Maths AI terms: I

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

IB Maths AI glossary: I | Augment Education

I

Identity functionHL only · also identity map, x ↦ x: The function that maps every input to itself, $x \mapsto x$ ; its graph is the line $y = x$ .
Introduced in 2.7 Composite and inverse functions
Identity matrixHL only · also unit matrix, identity, identity matrices, I_n: A square matrix with every element on the leading diagonal equal to 1 and every other element equal to 0, written $I$ ; for any square matrix $A$ of the same order, $AI = IA = A$ .
Introduced in 1.14 Matrices
ImageHL only · also images: The point, line or graph that results when a transformation is applied to an original point, line or graph.
Introduced in 2.8 Transformations of graphs
Imaginary partHL only · also Im(z), imaginary component: For a complex number $z = a + b\mathrm{i}$ with $a, b \in \mathbb{R}$ , the real number $b$ (the coefficient of $\mathrm{i}$
Imaginary unitHL only · also i, the number i: The number $\mathrm{i}$ defined by $\mathrm{i}^2 = -1$ , so that $\mathrm{i} = \sqrt{-1}$
In-degreeHL only · also in degree, indegree: The number of edges of a directed graph that end at (point into) a vertex.
Introduced in 3.14 Graph theory
Included anglealso included angles, angle between two sides: The angle between two given sides of a triangle, at the vertex where they meet.
Introduced in 3.2 Trigonometry in triangles
Increasing functionalso increasing, increasing on an interval, increasing functions, strictly increasing: A function is increasing on an interval if, for any two values $x_1 < x_2$ in the interval, $f(x_1) < f(x_2)$
Incremental algorithmalso incremental construction, adding a site, adding a site to a Voronoi diagram: A method of constructing a Voronoi diagram by adding the sites one at a time, updating the existing diagram after each new site is added.
Introduced in 3.6 Voronoi diagrams
Indefinite integralalso indefinite integrals, general anti-derivative: The family of all anti-derivatives of a function, written $\int f(x)\,\mathrm{d}x = F(x) + C$ , where $F'(x) = f(x)$
Independent and identically distributedHL only · also iid, i.i.d., independent and identically distributed random variables: Describes random variables that all have the same probability distribution and are mutually independent.
Introduced in 4.15 The central limit theorem
Independent eventsalso independent, independence, independent event: Events for which the occurrence of one does not change the probability of the other, so that $\mathrm{P}(A \mid B) = \mathrm{P}(A)$ and $\mathrm{P}(A \cap B) = \mathrm{P}(A)\,\mathrm{P}(B)$
Independent random variablesHL only · also independence of random variables, independent variables: Random variables for which the value taken by any one of them does not change the probability distribution of any of the others.
Introduced in 4.14 Linear transformations of random variables
Independent trialsalso independent trial, independence of trials: Repeated trials in which the outcome of any trial does not change the probabilities of the outcomes of any other trial.
Introduced in 4.8 The binomial distribution
Independent variablealso input variable, explanatory variable: The input of a function, whose values are chosen or given, usually plotted on the horizontal axis.
Introduced in 2.2 Functions, domain and range
Infinite sequence: A sequence that continues without end, so that every term is followed by another term.
Introduced in 1.2 Arithmetic sequences and series
Infinite seriesHL only · also infinite sum, infinite series of terms: The sum of the terms of an infinite sequence, $u_1 + u_2 + u_3 + \cdots$
Inflation ratealso inflation, annual inflation rate, rate of inflation: The percentage increase in the general level of prices over a year, usually measured by the change in the price of a fixed basket of goods and services.
Introduced in 1.4 Financial applications of geometric sequences
Initial positionHL only · also r₀, starting position, initial position vector: The position vector $\boldsymbol{r}_0$ of a moving object at time $t = 0$ .
Introduced in 3.12 Vectors in kinematics
Initial state vectorHL only · also initial state matrix, initial state probability matrix, initial state, s_0, initial distribution: The state vector $\boldsymbol{s}_0$ that describes a Markov chain before the first step, giving the probability of starting in each state or the number starting in each state.
Introduced in 4.19 Transition matrices and Markov chains
Initial valuealso starting value: The value of a model's output when the input is 0; for $f(x) = ka^x + c$ it equals $k + c$ .
Introduced in 2.5 Modelling with functions
Inner functionHL only · also inside function: In a composite function $y = g(f(x))$ , the function $f$ that is applied first, directly to $x$ ; its output $u = f(x)$
Instantaneous rate of changealso instantaneous rate, rate at an instant, rate of change at a point: The rate of change of a quantity at one particular value of the input, equal to the derivative at that value and to the gradient of the tangent there; it is the limit of the average rates of change over shorter and shorter intervals.
Introduced in 5.1 Limits and the derivative
