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# Enseigner les mathématiques en anglais

## Vocabulaire scolaire / School vocabulary

• BACK TO SCHOOL : rentrée des classes

• BOARDING SCHOOL : internat

• A boarding school is an institution where children live within premises(locaux) while being given formal instruction. The word "boarding" is used in the sense of "room and board(pension ici)", i.e. lodging and meals.

• CLASS/GROUPS : classe/groupe comme 4e1

1. MIDDLE-SCHOOL : Collège (attention College in inglish is Université in French)
(for United States)
• Y6 : sixième (First in United Kindom)
• Y7 : cinquième
• Y8 : quatrième
2. HIGH SHOOL : Lycée (à partir de la 3e)
(for United States)
• Y9 : troisième Y9 (grade 9) students are freshmen/women
• Y10 : seconde: Y10 (grade 10) students are sophomore students
• Y11 (Junior) : première / (Lower Sixth in United Kindom)
• Y12 (senior, age 17-18) : terminale / (Upper Sixth in United Kindom)
3. COLLEGE/UNIVERSITY : Université
• We've compiled a ranking of the best 100 US universities and colleges, according to the recently released QS World University Rankings
• 1. Harvard University
• 2. Stanford University
• 3. Massachusetts Institute of Technology (MIT)
• 4. University of California Berkeley (UCB)
• 5. University of California, Los Angeles (UCLA)
• 6. Yale University
• 7. Columbia University
• 8. Princeton University
• 9.  New York University (NYU)
• COURSE/CLASS/LESSONS : des cours
• The noun course can refer to a series of lectures, discussions, or other lessons in a particular subject.
• To graduate from high school, you have to take certain courses in English, social studies, math, and science. Naturally, you want to pass them!

• If you attend school, you probably have a favorite class — a series of lectures or discussions where you can learn about a particular subject, like English, math, or economics.

• These exercises help students understand the lesson. (Ces exercices aident les élèves à comprendre la leçon).
• The lesson benefitted everyone in the class.
• I structure my lessons according to the syllabus (CI-LABES, programme).
• Curriculum  or Program or SYLLABUS (CI-LABES) :  programme

• "The goal of our mathematics program is to provide our students with the skills and knowledge they will need to succeed in college and beyond.
Our math curriculum is rooted in the following core beliefs about quality math instruction."

• I structure my lessons according to the syllabus (CI-LABES, programme).
• To EDIFY : to make understand
• To edify is to help someone understand, whether it is books that edify those who want to learn a new language, or the explanations that hang beside paintings at a museum that edify visitors who aren't familiar with the artist.
• ELECTIVE : option

• EXAM
• To take (passer) an exam
• to pass (réussir) an exam
• GRADES/MARKS : notes

• My daughter is getting poor grades because she’s bored in school. She tunes out(décrocher). She’d be coasting in her classes if the teachers would just challenge her.

• GRADER :  correcteur

• HOMEWORK NOTEBOOK : Cahier de texte

• MAJORS/SUBJECTS/TOPICS : matières

• Maths is m'y favorite subject/what is your favorite subject.

• MARK : note / TO MARK : corriger, noter des test

• Marking exam/test papers is an awful grind (boulot)

• MOCK exam : examen blanc

• a mock exam is an examination, esp in a school, taken as practice before an official examination.
• PREP : synonyms : homework, preparation
• PREP is a preparatory school work done outside school (especially at home)
• Her father and her mother were both lawyers, so she spent a lot of time by herself in that big house when she wasn’t away at her prep school.
• PROCTOR : surveillant

• ROLL CALL : appel

• The entry of absences and tardiness

• SCHOLARSHIP : Bourse d'étude
• A scholarship is a form of financial aid awarded to students to further their education. Scholarships are awarded based upon various criteria, such as academic merit, diversity and inclusion, athletic skill, and financial need.
• SKILL BASED ASSESSMENT: évaluation par compétences

• TEST PAPER : interro ecrite

• TIME TABLE : EDT (Emploi du Temps)

• TUITION : cours ou fees in university/ private tuition : cours privés

• Tuition payments, usually known as tuition in American English and as tuition fees in Commonwealth English, are fees charged by education institutions for instruction or other services.
• TUNE (accorder, adapter)

• Teachers always tune their remarks to suit their audience

• TUNE OUT (décrocher)

• My daughter is getting poor grades because she’s bored in school. She tunes out(décrocher). She’d be coasting (avancer facilement) in her classes if the teachers would just challenge her.

