 − (kθ)²/2 = 1 − ½k²θ², ensuring the factor k is squared inside the bracket.WJEC
compound angle expansion: Expanding sin(x + h) or cos(x + h) using the correct compound angle formula, such as cos(x + h) = cos x cos h − sin x sin h.WJEC
compound angle formulas: Formulas that expand trigonometric ratios of compound angles, including sin(A ± B), cos(A ± B) and tan(A ± B).WJEC
Compound angle identities: Formulae for sin(A ± B), cos(A ± B) and tan(A ± B) that you must derive and state.AQA
compound events: Events such as P(X > 2) or P(1 ≤ X < 4), whose probabilities are evaluated by summing relevant individual probabilities.WJEC
compound growth and depreciation: Geometric series model compounding percentage growth and decay, such as compound interest or exponential depreciation of assets.WJEC
concave curves: A curve is concave on an interval if d²y/dx² ≤ 0, meaning the gradient is decreasing and chords lie below or on the curve.WJEC
Concave down: A curve that gives an underestimate of the true area under the rule.Pearson Edexcel
Concave up: A curve that lies below its chords, so the rule overestimates the true area.Pearson Edexcel, WJEC
Conditional probability: The probability of an event given that another event has already occurred, found by restricting the sample space to that event.AQA, Pearson Edexcel, WJEC
conditional probability formula: Rearranges to P(A|B) = P(A ∩ B) / P(B), where the denominator is always the probability of the conditioning event B.AQA, WJEC
Conditions for a binomial distribution: Fixed n, two outcomes, constant p and independence must all hold for a situation to fit this model.AQA
Conditions of use for formulae: The stated conditions attached to a formula or method, which must be satisfied in the situation before it is applied.Pearson Edexcel
confounding variables: A confounding third variable simultaneously influences both observed variables, so a strong correlation can arise through its presence.WJEC
Conjugate: For a denominator a ± √b, the conjugate a ∓ √b is used with the difference of two squares.AQA, Pearson Edexcel
conjugate pairs: For a binomial denominator containing surds, such as a + b√c, the expression a − b√c used to multiply it.WJEC
conjunction: Used as 'and' when a single continuous interval has x satisfying two simultaneous constraints, written as a double inequality or in set notation.WJEC
connected particles: Two or more masses linked by light, inextensible strings passing over smooth fixed pulleys or pegs.WJEC
Connected particles and pulleys: For a light inextensible string over a smooth pulley, tension is the same throughout and acceleration magnitude is the same for both particles.AQA
Connected rates: Use dy/dt = dy/dx × dx/dt, often with geometry formulae.AQA
connected rates of change: Link variables through time t via the chain rule.Pearson Edexcel, WJEC
Connected rates of change and inverse function derivatives: dy/dt = dy/dx × dx/dt links how quantities change together, and dx/dy = 1/(dy/dx) provided dy/dx ≠ 0.Pearson Edexcel
Connection to binomial probability: Binomial coefficients also appear in binomial probability calculations, linking algebra to statistics.AQA
constant acceleration: Acceleration that has the same value, including sign, throughout the time interval being modelled.AQA, WJEC
Constant acceleration as a linear velocity–time model: Along a straight line, velocity changes linearly with time, so v = u + at.Pearson Edexcel
constant acceleration equations: Five equations linking displacement s, initial velocity u, final velocity v, acceleration a and time t for rectilinear motion with uniform acceleration a.WJEC
Constant acceleration modelling: Using the SUVAT formulae, which link displacement, initial velocity, final velocity, acceleration and time, for motion in a straight line with constant…AQA
Constant acceleration under gravity: For motion in a straight line under gravity alone, use constant acceleration equations with a = ±g, taking up as positive or negative consistently.AQA
constant acceleration vectors: Straight-line suvat formulas generalize directly to two dimensions under constant vector acceleration a, and the vector equations can be derived by…WJEC
Constant downward acceleration under gravity: Acceleration is constant and directed downwards with magnitude g, approximately 9.8 m s⁻², giving a = −g ĵ.Pearson Edexcel
constant of integration: An arbitrary constant c representing vertical translation, produced when indefinite integration reverses differentiation to give the general family of…WJEC
Constant of proportionality: A constant k that must be included where a rate of change is proportional to a quantity.AQA
constant probability: The condition that the probability of success p is identical for every trial.Pearson Edexcel
constants of proportionality: Proportionality statements use a positive constant k, and the sign must be correct for increase or decrease.WJEC
contact and field forces: Forces arising through direct physical contact or via non-contact fields.WJEC
contextual enquiry: Using data to investigate questions arising in real contexts.WJEC
contextual interpretation: Evaluating mathematical solutions against the physical or contextual constraints of the original scenario and communicating them in the context of the…AQA, WJEC
Contextual interpretation of significance: The conclusion must state whether there is sufficient evidence at the α level to reject H₀, phrased in terms of the real quantity measured.Pearson Edexcel
Contextual meaning: Translating mathematical results back into the original situation, explaining what the numbers mean in real terms rather than just restating the number.Pearson Edexcel
contextual problem solving: Solving problems in real-world engineering, financial, and scientific applications by selecting and applying appropriate numerical methods.WJEC
Continuity and the intermediate value property: If a continuous function takes values of opposite sign at two points, then f(x) = 0 has at least one root between them.Pearson Edexcel
continuity correction: An adjustment applied when approximating a discrete distribution (like Binomial) with a continuous distribution (like Normal), by adding or subtracting 0.5 to…Pearson Edexcel
continuous: A function with no break, gap, hole or vertical asymptote on the stated interval.Pearson Edexcel
Continuous change: Change modelled using e, as in continuous compound interest A = Pe^(rt), where P is the principal, r the annual rate and t the time in years.Pearson Edexcel
Continuous distributions: Models where probabilities are found from areas under a curve, and P(X = x) = 0 for any single value.Pearson Edexcel
continuous probability density: Probability spread smoothly across intervals via a probability density function f(x) where ∫ f(x) dx = 1.WJEC
continuous random variable: A random variable that can take any value in an interval of possible values.Pearson Edexcel
continuous uniform distribution: Models a variable equally likely to fall anywhere within interval [a, b], with density f(x) = 1/(b − a) for a ≤ x ≤ b and 0 elsewhere.WJEC
continuous uniform suitability: Applies when outcomes are strictly bounded and all sub-intervals of equal length are equally likely, and is inappropriate if values cluster centrally.WJEC
Convergence: The property that successive values approach a limit, which must be justified and checked by choosing a start near the root.Pearson Edexcel, WJEC
Convergence and limiting sums: A geometric series converges when the modulus of the common ratio is less than one, and then the sum to infinity is a divided by one minus r.AQA
Convergence and sum to infinity: When |r| < 1 the terms shrink towards zero and the series converges to S∞ = a/(1 − r).Pearson Edexcel
Convergence and the gradient condition: The sequence converges when |g′(x)| < 1 near the root and diverges when |g′(x)| > 1 there, so convergence depends on the gradient of g near the root.Pearson Edexcel
convergence condition: The requirement that the common ratio satisfies |r| < 1, which corresponds to −1 < r < 1 in modulus notation.WJEC
convergence condition |g'(x)| < 1: If |g'(α)| > 1 the iteration diverges away from the root, so convergence depends on the gradient of g(x) near the root.WJEC
Convergent geometric series: A geometric series whose partial sums approach a finite limit; it converges when $|r|<1$.AQA, WJEC
Conversion between Cartesian and parametric forms: To convert to Cartesian form, eliminate the parameter; conversely, to parametrise a curve, choose a suitable parameter.AQA
Conversion between component and magnitude/direction form: Changing between the two forms, using x = r cos θ and y = r sin θ where r is the magnitude, or finding magnitude and direction from components.Pearson Edexcel
convex curves: A curve is convex on an interval if d²y/dx² ≥ 0 everywhere on that interval, meaning the gradient is increasing and chords lie above or on the curve.WJEC
Coordinate geometry of circles: The study of circles in the coordinate plane, using the standard equation to give the centre and radius.AQA
coplanar equilibrium: A particle is in static equilibrium under coplanar forces if the vector resultant of all forces acting upon it is zero.WJEC
Coplanar forces: Forces whose lines of action lie in the same plane.Pearson Edexcel
Correlation: An informal measure of how closely points follow a straight line, from strong positive through weak to strong negative.AQA, Pearson Edexcel
Correlation and association: Described informally using terms such as strong, weak, positive or negative, referring to how closely points follow a straight-line pattern.AQA
correlation direction: Describes whether y tends to increase as x increases, or y decreases as x increases, shown on a scatter diagram.WJEC
Correlation interpretation: Interpreting a given correlation coefficient using a given p-value or critical value, linking it to a linear relationship, without calculating the coefficient.AQA
correlation strength: Judged informally by how tightly data points cluster around a straight line: strong, moderate, or weak.WJEC
correlation versus causation: A statistical correlation between two variables demonstrates mutual co-variation, but does not establish that changes in one variable cause changes in the…WJEC
cosec(x): The cosecant function, defined as the reciprocal of the sine function: cosec(x) = 1/sin(x).Pearson Edexcel
cosecant: The reciprocal of sine, $\mathrm{cosec}\,x=1/\sin x$; it is undefined where $\sin x=0$.Pearson Edexcel
cosine rule: States a² = b² + c² − 2bc cos A, used to find a third side given two sides and the included angle, or rearranged to find an angle given all three sides.WJEC
cot(x): The cotangent function, defined as the reciprocal of the tangent function: cot(x) = 1/tan(x) = cos(x)/sin(x).Pearson Edexcel
cotangent: The reciprocal of tangent, $\cot x=1/\tan x=\cos x/\sin x$; it is undefined where $\sin x=0$.Pearson Edexcel
Coulomb friction model: A model of dry friction in which the friction force F satisfies the inequality F ≤ μR, where μ is the coefficient of friction and R is the normal reaction…WJEC
counter-example: A permitted example for which a universal statement fails; one is sufficient to disprove that statement.AQA, Pearson Edexcel
Counterexample: A value in the stated domain for which a claimed universal statement is false.WJEC
critical angle of tilt: The maximum tilt angle determined by combining the friction equation F = μR with the conditions for static equilibrium.WJEC
Critical evaluation: A reasoned judgement about the usefulness of a model in context, weighing strengths against limitations and supported by evidence from outputs and assumptions.Pearson Edexcel
Critical evaluation of applied models: Judging whether a model's assumptions, such as constant acceleration or a normal distribution, justify the method used, and commenting on the strength and…Pearson Edexcel
Critical reflection on model predictions: Evaluating whether the model's predictions are sensible, noting where results may be unreliable or where assumptions break down.AQA
critical region: The set of test statistic values leading to rejection of H₀, bounded by critical values.AQA, WJEC
Critical regions and p-values: The critical region is found using cumulative binomial probabilities, and the p-value is the probability of a result at least as extreme as the observed X.Pearson Edexcel
critical value comparison: Comparing the sample r against tabulated critical values for sample size n at significance level α, rejecting H₀ if |r| exceeds the critical value.WJEC
critical values: Values found for a quadratic inequality after rearranging to make one side zero, used with a sketch of the parabola to identify the correct regions.AQA, WJEC
Critique: Considering whether a presentation shows the distribution clearly, whether the scale is misleading, and whether the diagram suits the data type.AQA
Critiquing and refining mathematical models: Identifying limitations such as unrealistic long-term behaviour and suggesting refinements such as a logistic model or a restricted domain.AQA
Critiquing assumptions: Identifying each assumption, explaining why it may not hold, and stating whether the true probability would be higher or lower.AQA
Cumulative probabilities: Probabilities such as P(X ≤ 3), found directly with the binomial cumulative distribution function on your calculator.AQA
Cumulative probability: The probability that a random variable is less than or equal to a stated value, found by adding probabilities up to that value.Pearson Edexcel
curve intersections: Points where two curves meet on a single set of coordinate axes, allowing equations to be solved.WJEC
curve rearrangement: Rewriting an intractable equation into the form f(x) = g(x) so its roots can be estimated or analysed.WJEC
curve sketching: Reveals key geometric properties such as stationary points, intersections, asymptotes, and symmetry in pure mathematics.AQA, WJEC
curve symmetry: Rotational symmetry of order 2 about the origin for y = a/x, and line symmetry about the y-axis for y = a/x².WJEC

D

dashed and solid lines: Dashed boundary lines indicate strict inequalities, whereas solid boundary curves indicate that points on the boundary are included.WJEC
Dashed lines/curves: What strict inequalities are represented with graphically, shading the required region.AQA
data cleaning: The systematic process of identifying, correcting, or removing anomalies before undertaking statistical analysis.AQA, WJEC
data integrity: Evaluating whether an outlier is an authentic extreme phenomenon, an erroneous measurement, or a transcription error, and deciding whether it should be…WJEC
Decay constant: The positive magnitude of a continuous decay rate in a model y = Ae^(-kt), where k has reciprocal time units.AQA
decision rule: Comparing the p-value to α, or checking if x lies in the critical region, to decide whether to reject or not reject H₀.WJEC
decreasing functions: On an interval, if f'(x) ≤ 0 throughout, then f is decreasing.WJEC
decreasing sequences: A sequence that satisfies xₙ₊₁ ≤ xₙ for all n.WJEC
deduction (direct proof): A proof which starts from the given conditions and uses logical or algebraic steps to reach the required conclusion.AQA
definite evaluation: Evaluating definite integrals using the evaluation formula F(b) − F(a) between boundaries.WJEC
Definite integral: Used to find the area between two curves by integrating the difference between the upper curve and the lower curve across an interval [a, b].AQA, Pearson Edexcel, WJEC
definite integral definition: The exact definite integral written as the limit of the sum of f(x) δx as δx tends to zero.WJEC
definite integrals: Evaluated over intervals such as [a, c] and [c, b], giving a negative number when the curve falls below the x-axis.WJEC
Definite integrals and area under curves: Evaluated by finding an antiderivative of the integrand, then evaluating it at the upper and lower limits and subtracting.AQA
definite integration: A definite integral has specific lower and upper limits and evaluates to a unique numerical value without an arbitrary constant of integration.AQA, WJEC
Dependent events: Events where occurrence of one changes the probability of another.AQA
Dependent variable: The quantity whose value depends on the independent variable, such as depth H or velocity v.Pearson Edexcel
Derivation and manipulation of identities: Understanding how the identities are derived and using them to simplify expressions, prove other identities and solve trigonometric equations.AQA
Derivation from calculus and graphs: Obtaining the formulae from the definitions a = dv/dt and v = ds/dt by integration, or from a velocity–time graph.AQA
Derivation of Pythagorean identities: Dividing sin²θ + cos²θ = 1 by cos²θ gives sec²θ = 1 + tan²θ, and dividing by sin²θ gives cosec²θ = 1 + cot²θ.Pearson Edexcel
Derivative: The gradient of the tangent to the graph of y = f(x) at a general point (x, y), also representing an instantaneous rate of change.AQA, Pearson Edexcel, WJEC
derivative sign analysis: To find intervals, differentiate f(x), solve f'(x) ≥ 0 or f'(x) ≤ 0, factorise where possible, and analyse the sign of f'(x) across critical boundary points.WJEC
derived quantities: Velocity, acceleration, force, weight and moment, each derived from the fundamental quantities.AQA
derived quantity: A quantity formed by combining fundamental quantities through a mathematical relationship.AQA
Derived units and dimensional consistency: Quantities formed by combining the fundamental ones, and checking that every term in an equation has consistent units to detect errors.Pearson Edexcel
Diagram construction: Choosing a suitable scale and orientation, drawing forces as arrows from the correct points, and labelling magnitudes and directions.Pearson Edexcel
Diagram interpretation: Reading scales, labels, directions and units correctly from a given diagram.Pearson Edexcel
difference of squares: Expanding (a + b√c)(a − b√c) = a² − b²c, which produces a purely rational integer denominator.WJEC
Difference of Two Squares: The algebraic identity a² - b² = (a + b)(a - b).Pearson Edexcel
Differential equation: An equation involving a derivative, formed by translating a written or physical description.AQA, Pearson Edexcel
differential equation formulation: Translating a described rate of change into the correct derivative notation and formulating the complete first order differential equation representing the…WJEC
differential equations formulation: Constructing a differential equation translates verbal statements about rates of change into symbolic calculus relations, with constants clearly identified.WJEC
differential formulations: Governing relationships such as proportionalities and differential equations formulated from contextual descriptions, for instance where the rate of change is…WJEC
Differentiation and integration as inverse operations: Velocity is the time derivative of displacement and acceleration the derivative of velocity, while displacement follows from integrating velocity and velocity…Pearson Edexcel
differentiation from first principles: Taking the limit of [f(x + h) − f(x)] ÷ h as h tends to zero, for small positive integer powers of x and for sin x and cos x.Pearson Edexcel, WJEC
differentiation in kinematics: Determines instantaneous rates: velocity is the derivative of displacement and acceleration is the derivative of velocity.WJEC
Differentiation of exponential functions: Differentiating y = e^(kx) gives dy/dx = k e^(kx), so the gradient at any point equals k times the current value.AQA, Pearson Edexcel
Differentiation of parametric curves: Finding a gradient using dy/dx = (dy/dt) ÷ (dx/dt), with dx/dt not equal to zero.Pearson Edexcel
dimensional consistency: Vital across equations in mechanics problems, since substituting unstandardised units without prior conversion to SI base units introduces fatal calculation…WJEC
dimensionless constant: A scalar constant with no units, being the ratio of two forces such as limiting friction and normal reaction.WJEC
direct proportion: A proportional relationship such as y = kx or y = kx², where given points can be used to find the constant of proportionality k.AQA, WJEC
directed line segments: A representation of a vector that carries both magnitude and direction.Pearson Edexcel
direction: The angle θ from the positive x-axis, with tan θ = y/x, choosing the correct quadrant from the signs of x and y.AQA, WJEC
Direction and quadrant awareness: The angle measured from the positive x-axis, found using tan θ = y ÷ x with the correct quadrant selected from the signs of the components.Pearson Edexcel
Direction cosines in 3-D: A way of describing the direction of a three-dimensional vector, used instead of a single bearing, alongside angles with the axes.Pearson Edexcel
discontinuities and asymptotes: A vertical asymptote or discontinuity within the interval can cause a change of sign without any root existing.WJEC
Discrete distributions: Models where the probabilities of separate outcomes sum, and the addition rule applies to disjoint outcomes of a discrete random variable.Pearson Edexcel
discrete modelling: Sequences and series model discrete physical, financial, and biological processes.WJEC
Discrete probability distribution: A set of values of a random variable, each listed with its probability, where the probabilities sum to 1.Pearson Edexcel
discrete probability mass: Probability concentrated at isolated outcomes x_i such that 0 ≤ P(X = x_i) ≤ 1 and Σ P(X = x_i) = 1.WJEC
discrete random variable: Takes countable numerical outcomes with specified probabilities, defined via a table or formula P(X = x).Pearson Edexcel, WJEC
discrete uniform distribution: Models n equally likely outcomes, each with probability 1/n.Pearson Edexcel, WJEC
discrete uniform probabilities: For a discrete uniform distribution on n equally likely outcomes, P(X = r) = 1/n.WJEC
Discriminant: The value b²−4ac, which determines the number of real roots: positive gives two distinct real roots, zero gives one repeated root, negative gives no real roots.AQA, Pearson Edexcel, WJEC
discriminant and intersections: A repeated root with discriminant zero corresponds to tangential contact, and no real roots indicates that the curves do not meet.WJEC
disguised equations: Equations that are quadratic in form, solved by substituting a temporary variable u = g(x) and reversing each root through the inverse function.WJEC
disjunction: Used as 'or' to connect disjoint solution regions, such as the outer tails of a quadratic inequality, where no real number satisfies both.WJEC
Displacement: The change in position, a vector with both magnitude and direction.AQA, Pearson Edexcel, WJEC
Displacement vector: The vector from A to B, found by subtracting position vectors in the correct order, b - a, componentwise.Pearson Edexcel, WJEC
displacement versus distance: Displacement is a vector denoting directed distance from O, which can be positive, negative, or zero, while distance travelled is the total scalar path length…WJEC
displacement-time graph: A graph on which the gradient represents instantaneous velocity, a horizontal tangent signifies instantaneous rest, and a straight line indicates constant…WJEC
Disproof by counter example: Gives one valid case where the statement fails, providing a specific counter example that satisfies the conditions but makes the statement false.AQA, Pearson Edexcel
disproof by counterexample: Disproves a universal conjecture "for all x, P(x)" by exhibiting a single specific value x₀ for which P(x₀) is false.WJEC
Distance: The magnitude of the displacement between two points, found by applying the full distance formula and taking the square root.Pearson Edexcel
Distance between two points: The magnitude of the vector between the two points, the same whichever order the subtraction is done in.AQA
Distance travelled: The total length of path covered, a scalar, so it is never negative.AQA, Pearson Edexcel, WJEC
Distinct sections of the population: Two clusters or a group of points that follow a different pattern, which may indicate subgroups that should be described separately rather than forced into…Pearson Edexcel
Distinguishing between arithmetic and geometric change: Recognising whether a situation has a constant difference or a constant ratio, and checking whether the change is additive or multiplicative.AQA
distribution parameters: The parameters μ and σ define location and dispersion.WJEC
distribution selection: Choosing an appropriate probability distribution for a context, with appropriate reasoning, by comparing physical problem traits against distribution…WJEC
distribution shapes: Features such as symmetry, unimodality or skewness in sample diagrams that help statisticians choose candidate models, though shape alone is not decisive.WJEC
divergence: When f'(xₙ) is close to zero the tangent sends the subsequent iterate far from the root, or in fixed-point iteration whenever |g'(x)| > 1 near the root.Pearson Edexcel, WJEC
divisibility: a divides b, written a ∣ b, means that b = ak for some integer k.AQA
division by zero: What occurs in the iterative formula when f'(xₙ) = 0, because the horizontal tangent does not meet the x-axis.WJEC
Domain: The complete set of possible input values (x-values) for which the function is defined.AQA, Pearson Edexcel, WJEC
domain and range: Arcsin x has domain [−1, 1] and range [−π/2, π/2]; arccos x has domain [−1, 1] and range [0, π]; arctan x has domain ℝ and range (−π/2, π/2).WJEC
Domain and range in context: A sensible domain stated for the context, with out-of-range outputs such as a negative height rejected.Pearson Edexcel
Domain and range restrictions for functions: Arcsin and arccos have domain [-1, 1], arctan has domain all real numbers, and their restricted ranges make them functions.AQA
Domain and restrictions: Conditions such as cosθ ≠ 0 when using tanθ, which must be handled and stated explicitly in proofs.AQA
Domain and validity of solutions: Checking that solutions satisfy x>0 and y>0, and for combined expressions such as log_a(xy), requiring xy>0.AQA
Domain of a composite function: The set of x in the domain of g for which g(x) lies in the domain of f.Pearson Edexcel
Domain of f⁻¹: The range of f, while the range of f⁻¹ is the domain of f.AQA
domain restrictions: Conditions such as u > 0 for u = eˣ, u ≥ 0 for u = √x and −1 ≤ u ≤ 1 for trigonometric substitutions, rejecting invalid branches.WJEC
Domain restrictions on logarithms: The laws apply only when all logs share the same base and all arguments are positive.Pearson Edexcel
Domains of reciprocal functions: Values where the denominator is zero are excluded, so sec θ and tan θ are undefined where cos θ = 0, and cosec θ and cot θ where sin θ = 0.Pearson Edexcel
Double angle formulae: Results such as sin 2A = 2 sin A cos A, obtained by setting B = A in the addition formulae.Pearson Edexcel
double angle formulas: Identities derived directly from the compound angle formulas by setting B = A, giving forms for sine, cosine and tangent of 2A.WJEC
Double angle identities: Formulae used to express sin 2θ, cos 2θ and tan 2θ in terms of sin θ, cos θ and tan θ.AQA
doubling time: Found by setting y = 2y₀, giving T = (ln 2)/k.WJEC
Dynamics in a plane: Resolving forces into two perpendicular directions, adding components in each direction, then applying F = ma in each direction.Pearson Edexcel

