Maths AI terms: L

37 of the Maths AI glossary’s terms, each with the part of the syllabus where you first meet it.

IB Maths AI glossary: L | Augment Education

L

Largest empty circlealso maximum empty circle, largest empty circles: The largest circle, centred inside a given region, that has no site inside it; its centre solves the toxic waste dump problem and its radius is the distance from that centre to the nearest site.
Introduced in 3.6 Voronoi diagrams
Laws of exponentsalso exponent laws, index laws, laws of indices: The rules for calculating with powers: $a^m \times a^n = a^{m+n}$ , $a^m \div a^n = a^{m-n}$ , $(a^m)^n = a^{mn}$ , $(ab)^n = a^nb^n$ and $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$ , together with $a^0 = 1$ and $a^{-n} = \frac{1}{a^n}$ for $a \ne 0$ .
Introduced in 1.5 Exponents and introduction to logarithms
Laws of logarithmsHL only · also log laws, logarithm laws, rules of logarithms, laws of logs: The three rules $\log_a xy = \log_a x + \log_a y$
Leading diagonalHL only · also main diagonal, diagonal, principal diagonal: The elements of a square matrix whose row number equals their column number, running from the top left to the bottom right.
Introduced in 1.14 Matrices
Least squares regression curveHL only · also least squares curve, regression curve, least squares, least-squares regression curve: The curve of a chosen family (such as quadratic or exponential) whose parameter values make the sum of square residuals for the data as small as possible.
Introduced in 4.13 Non-linear regression
Leibniz notationalso dy/dx notation, Lagrange notation, prime notation, Leibniz's notation: The notation $\frac{\mathrm{d}y}{\mathrm{d}x}$ for the derivative of $y$ with respect to $x$ , which names both the quantity that changes (on top) and the variable it changes with (underneath); the alternative prime (Lagrange) notation writes the derivative of
Length of a walkHL only · also walk length, k-length walk: The number of edges in the walk, counting each repeated edge every time it is used.
Introduced in 3.15 Adjacency matrices
Limitalso limits, tends to, approaches, limiting value of a function: The value that $f(x)$ gets arbitrarily close to as $x$ gets closer and closer to a given value $a$ (or as $x$ increases without bound), written $\lim_{x \to a} f(x)$
Limitation of a modelalso limitation, limitations, limitations of a model, weakness of a model: A feature of the real situation that a model ignores or represents poorly, or a range of inputs where the model gives unreliable results.
Introduced in 2.6 The modelling process
Limits of integrationalso lower limit, upper limit, bounds of integration, limit of integration: The two values of the variable between which a definite integral is taken: the lower limit $a$ , written at the bottom of the integral sign, and the upper limit $b$ , written at the top.
Introduced in 5.5 Introduction to integration
Line of best fitalso line of best fit by eye, best-fit line, trend line: A straight line drawn by eye on a scatter diagram through the mean point, following the trend of the points so that they are balanced on either side of it.
Introduced in 4.4 Correlation and regression
Line of sightalso lines of sight, sight line: The straight line from an observer's eye to the object being observed.
Introduced in 3.3 Applications of trigonometry
Line segmentalso segment [AB], [AB], line segments: The part of a straight line between two endpoints, written $[AB]$ for the segment with endpoints $A$ and $B$ ; its length is written $AB$ .
Introduced in 3.1 Volume and surface area in three dimensions
Linear combination of random variablesHL only · also linear combination, sum of random variables, difference of random variables, linear combinations: A random variable of the form $a_1X_1 \pm a_2X_2 \pm \dots \pm a_nX_n$
Linear equationalso linear equations: An equation in which every term is either a constant or a constant multiplied by a single variable raised to the power 1.
Introduced in 1.8 Equations and systems using technology
Linear functionalso linear functions, straight-line graph, linear graph: A function whose graph is a straight line, with an equation of the form $f(x) = mx + c$ , where $m$ and $c$ are constants.
Introduced in 2.1 Equations of straight lines
Linear modelalso linear models: A model of the form $f(x) = mx + c$ , in which the output changes by the same amount $m$ for every increase of 1 in the input.
Introduced in 2.5 Modelling with functions
Linear relationshipalso linear association, linear relationships: A relationship between two variables in which the points of a scatter diagram lie close to a straight line, so that equal increases in $x$ go with roughly equal changes in $y$ .
