Author: paulpatenaude

Paul Patenaude a une expérience de plus de 35 années dans l'enseignement et l'animation pédagogique en mathématiques au primaire et au secondaire, au Québec et à l'étranger. Il est auteur ou co-auteur de nombreux ouvrages dédiés à l'enseignement des mathématiques dont ce lexique des termes utilisés avec les jeunes de 5 à 17 ans. Il peaufine ce lexique depuis plus de 30 ans. Prix d'excellence du GRMS (prix Claude Janvier) en 1997, prix du meilleur article de la revue l'Envol du GRMS (prix Euler) en 1992. Il adore voyager et a déjà exploré de nombreux pays sur les cinq continents, curieux à la fois des cultures et de l'histoire. Il apprécie recevoir vos commentaires et vos questions auxquelles il s'empressera de répondre.

Base of a Power

In an exponentiation, the number \(a\) that we raise to a certain power \(n\). In the expression \({a}^{n}\), the number \(a\) is called the base and the number \(n\) is the exponent. Example In the expression "7² = 49", the number 7 is the base of the 2nd power of 7.

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Profit

The difference between the sale price and the cost price of an item. Net balance of an investment, which is the difference between the capital invested and the value of this capital increased by accumulated interest. This is usually expressed as a percentage of the cost price. Example An item was purchased at a price [...]

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Biconditional

Relationship between two propositional forms P and Q, noted as "P ↔ Q" or "P is equal to Q", which is true when P and Q both simultaneously have the same truth value and false in other cases. Synonym for biconditional propositional form. The biconditional truth table is: P Q P ↔ Q T T T T [...]

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Base of an Exponential Function

Number that is affected by the independent variable. Example Consider the exponential function \(f\) defined by the equation \(f(x) = 5^{(x + 7)}\). The base of this function is 5.

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Base of an Exponentiation

The first element in an exponentiation operation (or in raising to a power). In the exponentiation \(b^n\), the number \(b\) is the base and the number \(n\) is the exponent. Example In the exponentiation 25 = 32, the number 2 is the base, the number 5 is the exponent and the number 32 is the result [...]

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Base of a 2-Dimensional Figure

An element (segment, polygon, etc.) identified for the purpose of providing a measure or a definition. Examples A triangle is a polygon with three sides, each of which can serve as its base to calculate the area. By definition, the base of a cone is the plane surface of the solid; the other face is [...]

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Axiom

In a theory, a proposition that is obvious on its own and is not subject to any demonstration. Example All mathematical theories are based on a set of definitions of mathematical objects and axioms that set the elementary properties of these objects. Traditional Euclidean geometry is based on these elements: basic objects: a point is [...]

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Attribute

Synonym for quality, characteristic, or property. Example In primary school, we often introduce the concept of classification using logic blocks, which are a set of blocks that have different attributes like: shape: triangle, circle, square, rectangle size: small or large thickness: thick or thin colour: yellow, blue, or red which makes a set of 48 [...]

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Approximation by Rounding

The process of replacing a number with another number so that the last digit retained is unchanged if it is followed by 0, 1, 2, 3 or 4, or increased by 1 if it is immediately followed by 5, 6, 7, 8 or 9. When rounding a number, we always specify the desired order of [...]

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Arithmetic

A branch of mathematics dedicated to the rules of calculation in the set of rational numbers. In arithmetic, we focus on the operations of addition, subtraction, multiplication, division and exponentiation (integer exponents). In addition to these basic operations, there are also factorials and absolute values. This discipline of mathematics was later extended by the inclusion of [...]

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Arrangement

In a set E of n elements, this is an ordered subset with k elements of E without repetition. Because an arrangement is an ordered subset, it is preferable to use the notation in the form of n-uplet to designate an arrangement. arrangement with repetition In a set E of n elements, it is an [...]

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Rounded Number

The result of an approximation by rounding. The rounded value of a number is an approximate value of this number obtained from its decimal expansion, and reducing the number of significant digits. Therefore, a rounded number produces a result that is less precise but easier to use in some calculations or estimations. Example The number [...]

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Associative Property

Property of an operation in which the terms can be grouped in different ways without modifying the result of the operation. Property of an operation that makes it possible to group terms without changing the result. This property helps to facilitate calculations. It also helps make mental calculations more efficient. Examples The operations of addition [...]

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Argument

Term often used as a synonym for independent variable. Example In the expression f(x) = cosec(x), the argument of the cosecant function is the real number x.

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Arc Secant

The arc secant of a real number x is a real number with a secant of x. The argument x of the arc secant relation is a real number between \(-\infty\) and \(+\infty\). The relation defined by y = arcsec(x) is not a function. Notation The symbol used for the arc secant of a number [...]

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Arc Tangent

The arc tangent of a real number x is a real number with a tangent of x. The relation defined by y = arc tan(x) is not a function. Notation The symbol used to refer to the arc tangent of a real number x is “arc tan(x)” which is read as “arc tangent of x.” [...]

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Are

Unit of area that corresponds to 100 square metres. Notation The symbol for are is "a" which stands for "are". 1 are is equal to 100 m\(^{2}\) and we write: 1 a = 100 m\(^{2}\). 1 hectare is equivalent to 100 ares and we write: 1 ha = 100 a.