E

Effect of transformations on key features and asymptotes: Key points, asymptotes and intercepts should be tracked through each transformation, and asymptotes transform with the graph.Pearson Edexcel
Effect on calculated probabilities: The likely direction of change, stating whether the probabilities would increase or decrease when an assumption is relaxed.AQA
Eliminating parameters: Forming the differential equation from a family of curves by removing arbitrary constants.AQA
Eliminating the parameter: Converting to Cartesian form by expressing the parameter from one equation and substituting into the other.AQA, Pearson Edexcel
eliminating variables: All instances of the original variable x must be completely eliminated before integrating with respect to u.WJEC
Elimination: A method where one or both equations are multiplied to make the coefficients of one variable equal, then added or subtracted to remove it.AQA
empirical 68-95-99.7% rule: Approximately 68% of data lie within μ ± σ, 95% within μ ± 2σ, and 99.7% within μ ± 3σ.WJEC
empirical to theoretical link: Empirical frequency presentations approximate theoretical probability models, and comparing observed proportions with theoretical probabilities assesses model…WJEC
enclosed regions: The region between two intersecting continuous curves, partitioned at each intersection point c when the curves cross multiple times within the domain.WJEC
end behavior: The degree n and the sign of the leading coefficient dictate this asymptotic behavior of the curve.WJEC
equating coefficients: Expanding and comparing coefficients of corresponding powers of x to evaluate the unknown constants A, B and C.Pearson Edexcel, WJEC
equation: Equates two expressions to determine specific unknown values.WJEC
Equation in a function of the unknown: An equation such as x⁴ − 5x² + 4 = 0, solved by substituting a single letter for that function, solving the resulting quadratic, then reversing the…Pearson Edexcel
equation of motion: Newton's second law parallel to the surface: the sum of parallel forces equals the driving force minus friction, which equals ma.WJEC
equation solving: Factorising or solving the quadratic equation to determine candidate trigonometric values, then solving for θ within the given interval.AQA, WJEC
Equations involving multiples of the unknown angle: Equations such as sin 2θ = k or cos(3θ + 30°) = k, solved by finding the general solution for the multiple angle, then dividing or adjusting to find θ.Pearson Edexcel
equations of motion: Choosing one axis parallel to acceleration and the other perpendicular simplifies analysis: ΣF_parallel = ma and ΣF_perp = 0.WJEC
Equilibrium: For a particle in equilibrium the resultant force is zero, so forces balance in two perpendicular directions, and under coplanar forces the vector sum of all…AQA, Pearson Edexcel
Equilibrium and constant velocity: A zero resultant force, leading to constant velocity, which may be zero, rather than necessarily rest.AQA
Equilibrium of a particle: The resultant force is zero: resolve forces in two perpendicular directions and set sum of components to zero.AQA
Equilibrium of rigid bodies: A rigid body is in equilibrium when the total clockwise moment about any point equals the total anticlockwise moment.AQA
equivalence: A two-way implication requiring both directions to hold.WJEC
Error: Grows as θ increases, so the approximations are only valid when θ is sufficiently small.Pearson Edexcel
error analysis: Analysing error sources in numerical approximations: truncation error from the algorithm and rounding error from finite precision.AQA, WJEC
Error bounds: A numerical limit on how far a solution may be from the true value, such as an interval width or a function-value tolerance.Pearson Edexcel
Error bounds and tolerance: To confirm a root to a specific accuracy, check for a sign change in f(x) between the upper and lower bounds of the rounded value, proving the root lies…AQA
Euclidean distance: The straight-line distance between points A and B, equal to the magnitude of the displacement vector AB, calculated using Pythagoras' theorem.WJEC
Euler's constant: The constant e ≈ 2.71828 used as the base of the natural exponential function.WJEC
Evaluate: To calculate the final numerical value of an expression.Pearson Edexcel
evaluating assumptions: Critiquing assumptions made and the likely effect of more realistic assumptions, explaining how adopting them alters predicted outcomes.WJEC
Evaluation: Judging whether a model's conclusions remain valid when assumptions change.Pearson Edexcel
evaluation of integrals: Integrating the function term by term to find an antiderivative, writing it in square brackets with the limits, then evaluating the upper limit and…WJEC
evaluation of validity: Comparing theoretical outputs against empirical data or physical realities to determine the model's domain of validity and whether it is appropriate.WJEC
even and odd symmetry: cos(−x) = cos x is an even function, while sin(−x) = −sin x and tan(−x) = −tan x are odd functions.WJEC
even function: A function satisfying `f(−x) = f(x)`, giving symmetry about the y-axis.Pearson Edexcel
even multiplicity root: A root at which the graph touches the x-axis and turns back instead of crossing it.Pearson Edexcel
Event: A subset of the sample space, representing one or more outcomes of interest.AQA, Pearson Edexcel
Exact forms and conjugates: Leaving answers in surd form, and multiplying a binomial surd denominator by its conjugate using the difference of two squares.Pearson Edexcel
exact logarithmic limits: If limits are present, combine logarithmic terms using logarithm laws ln P − ln Q = ln(P/Q) to express the final definite answer in exact compact form.WJEC
exact solutions: Solutions stated in terms of logarithms, such as x = (ln b) / (ln a), rather than evaluated decimals.WJEC
exact trigonometric values: Values of sin and cos for 0, π/6, π/4, π/3, π/2, π and multiples thereof, and of tan for 0, π/6, π/4, π/3, π and multiples thereof.AQA, WJEC
exact value: A value expressed without approximation, using integers, fractions and surds where appropriate.Pearson Edexcel
Exact values: Precise values of sin and cos at 0, π/6, π/4, π/3, π/2 and π, and of tan at 0, π/6, π/4, π/3 and π, allow work without a calculator.Pearson Edexcel
exclusion of formula derivation: Manual calculation of the Product Moment Correlation Coefficient r from raw summation formulas is excluded.WJEC
Expanding and collecting like terms: Multiplying out products of brackets and gathering like terms to give a simplified polynomial.Pearson Edexcel
experimental integration: Evaluating total distance travelled from irregular velocity data using numerical integration on experimental ordinates.WJEC
Explicit formula: A formula for the nth term, such as uₙ = 3n + 1, so any term can be found directly.Pearson Edexcel
Exploration of scenarios: Engaging with the situation mathematically by varying one input at a time to see how the output changes, or comparing several scenarios.Pearson Edexcel
exponential curves: The graph of y = eˣ passes through (0, 1) and (1, e), with y = 0 as a horizontal asymptote.WJEC
exponential decay: A model where k < 0, often written y(t) = y₀ e^(−λt) with λ > 0, so the initial value decreases towards zero as t → ∞.WJEC
exponential derivative: Applying the chain rule to the natural exponential function yields the fundamental derivative d/dx(e^(kx)) = k e^(kx).WJEC
exponential differentiation: For general exponential functions y = a^(kx) with base a > 0, rewrite using natural logarithms as y = e^(kx ln a), giving (k ln a) a^(kx).WJEC
Exponential function: A function with the variable in the exponent, written y = a^x where a is positive.AQA, Pearson Edexcel
exponential functions: The function f(x) = aˣ with base a > 0 is defined for all real x, with range f(x) > 0.WJEC
Exponential functions and their graphs: For a positive base a, a^x is defined for all real x and is always positive, and its graph passes through (0,1) and lies above the x-axis.AQA
Exponential functions with base e and general base a: The derivative of e^(kx) is k e^(kx), and the derivative of a^(kx) is k a^(kx) ln a.Pearson Edexcel
exponential growth: When a > 1 the function is strictly increasing, passes through the y-intercept (0, 1) and the point (1, a).WJEC
Exponential growth and decay: Quantities changing at a rate proportional to their current size, modelled with k > 0 for growth and k < 0 for decay.AQA
Exponential growth and decay models: Growth occurs when k > 0 and decay when k < 0, and the model is suitable whenever the rate of change is proportional to the amount present.AQA
exponential integrals: Integrating eᵏˣ gives (1/k) eᵏˣ + c, dividing by the linear coefficient k.WJEC
Exponential modelling: Using exponential growth and decay functions, such as y = Ae^(kt) or y = Ab^t, to represent quantities changing at a rate proportional to their current size.Pearson Edexcel
exponential models: Relationships of the form y = kbˣ, linearised by plotting ln y against x, where gradient m = ln b and vertical intercept c = ln k.WJEC
Exponential relationship: A model of the form $y=kb^x$, where k is a positive initial constant and b is a positive constant base.Pearson Edexcel
expression: Contains operations, terms, and variables without an equals sign.WJEC
extraneous solutions: Candidate solutions that must be checked algebraically or graphically and eliminated when solving equations of the form |ax + b| = cx + d.WJEC
extrapolation: A prediction that is unreliable because it lies far outside the range of observed explanatory data.Pearson Edexcel, WJEC

F

Factor theorem: A polynomial f(x) has a linear factor (x − a) if and only if f(a) = 0; more generally, (bx − a) is a factor if and only if f(a/b) = 0.AQA, Pearson Edexcel, WJEC
Factorial and combination notation: The notations n!, nCr and n r are used, with binomial coefficients nCr equal to n!AQA
factorials: Notation defined for non-negative integers by n!WJEC
factorisation: Used instead of dividing across by cos θ when cos θ can equal zero, as in cos θ (sin θ − 1) = 0.AQA, WJEC
factorisation in calculus: Algebraic factorisation producing a product of single-variable expressions before separation of variables is possible.WJEC
Factorisation involving a common factor: Some equations require factorisation first to reveal a common factor, such as taking out the common factor x from xy + x to give x(y + 1).Pearson Edexcel
Failure cases of numerical methods: A sign change may occur at a discontinuity where no root exists, an even number of roots can produce no sign change, and a repeated root touches without…Pearson Edexcel
Failure modes: A starting value near a stationary point, a cycle that never settles, or divergence away from the root.Pearson Edexcel
failure of sign change: Change of sign methods can fail through a discontinuity or vertical asymptote, or through an even number of roots in the interval.WJEC
Feasibility checking: Checking that the result is feasible and sensible within the context, since a negative time, a probability above 1 or a non-integer count of people signals…Pearson Edexcel
feasible regions: Regions in the Cartesian plane identified by testing a convenient test point not on the boundary, such as the origin.WJEC
Finite bounded region: A closed region with a limited area, enclosed by stated curves, straight lines or coordinate axes.Pearson Edexcel
finite expansion: A series of n + 1 terms produced when the index n is a positive integer.WJEC
Finite versus infinite binomial series: For positive integer n the series terminates after n + 1 terms, while for rational n the expansion continues indefinitely.Pearson Edexcel
First principles: The limiting definition f′(x)=lim as h→0 of [f(x+h)−f(x)]/h, derived from the gradient of a shrinking chord.WJEC
First-Order: A differential equation that involves only the first derivative ($\frac{dy}{dx}$), and no higher derivatives like $\frac{d^2y}{dx^2}$.Pearson Edexcel
Fitness for purpose: Whether a model is appropriate, judged by asking whether it predicts realistically and whether its assumptions are justified.Pearson Edexcel
Fixed point: A value alpha satisfying g(alpha)=alpha; it is an intersection of y=g(x) and y=x and may be the limit of a fixed-point iteration.Pearson Edexcel, WJEC
fixed-point iteration: Rearranging an equation f(x) = 0 into the form x = g(x), then choosing a starting value x₀ and computing x₁ = g(x₀), x₂ = g(x₁), and continuing.Pearson Edexcel, WJEC
force: An interaction that tends to alter the state of rest or uniform motion of a body, possessing both magnitude measured in newtons and direction.AQA, Pearson Edexcel, WJEC
Forces as vectors and equilibrium: Forces can be resolved and a resultant force found, and for equilibrium the resultant force is zero.AQA
formal notation: Standard conventions and notation used to structure step-by-step mathematical reasoning cleanly.WJEC
Forming and solving equations in n: Identify a and d, substitute into the correct formula, and solve the resulting linear or quadratic equation, rejecting non-integer or non-positive values of n.Pearson Edexcel
fractional coefficients: Coefficients such as k = 1/2 give (1/2) logₐ x = logₐ (x^(1/2)) = logₐ (√x), and k = −1/2 gives (−1/2) logₐ x = logₐ (1/√x).WJEC
fractional exponents: Fractional indices link to radicals, since a^(1/q) = ᑫ√a, so a^(p/q) = (ᑫ√a)ᵖ = ᑫ√(aᵖ).WJEC
Fractional exponents as roots and powers: For a > 0, a^(m/n) = (a^(1/n))^m = (a^m)^(1/n), where a^(1/n) is the nth root.Pearson Edexcel
free fall: Motion of a particle falling freely under gravity where air resistance is negligible, so the only force acting is weight and acceleration is constant at a = g…WJEC
Free-body diagrams in mechanics: Isolating one object and showing weight, normal reaction, tension, friction and applied forces with consistent directions.Pearson Edexcel
free-body force diagrams: Clear sketches showing all forces acting ON the particle.WJEC
Frequency density: The vertical axis quantity calculated via frequency density = frequency / class width when class intervals have unequal widths.AQA, Pearson Edexcel, WJEC
friction: A contact force that acts parallel to the contact surface and opposes relative motion or the tendency to move.Pearson Edexcel
Function: A mathematical mapping that assigns exactly one output value to each valid input value.AQA, Pearson Edexcel, WJEC
Function and algebraic language: Knowing what a symbol or phrase means and when it is legitimate, for example that f⁻¹(x) denotes the inverse function, not the reciprocal.AQA
function modelling: Selecting suitable function families, such as polynomial, exponential, trigonometric or rational, to represent physical scenarios.WJEC
Function transformations: Changes such as y = a^(x + c) shifting left by c, y = a^x + d shifting up by d, and y = a^(kx) stretching horizontally.Pearson Edexcel
functions and mappings: A mapping that assigns to each element x in the domain exactly one element y in the codomain, written y = f(x).WJEC
fundamental quantities: Length, time and mass, with SI units metre (m), second (s) and kilogram (kg).AQA
Fundamental S.I. quantities: Length measured in metres, time in seconds and mass in kilograms, the three quantities from which derived quantities are formed.Pearson Edexcel
Fundamental Theorem of Calculus: Links differentiation and integration, with two parts: if F(x) = ∫_a^x f(t) dt, then F'(x) = f(x); and ∫_a^b f(x) dx = F(b) - F(a), where F is any…AQA, Pearson Edexcel, WJEC
Fundamental trigonometric identities: Identities including tan θ = sin θ / cos θ and sin²θ + cos²θ = 1, used to simplify expressions, prove other identities and solve trigonometric equations.Pearson Edexcel

