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.

Scalar

Synonym for real number. Examples In an expression like A = 12x\(^{2}\), the number 12 is a scalar. It is important to distinguish scalar quantities from vector quantities: temperature and mass are scalar quantities while speed and force are vector quantities, because speed and force are not only characterized by their measure,but also by their [...]

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Secant of an Angle

Inverse ratio of the cosine of an angle. Notation The secant of x is noted as: “sec(x)” which is read as “secant of x.” Examples sec(60) = 2 sec(30) ≈ 1.155 Educational note The argument of the secant is a number and not an angle. Therefore, it’s a linguistic shortcut to say “secant of an [...]

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Result of an Operation

Each of the elements from the set of images of an operation. Examples In the addition operation 12 + 45 = 57, the result is 57. In the multiplication operation 12 × 7 = 84, the result is 84. Educational Note An operation is defined by a rule or a law of composition that determines [...]

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Favourable Outcome

Each of the elements (or results) of an event in a random experiment. Example Consider rolling an honest die with six faces numbered 1 to 6. Consider the event "A: rolling a number greater than 4". The possible outcomes of this random experiment are {1, 2, 3, 4, 5, 6}. The favourable outcomes for event [...]

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Possible Outcome

Each of the possible results of a random experiment. Synonym for outcome of a random experiment. Examples In the random experiment that consists of rolling an honest die with 6 faces numbered 1 to 6, the possible outcomes are: {1, 2, 3, 4, 5, 6}. In the random experiment that consists of drawing a ball [...]

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Remainder

Element left over from a quantity after subtracting or sharing (dividing) the elements in this quantity. In Euclidean division, a whole number r such as D = q × d + r, with r < d, where D is the dividend, d is the divisor and q is the quotient. The term remainder is sometimes used to [...]

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Network

Directed and valued connected graph. Example Here is a network of cycling trails on a mountain. The number indicated on each branch of the network corresponds to the distance in kilometres between rest stops. The letters A to G indicate rest stops. The arrows indicate the direction in which a cyclist should bike along each [...]

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Outcome of a Random Experiment

Possible result of a random experiment. Example In the random experiment that consists of rolling a regular die with six faces and noting the result that appears on the top face, the possible outcomes of this random experiment are: 1, 2, 3, 4, 5 and 6. See also: Possible outcome Random experiment

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Symmetric Relation

Relation defined in a set E so that, for every ordered pair of elements (x, y) of \(E\times E\), if x is in relation with y, then y is in relation with x. The arrow diagram of a symmetric relation in a set E includes a return arrow every time that there is an arrow [...]

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Transitive Relation

Relation defined in a set E so that, if the ordered pairs (x, y) and (y, z) belong to the relation, then the ordered pair (x, z) also belongs to the relation. The arrow diagram of a transitive relation in a set E includes a transit arrow (x, z) associated with every occurrence of two arrows (x, y) and (y, z) of [...]

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Step Function

Relationship that describes a phenomenon that varies constantly in sections. Therefore, it is a combination of relationship of zero variation and a relationship that characterizes the gaps (jumps between levels). A step function is a function that is constant over the intervals of the independent variable and that changes abruptly for certain values of the [...]

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Euler’s Formula

For any convex polyhedron, a formula that establishes a relationship between the number of vertices V, the number of faces F and the number of edges E, such that: V + F = E + 2. Examples In this pentagonal prism, there are 10 vertices (V), 7 faces (F) and 15 edges (E). Therefore, the [...]

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Reflexive Relation

Relation defined in a set E so that all elements x of E are related to themselves. The arrow diagram of a reflexive relation in a set E includes loops in each of its points. A relation in a set E that does not contain any loops is called anti-reflexive while a relation in E [...]

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Pattern

Rule that we identify in a sequence of numbers or images, when a term in the sequence (number or sign) can be deduced from the other terms in the sequence. Phenomenon that we find in arithmetic sequences, geometric sequences or arrangements of figures when a term in the sequence (number or figure) can be deduced [...]

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Equivalence Relationship

Relationship that connects elements that are similar by one of their properties. Relationship of a set E toward a set E that is reflexive, symmetric and transitive. In the case of relationships between units of measurement, it is acceptable to use the symbol =. However, when reading them, it is preferable to use the expression [...]

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Linear Regression

Linear regression is a mathematical process that replaces information provided by a scatter plot by a line that has the same general properties, assuming that the relationship that connects the two variables involved is linear. The line found in this way is a line of regression. The line of regression also allows us to interpolate [...]

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Connected Relation

Relation defined in a set E so that, for every distinct pair of elements (x, y) of E, either one of the ordered pairs (x, y) or (y, x) belong to the relation. The arrow diagram of a connected relation in a set E includes at least one arrow between any two elements of E. Examples The [...]