## Mathematics Symbols

### Remarques sur les notations

• La droite $$\left(AB\right)$$ se nomme line $$AB$$ en anglais et se note : $$\overleftrightarrow{AB}$$.
• Le segment $$\left[AB\right]$$ se nomme segment $$AB$$ en anglais et se note : $$\overline{AB}$$.
• Le vecteur $$\overrightarrow{AB}$$ se nomme ray $$AB$$ en anglais et se note : $$\overrightarrow{AB}$$.

## Mathematics Vocabulary and differences

### Vocabulary for demonstration and deduction

• à cet égard / therein
• à partir de rien / ex nihilo from scratch
• c’est-à-dire / in other words, that is, i.e. (latin for "id est")
• comme / as
• contraposée / contraposition
• contre-exemple /counter-example
• corollaire / corollary
• CQFD (ce qu’il fallait démontrer) / QED (quod erat demonstrandum)
• d’où / whence
• d’une part, ..., d’autre part, ... /  on one hand, ..., on the other hand, ...
• déduire / to deduce, to infer
• dans l’ensemble, globalement / by and large, on the whole
• dans la mesure où / insofar as, as far as
• démontrer / to demonstrate, to give a demonstration, to show
• démonstration par l’absurde / proof by contradiction
• en plus de / in addition to, over and above, on top of this
• élément de démonstration / proof hint
• étant donné que / given that
• implique / implies
• A statement A implies another statement B (written as A⇒B), if from the truth of the former, it necessarily follows the truth of the latter.
• induit / induced
• finir par, se retrouver avec / to end up with
• lemme / lemma
• par conséquent / consequently, thus, therefore, hence, so
• par récurrence sur ... / by induction on ...
• par exemple / for example, for instance, e.g. (latin for "exempli gratia")
• puisque / since, as, inasmuch as, for
• réciproque / converse
• sans perte de généralité / without loss of generality (abbreviated wlog)
• si, et seulement si (abrégé en ssi) / if, and only if (abbreviated iff)
• soit (le triangle ABC) / let (ABC) be (a triangle)
• supposer / to assume
• supposition /assumption

### Le vocabulaire sur le calcul algébrique et les équations en anglais

Équations / equations
Calcul algébrique / algebra

• équation / equation
• Équation produit nul / Zero-product property
• The zero product property states that if $$a⋅b=0$$ then either a or b equal zero. This basic property helps us solve equations like $$(x+2)(x-5)=0$$.
• équation du second degré / quadratic equation
• Résoudre une équation / to solve an equation
• solutions d'une équation ou racine ou zéro / solutions of an equation or roots or zero
• The values of x that satisfy the equation are called solutions of the equation, and roots or zeros of the expression on its left-hand side.
• système d’équations / simultaneaous equations or equation system

• développer / to expand
• factoriser / to factorise
• Factor out $$t$$
• forme canonique (d’un polynôme du second degré) / vertex form
• Inverse et opposé : Attention
• inverse multiplicatif / multiplicative inverse or reciprocal
• opposé / additive inverse
• membre de droite (resp. gauche) (e.g. dansune équation) / right (resp. left) hand side
• parenthèses / brackets
• simplifier (une fraction) / to cancel

### Le vocabulaire sur l'arithmétique (et les nombres) en anglais

Aritmétique / Arithmetic

• chiffre / digit
• crible (d’Eratosthène) / sieve (of Eratosthenes)
• critère de divisibilité / divisibility rule
• The basic rule for divisibility by 4 is that if the number formed by the last two digits in a number is divisible by 4, the original number is divisible by 4
• division euclidienne / Euclidean division or division with remainder
• In arithmetic, Euclidean division – or division with remainder – is the process of dividing one integer (the dividend) by another (the divisor), in a way that produces a quotient and a remainder smaller than the divisor.
• division posée / long division
• entiers premiers entre eux / coprime, relatively prime integers or mutually prime
• In mathematics, two integers a and b are coprime if the only positive integer that is a divisor of both of them is 1
• équation diophantienne / diophantine equation
• Inverse et opposé : Attention
• inverse multiplicatif / multiplicative inverse or reciprocal
• opposé / additive inverse
• multiple / multiple
• For the quantities a and b, it can be said that b is a multiple of a if $$b = na$$ for some integer n, which is called the multiplier.
If a is not zero, this is equivalent to saying that $$\dfrac {b}{a}$$ is an integer.
• ordre croissant / ascending or increasing order
• ordre décroissant / descending or decreasing order
• plus grand diviseur commun (PGCD) / greateast common divisor (GCD)
• plus petit diviseur commun (PPCM) / least common divisor (LCM)
• rapport / ratio
• reste de la division euclidienne / remainder