G

general addition rule: States that P(A ∪ B) = P(A) + P(B) − P(A ∩ B), used in combination with the multiplication rule to solve multi-step probability problems.WJEC
General and particular solutions: The analytical solution includes a constant of integration C, while a particular solution uses a given initial condition to find C.Pearson Edexcel
general form: A straight-line equation written as ax + by + c = 0, where a and b are not both zero.Pearson Edexcel
General linear form: The form ax + by + c = 0 covers vertical lines such as x = 4, which y = mx + c cannot.Pearson Edexcel
general multiplication rule: States that P(A ∩ B) = P(B) × P(A|B) = P(A) × P(B|A), provided P(A) > 0 and P(B) > 0.WJEC
general solution: The result of performing the integration, containing an arbitrary constant of integration C.Pearson Edexcel, WJEC
general solutions: The result of integrating both sides, containing an arbitrary constant of integration c.WJEC
Geometric: Describes a pattern with a constant ratio between terms.Pearson Edexcel
geometric interpretation: Extracting correct geometric or physical relationships, such as perpendicularity or force equilibrium, from a diagram.WJEC
Geometric modelling with vectors: Vectors model displacement, velocity and force in both dimensions, and can be used to solve geometric or physical problems such as finding a point dividing a…Pearson Edexcel
geometric progression: A sequence with a constant common ratio r between consecutive terms, where uₙ₊₁ / uₙ = r.WJEC
Geometric proof using vectors: Vectors may be used to prove geometric results, such as showing lines are parallel or points are collinear, or to find intersections of lines in 2D.AQA
Geometric properties of circles: Three properties used to find centres, radii, tangents and intersections, often combining algebra and geometry.AQA
Geometric sequence: A sequence in which each term is obtained by multiplying the previous term by a constant common ratio $r$.AQA, WJEC
geometric vector proofs: Vectors provide powerful synthetic tools to prove geometric theorems and solve configuration problems without coordinates.WJEC
Geometrical proof: A proof, such as using a unit circle or right-angled triangles, that establishes the compound angle formulae.AQA
Geometrical proofs: Proofs of the addition formulae using stacked right-angled triangles, where a triangle with angle B sits on the hypotenuse of one with angle A, and resolving…Pearson Edexcel
gradient: The rate of change of the vertical variable with respect to the horizontal variable on a straight-line graph, calculated as change in Y divided by change in X.Pearson Edexcel
gradient and intercept: Values read from the straight-line graph, used to estimate the unknown parameters by reversing the logarithmic transformations.WJEC
Gradient as a rate of change: On a displacement–time graph the gradient gives velocity, and on a velocity–time graph the gradient gives acceleration, since acceleration is the rate of…AQA, Pearson Edexcel
Gradient at a point: Found by substituting the x-coordinate into dy/dx.Pearson Edexcel
gradient formula: The gradient m of a line through points (x₁, y₁) and (x₂, y₂) is m = (y₂ − y₁)/(x₂ − x₁).WJEC
gradient of tangent: The gradient of the tangent to the graph of y = f (x) at a general point (x, y), taken as a limit.WJEC
Gradients and intercepts: The general form ax + by + c = 0 can be rearranged to find these, and in modelling they should be interpreted in context.AQA
Gradients and rates of change: Differentiation gives the gradient function, and to find the gradient at a point, substitute the x-coordinate into dy/dx.AQA
Graph of an inverse function: The reflection of y = f(x) in the line y = x, so points (a, b) and (b, a) correspond.Pearson Edexcel
Graph transformations: Changes that alter the position and shape of the graph of y = f(x) in predictable ways, operating either outside or inside the function.AQA, WJEC
Graphical behaviour including asymptotes and ranges: Sec and cosec have vertical asymptotes where cos or sin are zero with ranges |y| ≥ 1, while cot has asymptotes where sin is zero and range all real numbers.AQA
Graphical description of motion: Graph features such as intercepts, turning points and horizontal sections are used to describe the motion in words, where a horizontal line means the particle…Pearson Edexcel
Graphical interpretation and modelling: Graph features such as intercepts, turning points and asymptotes are used to describe motion qualitatively.AQA
Graphical interpretation of derivatives: Sketching the gradient function for a given curve by noting where f is increasing (f' > 0), decreasing (f' < 0), and stationary (f' = 0).AQA
Graphical interpretation of gradient and area: The gradient and area of velocity–time and displacement–time graphs are interpreted as acceleration and displacement respectively.Pearson Edexcel
Graphical interpretation of iteration: Cobweb diagrams show iterates alternating around the root, while staircase diagrams show them approaching monotonically.AQA
graphical intersections: The solutions seen as points where the corresponding graphs meet, such as a line intersecting a circle or parabola at two points, one point or no points.AQA, WJEC
Graphical representation: A diagram or sketch should be chosen to reveal structure, such as intercepts, turning points, asymptotes or regions, rather than a decorative picture.AQA
graphical solutions: Estimating or analysing roots by sketching two well-understood curves and locating where they meet.WJEC
Graphical transformations of functions: Simple transformations move or reshape the graph of y = f(x), including y = af(x), y = f(x) + a, y = f(x + a), y = f(ax) and combinations of these.Pearson Edexcel
Gravitational acceleration: The value g, in m s⁻², which near the Earth's surface is approximately 9.8 m s⁻², often used as 9.81 m s⁻² depending on required accuracy.Pearson Edexcel
gravitational acceleration g: The local acceleration due to gravity, taken near the surface of the Earth as 9.8 m s⁻², or 9.81 m s⁻² or 10 m s⁻² depending on specification instructions.WJEC
growth and decay models: Direct proportionality gives dy/dt = ky, where k is positive for growth or negative for decay (dy/dt = −ky with k > 0).WJEC

H

half-life: Found by setting y = 0.5y₀, giving t_(1/2) = (ln 2)/λ.WJEC
Half-life and decay constants: In radioactive decay N = N₀e^(−λt), λ is the decay constant and half-life is given by t½ = ln 2 ÷ λ.Pearson Edexcel
harmonic form: The equivalent form of a cos θ + b sin θ written as r cos(θ ± α) or r sin(θ ± α).AQA, OCR, WJEC
Harmonic form (R cos(θ ± α) or R sin(θ ± α)): The equivalent form of a cos θ + b sin θ, where R = √(a² + b²) and α satisfies cos α = a/R, sin α = b/R for R cos(θ - α).AQA
hidden quadratics: Equations that are quadratic in form, including quartics with even powers, exponential equations, equations involving surds and trigonometric quadratics.WJEC
Histogram: A diagram for single-variable data in which unequal class widths mean frequency is represented by the area of each bar, not its height.AQA, Pearson Edexcel
Histogram area as frequency: In a histogram, bars are drawn so that area, not height, represents frequency, which matters when class widths are unequal.AQA
histograms: Diagrams for single-variable data in which the area of each bar represents frequency.WJEC
horizontal and vertical scaling: The multiplier a indicates a horizontal stretch by scale factor 1/a, while a stretch vertically by scale factor a is parallel to the y-axis.WJEC
horizontal asymptotes: As x → −∞, aˣ approaches zero from above, so the line y = 0 is a horizontal asymptote.WJEC
horizontal tangent: A tangent line produced when f'(xₙ) = 0, which never intersects the x-axis and causes division by zero.WJEC
hyperbola: The shape of the reciprocal graph y = a/x, described in the note as a rectangular hyperbola.WJEC
Hypothesis testing: Using the language of statistical hypothesis testing, developed through a binomial model, to assess evidence against H0, not test H1.AQA

I

Idealised assumptions and their limitations: The model neglects air resistance and treats g as constant, so it applies only while the projectile is in free flight.Pearson Edexcel
Identity: Holds true for every value within the domain of the variables, denoted by the triple-bar symbol ≡.AQA, OCR, Pearson Edexcel, WJEC
Identity function: The function that leaves every input unchanged, mapping x to x.Pearson Edexcel
impending slip: The condition at which F = μR holds, occurring when the applied tangential force reaches the maximum static friction threshold.WJEC
implication: A directional inference in which truth of premise P necessitates conclusion Q, while the converse may fail.WJEC
Implicit differentiation: Differentiating each term of a relation with respect to x, applying the chain rule to terms containing y, then rearranging to make dy/dx the subject.AQA, Pearson Edexcel, WJEC
Improper fraction: A fraction where the numerator degree is not lower than the denominator degree, first divided to give a polynomial plus a proper fraction.Pearson Edexcel
improper fractions: Algebraic fractions where the degree of the numerator is greater than or equal to the degree of the denominator, requiring algebraic division.WJEC
Improper rational function: A rational function whose numerator has degree equal to or greater than its denominator.Pearson Edexcel
inclined plane dynamics: On a rough inclined plane of angle α, a body accelerating down the slope satisfies mg sin α − μ(mg cos α) = ma, yielding a = g(sin α − μ cos α).WJEC
inclined plane mechanics: On an inclined plane at angle α to horizontal, weight W = mg resolves into mg sin α down the slope and mg cos α perpendicular into the slope.WJEC
Increasing and decreasing functions and points of inflection: A function is increasing where dy/dx > 0 and decreasing where dy/dx < 0; a point of inflection is where the curve changes concavity.Pearson Edexcel
Increasing function: A function whose values rise as x increases over a stated interval; its first derivative is positive there.WJEC
increasing functions: On an interval, if f'(x) ≥ 0 throughout, then f is increasing.WJEC
increasing sequence: A sequence in which every term is greater than the one before.AQA, Pearson Edexcel
increasing sequences: A sequence that satisfies xₙ₊₁ ≥ xₙ for all n, meaning every term is greater than or equal to its predecessor.WJEC
Indefinite integral: The family of all antiderivatives of a function, written with an arbitrary constant $C$.AQA
independence: The condition that the outcome of one trial does not change the probability distribution of another trial.Pearson Edexcel
independence of components: Resolving horizontally gives zero acceleration so horizontal velocity remains constant, while resolving vertically gives a_y = −g.WJEC
Independence of horizontal and vertical motion: The horizontal acceleration is zero so the horizontal velocity component stays constant, while the vertical component changes linearly.Pearson Edexcel
independence violations: In reality, weather conditions create correlated risks, and disease transmission causes spatial clustering, so individual occurrences influence one another.WJEC
Independent: Events or trials are independent when the outcome of one does not change the probability of another.Pearson Edexcel
Independent events: Events that have no influence on each other, so P(A ∩ B) = P(A) × P(B), which is the key test and calculation tool.AQA, Pearson Edexcel, WJEC
Independent trials: Trials for which the outcome of one trial does not affect the outcome or probability of another trial.AQA
Independent variable: The input variable with respect to which change is measured, often time t in a model.Pearson Edexcel
Index: The variable in a sigma expression that runs through the stated integer values and is treated as a dummy variable.AQA
Index (Power/Exponent): The small number written above and to the right of the base, indicating how many times the base is multiplied by itself.Pearson Edexcel
index form conversion: Rewriting y = logₐ x as aʸ = x, where the base of the log becomes the base of the power.WJEC
index of summation: In the expression ∑_(r=1)ⁿ u_r, r is this, running from the lower limit to the upper limit.WJEC
inequality F ≤ μR: The condition the friction force F satisfies under the Coulomb model, where μ is the coefficient of friction and R is the normal reaction force.WJEC
inequality regions: Identified by sketching the parabola to visualise where the curve lies above or below the x-axis.WJEC
inextensible string: Modelling assumption meaning acceleration magnitude a is identical for both connected particles.Pearson Edexcel, WJEC
Inference from sample to population: The sample gives evidence about the unknown population proportion, so conclusions are inferences, not certainties.Pearson Edexcel
infinite binomial series: For any rational index n, negative or fractional, the binomial series continues with higher order terms and is valid when |x| < 1.WJEC
infinitesimal elements: Physical quantities are conceptualised as limits of sums of these elements.WJEC
infinity of primes: Proved by assuming a finite set of primes and constructing N, which implies either N is prime or has a prime factor not in the list.WJEC
informal inference: Examining sample characteristics and making reasoned deductions about the wider population while acknowledging the presence of sampling uncertainty.AQA, WJEC
Information collection and processing: Gathering measurements, given data or assumptions, then using calculation, algebra or statistical analysis on them.Pearson Edexcel
Initial and boundary conditions: Conditions applied to fix the arbitrary constant in the general solution of a differential equation.AQA
Initial condition: A known value of the dependent variable at a specified value of the independent variable.Pearson Edexcel
Initial conditions: A given condition, such as y = 1 when x = 0, is substituted to find the constant C for a particular solution.Pearson Edexcel
Initial conditions and constants of integration: Each indefinite integral needs a constant of integration fixed by initial conditions, while a definite integral between two times gives the change in the…Pearson Edexcel
Initial or boundary condition: A given value that determines the constant in the general solution.Pearson Edexcel
Initial value: The starting approximation $x_0$ used to begin an iterative process.Pearson Edexcel
Input selection: Choosing inputs that are meaningful in context, such as positive times or realistic speeds, and valid within the model's domain.Pearson Edexcel
inspection integration: Evaluating integrals of the form ∫ f'(x)/f(x) dx and ∫ f'(x)[f(x)]ⁿ dx by inspection.WJEC
instantaneous rest: When a particle reverses direction, its instantaneous velocity is momentarily zero, but its acceleration may be non-zero.WJEC
instantaneous velocity: Velocity at a particular instant, equal to the gradient of the tangent to a displacement–time graph at that instant.AQA
Integer: A whole number, which can be positive, negative, or zero.Pearson Edexcel
Integration by parts: A method that reverses the product rule, including more than one application of the method but excluding reduction formulae.AQA, Pearson Edexcel, WJEC
Integration by substitution: A method that reverses the chain rule, limited to cases where one substitution will lead to a function which can be integrated.AQA, Pearson Edexcel, WJEC
integration in kinematics: Reversing differentiation determines accumulated change, giving velocity from acceleration and displacement from velocity, including a constant of integration.WJEC
Integration of functions of x and y: Integrating both sides with respect to their respective variables, including the constant of integration.AQA
interacting bodies: The two different bodies on which third-law action-reaction pairs act.WJEC
intercept interpretation: The intercept c represents the initial value or fixed base charge at x = 0.WJEC
intercepts and stationary points: Mathematical features whose physical significance must be explained, such as a maximum of h(t) representing the greatest height achieved by the projectile.WJEC
Intermediate value theorem: If f(x) is continuous on a closed interval [a, b] and f(a) and f(b) have opposite signs, there exists at least one real root α ∈ (a, b) such that f(α) = 0.AQA, WJEC
Internal division: A point lies between two endpoints and divides the joining line segment in a stated ratio.WJEC
interpolation: A prediction that is reliable because it lies within the range of observed explanatory data.Pearson Edexcel, WJEC
Interpretation: Reading the mathematical result back in the original context and commenting on the reasonableness of the assumptions.Pearson Edexcel
Interpretation and validation: Interpreting results in the context of the original problem, checking reasonableness and units, and deciding whether the cycle needs repeating.AQA
Interpretation in context: Comparing model predictions with data or with what is plausible, and commenting on the adequacy of the model.Pearson Edexcel
Interpretation of mathematical results in context: Commenting on whether the assumptions make the result reasonable or limited, keeping the interpretation consistent with the stated assumptions.AQA
Interpretation of numerical solutions: Always relate the final value back to the original problem, checking it lies within the domain and makes sense practically.AQA
Interpretation of outputs: Reading the results the model produces in the context of the original situation, including units and practical meaning.AQA
Interpreting and evaluating mathematical models: Communicating findings clearly by interpreting the solution in context with appropriate units and realistic constraints, and discussing assumptions made and…AQA
Interpreting probabilities in context: Understanding the distribution's shape and context, for example the probability that exactly or at most a certain number of successes occur.AQA
Interpreting single-variable diagrams: Involves reading frequencies, identifying modal classes and estimating probabilities from diagrams for single-variable data.AQA
interquartile range: A measure of variation calculated as Q₃ − Q₁.AQA, WJEC
Intersection: Bounded regions represent intersections, written compactly as a single continuous interval using bounded inequalities.AQA, Pearson Edexcel, WJEC
intersection limits: The x-coordinates of the intersection points, found by solving the simultaneous equation f(x) = g(x), which define the limits of integration a and b.WJEC
Intersection points: Solving f(x) = g(x) graphically means finding the x-coordinates of the points where the two graphs meet.AQA, Pearson Edexcel
interval: The set of x-values between stated bounds, with inclusion or exclusion shown by the inequality or bracket notation.Pearson Edexcel
interval additivity: The property that the integral from a to c equals the integral from a to b plus the integral from b to c for any intermediate b.WJEC
interval inequalities: Setting up the inequality f'(x) ≥ 0 for increasing or f'(x) ≤ 0 for decreasing, then solving it.WJEC
invalid algebraic steps: Operations within a proof that are not valid, such as dividing by an expression that can equal zero.WJEC
invariant points: Points that stay fixed under a transformation, such as points lying on the x-axis when the graph is stretched vertically by scale factor a.WJEC
Inverse derivative relationship: If x is differentiable as a function of y and dx/dy is non-zero, then dy/dx = 1/(dx/dy).Pearson Edexcel
Inverse function: Reverses the mapping, so if f(a) = b then f⁻¹(b) = a, and exists only when f is one-to-one on its domain.AQA, Pearson Edexcel
inverse functions: Only one-to-one functions possess an inverse function f⁻¹(x), whose domain equals the range of f(x) and whose range equals the domain of f(x).Pearson Edexcel, WJEC
Inverse Normal: A calculation that finds a boundary value corresponding to a given cumulative probability.Pearson Edexcel
inverse Normal calculations: Given a cumulative probability p, the corresponding critical value x is found using calculator Inverse Normal functions, or by finding z from tables and…WJEC
inverse proportion: A proportional relationship such as y = k/x or y = k/x², where given points can be used to find the constant of proportionality k.AQA, WJEC
Inverse relationship between differentiation and integration: Differentiation and integration are inverse processes.AQA
inverse trigonometric function: A function that returns the principal angle whose sine, cosine or tangent is the given value, for example $\arcsin x$.Pearson Edexcel
inverse trigonometric functions: Arcsin x (sin⁻¹ x), arccos x (cos⁻¹ x) and arctan x (tan⁻¹ x) require restricted domains of the original functions to be one-to-one.WJEC
Inverse trigonometric functions and principal values: Arcsin, arccos and arctan return angles for given ratios, with restricted ranges that make them functions and give principal values.AQA
Irrational Number: A real number that cannot be written as a simple fraction; its decimal expansion goes on forever without repeating.AQA, Pearson Edexcel
irrationality of √2: Proved by assuming √2 = a/b in simplest form, showing a and b are both even, which contradicts the assumption that they have no common factors.WJEC
Isolating dy/dx: Rearranging the resulting equation correctly to make dy/dx the subject, including collecting like terms and factorising if necessary.AQA
Iteration: A numerical method that refines a solution, showing successive values and demonstrating that the sequence converges to the required root.Pearson Edexcel, WJEC
Iterative formula: The recurrence relation that calculates the next approximation from the current approximation, usually $x_{n+1}=g(x_n)$.Pearson Edexcel
Iterative processes: A valid iterative formula such as interval bisection or Newton-Raphson is applied accurately for at least two iterations, showing substituted values.AQA
Iterative processes and convergence: Methods such as Newton-Raphson can converge rapidly, but convergence is not guaranteed, as poor starting values or turning points can cause divergence.AQA
Iterative refinement: Repeating the cycle by refining initial assumptions, introducing additional parameters, and re-evaluating the revised model when discrepancies arise.AQA, Pearson Edexcel, WJEC