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Reflexivity

Property of being a reflexive relationship. Relationships of equivalence and relationships of order are reflexive relationships.

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Census

Statistical inquiry conducted among all the individuals in a given population, in order to study on or more of its characteristics. When dealing with objects instead of living individuals, the term inventory is used to refer to this practice. When the practice only involves a sample of the population, we use the term survey instead. [...]

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Reciprocal of a Function

The reciprocal relationship of a function f of X in Y is the relation noted f-1, of Y in X, so that, for all elements of the domain of f, if y = f(x), then x = f -1(y). When the reciprocal relationship of a function f is also a function, we call it the reciprocal function of f and [...]

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Golden Rectangle

Rectangle in which the ratio of the measure a of the largest side to the measure b of the smallest side is the same as between the half-perimeter (a + b) and the measure a of the large side. Consider this rectangle: Therefore: \(\dfrac{a}{b}\) = \(\dfrac{a+b}{a}\) The value of the golden ratio is about 1.618 and [...]

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Proportional Reasoning

Process of solving a problem using mathematical reasoning that involve ratios or a proportion. To solve a problem using proportional reasoning, it’s important to identify that one quantity or size is related to another one by a determined ratio in that situation. Example During a recent trip, Robert drove 483 kilometres in 7 hours. What [...]

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Rank of a Term

Measure of position in a set of data. In a sequence of numbers, the rank of a term is the ordinal that characterizes the position of this term. Example Consider this number sequence: 1, 2, 4, 8, 16, 32, 64, ... The number 16 is the 5th term in the sequence, so we say that its [...]

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Mathematical Reasoning

Argumentation or way of reasoning by analogy, induction, deduction, and proportional reasoning, as well as algebraic, geometric, arithmetic, probabilistic, or statistical reasoning. Mathematical reasoning refers to rules of inference and deduction that uses definitions, accepted statements as premises, laws, or properties, results previously obtained also using reasoning, in order to demonstrate hypotheses or conjectures. By [...]

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Nth Root of a Real Number

In the equation an = A, the real number a that, that, when raised to the power n, is equal to A. Examples The 4th roots of 81 are 3 and –3, since 34 = 81 and (–3)4 = 81. The square roots of 81 are 9 and –9, since 9\(^{2}\) = 81 and (–9)\(^{2}\) [...]

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Digital Root

The digital root or remainder of a whole number is the iterative sum of the values associated with each of its digits. Casting out nines uses the digital root of a number. Examples Consider the number 457. We add the values associated with each of its digits, then repeat the process with the values associated [...]

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Square Roots of a Real Number

In the equation n\(^{2}\) = N, each real-number n whose square is equal to N is a square root of the real number N. Symbols The square roots of the number N are written as – \(\sqrt{N}\) and + \(\sqrt{N}\) which are read as "the negative square root of N" and "the positive square root of N". Properties All positive [...]

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Root of a Polynomial

Real number that makes the polynomial function associated with the polynomial equal to zero. Examples Consider the polynomial x2 – 7x + 12. The numbers 4 and 3 are roots of the polynomial; since, when x = 4 or x = 3, the polynomial is equal to 0. Consider the polynomial 6x2 + 11x – 10. The numbers \(\frac{2}{3}\) and – [...]

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Quotient

Result of the division of two numbers. Examples In the operation 24 ÷ 4 = 6, the number 6 is the quotient. The number 24 is the dividend and the number 4 is the divisor. In the operation 48.6 ÷ 3 = 16.2, the number 16.2 is the quotient. In the operation 5 ÷ 25 [...]

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Discount

Percentage subtracted from an initial amount. A discount is a decrease in the initial value. Example If a TV with an initial sale price of $500 is sold for $400, then this is a reduction of $100, because 500 − 400 = 100. This represents a 20% discount, because 100 ÷ 500 = 0.2 and [...]

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Root

Term used in several mathematical expressions in reference to the structure of a particular object or some of its properties. See also : Without being exhaustive, these references illustrate the variety of uses of the term root. Square root of a real number Cube root of a real number Root of an equation Root of [...]

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Cube Root of a Real Number

In the equation n\(^{3}\) = N, the real number n whose cube is equal to N. Symbols The cube root of N is written as \(\sqrt[3]{N}\) and is read as "the cube root of N". Examples If x\(^{3}\) = 1000, then \(\sqrt[3]{1000}\) = 10, since 10 × 10 × 10 = 1000. If x\(^{3}\) = –1000, then \(\sqrt[3]{–1000}\) [...]

