Maths AI terms: G

G

Gainalso net winnings, expected gain, net gain

The amount a player receives from a game minus the amount paid to play, so that a loss is a negative gain.

Introduced in 4.7 Discrete random variables

Galton boardalso quincunx, bean machine, Galton box

A device in which balls fall through rows of pins, bouncing left or right at each pin, and collect in slots at the bottom, so that the number of balls in each slot follows a binomial distribution.

Introduced in 4.8 The binomial distribution

General form of a linealso general form, ax + by + d = 0, general form of a straight line

The equation of a straight line written as $ax + by + d = 0$, where $a$, $b$ and $d$ are constants, usually integers, and $a$ and $b$ are not both zero.

Introduced in 2.1 Equations of straight lines

General solutionHL only · also general solutions, family of solutions

The solution of a differential equation that contains an arbitrary constant (one constant for a first-order equation), so that it describes the whole family of functions satisfying the equation.

Introduced in 5.14 Setting up differential equations

General termalso nth term, nth term formula, formula for the nth term

A formula for $u_n$ in terms of the position $n$, from which any term of a sequence can be calculated directly.

Introduced in 1.2 Arithmetic sequences and series

Geometric sequencealso geometric progression, geometric sequences, GP

A sequence in which each term after the first is found by multiplying the term before it by the same non-zero constant, called the common ratio.

Introduced in 1.3 Geometric sequences and series

Geometric seriesalso geometric series sum, sum of a geometric sequence, geometric progression sum

The sum of the terms of a geometric sequence, $u_1 + u_1 r + u_1 r^2 + \cdots$

Global maximumalso absolute maximum, greatest value, global max, maximum value on a domain

The greatest value that a function takes on its whole domain, which may occur at a local maximum or at an end point of the domain.

Introduced in 5.6 Stationary points

Global minimumalso absolute minimum, least value, global min, minimum value on a domain

The least value that a function takes on its whole domain, which may occur at a local minimum or at an end point of the domain.

Introduced in 5.6 Stationary points

Googolalso googols

The number $10^{100}$, a 1 followed by one hundred zeros.

Introduced in 1.1 Scientific notation

Googolplexalso googolplexes

The number $10^{\text{googol}} = 10^{10^{100}}$, a 1 followed by a googol of zeros.

Introduced in 1.1 Scientific notation

Gradientalso slope, gradients, gradient of a line

The steepness of a straight line, equal to the vertical change divided by the horizontal change between any two points on the line.

Introduced in 2.1 Equations of straight lines

Gradient formulaalso gradient formula for two points, m = (y2 − y1)/(x2 − x1)

The formula $m = \frac{y_2 - y_1}{x_2 - x_1}$

Gradient of a curvealso gradient at a point, steepness of a curve, slope of a curve, gradient of the curve

The gradient of the tangent to a curve at a given point, equal to the limit of the gradients of secants through the point as the second point approaches it.

Introduced in 5.1 Limits and the derivative

Gradient-intercept formalso y = mx + c, slope-intercept form, gradient–intercept form

The equation of a straight line written as $y = mx + c$, where $m$ is the gradient and $c$ is the y-coordinate of the y-intercept.

Introduced in 2.1 Equations of straight lines

Graph (graph theory)HL only · also graphs, network graph

A set of vertices together with a set of edges, where each edge joins two vertices (or one vertex to itself).

Introduced in 3.14 Graph theory

Graph of a functionalso graph, graph of f, graphs of functions

The set of all points $(x, y)$ in the plane with $x$ in the domain of the function and $y = f(x)$.

Introduced in 2.3 Graphing functions with technology

Graph theoryHL only

The branch of mathematics that studies graphs, structures made of objects (vertices) and connections between pairs of them (edges).

Introduced in 3.14 Graph theory

Graphic display calculator (GDC)also GDC, graphing calculator, graphic display calculators, graphics calculator

A hand-held calculator that draws graphs of functions and has built-in tools for solving equations, statistics, probability distributions, matrices and finance; one is used on every paper of the course.

Graphical solutionalso solving graphically, graphical method, graphical solutions, solve graphically

A solution of an equation $f(x) = g(x)$ found as the $x$-coordinate of a point of intersection of the graphs of $y = f(x)$ and $y = g(x)$

Greedy algorithmHL only · also greedy, greedy algorithms

An algorithm that makes the choice that looks best at each step, without reconsidering earlier choices.

Introduced in 3.16 Tree and cycle algorithms

Grouped dataalso grouped frequency table, grouped frequency distribution, grouped frequency tables

Data that have been sorted into classes, so that the table gives the number of values in each class rather than each individual value.

Introduced in 4.2 Presenting data

Growth factoralso multiplier, growth multiplier, growth factors

The number greater than 1 by which a quantity is multiplied in each time period when it increases by a fixed percentage; for an increase of $p\%$ it equals $1 + \frac{p}{100}$.

Introduced in 1.3 Geometric sequences and series