K

kinematic decay and drag: Solving m dv/dt = −kv produces velocity decay v(t) = v₀ e^(−kt/m), showing that velocity approaches zero asymptotically as t → ∞.WJEC
Kinematics: The study of motion in a straight line or in two dimensions, connecting displacement, velocity and acceleration through calculus.AQA
Kinematics and motion: A context in which the solution of a differential equation is interpreted, for example speed decaying exponentially.AQA
Kinematics with constant acceleration in vector form: For kinematics with constant acceleration, vector equations such as r = r0 + ut + ½at² are used, applying them to each component.AQA
kinetic friction: Dynamic friction acts parallel to the contact surface in the direction directly opposing the relative motion, operating at its maximum value F = μR because…WJEC

L

large data sets: Data that must be real and sufficiently rich to enable the concepts and skills of data presentation and interpretation in the specification to be explored.WJEC
LATE priority rule: The choice of u follows this priority rule: Logarithmic, Algebraic, Trigonometric, Exponential.WJEC
laws of indices: The three core rules a^m × a^n = a^(m+n), a^m ÷ a^n = a^(m-n) and (a^m)^n = a^(mn), which hold for all rational m and n.AQA, WJEC
laws of logarithms: Rules that let you combine or split logarithms of the same base: adding gives the log of the product, subtracting gives the log of the quotient, and a…Pearson Edexcel, WJEC
light inextensible string: An ideal string with negligible mass that does not stretch; when taut it transmits equal tension and constrains connected particles to equal acceleration…AQA
light string: Modelling assumption meaning string mass is zero, so tension T is uniform throughout.WJEC
Like surds: Surds that can be combined through addition and subtraction, such as 3√2 + 5√2 = 8√2.AQA
limit of a sum: The sum of areas of rectangles tends to a value as the number of strips increases without bound and the width of each strip tends to zero.AQA, WJEC
Limit of a sum as n → ∞: The value the sum Σ f(xᵢ)Δx approaches as n → ∞ and Δx → 0, which defines the definite integral when it exists.Pearson Edexcel
limit of chord gradient: Taking the limit as h → 0 of the chord gradient yields the derivative f'(x).WJEC
Limitations: Restricted domains, unrealistic long-term behaviour, and assumptions such as constant acceleration or negligible resistance.Pearson Edexcel
Limitations and model criticism: The binomial is inappropriate if trials are not independent, the number of trials is not fixed or p changes; the Normal is inappropriate for strongly skewed…Pearson Edexcel
Limitations of mathematical models: Unrealistic values such as negative speed or unbounded growth, or validity only for a restricted time interval.AQA
Limitations of numerical methods: Change of sign methods can fail if f is not continuous, if there is an even number of roots, if the interval is too large, or if the graph touches the axis.AQA, Pearson Edexcel, WJEC
limiting equilibrium: The state in which friction has reached its maximum possible value F_max = μR and the body is on the point of slipping.AQA, Pearson Edexcel, WJEC
Limiting equilibrium and static friction: When a body is in limiting equilibrium, friction takes its maximum value F = μR; when it is stationary but not at the point of sliding, F < μR.AQA
Limiting value: The value a model approaches as the independent variable becomes arbitrarily large.Pearson Edexcel
Limiting values: Values found as θ → 0, which the approximations are used to find.Pearson Edexcel
Limits and first principles: The gradient of the tangent defined as the limit of [f(x+h) - f(x)]/h as h tends to 0, used to differentiate from first principles.AQA
limits of integration: The specific lower limit a and upper limit b of a definite integral, at which the antiderivative is evaluated.Pearson Edexcel, WJEC
line of action: The infinite straight line through a force in the direction in which the force acts.Pearson Edexcel
Line of best fit: A straight line drawn through plotted transformed variables, from which the gradient is estimated using two well-separated points.Pearson Edexcel
linear association: The relationship between two quantitative variables whose direction and strength correlation describes.WJEC
linear association scope: r measures only linear association and cannot detect curved relationships.WJEC
linear association test: Testing whether an observed sample correlation r indicates a genuine linear association in the population, rejecting H₀ in favour of significant linear…WJEC
Linear factor: A first-degree factor of the form $ax+b$, where $a\ne0$.Pearson Edexcel
linear inequalities: Solved like linear equations, except multiplying or dividing by a negative quantity reverses the inequality sign.WJEC
Linear inequalities and sign reversal: Solved like an equation, but multiplying or dividing by a negative number reverses the inequality sign; brackets are expanded first and fractions cleared by…Pearson Edexcel
linear interpolation: A method used to estimate values within classes, including frequencies or percentiles within a class interval.WJEC
linear model: A model in which one variable changes at a constant rate with another, represented by a straight-line equation.Pearson Edexcel
linear modelling: Using straight line models in a variety of contexts, where a dependent variable changes at a constant rate with respect to an independent variable.Pearson Edexcel, WJEC
linear operator: Differentiation is one: the constant multiple rule gives d/dx(c f(x)) = c f'(x), and the sum and difference rule gives d/dx(f(x) ± g(x)) = f'(x) ± g'(x).WJEC
Linearisation: A transformation of variables that converts a non-linear relationship into a straight-line relationship so parameters can be estimated from gradient and…AQA, Pearson Edexcel
linearising exponents: Using the power law k ln x to bring the exponent down, giving x ln a = ln b as a linear equation in x.WJEC
linearity of summation: Properties allowing constants to factor out, ∑ c u_r = c ∑ u_r, and sums to split term-by-term, ∑ (u_r + v_r) = ∑ u_r + ∑ v_r.WJEC
Links between index laws and log laws: The logarithm laws follow from the index laws because logs are exponents.Pearson Edexcel
Local behaviour: The shape or value of a function in a small region around a particular point, here around θ = 0.Pearson Edexcel
Logarithm: log_a x is the power to which the valid base a must be raised to obtain x, where a>0, a≠1 and x>0.AQA, WJEC
logarithm definition: The inverse of an exponential function, where y = logₐ x is equivalent to aʸ = x, with base a > 0 and a ≠ 1 and argument x > 0.WJEC
Logarithm laws: The addition law combines logs as log_a(x)+log_a(y)=log_a(xy), the subtraction law gives log_a(x)−log_a(y)=log_a(x/y), and the power law gives k…AQA
logarithmic antiderivatives: Integrating term by term uses the standard logarithmic integral ∫ [1/(ax + b)] dx = (1/a) ln|ax + b| + c.WJEC
logarithmic domain: The graph of y = logₐ x has domain x > 0, since logₐ 0 is undefined.WJEC
Logarithmic graphs and asymptotes: The graph of log_a(x) passes through (1, 0) with the y-axis as a vertical asymptote, and the domain is x > 0.Pearson Edexcel
logarithmic integration: Integrating 1/x gives ln|x| + c for x ≠ 0, with absolute value brackets ensuring the logarithm is defined for negative domain values.WJEC
logarithmic integration pattern: Integrals of the shape ∫ [f'(x)/f(x)] dx, which integrate immediately to ln|f(x)| + c.WJEC
logarithmic linearisation: Taking logarithms of both sides to transform a relationship into the straight-line form Y = mX + c.WJEC
Logical deduction: Building logical arguments that establish trigonometric identities or solve equations by proof, with each step justified and without assuming the result.AQA
logical fallacies: Errors in a mathematical argument that can be identified by scrutinising each deductive transition.WJEC
Logical sequencing and justification: Each step is justified by a named identity or algebraic operation, and the result being proved must not be assumed.Pearson Edexcel
Logical structure and deduction: Each line follows from the previous one, using 'since', 'therefore', 'if … then' and 'if and only if' accurately.AQA
Logical structure and implication: The link between consecutive lines of an argument, which must be checked to see whether a stated implication is valid in the direction used.Pearson Edexcel
logical structuring: Linking intermediate sub-goals into a coherent, continuous multi-stage mathematical deduction.WJEC
Lower limit: The starting value of the index in a sigma expression, from which counting to the upper limit inclusive gives the number of terms.AQA
lowest terms: A fraction whose numerator and denominator have no common factor greater than 1.AQA

M

Magnitude: Calculated using Pythagoras in 2D or 3D, as the square root of the sum of the squares of the components.AQA, Pearson Edexcel, WJEC
magnitude and direction: The size of the resultant force given by the square root of the sum of squared components, and its direction angle relative to the x-axis.AQA, WJEC
magnitude and spatial distance in three dimensions: Extends Pythagoras as the square root of the sum of the three squared components, and the distance between two points uses the magnitude of their displacement.WJEC
Magnitude formula: The square root of the sum of the squared component differences, extending to three dimensions by adding the squared difference of the z coordinates.Pearson Edexcel
magnitude/direction form: A representation using r, the magnitude, and theta, the direction, converted back using x = r cos(theta) and y = r sin(theta).AQA, Pearson Edexcel
Many-one function: A function in which two or more different inputs can give the same output.Pearson Edexcel
mass and acceleration: For a particle of constant mass m, the acceleration a is directly proportional to the net resultant force ΣF and acts in the identical direction.WJEC
mathematical abstraction: Recognising the underlying mathematical structure in a situation and simplifying and abstracting appropriately to enable problems to be solved.WJEC
Mathematical communication: Presenting mathematics as a reasoned argument, not just producing an answer, through appropriate use of diagrams, sketches, logical deduction and precise…AQA
mathematical diagrams: Tools for visualising structural relationships and setting up algebraic equations, constructed to represent geometric and physical scenarios.WJEC
mathematical fidelity: The descriptive accuracy of a model, which refinement improves and which must be balanced against increased mathematical complexity.WJEC
mathematical idealisations: Assumptions in applied contexts, such as treating objects as point masses or neglecting air resistance, whose validity across the operating domain is evaluated.WJEC
Mathematical model: A simplification, not the reality, obtained by translating a situation in context into mathematical form.AQA, Pearson Edexcel
Mathematical modelling: Transforms complex real-world situations into tractable mathematical formulations, requiring identification of key dependent and independent variables and the…AQA, WJEC
Mathematical modelling in context: In context, you may need to set up the equation from given information and decide on a sensible starting value.AQA
mathematical proof: Establishes universal truth from initial axioms through a deductive chain, proceeding from given assumptions through a series of logical steps to a conclusion.WJEC
Mathematical representation: The expression of relationships using functions, equations or graphs.Pearson Edexcel
mathematical strategy: The process begins by identifying given information and the ultimate goal, formulating intermediate sub-goals, and selecting appropriate mathematical tools.WJEC
mathematical syntax: The proper deployment of operational symbols, brackets to establish order of precedence, and set-builder notation, ensuring unambiguous mathematical discourse.WJEC
maximum and minimum values: The harmonic form reveals the maximum value R, occurring when cos(θ − α) = 1, and the minimum value −R.WJEC
maximum static friction: The threshold that a tangential force attempting to cause motion must not exceed for a body resting on a rough surface to remain in equilibrium.WJEC
Mean (μ): The centre of symmetry of the Normal curve.AQA, Pearson Edexcel
Measures of central tendency: The mean, median and mode, which are interpreted and calculated in this topic.AQA, Pearson Edexcel
Measures of variation: The range, interquartile range and standard deviation, which are interpreted and calculated in this topic.AQA, Pearson Edexcel
Method mark: A mark awarded for a valid mathematical method or intermediate step, even if a later arithmetic error occurs.Pearson Edexcel
methodological evaluation: Critiquing proposed sampling designs by identifying coverage errors and selection bias, and selecting and justifying appropriate sampling techniques for…WJEC
midpoint position vector: The position vector OM of the midpoint M of the line segment AB, given by ½(OA + OB).WJEC
misleading graphical features: Misleading traits such as truncated vertical axes, unequal bar widths, or distorted 3D perspective.WJEC
missing data: Missing observations, described as null entries, present in raw datasets.WJEC
mixed angle equations: Equations with mixed arguments, such as sin 2x = sin x, rewritten in a single angle x and factorised using double angle formulas.WJEC
model critique: Identifying a specific violated assumption, such as non-constant probability or dependence, in order to reject an inappropriate probability model.WJEC
model evaluation: Evaluating whether the outcome is realistic, consistent with known boundary conditions, and sufficiently accurate, and articulating specific modifications…WJEC
model extrapolation: Linear extrapolation beyond observed data ranges assumes the rate remains constant indefinitely.WJEC
Model limitation: A reason why a mathematical model may not accurately represent the real situation outside a stated range or assumption.Pearson Edexcel
model limitations: Physical constraints and practical limitations of differential equation models, such as resistance laws failing at high speeds or capacity constraints.AQA, WJEC
Model limitations and refinements: Models assume constant rates and unlimited resources, so limitations include resource limits, varying drug clearance and changing decay rates; refinements…Pearson Edexcel
model refinement: Considering a model's outputs and simplifying assumptions to improve it, balancing improved descriptive fidelity against increased mathematical complexity so…AQA, Pearson Edexcel, WJEC
Model selection: Choosing a probability model that fits the random variable and justifying the choice with reference to the context.AQA
Model selection and assumptions: Matching the context's structure to a distribution's assumptions, then stating the model, its parameters and the reason in context.Pearson Edexcel
Modelling: Translates a real situation into a sequence of individual terms or a series of cumulative totals.Pearson Edexcel
Modelling assumptions: A fixed number of independent trials, two outcomes per trial, and a constant probability of success, which must be recognised as appropriate.AQA, Pearson Edexcel, WJEC
Modelling real situations with derivatives: Translating a written rate relationship into an equation containing a derivative, defining every symbol and keeping units consistent.Pearson Edexcel
Modelling real-world situations with sequences and series: Applying sequences and series to real-world situations by translating a verbal description into mathematical notation and solving using sum formulae.AQA
Modelling with trigonometry: Applying trigonometric functions to model and solve real-world problems, interpreting the context and setting up equations.AQA
modulus function: Maps real numbers to non-negative values, with |x| = x for x ≥ 0 and |x| = −x for x < 0.WJEC
Modulus graph: A V-shape drawn by reflecting the negative part of the line in the x-axis, with vertex where mx + c = 0.Pearson Edexcel
Modulus notation: The notation |r| < 1 means r lies strictly between −1 and 1.Pearson Edexcel
Modulus notation and inequalities: The notation |r|<1 means -1<r<1, which is stronger than r<1 alone and includes negative ratios with magnitude less than one.AQA
modulus of common ratio: Written |r|, it must be less than 1 for an infinite geometric series to converge to a finite limit.WJEC
Modulus signs: Used inside logarithms where appropriate, because the argument of a logarithm must be positive.AQA
Modulus transformation: A transformation using absolute value that replaces negative outputs with their positive magnitudes.Pearson Edexcel
moment: A measure of the turning effect of a force about a point, equal to Fd for a force F acting at perpendicular distance d from a pivot.AQA, Pearson Edexcel
Moment and perpendicular distance: The turning effect of a force about a point, defined as force times perpendicular distance, with unit N m.Pearson Edexcel
moment of a force: Measures its turning effect about a chosen point or axis of rotation, defined as the product of the force magnitude F and the perpendicular distance d.Pearson Edexcel, WJEC
monotonic: Strictly increasing or strictly decreasing on an interval.Pearson Edexcel
Monotonicity: A function is increasing where dy/dx > 0 and decreasing where dy/dx < 0.AQA
More realistic assumptions: Changes to a model that often make it more complex but more accurate, altering its predictions.AQA
motion in a plane: Parametric equations model closed loops and spirals that cannot be represented as single-valued Cartesian functions y = f(x).WJEC
Motion in a straight line: Motion where displacement r(t) gives velocity v = dr/dt and acceleration a = dv/dt = d²r/dt², with integration giving velocity and displacement.AQA
Motion on rough surfaces and Newton’s second law: When a body moves, friction is usually modelled as F = μR opposing motion, and Newton’s second law is applied along the surface, including friction, to find…AQA
Motion under gravity: Motion in a straight line under gravity alone, where a particle accelerates downwards at g so equations of constant acceleration apply with a = g.Pearson Edexcel
multi-step arguments: Each deductive stage must connect logically to the next, maintaining dimensional consistency and exact values where required until the final contextual…WJEC
Multi-step reasoning: Maintaining logical flow across multiple steps, ensuring each conclusion follows from previous work and is clearly justified.AQA, Pearson Edexcel
multiple-angle equations: Equations such as sin(2x + 30°) = 0.5 where the interval for the composite angle is transformed first, all solutions for that angle are found, and finally x…WJEC
multiplication rule: Independence is defined formally by the multiplication rule P(A ∩ B) = P(A) × P(B), or equivalently P(A|B) = P(A).AQA, WJEC
multivariate data: Rich records from which summary statistics or graphical displays are interpreted in context.WJEC
mutually exclusive events: Two events A and B are mutually exclusive if they cannot occur simultaneously, meaning A ∩ B = ∅ and P(A ∩ B) = 0.AQA, Pearson Edexcel, WJEC