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Root of an Equation

Synonym for solution to an equation. In the equation 0x = 0, all values of x are solutions or roots of the equation. The equation ax + b = o, where a ≠ 0, has only one root, that is x = – \(\frac{\textrm{b}}{\textrm{a}}\). Examples The solution set of the equation 3x + 4 = 7 [...]

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Quantile

 

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Fourth Proportional

Fourth term in a proportion with four terms. In the proportion with four terms \(\dfrac {a}{b} =\dfrac {c} {d}\), the term d is the fourth proportional. Example \(\dfrac {5}{8} =\dfrac {25} {x}\) By calculating, we find that the 4th proportional, which is the value of the unknown x, is 40.

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Quartile

Each of the three values that divide an ordered statistical series into four parts with equal frequencies. Notation The three quartiles that divide a distribution of statistical data are noted as \(\textrm{Q}_1\), \(\textrm{Q}_2\) and \(\textrm{Q}_3\), where \(\textrm{Q}_2\) is also the median of the distribution. See also: Box and whisker plot

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Quintile

Each of the four values that divide an ordered statistical series into five parts with equal frequencies.

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Quality

Synonym for attribute, characteristic, or property, depending on the mathematical context in which the term is used. This term is often used in statistics to designate the different values taken by a qualitative statistical characteristic.

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Power

Result of an exponentiation. Examples In the operation 3\(^{4}\) = 81, the number 81 is the power of 3 raised to the exponent 4. In the operation 25\(^{\frac{1}{2}}\) = 5, the number 5 is the power of 25 raised to the exponent \(\frac{1}{2}\).

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Pythagoras (c. 580 – c. 495 BCE)

Greek mathematician born in the first half of the 6th century BCE on the Aegean island of Samos in Ionia, near Miletus. He died circa 500 BCE in Metapontum, where he was exiled. Dates are approximate because Pythagoras, although many times quoted by the ancients, has never written anything himself and we do not have any [...]

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Proposition

Statement that is either true or false. A proposition does not contain any variable elements. A mathematical proposition is an assembly of symbols and letters formed by following certain rules, with the help of logical connectors. In the calculation of propositions, the propositions used may not have a particular meaning. We can replace a proposition [...]

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Properties of an Operation

An operation defined in a set of objects has specific characteristics called properties. The properties of an operation are very diverse and depend on the type of operation. Here is a list of the most commonly encountered properties: Commutative property Associative property Distributive property over another operation defined in the same set of objects Existence [...]

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Parallel Projection

Geometric transformation in geometric space characterized by a projection direction and a target figure. The target figure can be a line, a plane, a sphere, etc. parallel projection on a line in a plane Transformation in a plane determined by two intersecting lines d (line on which the figures are projected) and d1 (which determines [...]

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Property

That which is unique or particular to a mathematical object. Synonym for attribute, characteristic, or quality, according to the mathematical context in which this term is used. A mathematical object is often defined by a set of properties. Examples A square is a quadrilateral in which the four sides are isometric and the four angles are [...]

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Central Projection

Geometric transformation of an object in three-dimensional space characterized by one or more fixed points called centres of projection and a projection plane that does not contain these points. The central projections are also called conic projections because all of the vanishing lines relative to a fixed point pass through the apex of a cone [...]

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Isometric Projection

Axonometric projection in which the three main axes create isometric angles, at an angle of 120°.

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Oblique Projection

Parallel projection of three-dimensional space on a plane in which at least one of the three axes of projection is not perpendicular to the two others. Like axonometric projections, oblique projections make it possible to represent an object on a plane by suggesting the effect of depth. In an oblique projection, one face of the [...]

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Orthogonal Projection

Parallel projection in which the projection direction is perpendicular to the projection target (or screen). The target figure can be a line, a plane, a sphere, etc. Orthogonal projection on a line in a plane Transformation in a plane determined by two perpendicular lines d (line on which the figures are projected) and d1 which [...]

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Arithmetic Progression

Number sequence in which the rule is that each term must be equal to the preceding term increased by a constant. Examples Consider this sequence: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, … Each term is increased by 2 to find the next term in the sequence. Consider the sequence: 2, 6, [...]

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Geometric Progression

Numerical sequence in which the rule is that each term must be equal to the preceding term multiplied by a constant. Examples Consider this sequence: 1, 2, 4, 8, 16, 32, 64, 128, 256, … Each term in the sequence is multiplied by 2 to find the next term. Consider this sequence: 1, 3, 9, [...]

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Axonometric Projection

Parallel projection of three-dimensional space on a plane in order to show the three perpendicular axes of three-dimensional space. The result obtained is a representation in which the three main axes called x, y and z appear. These axes create angles that characterize the type of axonometric projection. Properties Axonometric projections preserve the parallelism of [...]