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Arc Cotangent

The arc cotangent of a real number x is a real number for which the cotangent is x. The relation defined by y = arccot(x) is not a function. Notation The symbol used to indicate the arc cotangent of a real number x is “arccot(x)” which is read as “arc cotangent of x.” Examples In [...]

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Arc Sine

The arc sine of a number x is a real number for which the sine is \(x\). The argument \(x\) of the arc sine relationship is a real number between \(-1\) and \(+1\). The relation defined by \(y \)= arcsin(\(x\)) is not a function. Notation The symbol used for the arc sine of a number [...]

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Approximation

A quantity that we accept as sufficiently close to a known or unknown quantity. This approximation can be obtained by rounding, estimating or truncating. Symbol The symbol of approximation is "≈" which is read as “is approximately equal to”. Examples π ≈ 3.1416 e ≈ 2.7183

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Tree

Connected graph without a cycle. Using trees as a form of representation makes it possible to illustrate the process of counting cases that result in a specific study, such as counting and representing prime factors d'un nombre naturel, of a whole number, counting the possible outcomes of a random experiment, or representing the probabilities associated [...]

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Arc Cosecant

The arc cosecant of a number x is a real number for which the cosecant is x. In a trigonometric context, the cosecant of an angle A is the multiplicative inverse of the sine ratio of angle A. The cosecant relationship of an angle x is a function, but the inverse relationship defined by y [...]

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Arc Cosine

The arc cosine of a number x is a real number for which the cosine is x. The argument x of the arc cosine relationship is always a real number between -1 and 1. The relation defined by y = arccos(x) is not a function. Notation The symbol used for the arc cosine of a [...]

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Antecedent

That which precedes or premises in reasoning. In mathematical logic, the first of two terms in conditional propositional form or in an implication. Example In the statement "if a quadrilateral has one pair of parallel sides, then this quadrilateral is a trapezoid", the antecedent is the proposition "a quadrilateral has one pair of parallel sides", [...]

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Exterior Angle of a Polygon

Angle formed by one side of a convex polygon and the extension of an adjacent side. An angle inside a polygon that is not adjacent to an exterior angle is called a remote interior angle. Example In the figure below, angle BDE is an exterior angle of polygon ABCD. It is formed by side BD [...]

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Amplitude

Synonym for magnitude. See also : Amplitude of an interval Amplitude of a periodic function Amplitude of a sinusoidal function Amplitude of a statistical class

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Amortization

In financial operations, this word designates the repayment terms for the capital borrowed without accounting for the interest charges. These payments occur regularly in equal instalments called annuities (annual payments) or monthly payments. Formula Calculating the amount of the amortization of a loan in accordance with the repayment terms is based on calculating logarithmic or exponential expressions. [...]

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Area

Measure of a two-dimensional closed surface. Synonym for surface area. The term surface area is generally used in the case of large surfaces. Area is a quantity that is almost always expressed using denominate numbers. Examples The side c of a square measures 10 cm. The area A of this square is 100 cm², because: A [...]

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Random

That which depends entirely on chance. See also: Random sample Random experiment Random number Random variable

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Addition

 

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Addition of Real Numbers

An operation in which any pair \((a, b)\) of real numbers is made to correspond to a real number written \((a + b)\) called the sum of a and b. The addition of real numbers is one of the operations in arithmetic. We add one number to another, one quantity to another, one value to [...]

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Adding Functions

Binary operation under which each pair (f, g) of functions defined in a set E toward a set F, is made to correspond to a new function, noted as f + g, called the sum of these functions. To obtain the value of the sum of the two functions f and g of variable x, [...]

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Adding Fractions

Operation under which each pair \(\left( \frac {a} {b},\frac {c} {d}\right) \) of fractions is made to correspond to a new fraction \(\frac {ad\space+\space bc} {bd}\) called the sum of these fractions. Generally, we calculate the sum of two fractions using this algorithm: \(\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad}{bd} + \dfrac{bc}{bd}=\dfrac{ad+bc}{bd}\) Examples \(\dfrac {2} {5}+\dfrac {1} {6}= \dfrac{2x6}{5x6} +\dfrac{5x1}{5x6}=\dfrac{12}{30}+\dfrac{5}{30}=\dfrac{12+5}{30}=\dfrac{17}{30}\) If the denominators [...]

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Abacus

A device with beads or washers that slide along wires and are used to represent numbers and carry out basic arithmetic operations. Depending on the region and the era, the abacus was called a soroban (Japan), a suan pan (China) or a S’choty (Russia), among others, and occurred in many different configurations. It is also [...]

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Acre

Ancient agricultural unit of measurement (of area). This unit of measurement is equivalent to about 52 ares in France and varies from one country to another. The acre is an ancient unit of measurement for area that is still used today. Note The acre is a unit of measurement that is still used in some [...]

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X-Intercept

The x-intercept of a graph of a function f represented in a Cartesian plane is the name given to the x-coordinate of each of the points where the graph of f intersects with the x-axis, or the point(s) of the graph for which \(f(x) = 0\). The expression "x-intercept" can also indicate each of the [...]

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