N

natural exponential: The function f(x) = eˣ, which uses Euler's constant e ≈ 2.71828 as its base.WJEC
Natural exponential function: The exponential function y = e^x, where e is Euler's number, approximately 2.71828.AQA
natural logarithm: The function y = ln x is defined as the logarithm to base e, so y = ln x ⇔ eʸ = x.AQA, WJEC
nature of roots: Determined by the discriminant: if Δ > 0 there are two distinct real roots, if Δ = 0 one repeated real root, and if Δ < 0 no real roots.WJEC
negative area regions: Parts where the curve falls below the x-axis, whose physical area is the absolute value of the integral.WJEC
Negative exponent: A power written as a^(-n), which equals 1/a^n.AQA
Negative exponents as reciprocals: Negative exponents give reciprocals, so a^(−p) = 1/a^p.Pearson Edexcel
negative reciprocal: The number obtained by inverting a non-zero number and changing its sign; for example, the negative reciprocal of 3/2 is −2/3.Pearson Edexcel
newton metre unit (N m): The derived SI unit for a moment, to be stated clearly with a space and distinguished from joules.WJEC
Newton-Raphson: A method that uses the tangent to the curve, giving from an estimate xₙ the next value xₙ₊₁ = xₙ − f(xₙ)/f′(xₙ).Pearson Edexcel
Newton-Raphson method: Uses tangent lines to generate root approximations, with the formula xₙ₊₁ = xₙ − f(xₙ)/f'(xₙ).Pearson Edexcel, WJEC
Newton's first law: A body remains at rest or moves with constant velocity unless acted on by a resultant force.AQA, Pearson Edexcel, WJEC
Newton's second law: Governs the dynamic response of a particle of constant mass m subjected to an unbalanced resultant force, where the acceleration is directly proportional to…AQA, Pearson Edexcel, WJEC
Newton’s second law in two dimensions: Applying F_net = ma in vector form, with separate equations for two perpendicular directions and acceleration in the direction of the resultant force.AQA
Newton’s third law: If body A exerts a force on body B, then B exerts an equal and opposite force on A, and these act on different bodies.AQA, Pearson Edexcel, WJEC
nominal significance level: The stated level such as 5%, which in discrete distributions may be strictly greater than the actual significance level determined by discrete critical regions.WJEC
non-linear patterns: A curved or quadratic association that linear metrics cannot detect, so zero linear correlation does not imply an absence of relationship.WJEC
non-linear relationships: Correlation coefficients close to zero do not preclude strong non-linear relationships.WJEC
Normal: A line perpendicular to the tangent at the point of contact with a curve.AQA, WJEC
Normal approximation: Using a Normal distribution N(np,np(1-p)) to estimate probabilities from a suitable Binomial distribution B(n,p).Pearson Edexcel
Normal approximation to the binomial: Using the Normal distribution to approximate the binomial when n is large and p is close to 0.5, with no continuity correction required.AQA
Normal approximation to the binomial distribution: Approximates a binomial distribution B(n, p) when n is large and p is close to 0.5, using μ = np and σ² = np(1 − p).Pearson Edexcel
Normal conditions: A continuous symmetric bell shape, often justified by the context or underlying normal variation.AQA
Normal distribution: A continuous probability distribution that is symmetric and bell-shaped, defined by its mean μ and variance σ².AQA, Pearson Edexcel
Normal distribution limitations: Inappropriate if data exhibit significant skewness, multi-modality, or strict physical boundaries where a Normal model would predict impossible negative values.WJEC
Normal distribution model: Models continuous variables exhibiting a symmetrical, bell-shaped distribution about mean μ with variance σ².WJEC
Normal distribution probabilities: These correspond to areas under the bell curve for a Normal variable X ~ N(μ, σ²), evaluated via calculator functions (Normal CD) or standardisation.WJEC
Normal hypothesis testing: Testing a claim about the mean of a Normal population when the variance is known, given or assumed, by setting up a null and alternative hypothesis.AQA
Normal mean hypothesis test: A statistical hypothesis test for the mean of a Normal distribution with known, given or assumed variance, interpreting the results in context.WJEC
normal reaction: The force R in the friction model, which is calculated by balancing forces perpendicular to the contact surface.AQA, Pearson Edexcel, WJEC
normal reaction determination: Resolving forces correctly is required to evaluate normal reaction R and dynamic friction before computing acceleration, formulating ΣF_perp = 0 to determine…WJEC
Normal reaction on horizontal and inclined surfaces: For a body on a rough horizontal surface R is often equal to weight, but on an incline R = mg cos θ.AQA
Normalise: To divide a non-zero vector by its magnitude so that the resulting vector has magnitude 1.Pearson Edexcel
Notation and syntax: The grammar of the subject, covering brackets, order of operations, the scope of a summation or integral, and the difference between an expression, an…AQA
Nth term: Given by a + (n-1)d, where a is the first term and d is the common difference.AQA
nth term formula: The nth term is uₙ = a + (n − 1)d, where a is the first term and d is the common difference.Pearson Edexcel
nth term formulas: A formula such as xₙ = 3n − 2 or xₙ = 2ⁿ which allows any term to be calculated directly by substituting n.WJEC
null hypothesis: A claim about a population parameter, usually written H₀, with which a hypothesis test starts.Pearson Edexcel, WJEC
Null hypothesis (H₀): The initial statement about a population parameter that is assumed true when calculating the test probability; it contains an equality.AQA
number of roots: The count of real roots of the original equation, which equals the number of intersection points.WJEC
number systems: Number sets: ℕ = {1, 2, 3, ...}, ℤ, ℚ, ℝ.WJEC
Numerical fractions: Fractions such as (x+1)/2 > (2x−3)/3, cleared by multiplying by the positive common denominator rather than by algebraic denominators.AQA
numerical methods: Systematic algorithms that provide approximations to solutions to any desired degree of precision when problems cannot be solved analytically.Pearson Edexcel, WJEC

O

odd function: A function satisfying `f(−x) = −f(x)`, giving rotational symmetry of 180° about the origin.Pearson Edexcel
One-tailed and two-tailed critical regions: A two-tailed test at significance level α rejects H₀ if |z| exceeds z_(α/2), while a one-tailed test compares z with z_α in the correct direction.Pearson Edexcel
One-tailed and two-tailed tests: For a one-tailed test the probability is compared to the significance level α; for a two-tailed test the observed tail probability is compared to α/2.AQA
One-tailed test: A test with a critical region in one tail of the distribution because H₁ uses < or >.AQA
One-to-one: A property f must have on its domain for f⁻¹ to exist as a function; restricting the domain can achieve this.AQA
One-to-one function: A function in which each output is associated with only one input; distinct inputs have distinct outputs.Pearson Edexcel
one-to-one functions: A function is one-to-one (injective) if distinct inputs yield distinct outputs.WJEC
one-to-one mapping: A condition under which an inverse function exists; if a function is not one-to-one, its domain must be restricted to define an inverse.WJEC
Operations with surds: Adding or subtracting like surds by combining their coefficients, and multiplying using √a × √b = √(ab).Pearson Edexcel
Opportunity sample: A sample made from people or items that are available or convenient at the time of selection.AQA
Opportunity sampling: Chooses subjects who are readily available; while swift and inexpensive, it introduces severe selection bias.AQA, Pearson Edexcel, WJEC
optimisation: Practical constraints link variables to express the target quantity as a single-variable function.WJEC
Order of combined transformations: Combinations apply in sequence, and the order matters when stretches and translations are mixed, so y = af(x + b) translates first and then stretches.Pearson Edexcel
order of operations: For y = af(x) + b, stretch vertically by scale factor a parallel to the y-axis, then translate by vector (0, b).WJEC
order of periodicity: The smallest positive integer k for which the identity xₙ₊ₖ = xₙ holds.WJEC
orthogonal components: Force and velocity vectors are resolved into orthogonal components using trigonometric functions, such as projectile velocities resolving into horizontal u…WJEC
orthogonal equilibrium equations: Resolving into two non-parallel directions, usually orthogonal horizontal x and vertical y axes, yields two simultaneous scalar equilibrium equations.WJEC
orthogonal force analysis: Forces acting perpendicular to the line of motion remain balanced, while along the axis of motion the resultant driving force minus resistive forces produces…WJEC
Outlier: A value that lies far from the rest of the data, which may be a genuine extreme value or an error.AQA, Pearson Edexcel
outlier boundaries: Values given by Q₁ − 1.5 × IQR and Q₃ + 1.5 × IQR, used to classify a data point as an outlier.WJEC
outliers: Extreme values in a dataset that data cleaning may identify, correct, or remove.WJEC
Over-estimate: An estimate that lies above the true value, occurring when the curve is convex over the interval.AQA
overestimate and underestimate: Where the curve is convex the straight chords lie above the curve, so the rule overestimates; where concave the chords lie below, so it underestimates.WJEC

P

p-value: The probability of observing a result at least as extreme as the test statistic under H₀.AQA, WJEC
P(Type I error): The probability of the critical region under H₀, which equals the actual significance level.WJEC
P(Type II error): β, the probability of the acceptance region under the alternative parameter p₁.WJEC
parabola sketching: Requires labelling the vertex, line of symmetry, and all axis intercepts accurately.WJEC
parabolic trajectory equation: Eliminating t yields the cartesian equation y = x tan θ − (g x²)/(2 u² cos²θ).WJEC
Parallel: Two vectors are this when one is a non-zero scalar multiple of the other, which also tests collinearity.AQA
Parallel and perpendicular gradients: Two lines are parallel when their gradients are equal, m₁ = m₂, and perpendicular when m₁m₂ = −1, so a perpendicular gradient is the negative reciprocal.Pearson Edexcel
Parallel and perpendicular lines: For two lines, parallel means equal gradients, while perpendicular means gradients multiply to −1, unless one is vertical and the other horizontal.AQA
parallel box plots: Plots for comparing multiple groups on a shared numerical scale, displaying median, spread, and skewness simultaneously.WJEC
parallel lines: Distinct coplanar lines that remain a constant distance apart and have equal gradients, m₁ = m₂.Pearson Edexcel
Parallel vectors: Two non-zero vectors a and b are parallel if and only if one is a scalar multiple of the other: a = kb for some scalar k.AQA, Pearson Edexcel, WJEC
Parallelogram law: This is the triangle law extended to the case when two vectors share a starting point.AQA
parallelogram proofs: Proving that opposite vector displacements are equal, such as AB = DC, proves that ABCD is a parallelogram.WJEC
Parameter: A third variable, often time t, in terms of which x and y are separately expressed to describe a curve.AQA, Pearson Edexcel
parameter determination: Setting up simultaneous equations enables solving for unknown μ and σ.WJEC
parameter elimination: Rearranging one equation to isolate t and substituting into the other, or using fundamental identities when equations involve trigonometric functions of t.WJEC
parameter estimation: Reading the gradient and vertical intercept from a logarithmic graph and converting the intercept back to a or k by exponentiating with the chosen base.Pearson Edexcel, WJEC
Parameter interpretation in context: Explaining A as the initial value and k (or ln b) as the continuous rate constant within the situation being modelled.AQA
Parameterisation: Defining x and y separately in terms of a third variable, the parameter, such as x = 2t and y = t² − 1.Pearson Edexcel
Parametric curve: A curve whose coordinates are both expressed in terms of a third variable, commonly t.Pearson Edexcel
Parametric differentiation: For parametric curves, x and y are given in terms of a parameter t, and the first derivative is dy/dx = (dy/dt)/(dx/dt), provided dx/dt ≠ 0.AQA, Pearson Edexcel, WJEC
parametric equations: Equations that express the Cartesian coordinates x and y independently as functions of a third variable or parameter t, so x = f(t) and y = g(t).AQA, WJEC
parametric modelling: Using parametric equations in modelling in a variety of contexts, including kinematics and physical modelling.WJEC
Parametric representation: Describes a curve using a third variable, usually t or θ, giving equations for x and y in terms of that variable.AQA
Partial fractions: Simpler fractions into which a proper algebraic fraction is decomposed, facilitating integration and binomial expansion.AQA, WJEC
partial fractions integration: Integrating algebraic rational functions where the denominator factors into linear terms requires partial fraction decomposition prior to integration.WJEC
Partial-fraction decomposition: Writing a rational function as a sum of simpler fractions whose denominators are factors or powers of factors of the original denominator.Pearson Edexcel
Particle: A model of an object with mass but negligible dimensions.Pearson Edexcel
particle equilibrium: A state in which the resultant force on a particle vanishes in both perpendicular directions, so that the sum of force components equals zero.WJEC
particles: Objects treated with mass concentrated at a point, neglecting dimensions, rotational energy and aerodynamic effects.WJEC
particular solution: Found by substituting given initial or boundary conditions to determine the unique numerical value of C.Pearson Edexcel, WJEC
particular solutions: Obtained when an initial condition or boundary pair (x₀, y₀) is supplied, allowing the unique numerical value of c to be determined.WJEC
Pascal's triangle: An arithmetic layout where each term is the sum of the two terms directly above it.WJEC
Percentile: A value below which a stated proportion of observations lies.AQA
Perfect Square: An integer that is the square of an integer (e.g., 1, 4, 9, 16, 25).Pearson Edexcel
period: The smallest positive length of the input interval over which a periodic function repeats its values.AQA, OCR, Pearson Edexcel
periodic cycle: A failure mode where Newton-Raphson oscillates indefinitely between two values without converging, occurring if the curve oscillates or has inflection points…WJEC
periodic sequence: A sequence in which a block of terms repeats indefinitely, with the period stating the length of that repeating block.AQA, Pearson Edexcel
periodic sequences: A sequence that repeats the exact same cycle of values indefinitely, satisfying xₙ₊ₖ = xₙ for all n.WJEC
periodic solutions: Further solutions generated by adding or subtracting integer multiples of the period, which is 360° for sin and cos and 180° for tan.WJEC
Periodicity: Sine and cosine have period 2π, while tangent has period π, and multiples follow from this property.AQA, Pearson Edexcel
perpendicular bisector: Finding these combines the midpoint formula with perpendicular gradients.WJEC
perpendicular bisector of chord: The perpendicular bisector of any chord passes through the centre of the circle, allowing the centre to be found as the intersection of perpendicular…WJEC
perpendicular distance: The distance from the point to the line of action of the force, used in moment calculations, or found by resolving the force into components perpendicular to…AQA, Pearson Edexcel, WJEC
Perpendicular distance and components: For a force at an angle, use the perpendicular component F sin θ or the perpendicular distance, not the full force along the rod.AQA
Perpendicular from the centre to a chord: It bisects the chord, which lets you find a midpoint or a length.Pearson Edexcel
perpendicular lines: Lines that meet at a right angle.Pearson Edexcel
perpendicular resolution: Resolving coplanar forces into two mutually perpendicular axes, typically horizontal x and vertical y, to enable systematic analysis.WJEC
phase angle: The acute angle α, found from tan α = b/a, by which the single wave is shifted.WJEC
phase shifts: Additive links between angles in equations that compound angle formulas are deployed to solve.WJEC
physical asymptotes: Mathematical features connected to real-world limiting capacities, such as asymptotic ceilings in rational functions.WJEC
Pivot: The point about which moments are taken; choosing a convenient one can eliminate unknown forces.Pearson Edexcel
PMCC interpretation: Interpreting a provided sample correlation coefficient r in terms of strength and direction.WJEC
Point of inflection: A point indicated by a change of sign in the second derivative.AQA, Pearson Edexcel
point probabilities: The probability of any single point, which is zero for continuous variables: P(X = c) = 0.WJEC
Point-gradient form: The form y − y₁ = m(x − x₁) builds the line through (x₁, y₁) with gradient m.Pearson Edexcel
point-slope form: The form y − y₁ = m(x − x₁) directly generates the equation of a line passing through a known point with known gradient.WJEC
points of inflection: The mathematical points on the density curve occur precisely at x = μ ± σ, where the curve transitions from concave downward to concave upward.AQA, WJEC
Poisson distribution model: Models event counts in a fixed interval of space or time, assuming events occur singly, independently, and at a constant average rate.WJEC
Poisson probability calculations: For X ~ Po(λ), P(X = r) = (e^(−λ) λ^r)/r!WJEC
polynomial curves: Curves defined by simple equations, including polynomials, whose graphs are understood and sketched.WJEC
Polynomial division: Performed first when the degree of the numerator is not less than the denominator, to obtain a proper fraction.AQA
Polynomial expansion: Multiplying every term in one bracket by every term in the other, then collecting like terms.AQA
Population: The entire collection of individuals, objects, or measurements about which information is sought in a statistical investigation.AQA, Pearson Edexcel, WJEC
Population correlation coefficient (ρ): The parameter measuring the strength and direction of linear correlation in the whole population.AQA
population correlation ρ: The correlation coefficient in the population about which hypotheses are formulated, with H₀: ρ = 0 against H₁: ρ > 0, ρ < 0, or ρ ≠ 0.WJEC
position: The location of a particle relative to a chosen origin, normally represented by a signed coordinate or position vector.AQA, WJEC
position and displacement: Position is calculated from displacement using r = r_0 + ut + ½at², adding the initial position vector r_0.WJEC
position and velocity vectors: The vector velocity equation is v = u + at, and the vector displacement equation is r = ut + ½at², with position vector r = r₀ + ut + ½at² from initial…WJEC
Position vector: A vector that gives the displacement of a point from a fixed origin, usually written as a column vector or in i, j, k form.AQA, Pearson Edexcel, WJEC
position vectors: The vector of a point relative to a fixed origin, denoted by r_A or OA, representing the displacement from the origin to A.AQA, WJEC
Position vectors and displacement: The vector between two points is found by subtracting position vectors, so AB is b − a.Pearson Edexcel
Positive direction: A direction that must be defined, with units kept consistent, before resolving in a context.Pearson Edexcel
Possible outlier: An observation unusually far from the overall pattern that should be investigated because it may be an error, a genuine extreme or a different group.AQA
power law: This states logₐ (xᵏ) = k logₐ x, corresponding to (aᵐ)ᵏ = a^(mk).WJEC
power law models: Relationships of the form y = axⁿ, linearised by plotting ln y against ln x, where gradient m = n and vertical intercept c = ln a.WJEC
power reduction identities: Rearranged cosine double angle formulas, cos²A = ½(1 + cos 2A) and sin²A = ½(1 − cos 2A), essential for integrating even powers of sine and cosine.WJEC
Power relationship: A model of the form $y=ax^n$, where a is a positive constant and n is a constant exponent.Pearson Edexcel
power rule: States that for any real or rational constant n, d/dx(xⁿ) = n x^(n−1).WJEC
power rule for integration: Reverses the power rule of differentiation: for any rational power n ≠ −1, ∫ xⁿ dx = (x^(n+1)) / (n + 1) + c.WJEC
Power rule for rational indices: For a power xⁿ with rational n, the derivative is n x^(n−1), which works for positive, negative and fractional indices.Pearson Edexcel
Precise use of terminology: Correct vocabulary is required, such as calling 3x² + 2x − 1 an expression, 3x² + 2x − 1 = 0 an equation, and sin²θ + cos²θ = 1 an identity.AQA
precision and tolerance: Choosing appropriate step sizes h or tolerances and performing iterations to required contextual precision.WJEC
Precision in communication: Correct syntax lets an examiner follow your method, whereas incorrect syntax can change the meaning of a correct idea.AQA
Price and demand as related changing quantities: If demand x falls at a rate proportional to its current value, the equation is dx/dt = −kx.Pearson Edexcel
Principal ranges: Restricted ranges of the inverses: arcsin x has range [−π/2, π/2], arccos x has range [0, π] and arctan x has range (−π/2, π/2).Pearson Edexcel
principal value: A value α = arcsin(k), arccos(k), or arctan(k) calculated before secondary solutions in the base cycle are determined using symmetry.AQA, OCR, Pearson Edexcel, WJEC
principle of moments: For a rigid body in equilibrium, the sum of clockwise moments about any point equals the sum of anticlockwise moments about that point.Pearson Edexcel, WJEC
probabilistic modelling: Applying probability models to real-world phenomena requires simplifying assumptions, most notably that trials are independent and event probabilities remain…WJEC
probability density: A continuous curve towards which a relative frequency histogram smooths as sample size grows and class intervals narrow, where total area equals 1.Pearson Edexcel, WJEC
probability density functions: Functions f(x) by which continuous random variables are modelled.WJEC
Probability distribution: A rule or table giving the probability associated with each possible value of a random variable.Pearson Edexcel
probability distribution table: A way of defining a discrete random variable, alongside a formula, giving the specified probabilities of its countable numerical outcomes.WJEC
Probability modelling: Representing a real situation with a probability model, then judging how well that model fits.Pearson Edexcel
Problem formulation: Formulating equations, functions or models that capture the essential structure.AQA
problem reformulation: Transforming the contextual problem into an abstract mathematical form, such as a quadratic or differential equation, so that symbolic algebra can yield…WJEC
Problem specification: Defining variables, units and what counts as a solution before any calculation begins.Pearson Edexcel
problem-solving cycle: A workflow comprising four core stages: specifying the problem, collecting relevant data, processing and representing information mathematically, and…WJEC
processing information: Translating constraints into algebraic equations, geometric constructions, or calculus models.WJEC
product law: The sum of two logarithms sharing the same base equals the logarithm of their product, for positive arguments.WJEC
Product rule: Gives d/dx(uv) = u(dv/dx) + v(du/dx) when differentiating a product.AQA, Pearson Edexcel, WJEC
product rule in implicit terms: For product terms like xy, the product rule yields d/dx(xy) = x(dy/dx) + y.WJEC
projectile: A particle moving under gravity in a vertical plane after projection, with air resistance neglected in the standard model.AQA, WJEC
projectile motion: Models a particle launched with initial velocity u at angle θ to the horizontal, moving under uniform downward gravity g in a vertical plane with negligible…WJEC
Projectile motion in two dimensions: Modelling motion by taking horizontal acceleration as zero and vertical acceleration as constant, usually −g, with a = (0, −g) under gravity.AQA
projectile trajectories: For projectile motion under gravity, x(t) = (V cos θ)t and y(t) = (V sin θ)t − ½gt² parameterise the flight path, with the parameter domain restricted to 0 ≤…WJEC
Proof: A logically valid argument that begins with accepted assumptions and establishes a conclusion for every case covered by those assumptions.AQA, Pearson Edexcel, WJEC
Proof and simplification of expressions: Using the identities to simplify expressions and to prove other identities by manipulating one side to match the other.AQA
Proof by contradiction: Assumes the opposite and derives an impossibility, then concludes the original statement is true; classic examples prove that √2 is irrational and that there…AQA, Pearson Edexcel, WJEC
Proof by deduction: Starts with clear algebraic definitions, such as an even integer expressed as 2k and an odd integer as 2k + 1 for k ∈ ℤ, and uses algebraic expansion and…AQA, Pearson Edexcel, WJEC
Proof by exhaustion: Checks every possible case, such as testing all residue classes modulo 3, and confirms that every possible case has been considered.AQA, Pearson Edexcel, WJEC
Proof completeness and generality: Whether a justification establishes its conclusion for all required cases, tested by considering special cases, boundary cases or a counterexample.Pearson Edexcel
proof of geometric sum: Writing S_n and r S_n, then subtracting the second equation from the first so all intermediate terms cancel, leaving (1 − r)S_n = a(1 − rⁿ).WJEC
Proof techniques: Techniques including factorising, combining fractions, multiplying numerator and denominator by a conjugate, and substituting equivalent expressions.Pearson Edexcel
Proper rational function: A rational function whose numerator has degree lower than its denominator.Pearson Edexcel
proportional growth: The instantaneous rate of change of y = A e^(kx) is directly proportional to the current value of y, satisfying dy/dx = ky.WJEC
Proportional rate of change: A rate of change that is a constant multiple of the current amount, written dy/dt = ky.AQA
Proportional rates of change: The rate of change is proportional to the current value, dy/dx = ky, which is exactly the relationship modelled by growth and decay processes.Pearson Edexcel
Proportional relationship: A relationship giving a straight-line graph through the origin, written as y = kx.Pearson Edexcel
Proportionality and constants of proportionality: A rate relationship written with a constant of proportionality, such as dP/dt = kP, where k is stated to be a positive constant.Pearson Edexcel
Proportionality and differential equations: The rate of change is proportional to the quantity present, with constant of proportionality k, so the derivative is a constant multiple of the function.AQA
proportionality constant: The constant k ≠ 0 in a proportional relationship, evaluated by substituting known paired values (x₁, y₁).WJEC
proportionality graphs: Direct proportion gives a straight line through the origin, while inverse proportion gives a rectangular hyperbola with the coordinate axes as asymptotes.WJEC
proportionality in calculus: Statements of direct proportionality translate to dy/dt = ky, where k is a positive constant for growth or negative for decay.WJEC
Pythagorean identity: cos²θ + sin²θ = 1, which applies Pythagoras' theorem to the right-angled triangle formed in the unit circle.WJEC
Pythagorean trigonometric identities: Three fundamental identities: sin²θ + cos²θ ≡ 1, sec²θ ≡ 1 + tan²θ and cosec²θ ≡ 1 + cot²θ.AQA