### Ensembles de Nombres / Set of numbers

• décimal / decimal
• entiers naturels
• Whole numbers {0,1,2,3,...}
• Natural numbers {1,2,3,...} ou counting numbers
• Some definitions begin the natural numbers with 0, corresponding to the non-negative integers 0, 1, 2, 3, ..., whereas others start with 1, corresponding to the positive integers 1, 2, 3, ...Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, while in other writings, that term is used instead for the integers (including negative integers)
• entier relatif / integer
• impair / odd
• pair / even
• premier / prime
• rationnel, irrationnel / rational, irrationnal
• réel / real

### Fraction / fraction

• dividende, diviseur / dividend, divisor
• fraction irréductible / Irreducible fraction, simple fraction (or fraction in lowest terms, simplest form or reduced fraction)
• An irreducible fraction is a fraction in which the numerator and denominator are integers that have no other common divisors than 1
• numérateur, dénominateur / numerator, denominator
• simplifier (une fraction) / to cancel

### Le vocabulaire sur les fonctions

Fonction / Function, map, mapping

• abscisse (d’un point), ordonnée / x-coordinate, y-coordinate
• accolade / brace
• analyse (en tant que domaine des mathématiques) / calculus
• axe des abscisses, axe des ordonnées  / x-axis, y-axis
• coefficient directeur / slope
• cosinus, sinus / cosine, sine
• courbe paramétrée / parametric curve
• courbe représentative / graph
• associer y à x / to map x onto y
• antécédent / pre-image (less frequently : counterimage or inverse image)
• comportement aux infinis (d’une fonction) / end behaviour
• continu (par morceaux) / (piecewise) continuous
• décroissance exponentielle / exponential decay
• dérivée / derivative
• dériver / to differentiate
• fonction / function, map, mapping
• Injective, bijective, surjective
• fonction bijective / bijective function, one-to-one correspondence (≠ one-to-one function)
• fonction injective / injective function, one-to-one function (≠ one-to-one correspondence cf. above)
• fonction surjective / surjective function, onto function

• forme canonique (d’un polynôme du second degré) / vertex form
• la limite de f (x) quand x tend vers a est l / the limit of f as x approaches a equals/is l
• fonction définie par morceaux / piecewise-defined function
• a piecewise-defined function is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain.
• ordonnée à l’origine / y-intercept
• point d’inflexion / inflection point
• primitive / antiderivative, primitive function, indefinite integral
• système de coordonnées, repère / coordinate system

#### Monotonie / monotonic, monotone function

• fonction croissante / increasing function or nondecreasing function
• fonction décroissante / decreasing function or nonincreasing function
• fonction monotone / monotonic function, monotone function
• In calculus, a function $$f$$ defined on a subset of the real numbers with real values is called monotonic if and only if it is either entirely non-increasing, or entirely non-decreasing.
• A function is called monotonically increasing (also increasing or non-decreasing), if for all $$x$$ and $$y$$ such that $$\displaystyle x\leq y$$ one has $$\displaystyle f\left(x\right)\leq f\left(y\right)$$, so $$f$$ preserves the order .
• Likewise, a function is called monotonically decreasing (also decreasing or non-increasing) if for all $$x$$ and $$y$$ such that $$\displaystyle x\leq y$$ one has $$\displaystyle f\left(x\right)\geq f\left(y\right)$$,, so it reverses the order
• Attention, l’anglais est trompeur ici : la négation de « $$f$$ est croissante » n’est pas « $$f$$ est décroissante » et réciproquement.

#### Fonction affine et linéaire

• Fonctions affines / linear function (or affine)
• coefficient directeur / slope
• ordonnée à l'origine / y-intercept
• Fonctions linéaires /  homogeneous linear function
• A linear function is a polynomial function in which the variable x has degree at most one: $$f ( x ) = a x + b$$ .
• Such a function is called linear because its graph, the set of all points $$( x , f ( x ) )$$ in the Cartesian plane, is a line.
• The coefficient a is called the slope of the function and of the line (see below)
• The coefficient b is called the y-intercept
• If the slope is $$a = 0$$ , this is a constant function $$f ( x ) = b$$ defining a horizontal line, which some authors exclude from the class of linear functions.
• If $$b = 0$$ then the linear function is said to be homogeneous.
• Such function defines a line that passes through the origin of the coordinate system, that is, the point $$( x , y )= ( 0 , 0 )$$ .
• In advanced mathematics texts, the term linear function often denotes specifically homogeneous linear functions, while the term affine function is used for the general case, which includes $$b \neq 0$$.