Introduced in 4.4 Correlation and regression
Linear system of differential equationsHL only · also coupled linear differential equations, ẋ = Mx, linear systems of differential equations, linear coupled system: A pair of coupled differential equations $\dot{x} = ax + by$ , $\dot{y} = cx + dy$
Linear transformation of a random variableHL only · also aX + b, E(aX + b), Var(aX + b), linear transformation: A new random variable $Y = aX + b$ formed from a random variable $X$ by multiplying every value by a constant $a$ and adding a constant $b$ ; it has $\mathrm{E}(Y) = a\mathrm{E}(X) + b$
LinearizationHL only · also linearisation, linearizing, linearising, linearize, linearise, linearising data: Transforming one or both variables of a data set, usually by taking logarithms, so that the relationship between the transformed variables is a straight line whose gradient and intercept give the parameters of the original model.
Introduced in 2.10 Scaling very large and small numbers using logarithms
Loanalso loans, borrowing, borrow: An amount of money borrowed from a lender, such as a bank, that the borrower agrees to repay with interest under agreed conditions.
Introduced in 1.7 Amortisation and annuities
Loan termalso term of a loan, repayment period, loan terms: The length of time over which a loan is to be fully repaid, usually given in years.
Introduced in 1.7 Amortisation and annuities
Local linearityalso locally linear, local linear approximation, linear approximation: The property of a smooth curve that, close enough to any point on it, the curve is almost indistinguishable from its tangent at that point, so the tangent gives a good approximation to the curve there.
Introduced in 5.4 Tangents and normals
Local maximumalso local maxima, relative maximum, maximum point, local max: A point on a graph whose $y$ -coordinate is greater than or equal to the $y$ -coordinates of all nearby points on both sides of it.
Introduced in 2.4 Key features of graphs
Local minimumalso local minima, relative minimum, minimum point, local min: A point on a graph whose $y$ -coordinate is less than or equal to the $y$ -coordinates of all nearby points on both sides of it.
Introduced in 2.4 Key features of graphs
Locusalso loci, locus of points: The set of all points that satisfy a given condition.
Introduced in 3.5 Perpendicular bisectors
Log-log graphHL only · also log-log plot, log-log graphs, logarithmic graph, double-log graph: A graph in which both axes are logarithmic, or equivalently a graph of $\ln y$ against $\ln x$ (or $\log y$ against $\log x$ ); power relationships appear on it as straight lines whose gradient is the power.
Introduced in 2.10 Scaling very large and small numbers using logarithms
Logarithmalso log, logarithms, log_a b: For a base $a > 0$ , $a \ne 1$ , and a positive number $b$ , the logarithm $\log_a b$
Logarithmic equationHL only · also logarithmic equations, log equation, log equations: An equation in which the unknown appears in the argument of a logarithm.
Introduced in 1.9 Laws of logarithms
Logarithmic identitiesHL only · also log identities, log_a 1 = 0, log_a a = 1, logarithmic identity: The results $\log_a 1 = 0$ , $\log_a a = 1$
Logarithmic scalealso log scale, logarithmic scales: A scale on which equal distances represent multiplication by the same factor, so that a value is placed according to its logarithm (usually its common logarithm) rather than its size.
Introduced in 1.5 Exponents and introduction to logarithms
Logistic modelHL only · also logistic function, logistic growth, logistic curve, logistic growth model: A model of the form $f(x) = \frac{L}{1 + C\mathrm{e}^{-kx}}$ , where $L, C, k > 0$
Long-term probabilityHL only · also long-term probabilities, limiting probability, long-run probability, long-run proportion: The limit of the probability of being in a given state after $n$ steps of a Markov chain as $n$ becomes very large; for a regular chain it equals the corresponding entry of the steady state.
Introduced in 4.19 Transition matrices and Markov chains
LoopHL only · also loops, self-loop: An edge that joins a vertex to itself.
Introduced in 3.14 Graph theory
Lower boundalso lower bounds, least possible value: The smallest value that a rounded number could have had before it was rounded; for a value rounded to the nearest unit $u$ , it is the rounded value minus $\frac{u}{2}$ .
Introduced in 1.6 Approximation and error
Lower quartilealso Q1, Q₁, first quartile, quartile, quartiles: The value below which one quarter (25%) of the data lie when the data are arranged in order; it is written $Q_1$ .
Introduced in 4.2 Presenting data