Q

Q.E.D.: Abbreviation for 'quod erat demonstrandum', meaning 'which was to be demonstrated'.Pearson Edexcel
quadrant analysis: Identifying the correct quadrant from the signs of the components so that negative components are handled accurately.WJEC
quadratic approximations: In equation solving, substituting small-angle approximations reduces trigonometric expressions to solvable quadratic or linear equations in θ.WJEC
Quadratic equations in trigonometric functions: Equations in sin θ, cos θ or tan θ rearranged to standard form, then factorised or solved with the quadratic formula, rejecting roots outside the range.Pearson Edexcel
quadratic expressions: Expressions of the form ax² + bx + c, rewritten by factoring out the leading coefficient a from the terms in x² and x.WJEC
quadratic functions: A function taking the form f(x) = ax² + bx + c with a ≠ 0, producing a parabolic curve.WJEC
Quadratic in a function of the unknown: An equation solved by substituting, such as u=x², then solving the resulting quadratic and back-substituting.AQA
quadratic inequalities: Solving problems often involves forming and solving inequalities in an unknown parameter k from the discriminant conditions.WJEC
Quadratic inequalities and critical values: Solved by finding the critical values where the expression equals zero, then testing intervals or sketching the parabola; for a > 0, greater than lies outside…Pearson Edexcel
quadratic substitution: A temporary variable u = g(x) is substituted to reduce an equation to the form au² + bu + c = 0.WJEC
quantity: A measurable property of an object, system or motion, such as length, time or mass.AQA
Quartiles and interquartile range: Summaries used to identify possible outliers, being resistant to extreme values where the mean and range are not.Pearson Edexcel
quotient identity: tan θ = sin θ / cos θ, valid for all angles θ where cos θ ≠ 0, excluding odd multiples of 90° or π/2 radians.WJEC
quotient law: The subtraction law states logₐ x − logₐ y = logₐ (x/y), corresponding to aᵐ / aⁿ = a^(m−n).WJEC
Quotient rule: Differentiates y = u/v as (v du/dx − u dv/dx)/v², where du/dx is the derivative of the numerator u and dv/dx is the derivative of the denominator v.AQA, Pearson Edexcel, WJEC

R

R-alpha method: Equating coefficients after expanding gives R cos α = a and R sin α = b, with R = √(a² + b²) and tan α = b/a.WJEC
Radian: The angle subtended at the centre of a circle by an arc whose length equals the radius.AQA, OCR, Pearson Edexcel, WJEC
Radian measure: An alternative to degrees, converted using π radians = 180°, and used for arc length l = rθ and sector area A = ½r²θ.AQA, Pearson Edexcel
Radians: The unit in which θ must be measured for the approximations to hold; they are not valid for degrees without conversion.Pearson Edexcel
radical integrands: For integrands involving roots, let u equal the expression under the root, or set u² equal to it.WJEC
Random variable: A variable whose numerical value is determined by the outcome of a random process.AQA, Pearson Edexcel
Range: The corresponding set of output values (y-values or f(x)) of a function.AQA, Pearson Edexcel
Range of validity: The values for which an expansion is guaranteed to be valid; for a rational binomial series $(1+x)^n$, this is $|x|<1$.WJEC
rate of change: The gradient m in an applied equation, representing the constant rate of change such as cost per mile or price increase per year.AQA, WJEC
rate of change of gradient: Geometrically, it measures the rate at which the gradient of the curve is changing.WJEC
rates of change: Instantaneous rates of change given by derivatives dy/dt, such as litres per minute or metres per second squared, articulated with their contextual meaning.WJEC
Rational exponent: An exponent that is a fraction, where a^(1/n) is the nth root of a and a^(m/n) is the nth root of a raised to the power m.AQA
rational exponents: Surds and reciprocals are converted into this form: 1/x³ = x⁻³ and ᵌ√x = x^(1/3).WJEC
Rational expression simplification: Factorising numerator and denominator fully, then cancelling common factors, remembering that the cancelled factor must not be zero.AQA
rational expressions: Expressions of the form f(x)/g(x) that are simplified by factorising the numerator and denominator into linear or irreducible quadratic factors and cancelling…WJEC
Rational function: A function that can be written as a quotient of two polynomials, with a non-zero denominator.Pearson Edexcel
Rational indices: Indices that may be negative and fractional, for which d/dx(x^n)=n x^{n-1} applies.AQA
Rational Number: A number that can be written as a fraction $\frac{a}{b}$, where $a$ and $b$ are integers and $b \neq 0$.AQA, Pearson Edexcel
rational powers: Indices n that are negative or fractional, for which the binomial series is infinite.WJEC
Rationalising denominators: Multiplying numerator and denominator by a suitable surd or conjugate so the denominator no longer contains a surd.Pearson Edexcel
rationalising the denominator: Eliminating radicals to express values in standard form.AQA, WJEC
Real-world validation: Comparing model predictions with real-world data or expectations to assess whether the model is appropriate for its intended purpose.AQA
Realism checking: Considering whether the output is realistic and identifying any limitations or anomalies, such as a negative height or a probability greater than 1.Pearson Edexcel
Reasonableness checking: Comparing the result with the context, such as checking that a length is positive or a probability is between 0 and 1.AQA
Reasoned estimate: A judgement of a solution's value made from a rough sketch, a simpler model, or bounds.AQA
Reasoned estimation: Judging accuracy by checking the sign and size of the answer, comparing with a graph, or using a simpler model.Pearson Edexcel
Reciprocal: One divided by a number.Pearson Edexcel
reciprocal derivative: The derivative of the natural logarithm function is d/dx(ln x) = 1/x for x > 0.WJEC
reciprocal logarithms: When k = −1, −logₐ x = logₐ (x⁻¹) = logₐ (1/x), expressing the logarithm of a reciprocal as the negative logarithm.WJEC
Reciprocal relationships in trigonometry: Secant, cosecant and cotangent are defined as the reciprocals of cosine, sine and tangent, with cotangent equivalently given as cos θ/sin θ.AQA
reciprocal trigonometric function: A function formed by taking the reciprocal of a trigonometric function: $\sec x=1/\cos x$, $\mathrm{cosec}\,x=1/\sin x$ and $\cot x=1/\tan x$.Pearson Edexcel
reciprocal trigonometric functions: Defined as sec θ = 1/cos θ, cosec θ = 1/sin θ, and cot θ = 1/tan θ = cos θ / sin θ.Pearson Edexcel, WJEC
rectilinear dynamics: Motion in a straight line along one axis when unbalanced forces act, while equilibrium is maintained perpendicular to it.WJEC
recurrence relation: A relation linking each term to the previous one, applied repeatedly while carrying forward the previous term accurately.AQA, Pearson Edexcel, WJEC
Recurrence relations: Relations of the form xₙ₊₁ = g(xₙ) that generate successive approximations, converging when the iteration is stable near the root.AQA, Pearson Edexcel, WJEC
recurring decimals: These can be evaluated as infinite geometric series, for example 0.454545...WJEC
Recursive definition: A relation like xₙ₊₁ = f(xₙ) where each term depends on the previous one, so a starting value is needed.Pearson Edexcel
reference angle: The positive acute angle between the terminal arm of an angle and the x-axis.Pearson Edexcel
reference angles: The acute angle with the x-axis, found first before attaching the correct quadrant sign.WJEC
reference triangles: Standard triangles from which exact trigonometric ratios derive: the equilateral triangle of side 2 split in half, and the isosceles right-angled triangle…WJEC
Refinement: Identifying a limitation of a model and suggesting a more realistic assumption where appropriate.Pearson Edexcel
Refinement of models: A specific improvement such as adding a term to account for a neglected factor or restricting the domain.AQA
Refinement of models when assumptions fail: Recognising when a model is inappropriate and suggesting a refinement, such as including air resistance for a falling object.AQA
Refinement using data: Adjusting the function, domain or constants to fit data better, such as adding a drag term or restricting t.Pearson Edexcel
Reflection in the x-axis: A transformation mapping each point (x, y) to (x, -y).Pearson Edexcel
Reflection in the y-axis: A transformation mapping each point (x, y) to (-x, y).Pearson Edexcel
reflection in y = x: The graph of y = f⁻¹(x) is the reflection of y = f(x) in the line y = x, and points of intersection between a function and its inverse lie along y = x.WJEC
Regression line: A line that models the average linear relationship between two variables and can support interpolation within the observed range.AQA
regression lines: The least-squares line y = a + bx modelling how the dependent response variable y changes in response to the independent explanatory variable x.Pearson Edexcel, WJEC
Regression lines as models: A given line that helps predict one variable from another, but only within the observed range.AQA
relative frequency: Observed proportions in sample presentations that approximate theoretical probability models and can be compared with theoretical probabilities to assess…Pearson Edexcel, WJEC
Relative frequency and probability: Relative frequencies from data can estimate probabilities, and the shape of a histogram can suggest an underlying distribution.AQA
Repeated integration by parts: Applying the method more than once where necessary, for example for ∫ x² eˣ dx, but reduction formulae are excluded.Pearson Edexcel
Repeated linear factor: A factor such as (x − 1)² that requires two terms, A/(x − 1) + B/(x − 1)², one for each power of that factor.Pearson Edexcel
repeated linear factors: Factors in the denominator that require an escalating denominator, with a single linear term and a squared term.AQA, WJEC
repeated linear integrals: When repeated linear factors occur in the denominator, such as C/(cx + d)², rewrite as C(cx + d)⁻² and integrate using the power rule.WJEC
Repeated real root: The single root that arises when the discriminant equals zero.Pearson Edexcel
Repeated root: A real root occurring twice, produced when the discriminant is zero; the quadratic graph touches the x-axis at that root.AQA
repeated roots: A repeated squared factor means the curve touches the x-axis tangentially without crossing, and a repeated cubic factor produces a stationary point of…WJEC
Representation of results: Choosing a table, graph, diagram or equation that reveals structure in the processed information.Pearson Edexcel
Representative: Describing a sample that reflects relevant characteristics of the population sufficiently well for the purpose of an investigation.AQA
representativeness: Whether an extracted sub-sample provides an accurate representation of the wider data set, considering sampling bias before generalising.WJEC
Resolution of forces: Resolving forces in 2 dimensions using components, with trigonometry, allows F = ma to be applied along the line of motion.Pearson Edexcel
Resolving a force: Splitting a force into perpendicular components whose vector sum is the original force.Pearson Edexcel
Resolving forces: Splitting forces into components using trigonometry, such as F cos θ and F sin θ, where θ is the angle to the chosen axis.AQA
Resolving forces in two dimensions: Forces at angles are split into components using trigonometry, typically parallel and perpendicular to motion.AQA
Restricted domain: A range of the parameter limited by the physical situation, such as restricting t to t ≥ 0.Pearson Edexcel
restricted sample space: Conditioning reduces the relevant sample space from S to B.WJEC
Resultant: Runs from the first tail to the final head when the tail of the second vector is placed at the head of the first, forming a triangle or parallelogram.Pearson Edexcel
resultant displacement: The vector displacement found by combining component displacements in two or more directions.AQA
Resultant force: The overall force found by identifying all forces and resolving if needed; when it is zero, acceleration is zero, and when it is not, motion changes.AQA, Pearson Edexcel, WJEC
Resultant force and acceleration: The vector sum of all forces is used in F = ma, so the applied force alone must not be used.AQA
resultant force equation: Written as ΣF = ma, where the acceleration a is directly proportional to the net resultant force ΣF and acts in the identical direction.WJEC
resultant force vector: The vector sum of multiple forces acting on a particle, written as R = ΣF_i = (Σx_i)i + (Σy_i)j.WJEC
resultant summation: Combining multiple concurrent coplanar forces by summing their respective orthogonal components, R_x = ΣF_x and R_y = ΣF_y.WJEC
Resultant vector: The single vector equal to the combined effect of two or more vectors.Pearson Edexcel
reverse chain rule: The process of integration by substitution, which reverses the chain rule.WJEC
reverse product rule: The process of integration by parts, which reverses the product rule.WJEC
Riemann sum: A total approximate area found by summing all thin vertical strips, each of width δx, over the interval [a, b].WJEC
Riemann sums and partition of an interval: Splitting the interval [a, b] into n strips of width Δx = (b − a)/n and forming the sum Σ f(xᵢ)Δx.Pearson Edexcel
rigid body: An object whose shape is assumed not to change when forces act on it.Pearson Edexcel
root: A value α for which f(α)=0; graphically, an x-coordinate where y=f(x) meets the x-axis.Pearson Edexcel
Root (zero): A value of x for which f(x)=0; graphically, an x-coordinate where the graph meets or touches the x-axis.WJEC
root interpretation: The number of real algebraic roots reveals the number of intersection points between the curves.WJEC
root location: Locating roots of f(x) = 0 by considering changes in sign of f(x) in an interval of x in which f(x) is sufficiently well-behaved.WJEC
rotational equilibrium: A condition in which the resultant turning effect about any chosen pivot is zero.WJEC
rotational sense: Moments possess this, being either clockwise or anticlockwise, and it must be assigned to calculated moments.WJEC
rough: Surfaces modelled as rough impose F ≤ μR.WJEC
rounding bounds: The lower and upper limits of values that round to a stated value at a given degree of accuracy.Pearson Edexcel
rounding bounds verification: Evaluating f(x) at the upper and lower rounding bounds [α − 0.5 × 10⁻ᵏ, α + 0.5 × 10⁻ᵏ], where a sign change between these bounds confirms the root rounds…WJEC