#### Fonction inverse, fonction réciproque, opposé

• La fonction bijection réciproque (ou fonction réciproque ou réciproque) / the inverse function of
• In mathematics, the inverse function of a function $$f$$ (also called the inverse of $$f$$) is a function that undoes the operation of $$f$$.
• The inverse of $$f$$ exists if and only if $$f$$ is bijective, and if it exists, is denoted by $$\displaystyle f^{-1}$$.
• The inverse sine of $$x$$ denoted by $$sin^{-1} x$$  or $$\arcsin x$$.
• The function $$f$$ is invertible if and only if it is bijective.

• La fonction inverse : $$x \longmapsto \dfrac1x$$ / the reciprocal function
• The reciprocal function, the function $$f$$ that maps $$x$$ to $$\dfrac1x$$, is one of the simplest examples of a function which is its own inverse (an involution).
• The reciprocal function: $$y = 1/x$$. For every $$x$$ except 0, $$y$$ represents its multiplicative inverse. The graph forms a rectangular hyperbola.

• Inverse d'un nombre, d'une fonction / multiplicative inverse or reciprocal ou just inverse
• In mathematics, a multiplicative inverse or reciprocal for a number $$x$$, denoted by $$\dfrac1x$$ or $$x^{-1}$$, is a number which when multiplied by $$x$$ yields the multiplicative identity, 1.

• In the phrase multiplicative inverse, the qualifier multiplicative is often omitted and then tacitly understood (in contrast to the additive inverse).
• The notation $$f^{-1}$$ is sometimes also used for the inverse function of the function $$f(x)$$, which is not in general equal to the multiplicative inverse.
• For example, the multiplicative inverse $$\dfrac{1}{\sin x} = (sin x)^{-1}$$ is the cosecant of $$x$$, and not the inverse sine of $$x$$ denoted by $$sin^{-1} x$$  or $$\arcsin x$$.

• Opposé d'un nombre / additive inverse, opposite number
• In mathematics, the additive inverse of a number $$a$$ is the number that, when added to $$a$$, yields zero.
• This number is also known as the opposite (number), sign change, and negation.
• For a real number, it reverses its sign: the additive inverse (opposite number) of a positive number is negative, and the additive inverse of a negative number is positive. Zero is the additive inverse of itself.

• Inverse function rule
• In calculus, the inverse function rule is a formula that expresses the derivative of the inverse of a bijective and differentiable function $$f$$ in terms of the derivative of $$f$$.
• More precisely, if the inverse of $$f$$ is denoted as $$f^{-1}$$, then the inverse function rule is, in Lagrange's notation : $$\left(f^{-1}\right)'(a) = \dfrac{1}{f'\left(f^{-1}\right)(a)}$$

### Le vocabulaire sur la Géométrie / Geometry

Géométrie / Geometrie

#### Outils / geometry tools, drawing tool

• compas / compass
• A compass, more accurately known as a pair of compasses, is a technical drawing instrument that can be used for inscribing circles or arcs. As dividers, it can also be used as a tool to step out distances, in particular, on maps.
• crayon papier, stylo / pencil, pen
• equerre / try squarre
• rapporteur / protractor
• règle / ruler

#### Geometry Vocabulary

• angle aigu (resp. obtus) / acute (resp. obtuse) angle
• arête / edge
• bissectrice / bisector
• centre de gravité / centroid
• centre du cercle circonscrit / circumcentre
• centre du cercle inscrit / incenter
• cercle circonscrit / circumcircle
• se chevaucher / to overlap
• circonférence / circumference
• coefficient directeur / slope
• coin (e.g. d’une figure) / wedge
• confondu (pour un point) / coincident
• corde (d’un cercle) / chord
• cosinus, sinus / cosine, sine
• courbure / curvature
• couronne (géométrique) / annulus
• courbe paramétrée / parametric curve
• courbe représentative / graph
• dessin à l’échelle / scale drawing
• enveloppe convexe / convex hull
• extrémité / endpoint
• forme / shape
• hauteur / altitude
• homothetie / homothety (or homothecy, or homogeneous dilation)
• hyperbole / hyperbola
• isocèle / isosceles
• losange / rhombus
• milieu / midpoint
• médiane / median
• médiatrice / perpendicular bisector
• orthocentre / orthocentre
• parallélépipède rectangle / cuboid
• pavage / tiling, tessellation
• A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps.
• point col / saddle point
• point de rebroussement / cusp
• rayon (d’un cercle) / radius
• repère cartésien / Cartesian coordinate system
• A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length.
• réseau / lattice
• sens des aiguilles d’une montre, horaire / clockwise, Normal left rotation
• sens inverse des aiguilles d’une montre, antihoraire, sens trigonométrique / counterclockwise, Normal right rotation
• sommet / vertex
• système de coordonnées, repère / coordinate system