Instantaneous restHL only · also at rest, momentarily at rest, instantaneously at rest: The state of a moving object at an instant when its velocity is zero, $v = 0$ .
Introduced in 5.13 Kinematics
Integeralso integers, ℤ, whole number, whole numbers: A whole number that may be positive, negative or zero; the set of integers is written $\mathbb{Z} = \{\ldots, -2, -1, 0, 1, 2, \ldots\}$ .
Introduced in 1.1 Scientific notation
Integrandalso integrands: The function that is being integrated, written between the integral sign and $\mathrm{d}x$ .
Introduced in 5.5 Introduction to integration
Integrationalso integrate, integrating, integrated: The process of finding an anti-derivative of a function, or of finding the accumulated total of a function between two values of the variable.
Introduced in 5.5 Introduction to integration
Integration by inspectionHL only · also inspection, integrating by inspection, recognition: Finding an integral by recognising the integrand as the result of differentiating a known function, writing that function down and adjusting it by a constant factor so that its derivative matches the integrand exactly.
Introduced in 5.11 Further integration
Integration by substitutionHL only · also substitution, u-substitution, change of variable, integrating by substitution: A method that replaces an inner function $g(x)$ by a new variable $u = g(x)$ and $g'(x)\,\mathrm{d}x$
Interestalso interest earned, interest paid: The money paid by a borrower to a lender, or earned by a saver, for the use of money over a period of time.
Introduced in 1.2 Arithmetic sequences and series
Interpolationalso interpolate, interpolating, interpolated: Using a model to predict a value for an input that lies within the range of the input values used to build or test the model.
Introduced in 2.6 The modelling process
Interquartile range (IQR)also IQR, inter-quartile range: The difference between the upper and lower quartiles, $Q_3 - Q_1$ , which measures the spread of the middle 50% of the data.
Introduced in 4.2 Presenting data
Intersecting linesHL only · also lines that meet, intersecting line: Two lines that have exactly one point in common, their point of intersection.
Introduced in 3.11 Vector equations of lines
Intersectionalso A ∩ B, and, intersections: The event $A \cap B$ that both $A$ and $B$ occur; it contains only the outcomes that are in $A$ and in $B$ .
Introduced in 4.6 Combined events
Interval notationalso intervals, interval, bracket notation: A way of writing a set of real numbers between two endpoints, with $[a, b]$ including both endpoints, $]a, b[$ excluding both, and $[a, b[$ or $]a, b]$
Invariant lineHL only · also invariant lines: A line that is mapped onto itself by a transformation; if every point on the line stays fixed, it is a line of invariant points.
Introduced in 2.8 Transformations of graphs
Invariant pointalso invariant points: A point that is mapped to itself by a transformation, so that its coordinates are unchanged.
Introduced in 2.2 Functions, domain and range
Inverse functionalso f inverse, inverse functions, f⁻¹, inverse of a function: The function $f^{-1}$ that reverses the effect of a one-to-one function $f$ , so that if $f(a) = b$ then $f^{-1}(b) = a$
Inverse matrixHL only · also inverse of a matrix, A⁻¹, matrix inverse, A^-1, inverse matrices: For a square matrix $A$ , the matrix $A^{-1}$ of the same order such that $AA^{-1} = A^{-1}A = I$
Inverse normal calculationalso inverse normal, inverse normal calculations, invNorm, inverse normal function: Finding the value $k$ of a normally distributed variable for which the area on one side of $k$ , or a central area around the mean, equals a given probability.
Introduced in 4.9 The normal distribution
Inverse square lawalso inverse-square law, inverse square relationship: A relationship in which a quantity is inversely proportional to the square of the distance from its source, $I = \frac{k}{d^2}$ .
Introduced in 2.5 Modelling with functions
Inverse trigonometric functionalso sin⁻¹, cos⁻¹, tan⁻¹, arcsin, arccos, arctan, inverse sine, inverse cosine, inverse tangent, inverse trig functions: A function, $\sin^{-1}$ , $\cos^{-1}$ or $\tan^{-1}$
Inverse variationalso inverse proportion, inversely proportional, varies inversely: A relationship $y = \frac{a}{x^n}$ with $n$ a positive integer (equivalently $y = ax^{-n}$
Irrational numberalso irrational numbers, irrational: A real number that cannot be written as a fraction of two integers; its decimal expansion neither terminates nor repeats.
Introduced in 1.1 Scientific notation
IsoclineHL only · also isoclines: A curve along which every solution of a differential equation $\frac{\mathrm{d}y}{\mathrm{d}x} = f(x, y)$ has the same gradient $c$
Iterated function systemHL only · also IFS, chaos game, iterated function systems: A finite set of transformations, usually affine, that are applied repeatedly, either all together to a shape or one at a time chosen at random to a point, to generate a fractal.
Introduced in 3.9 Matrix transformations
IterationHL only · also iterate, iterative process, iterations, iterating: The process of applying the same rule repeatedly, each time to the result of the previous application.
Introduced in 3.9 Matrix transformations