S

S.I. units: The units to always use: weight in N, mass in kg, and g in m s⁻².Pearson Edexcel
Sample: A subset selected from the population, used to make informal inferences about it.AQA, Pearson Edexcel, WJEC
Sample mean distribution: Under the null hypothesis, the sample mean of n independent observations follows a Normal distribution with mean μ0 and variance σ²/n.AQA
sample size impact: Larger samples reduce sampling variability, producing more reliable informal estimates, so sample size governs precision.WJEC
sample space: Events are subsets of a sample space S, where the addition rule for probability uses union and intersection notation.AQA, Pearson Edexcel, WJEC
Sampling bias: A systematic tendency for a sampling process to favour some members or outcomes over others.AQA
sampling constraints: Practical limitations such as prohibitive costs, excessive time constraints, or the destructive nature of testing that make a census unfeasible.WJEC
sampling critique: Assessing coverage errors, non-response bias, exclusion of key demographics, and sampling frame availability, proposing refined probability-based alternatives.WJEC
sampling distribution of X̄: For a sample of size n, the sample mean follows X̄ ~ N(μ, σ²/n).WJEC
sampling frame: A list numbered from 1 to N from which items are picked via pseudo-random numbers without replacement in simple random sampling.AQA, WJEC
sampling uncertainty: The presence of uncertainty that must be acknowledged when making an inferred conclusion about a population from a sample.WJEC
sampling variation: Independent random samples drawn from the identical population will naturally yield varying estimates due to sampling variability.WJEC
Scalar: A quantity that has only magnitude and no direction.Pearson Edexcel
scalar multiple: A vector formed by multiplying another vector by a scalar.AQA
scalar multiplication: Multiplication by a scalar k scales the vector's magnitude by |k|: k(xi + yj) = (kx)i + (ky)j, with direction unchanged if k > 0 and reversed if k < 0.AQA, Pearson Edexcel, WJEC
scalar product and angles between vectors: The sum of the products of corresponding components, and a · b = |a||b|cos θ gives the angle between vectors.WJEC
Scale, direction and units: Stating the scale, keeping a consistent orientation, and labelling all quantities with units on a constructed diagram.Pearson Edexcel
scatter diagrams: Plots of bivariate data showing the relationship between two quantitative variables, which must be inspected for distinct clusters or sub-groups.Pearson Edexcel, WJEC
sec(x): The secant function, defined as the reciprocal of the cosine function: sec(x) = 1/cos(x).Pearson Edexcel
secant: The reciprocal of cosine, $\sec x=1/\cos x$; it is undefined where $\cos x=0$.Pearson Edexcel
Secant, cosecant and cotangent: Reciprocal trigonometric functions defined by sec θ = 1/cos θ, cosec θ = 1/sin θ and cot θ = 1/tan θ = cos θ/sin θ.Pearson Edexcel
second derivative: The rate of change of the gradient; where it is greater than zero the curve is convex, where less than zero it is concave.Pearson Edexcel, WJEC
Second derivative and concavity: The derivative of f'(x), measuring how the gradient changes; where f'' > 0 the curve is convex, where f'' < 0 it is concave, and a point of inflection occurs…AQA
sector area: Given by Area_sector = ½r²θ, with θ in radians.WJEC
segment area: Found by subtracting the area of the isosceles triangle formed by the radii and chord from the sector area.WJEC
Selecting or critiquing presentation: Choosing a diagram or summary that suits the data and explaining the strengths and limitations of that choice.Pearson Edexcel
Selection and justification of input values: Choosing input values that are meaningful and within the domain of the model, explaining why those values are chosen.AQA
selection bias: Systematic bias introduced by non-random methods like opportunity sampling that cannot be mitigated by merely increasing sample size.WJEC
Separable differential equation: A first-order differential equation whose variables can be rearranged so all $y$-terms accompany $dy$ and all $x$-terms accompany $dx$.AQA
Separable first order differential equations: A first order differential equation with separable variables can be written as dy/dx = f(x)g(y), then separated and integrated on both sides.Pearson Edexcel
separable variables: Variables separated into a product of single-variable expressions, allowing division to isolate them.Pearson Edexcel, WJEC
separation of variables: A method for solving first order differential equations of the form dy/dx = f(x)g(y) by rewriting as ∫ (1/g(y)) dy = ∫ f(x) dx.WJEC
Separation of variables technique: Rearranging the equation so that all terms involving y are on one side and all terms involving x are on the other.AQA
Sequence: An ordered set of terms, usually generated by an explicit formula or a recurrence relation.AQA, WJEC
sequence limits: If a recurrence converges to a limit L as n → ∞, the limit satisfies the fixed-point equation L = f(L), which can be solved algebraically.WJEC
sequences: An ordered list of terms x₁, x₂, x₃, ...WJEC
Series: Represents cumulative totals, as opposed to a sequence of individual terms.Pearson Edexcel, WJEC
series splitting: Evaluating ∑_(r=k)ⁿ u_r by subtracting ∑_(r=1)^(k−1) u_r from ∑_(r=1)ⁿ u_r.WJEC
set intersections: The region where events overlap, such as A ∩ B, which is entered first when populating a diagram.WJEC
Set notation: Written with set-builder braces and membership symbols, using intersection for a bounded single interval and union for disjoint intervals.AQA, Pearson Edexcel, WJEC
Set notation and interval language: Solutions may be written with ‘and’ or ‘or’, or in set notation such as {x : x < −1} ∪ {x : x > 3}, using the correct symbols for union or intersection.Pearson Edexcel
set theory: Supplies the language for domains, ranges and solution sets, where a set collects distinct elements.WJEC
set-builder and interval notation: Intervals use [a, b] for closed, (a, b) for open, and mixed forms such as (a, b]; set-builder form is {x ∈ ℝ : 1 < x ≤ 5}.WJEC
Shape descriptors and points of inflection: Points of inflection occur at μ ± σ; reading left to right, the curve changes from convex to concave at μ − σ, and from concave to convex at μ + σ.Pearson Edexcel
SI base units: The fundamental mechanical base quantities are length, measured in metres (m); time, measured in seconds (s); and mass, measured in kilograms (kg).WJEC
SI system: The international coherent system of units used as the standard in mechanics calculations.AQA
SI units and accuracy: In SI, g is measured in m s⁻²; use g = 9.8 or 9.81 as required, stating the value of g used and its direction.AQA
sigma notation: A compact way to represent a sum, in which an index runs through stated integer values and the expression is evaluated at each and added.AQA, WJEC
sign change: A change of sign occurs when f(a) and f(b) have opposite signs, so that f(a) × f(b) < 0.WJEC
Sign change as a root-locating test: Evaluating f at successive x-values and looking for a sign change locates a root, provided the function is continuous and genuinely crosses.Pearson Edexcel
sign change of curvature: Testing the sign of f''(x) just to the left and just to the right of the candidate point; if it changes sign, the point is an inflection point.WJEC
sign convention: A consistent choice of positive direction, for example upwards positive so that a = −g = −9.8 m s⁻², applied when using constant acceleration equations.WJEC
sign conventions: Consistent directional signs maintained throughout, for example upwards positive, so that vector quantities such as velocity and acceleration keep the correct…WJEC
Sign-change location: Evaluating a function at successive values to locate a sign change, giving an interval containing the root.Pearson Edexcel
Signed area: What the integral gives if the curve dips below the x-axis; for total area, split the interval at roots and take absolute values.AQA, Pearson Edexcel
Signed area and the definite integral: The definite integral is a number given by the limit of a sum, explaining why integration gives signed area.Pearson Edexcel
Signed displacement versus total distance: Displacement is found by summing signed areas, while total distance travelled is the sum of the magnitudes of these areas.Pearson Edexcel
Signed quantities in one-dimensional motion: Negative gradients and areas below the time axis are interpreted as motion in the opposite direction or negative displacement.AQA
significance level: The maximum acceptable probability of committing the mistake of incorrectly rejecting the null hypothesis H₀ when it is entirely true.AQA, Pearson Edexcel, WJEC
Significance level and Type I error: The probability of incorrectly rejecting a true null hypothesis; the p-value is compared with it to decide whether to reject the null hypothesis.AQA
Significance level as a probability of incorrect rejection: The probability of incorrectly rejecting H₀ when it is true.Pearson Edexcel
Significance levels: A level chosen for the test, against which the p-value is compared so that H0 is rejected if p is less than it.AQA
Simple random sample: A sample chosen so that every member of the population has an equal chance of being selected.AQA
Simple random sampling: Allocates every member an equal probability of selection, typically executed by numbering a sampling frame from 1 to N and picking items via pseudo-random…AQA, Pearson Edexcel, WJEC
Simplification: Removing irrelevant detail and replacing complex features with manageable approximations.AQA
Simplification and idealisation: Stripping away irrelevant information, perhaps by choosing sensible units, ignoring negligible effects, or replacing a real object with an idealised one.Pearson Edexcel
Simplification and proof in trigonometry: Using the identities to simplify expressions and prove other identities, starting from the more complicated side and stating any restrictions on θ.Pearson Edexcel
Simplification of surds: Removing square factors from a surd, for example √50 = √(25 × 2) = 5√2.Pearson Edexcel
Simplifying assumptions: Introduced to reduce algebraic complexity, each must be stated explicitly, acknowledging that it defines the operational boundaries and potential error…AQA, Pearson Edexcel, WJEC
Simplifying rational expressions: Factorising numerator and denominator completely, then cancelling common factors, remembering that the cancelled factor must not be zero.Pearson Edexcel
Simultaneous equations: Pairs of equations in two variables that must be solved together, with each solution pair satisfying both original equations.AQA
simultaneous equations in AP: Setting up and solving simultaneous linear equations from two pieces of information, which uniquely determines the first term a and common difference d.WJEC
simultaneous force balance: The resulting simultaneous equations are solved to determine unknown force magnitudes, tensions in strings, or angles of inclination.WJEC
Sine and cosine rules: Rules that solve any triangle, with the sine rule written as a/sin A = b/sin B = c/sin C and the cosine rule as a² = b² + c² - 2bc cos A.AQA
sine rule: States a/sin A = b/sin B = c/sin C, used when given two angles and one side, or two sides and a non-included angle.WJEC
Sketching and key features: Marking key features such as intercepts, turning points and asymptotes after transformation, with the correct overall shape.AQA
sketching gradient functions: Identifying stationary points of f(x) where f'(x) = 0, giving x-intercepts of f', and intervals where f(x) is increasing or decreasing.WJEC
slope-intercept form: The form y = mx + c displays the gradient m and y-intercept (0, c).WJEC
small angle formulas: sin θ ≈ θ, cos θ ≈ 1 − θ²/2 and tan θ ≈ θ, where θ is in radians.WJEC
small-angle approximation: An algebraic expression used as a close estimate of a trigonometric function for an angle close to zero in radians.AQA, Pearson Edexcel
Small-angle approximations: For small angles measured in radians, sine and tangent can be replaced by θ, and cosine by 1 − θ²/2.Pearson Edexcel
small-angle limits: As h → 0 in radians, (sin h)/h → 1 and (cos h − 1)/h → 0.WJEC
smooth: Surfaces modelled as smooth remove friction.WJEC
smooth pulley: Modelling assumption meaning no frictional resistance, so tension is equal on both sides.WJEC
Smooth pulleys: For a light inextensible string over a smooth pulley the tension is the same throughout, and connected particles share the same magnitude of acceleration.Pearson Edexcel
solution interpretation: Interpreting the solution of a differential equation in the context of solving a problem, including identifying limitations of the solution.WJEC
solving exponential equations: The inverse relationship lets you solve equations by taking logs or exponentiating both sides, for example converting e^(2x) = 7 into 2x = ln 7.Pearson Edexcel, WJEC
Solving exponential equations by equating indices: Solve equations such as 2^(3x) = 4^(x+1) by writing both sides with the same base.Pearson Edexcel
Solving exponential equations using logarithms: Finding unknown times or rates by taking logarithms where necessary when solving problems involving exponential models.AQA
Solving logarithmic and exponential equations: The laws let you solve logarithmic equations by condensing to a single log, and change the subject in exponential models.Pearson Edexcel
solving logarithmic equations: Solving a logarithmic equation such as ln(3x + 1) = 4 requires taking exponentials, giving 3x + 1 = e⁴.WJEC
Solving trigonometric equations: Applying the identities to convert between functions in order to solve trigonometric equations.AQA
Solving trigonometric equations in a given interval: Finding all angles in a specified interval that satisfy an equation, using the inverse function for the principal value and symmetry and periodicity to find…Pearson Edexcel
Solving trigonometric equations using identities: Replacing terms such as sin²θ with 1 − cos²θ so an equation can be solved, checking whether a value of θ makes a denominator zero.Pearson Edexcel
special angles: The angles 0, π/6, π/4, π/3, π/2 and π for which exact values of sine, cosine and tangent are stated.WJEC
Speed: The magnitude of velocity; it is non-negative.WJEC
speed and direction of motion: Particle speed is found as the vector magnitude |v| and direction of motion using trigonometry.WJEC
speed and distance in 3D: Speed is computed as the magnitude of the velocity vector |v| and distance from origin as |r|.WJEC
spreadsheet analysis: Using technology such as spreadsheets or specialist statistical packages to explore data sets.WJEC
spurious correlation: A strong correlation can arise through mere coincidence, reverse causality, or the presence of a confounding third variable.WJEC
staircase diagram: An iterative path where successive iterations approach the root monotonically from one side, produced when the gradient g'(x) near the root α is positive (0 <…Pearson Edexcel, WJEC
standard derivatives: The derivatives required at A-level, including d/dx(x^n)=n x^{n-1} for any rational n, d/dx(e^{kx})=k e^{kx}, d/dx(a^{kx})=k a^{kx} ln a, d/dx(sin kx)=k cos…AQA, WJEC
standard deviation: Measures root mean square spread about the mean, and a larger value means greater variability or lower consistency in performance.AQA, Pearson Edexcel, WJEC
Standard error: The standard error is σ/√n, the square root of the variance σ²/n of the sample mean from n independent observations.Pearson Edexcel
standard error σ/√n: The standard deviation of the sample mean, since the variance of the sample mean is σ²/n.WJEC
standard integrals: Indefinite integrals that reverse standard derivatives, covering eᵏˣ, 1/x, sin kx and cos kx and related sums, differences and constant multiples.WJEC
Standard integrals as inverses of derivatives: Standard integration reverses standard differentiation, so powers, exponentials and trigonometric functions integrate back to related standard forms.Pearson Edexcel
Standard Normal distribution: The Normal distribution Z ∼ N(0, 1), with mean 0 and variance 1.Pearson Edexcel
Standardisation: Transforming any Normal variable using Z = (X - μ)/σ to the standard Normal, essential when μ or σ are unknown.AQA, Pearson Edexcel
Standardisation and cumulative probabilities: Finds probabilities using the cumulative Normal function on a calculator, or by standardising with z = (x − μ)/σ.Pearson Edexcel
Standardisation and z-scores: Converting the observed sample mean using z = (x̄ − μ0)/(σ/√n), which has a standard Normal distribution.AQA
standardisation Z = (X − μ)/σ: This maps X to the standard Normal variable Z ~ N(0, 1).WJEC
Stationary point: A point on a differentiable curve where the first derivative is zero, so the tangent is horizontal.AQA, Pearson Edexcel, WJEC
stationary points: Points where dy/dx = 0; solving gives their x-coordinates and substituting into f(x) gives the corresponding y-values.WJEC
Stationary points and their classification: Occur where dy/dx = 0; d²y/dx² > 0 gives a minimum, d²y/dx² < 0 gives a maximum, and d²y/dx² = 0 requires further checking.Pearson Edexcel
Stationary points and their nature: These occur where dy/dx = 0, and are classified using the second derivative: if d²y/dx² > 0 it's a minimum, if < 0 a maximum, and if = 0 further investigation…AQA
stationary vs non-stationary inflection: If f''(x) = 0 and dy/dx = 0 at the point it is a stationary point of inflection; if dy/dx ≠ 0 it is an oblique point of inflection.WJEC
Statistic: A numerical value calculated from sample data, such as a sample mean or sample proportion.AQA
Statistical inference from sample to population: A sample is used to make an inference about the population, providing evidence about the unknown population proportion.AQA
Stopping criterion: A condition such as an interval width or a function-value tolerance used to decide when the required accuracy is reached.Pearson Edexcel
Straight line equations: These can be written in forms such as y − y₁ = m(x − x₁) and ax + by + c = 0, and can be converted between forms.AQA
Strategic planning: Devising a strategy and sequence of steps before committing to detailed calculation, so the main stages are planned first.Pearson Edexcel
strategic substitution: Substituting strategic roots, values of x that make individual linear factors zero, to evaluate the unknown constants.WJEC
Stretch parallel to the x-axis: A transformation that multiplies all x-coordinates by a scale factor.Pearson Edexcel
Stretch parallel to the y-axis: A transformation that multiplies all y-coordinates by a scale factor, represented by y = af(x).Pearson Edexcel
stretches and reflections: y = af(x) stretches the graph vertically by scale factor a parallel to the y-axis; y = f(ax) stretches it horizontally by scale factor 1/a parallel to the…WJEC
Stretches and translations: A stretch reshapes the graph, as y = af(x) stretches vertically by scale factor a, while a translation moves it, as y = f(x) + a translates by a units…Pearson Edexcel
Strip width: Equal width h = (b − a) ÷ n, dividing the interval width by the number of strips.Pearson Edexcel
strip width and ordinates: The strips have equal width h = (b − a)/n and are bounded by n + 1 ordinates y₀, y₁, …, y_n.WJEC
Structural recognition: Seeing past surface detail to the mathematics underneath by identifying the quantities, their relationships and the operations that connect them.Pearson Edexcel
Structured problem solving: A structured approach in which the problem is specified, information is collected, information is processed and represented, and results are interpreted.AQA
subpopulations: Distinct clusters or sub-groups on a scatter plot representing separate sections of the population, for which separate regression lines are required.WJEC
Substitution: Rearranging one equation to make a variable the subject and putting that expression into the other equation.AQA
Substitution and computation: Putting suitable inputs into the model and computing outputs accurately, maintaining accuracy and carrying units through the calculation.Pearson Edexcel
successive approximations: Values generated by numerical methods that converge toward the true root or value.WJEC
suitable substitution: Finding one that will lead to a function which can be integrated.WJEC
Sum of a finite geometric series: The sum of the first n terms is Sₙ = a(1 − rⁿ)/(1 − r) for r ≠ 1, or equivalently a(rⁿ − 1)/(r − 1).Pearson Edexcel
Sum of an arithmetic series: The sum of the first n terms is Sₙ = n/2[2a + (n − 1)d], equivalently Sₙ = n/2(a + l) when the last term l is known.Pearson Edexcel
sum of arithmetic series: The sum of the first n terms, given by S_n = ½n(2a + (n − 1)d), or equivalently S_n = ½n(a + L), where L = uₙ is the last term.WJEC
sum of geometric series: The sum of the first n terms of a finite geometric series, S_n = a(1 − rⁿ) / (1 − r) for r ≠ 1.WJEC
sum to infinity: The finite limit that an infinite geometric series converges to, given by S_∞ = a / (1 − r).WJEC
Sum to n terms: Given by n/2[2a + (n-1)d] or n/2(a + l), where l is the last term.AQA
Summary statistics: Quantities such as sum of x, sum of x squared and n, from which a standard deviation can be found without the raw data.AQA, Pearson Edexcel, WJEC
Surd: An irrational number that can be expressed as a root (e.g., square root or cube root) of a rational number.Pearson Edexcel
surd ratios: Exact values of sin, cos and tan for π/6, π/4 and π/3 stated in surd form.WJEC
surface roughness: The microscopic roughness and adhesiveness between two contacting surfaces, which the coefficient of friction characterises.WJEC
suvat derivations: Obtained from linear velocity-time graphs, where gradient gives a = (v − u)/t and area of a trapezium gives s = ½(u + v)t, with algebraic elimination giving…WJEC
Symmetries: Relations such as sin(π − θ) = sin θ, cos(−θ) = cos θ and tan(π + θ) = tan θ give values at related angles.AQA
Symmetry: Sine and tangent are odd functions, whereas cosine is even, giving sin(−x) = −sin x, cos(−x) = cos x and tan(−x) = −tan x.Pearson Edexcel
symmetry and area: The Normal distribution is symmetrical about mean μ, and the total area under both density curves equals 1.WJEC
systematic sampling: Selects every k-th member, where k ≈ N/n, from an ordered list following a random starting point between 1 and k, but risks bias if the list possesses…WJEC