• transformation (du plan) / geometric transformation (plane)
• Déplacements / Displacements
Displacements preserve distances and oriented angles (e.g., translations)
• homothetie / homothety (or homothecy, or homogeneous dilation)
• Isométrie / Isometrie
Isometries preserve angles and distances (e.g., Euclidean transformations)
• rotation / rotation
• symétrie axiale, reflexion, pliage / line symmetry, reflection, reflect about line
• symétrie centrale / point reflection, central inversion, inversion in a point, through a point, reflect about point
• In geometry, a point reflection is a type of isometry of Euclidean space. In two dimensions, a point reflection is the same as a rotation of 180 degrees.
• translation / translation
In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction.

• trapèze / trapezium
• triangle rectangle / right-angled triangle
• vecteur / vector
• In mathematics, physics and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction.

### Le vocabulaire sur les Probabilités/Probability en anglais

Français /  English

• chance / likelihood, chance (often plural), odds
• dé / die (plural : dice)
• diagramme / circulaire pie chart
• diagramme en barre / bar chart
• diagramme en bâtons / stroke chart
• diagramme en boîte / box plot
• discret (i.e. discontinu) / discrete (, discreet)
• écart-type / standard deviation
• échantillon / sample
• échantillonnage / sampling
• effectif / frequency (false friend)
• effectif cumulé / cumulative frequency (false friend)
• espérance / expected value
• événement / event
an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned
• évènement élémentaire / elementary event
• An event consisting of only a single outcome is called an elementary event or an atomic event; that is, it is a singleton set.
• événements incompatibles / mutually exclusive events
• évènement contraire ou complémentaire / complementary event
• évènement certain / absolutely certain event
• évènement impossible  / impossible event
• The probability of an impossible event is 0. The probability of an absolutely certain event is 1.
• expérience / experiment or trial
• expérience aléatoire/ random experiment
• fréquence / relative frequency
• intervalle de confiance / confidence interval
• intervalle de fluctuation / prediction interval
• issue / possible outcome
• loi de probabilité / Probability distribution
• loi des grands nombres / law of large numbers (LLN)
• In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value and tends to become closer to the expected value as more trials are performed.
• médiane / median
• moyenne / average, mean
• nuage de points / scatter graph
• univers / sample space
• A sample space is the set of all possible outcomes.
• variable aléatoire centrée réduite / standardized random variable

### Le vocabulaire sur les Statistiques en anglais

Statistiques / Statistics

• chance / likelihood, chance (often plural), odds
• dé / die (plural : dice)
• diagramme / circulaire pie chart
• diagramme en barre / bar chart
• diagramme en bâtons / stroke chart
• diagramme en boîte / box plot
• discret (i.e. discontinu) / discrete (discreet)
• écart-type / standard deviation
• échantillon / sample
• échantillonnage / sampling
• effectif / frequency (false friend)
• effectif cumulé / cumulative frequency (false friend)
• espérance / expected value
• étendue / range
• fréquence / relative frequency (false friend)
• médiane / median
• moyenne / average, mean
• nuage de points / scatter graph

## Divers particularités

Beaucoup de théorèmes ont des noms différents en anglais pour des raisons historiques et culturelles. Par exemple, le principe des tiroirs s’appelle en anglais pigeonhole principle.

Les français ont également une fâcheuse tendance à vouloir donner un nom aux théorèmes ; par exemple, le lemme des bergers n’a pas de nom équivalent en anglais.
— Les noms de mathématiciens ne sont pas anglicisés : l’Eratosthène francisé devient en anglais Eratosthenes ; Pythagore devient Pythagoras ; etc.

• Le théorème de Thales/Intercept theorem
• Le Théorème que nous nommons théorème de Thalès en France est dans les pays anglosaxons (et en allemagne) appelé intercept theorem.
• The Thales's theorem est dans les pays anglosaxons (et en allemagne) le théorème de géométrie qui affirme que l'angle inscrit dans un demi-cercle est droit.

Thales's theorem: if AC is a diameter and B is a point on the diameter's circle, the angle ABC is a right angle.