T

tail probability calculation: For an upper-tail test with observed x, computing P(X ≥ x); for a lower-tail test, computing P(X ≤ x); for a two-tailed test, doubling the tail probability or…WJEC
taking logarithms: Applying logarithms to both sides of an exponential equation, which for natural logarithms gives ln(aˣ) = ln b.WJEC
Tangent: A straight line that has the same instantaneous gradient as a curve at the point of contact.AQA, Pearson Edexcel, WJEC
Tangent and chord relationships: The perpendicular from the centre to a chord bisects the chord, and the radius at a point is perpendicular to the tangent there.AQA
Tangent and normal lines: The tangent has gradient m = dy/dx and equation y − y₁ = m(x − x₁); the normal is perpendicular with gradient −1/m when m ≠ 0.Pearson Edexcel
tangent definition: Originates directly from unit circle definitions where x = cos θ, y = sin θ, and gradient tan θ = y/x.WJEC
tangent gradient: The gradient of the tangent at any point (x, y) on y = eˣ equals y itself.WJEC
tangent perpendicular to radius: The tangent at point P is perpendicular to the radius OP, so the tangent has gradient m_(tan) = −1/m_(rad).WJEC
tangents and normals: The tangent at a point has equation y - y1 = m(x - x1), where m is the gradient, and the normal is perpendicular, so its gradient is -1/m provided m ≠ 0.AQA, WJEC
tangents and secants: A secant line cuts the curve twice, while a tangent line touches the curve at a point of contact.WJEC
tangents to curves: Tangents and normals are formed using coordinates (f(t), g(t)) and the calculated gradient.WJEC
Technique selection: Choosing appropriate techniques and applying them accurately within the argument.Pearson Edexcel
tension: The pulling force exerted by a taut string or rope on an attached particle, acting along the string away from the particle.AQA, Pearson Edexcel
Term-by-term differentiation: Applying the constant multiple, sum and difference rules to differentiate each term of an expression separately, preserving coefficients.AQA
Term-by-term integration of sums and differences: Sums, differences and constant multiples are integrated term by term, carrying the constant of integration c.Pearson Edexcel
Terminal velocity: A constant velocity approached when acceleration tends to zero because forces balance in the model.Pearson Edexcel
Test statistic: A value calculated from the sample; for a binomial model it is the number of successes X ~ B(n, p).AQA, Pearson Edexcel
The exceptional case of 1/x: The power rule is valid for all n except n = −1, where 1/x integrates as ln|x| + c instead.Pearson Edexcel
The natural exponential base e: The base e≈2.718 is defined so that the gradient of e^x at x=0 is exactly 1, giving the self-derivative property.AQA
The natural logarithm and base e: ln x is log_e(x), the inverse of e^x, so ln(e^x) = x and e^(ln x) = x for x > 0.Pearson Edexcel
The special constant e: A base of approximately 2.718, defined so that the curve y = e^x has gradient equal to its own value at every point.Pearson Edexcel
time as parameter: In kinematics and physical modelling, the parameter t naturally represents time, with x(t) and y(t) describing horizontal and vertical positions simultaneously.WJEC
time of flight and range: Setting y = 0 gives the time of flight, and substituting this into x determines the horizontal range.WJEC
Tolerance: The specified accuracy to which an interval is narrowed or an iteration continued until the required degree is met.Pearson Edexcel
total distance travelled: Obtained by summing the absolute geometric areas above and below the time axis.WJEC
total probability axiom: Across the support, Σ P(X = x) = 1, alongside 0 ≤ P(X = x) ≤ 1 for every outcome x.WJEC
trajectory analysis: Trigonometric identities such as sin²θ + cos²θ = 1 and sec²θ = 1 + tan²θ help eliminate angles in trajectory equations.WJEC
transcendental equations: Equations, such as x = cos x or e^(−x) = x, that have no elementary algebraic solution.WJEC
transcription errors: Errors in raw datasets such as negative heights or impossible ages.WJEC
transformations of graphs: Translations and scalings applied to reciprocal curves, shifting the vertical asymptote to x = h and the horizontal asymptote to y = k.WJEC
transformed asymptotes: Landmarks such as asymptotes are tracked through each step to confirm the result.WJEC
Transformed variable: A new variable made from original data, such as $\log x$ or $\log y$, used to produce a linear graph.Pearson Edexcel
Translation: A transformation that moves every point by the same vector without changing the graph’s shape, size or orientation.Pearson Edexcel
translational equilibrium: When the resultant force acting on a particle is zero, its acceleration is identically zero and its velocity vector remains constant.WJEC
translations: Vertical transformations operate outside the function: y = f(x) + a translates the graph vertically by vector (0, a); y = f(x + a) translates the graph…WJEC
Trapezium rule: Approximates a definite integral by dividing the area under the curve into n strips of equal width, each strip treated as a trapezium with parallel vertical…AQA, Pearson Edexcel, WJEC
Tree diagrams: Show sequential events, with branch probabilities multiplied along a path and added across paths, and the second set of branches carries conditional…AQA, Pearson Edexcel, WJEC
Trend description: Commenting on trends or comparing outputs where multiple values are calculated as part of interpreting the model.Pearson Edexcel
Trial: One repetition or opportunity for the defined success or failure to occur.Pearson Edexcel
Triangle law: Vectors can be added by placing them tip to tail, with the resultant being the arrow from the start of the first vector to the tip of the last.AQA
triangle law of vectors: Adding vector b to vector a by placing the tail of b at the nose of a to form the resultant a + b.WJEC
triangle of forces: For three concurrent forces in equilibrium, the forces can be arranged head-to-tail to form a closed vector triangle.WJEC
trigonometric asymptotes: Vertical asymptotes occur wherever the denominators vanish: sec θ where cos θ = 0, cosec θ where sin θ = 0, and cot θ where sin θ = 0.WJEC
trigonometric definitions: For a radius making an angle θ anticlockwise from the positive x-axis, the terminal point is (cos θ, sin θ), with tan θ = y/x for cos θ ≠ 0.WJEC
trigonometric derivatives: Differentiating sin kx gives k cos kx, cos kx gives −k sin kx, and tan kx gives k sec²kx.WJEC
Trigonometric derivatives with argument kx: The derivatives are k cos kx for sin kx, −k sin kx for cos kx, and k sec² kx for tan kx.Pearson Edexcel
Trigonometric functions for all angles: Sine, cosine and tangent defined for all arguments via the unit circle, where tan θ = sin θ/cos θ is undefined wherever cos θ = 0.AQA
Trigonometric identities: Known identities used to manipulate expressions, such as sin² θ + cos² θ = 1, tan θ = sin θ / cos θ, and the addition, double angle and harmonic form formulae.AQA, Pearson Edexcel
trigonometric integration: Integrating sin(kx) gives −(1/k) cos(kx) + c and integrating cos(kx) gives (1/k) sin(kx) + c, with angles in radians.WJEC
trigonometric quadratics: Quadratic equations in mixed trigonometric ratios that can be transformed into a single trigonometric variable by substitution.WJEC
trigonometric resolution: Using trigonometric functions to resolve a force F inclined at angle θ to an axis into an adjacent component F cos θ and an opposite component F sin θ.WJEC
trigonometric simplification: Applying tan θ = sin θ / cos θ to simplify expressions or transform equations.WJEC
Turning effect of a force: A moment measures the turning effect of a force about a point.AQA
turning points: The stationary vertex of the parabola, located at (−b/(2a), c − b²/(4a)) from the completed square form.WJEC
Two-tailed test: A test with critical regions in both tails because H₁ states that the parameter is not equal to the stated value.AQA
Two-way tables: Organise counts by two categories, and conditional probability is a row or column proportion, not a proportion of the whole table.AQA, Pearson Edexcel, WJEC
Type I error: Incorrectly rejecting the null hypothesis H₀ when it is entirely true, a mistake whose probability the significance level α specifies as a maximum.WJEC
Type II error: Occurs when H₀ is not rejected (accepted) when H₀ is in fact false, so an alternative parameter value p₁ applies.WJEC

U

undefined: Having no numerical value in the stated expression.Pearson Edexcel
Under-estimate: An estimate that lies below the true value, occurring when the curve is concave over the interval.AQA
uniform gravitational field model: A model in which gravitational acceleration near the Earth's surface is treated as a uniform constant.WJEC
union: The symbol ∪ expresses disjoint solution regions as a set, connecting intervals that cannot be satisfied simultaneously by any real number.AQA, Pearson Edexcel, WJEC
union and intersection: Union A ∪ B contains elements in A, in B, or in both, matching "or"; intersection A ∩ B contains elements in both, matching "and".WJEC
unit: An agreed standard used to measure and state the size of a quantity.AQA
unit base vectors i and j: Written as i = (1; 0) and j = (0; 1), they allow a vector to be written as v = xi + yj.WJEC
unit circle: The circle x² + y² = 1 centred at the origin, used to define trigonometric ratios for any real angle θ.Pearson Edexcel, WJEC
unit conversion: Operating fluently with metric prefixes, converting kilometres to metres, grams to kilograms, and minutes or hours to seconds.WJEC
Unit vector: A vector of magnitude 1; $\mathbf i$ and $\mathbf j$ point in the positive coordinate directions.AQA, Pearson Edexcel, WJEC
unit vectors in 3D: A vector divided by its magnitude, written r̂ = r / |r|.WJEC
Units and accuracy: Attaching correct units and an appropriate degree of accuracy to the answer when presenting it.Pearson Edexcel
units and dimensions: Expressing solutions in appropriate units, such as metres, seconds, or pounds sterling, converting abstract mathematical variables back into the contextual…WJEC
units and meaning: Calculated numerical values interpreted as specific physical or contextual quantities with units, stated with appropriate degrees of precision.AQA, WJEC
Universal set: The set denoted by ξ, which must always be defined before complements are used.AQA
Universal statement: A statement claiming that a property holds for every value in a specified domain.WJEC
unstructured problem solving: Problems lack explicit scaffolding, requiring learners to design a multi-stage solution pathway independently.WJEC
Upper and lower bounds: Limits between which the true area must lie, determined for example by using rectangles or considering the nature of the curve.AQA
Upper limit: The final value of the index in a sigma expression, at which the general term is evaluated before adding.AQA
Using formulae for nth term and sum: Setting up the general term or sum formula correctly and defining variables clearly, such as a for first term, d for common difference, r for common ratio and…AQA
Using formulae to model and solve sequence problems: Identify a and r, choose the correct formula, and substitute, using ar^(n-1) for the nth term and the finite sum formulae for r≠1.AQA
Using periodicity and symmetry of trigonometric functions: Applying the periodic nature and symmetry of the sine, cosine and tangent graphs to find all solutions in the given interval.Pearson Edexcel

V

V-shaped graphs: For a linear function y = |ax + b|, the graph forms a characteristic V-shape with a vertex where the argument equals zero.WJEC
Validity and limitations of models: Judging whether a conclusion is still useful, and stating whether the model overestimates or underestimates the real value and why.AQA
Validity condition: The expansion for rational n is valid only when |bx/a| < 1, which ensures the infinite series converges.AQA, Pearson Edexcel
Validity conditions for infinite series: For rational n the expansion becomes an infinite series, valid only when the absolute value of bx over a is less than 1.AQA
Validity of mathematical statements: Maintaining correct syntax through multi-step working so that each line is a valid mathematical statement.AQA
validity of solutions: Checking mathematical roots against contextual constraints and rejecting unphysical values, such as a negative time value that is physically inadmissible.WJEC
variable acceleration: Acceleration that varies as a function of time, so that suvat equations are invalid and calculus must be used.WJEC
variable definition: Identifying the primary variables and defining them with appropriate notation and units.WJEC
Variables: Key quantities identified from the context, defined clearly and consistently, including units where appropriate.AQA
Variables and units: The key quantities identified from the context, each given suitable units.Pearson Edexcel
Variance (σ²): The square of the standard deviation; it measures spread in the notation N(μ, σ²).AQA, Pearson Edexcel
variance formula: σ² = (Σx²/n) − x̄², into which summary values are substituted before extracting the positive square root.WJEC
variation of g with location: g is not a universal constant but depends on location, being approximately 9.81 m s⁻² in the UK, lower at the equator and higher at the poles.AQA, WJEC
Vector: A quantity with both magnitude and direction.AQA, Pearson Edexcel, WJEC
vector addition: Combines displacements, either diagrammatically using the triangle law or parallelogram law, or algebraically by adding components: (x₁; y₁) + (x₂; y₂) = (x₁…WJEC
Vector addition and resolution of forces: Combining multiple forces into a single resultant, often by resolving into perpendicular components or using vector addition.AQA
Vector addition of forces: Forces given as 2D vectors are added to find the resultant force before using F = ma.AQA, Pearson Edexcel
Vector algebra in 2D and 3D: Vectors are added, subtracted and multiplied by scalars component-wise, keeping i, j and k terms separate.AQA
vector and force resolution: Constructing free-body force diagrams or vector triangles enables the resolution of forces into orthogonal components using trigonometry.WJEC
Vector arithmetic and scalar multiplication: Adding and subtracting vectors component by component, and multiplying by a scalar, with the same component rules applying in 2-D and 3-D.Pearson Edexcel
Vector between two points: Found by subtracting their position vectors in a consistent order, giving AB = b - a or a - b.AQA
vector constants of integration: Constants c = c_x i + c_y j and d = d_x i + d_y j that must be determined using initial vector conditions at t = 0.WJEC
vector differentiation: Differentiating position vector components to find velocity v = dr/dt, or velocity to find acceleration a = dv/dt.WJEC
vector direction and bearings: An angle relative to a reference axis, found using trigonometry, or measured clockwise from North for bearings.WJEC
vector dynamics ΣF = ma: Newton's second law in vector form, where acceleration a is in the direction of resultant force R.WJEC
vector integration: Integrating acceleration vectors to find velocity, or velocity to find position, including vector constants of integration.WJEC
vector kinematics: Kinematic relationships under constant acceleration extended directly to vectors, such as v = u + at and r = r_0 + ut + ½at².WJEC
vector magnitude: Calculated via Pythagoras' theorem as the square root of x squared plus y squared.WJEC
Vector modelling of motion in a vertical plane: Using r = r₀ + u t + ½a t² with a = −g ĵ and applying it componentwise to motion in a vertical plane.Pearson Edexcel
Vector modelling of real-world situations: Vectors model quantities with both magnitude and direction, such as forces and velocities, and problems are solved by drawing a diagram, defining a coordinate…AQA
Vector resolution: Resolving a vector or force into perpendicular components using sine and cosine.AQA
Vector resolution and components: Resolving vector quantities into perpendicular components, solving each component independently, then combining them.AQA
vector signs in kinematics: The sign of velocity indicates direction of travel, and displacement can be positive, negative, or zero.WJEC
Vectors: Quantities with components, used to extend kinematics to two dimensions by treating each component separately.AQA
Velocity: The rate of change of displacement, a vector, so a negative value indicates motion in the negative direction.AQA, Pearson Edexcel, WJEC
velocity versus speed: Velocity is the vector rate of change of displacement, whose sign indicates direction of travel, while speed is the scalar magnitude of velocity.WJEC
velocity-time graph: A graph on which the gradient represents instantaneous acceleration, while the area enclosed between the curve and the time axis represents displacement.WJEC
Venn diagrams: Visually represent a sample space and compound events as intersecting regions, dividing the universal set into mutually disjoint compartments.Pearson Edexcel, WJEC
Vertex: A point of a parabolic graph, identified from the completed-square form a(x−h)²+k as (h, k).AQA
vertex coordinates: Converting to completed square form a(x − h)² + k immediately identifies these at (h, k).WJEC
vertical asymptote: The y-axis (x = 0) is a vertical asymptote, with ln x → −∞ as x approaches 0 from the right (x → 0⁺).Pearson Edexcel, WJEC
Vertical intercept: The value of the vertical variable when the horizontal variable is zero; in $Y=mX+c$, it is c.Pearson Edexcel
violation of independence: A failure of the condition that events do not influence one another, which means the Poisson model is not appropriate.WJEC

W

weight: The force of gravity on a mass, calculated as W = mg, where m is mass in kg and g is gravitational acceleration in m s⁻².AQA, Pearson Edexcel, WJEC
Weight as a force: The force of gravity on a mass, W = mg, measured in newtons, where g is about 9.8 m s⁻² near the Earth's surface.Pearson Edexcel

X

x-intercepts: Points where the curve crosses the x-axis at a root x = c within the interval [a, b], at which the integral must be split.WJEC

Y

y-intercept: The value of y where a graph crosses the y-axis; in y = mx + c it is c.Pearson Edexcel

Z

Z-test statistic: The standardised score Z = (X̄ − μ₀) / (σ / √n), compared to standard normal critical values or used to calculate the p-value.WJEC
Zero exponent: A power written as a^0, which equals 1 provided a ≠ 0.AQA
zero resultant force: Implies zero acceleration and constant velocity or rest, and in orthogonal directions requires opposing forces to balance exactly.WJEC
Zero vector: The vector with every component zero; it has magnitude zero and no direction.Pearson Edexcel

Other terms

2D Newton's second law: Extend Newton's second law to situations where forces need to be resolved, restricted to two dimensions, by establishing two mutually perpendicular reference…WJEC
2D particle dynamics: Applying Newton's second law so that the resultant force causes acceleration in the identical direction, with acceleration vector a = R/m.WJEC
2D vector kinematics: Extending, using and deriving the formulae for constant acceleration for motion in a straight line to 2 dimensions using vectors.WJEC
3D Cartesian vectors and components: Positions, velocities and forces represented using orthogonal unit vectors i, j and k along the x, y and z axes, or as a column vector.WJEC
3D dynamics ΣF = ma: Under Newton's second law, the sum of forces equals mass times acceleration, applied in three dimensions.WJEC
3D force equilibrium: When multiple 3D forces act on a body, the resultant vector is zero, requiring balance in all three axes.WJEC
3D kinematics and calculus: Kinematic equations with constant 3D acceleration extend to v = u + at and r = r₀ + ut + ½at², while for variable acceleration calculus applies component-wise.WJEC

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