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Theoretical Probability

Probability of an event determined by a process of calculations. This theoretical method can be applied to one or more modes of representation, such as a grid, tree diagram, written calculations, etc. Example A tree diagram can be used to illustrate the possible outcomes and the probabilities of these outcomes occurring in the case of [...]

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Product

Result of a multiplication operation. In a very general way, this term represents the result of a multiplication operation in which the quantities can be numbers, algebraic expressions, sets, vectors, functions, etc. If the multiplication has numbers as quantities it is an arithmetic product of two numbers. If the quantities are algebraic expressions, it is an [...]

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Digital Product

Product of the values associated with the digits of a whole number. Examples The digital product of the number 107 is 0, because 1 × 0 × 7 = 0. The digital product of the number 324 is 24, because 3 × 2 × 4 = 24.

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Cartesian Product of Sets

The Cartesian product of set A by set B is the set of all ordered pairs for which the origin is an element of set A and the endpoint is an element in set B. Symbol The symbolism "A ☓ B" is read as: "A Cartesian product B". The Cartesian product is not commutative. The [...]

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Probability

Branch of mathematics that is concerned with the probable nature of an event. The calculation of probabilities consists of measuring the probable nature with the greatest precision possible in very diverse contexts such as games, weather, finances, chemistry, or even medicine. See also: Probability of an event

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Conditional Probability

If A and B are two events in a random experiment, then the conditional probability of the event A, once event B has occurred, is the ratio of the probability that A and B occur simultaneously to the probability of B (considered to be non-zero here). Notation The way to note the “conditional probability of [...]

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Probability of an Event

Ratio of the number of favourable outcomes for an event to the number of possible outcomes, when each outcome has the same number of chances of occurring. Ratio of the number of elements (favourable outcomes) of an event to the total number of possible outcomes of a random experiment, when each result has just as [...]

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Experimental or Frequential Probability

The experimental probability of an event A in a random experiment is the ratio of the number of times that the event A occurs to the number of times the experiment was conducted. Out of a relatively large number of attempts, the experimental probability of an event tends to get closer and closer to the [...]

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Geometric Probability

The probability, in a geometric or measurement context, is the ratio of the measure of one part of a geometric object G with n dimensions and one part A with n dimensions of G (the target). Formula Consider a geometric object G with one dimension that has a finite length and A, a part with [...]

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Subjective Probability

Probability estimated based on the personal experience of the person doing the assessment or an organization that has some information about the study topic. Examples Choosing the winning team in a sports competition is based on subjective probability. The probability of a snow storm today is a subjective probability.

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Priority of Arithmetic Operations

Conventions that determine the order in which we operate when finding the value of a sequence of operations. The order that we must follow is: (1) Solve operations in parentheses (P) (2) Solve exponents (E) (3) Solve multiplication and division from left to right (MD) (4) Solve addition and subtraction from left to right (AS) [...]

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Cost Price

In a business situation, the price paid by a vendor to acquire an item to offer for sale. The cost price represents the sum of the costs incurred for the production and distribution of a good or service. Determining the cost price is essential to avoid selling at a loss. Example The purchase price of [...]

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Sale Price

In a business situation, the price paid by the purchaser to buy an item. The sale price is the cost price increased by the vendor profits.

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Unit Price

Price per unit. Examples A merchant must sell 10 office chairs. The unit price for each chair is $89. The total cost of the chairs is $890, because: 89 × 10 = 890. A customer bought 20 dictionaries for a school. The purchase cost is $600. The unit price (price per dictionary) is given by: [...]

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Mathematical Proof

Sequence of logically ordered statements based on a certain number of hypotheses and that should lead to an expected conclusion. The proof can involve results that were previously demonstrated or other statements of the theory such as axioms, postulates or definitions of terms in the theory. The term "proof" is synonymous with "demonstration". Example Here [...]

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Lowest Common Multiple

If m and n are integers, the lowest multiple shared by m and n is the lowest strictly positive integer that is a multiple of both m and n. Notation The notation for the "lowest common multiple" of several numbers is "LCM(a, b, …, z)" which means "the lowest common multiple of a, b, …, z". [...]

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Percentage

Ratio in which the second term is 100. Symbol The symbol "%" means "divided by 100" and is read as "percent". When writing a percentage in English, we do not leave a space between the number and the percentage symbol. A percentage is a specific kind of ratio, which is a comparison between two sizes or [...]

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Population

Finite set of all the individuals or units of the same type on which a statistical study is focused. Examples The population of a city, which is to say the inhabitants of this city. The population of a river, which is to say all of the fish in this river. The population of a school, [...]

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Frequency Polygon

Cartesian graph of the distribution function of a statistical variable or of the distribution function of a random variable. Examples This frequency polygon describes the number of passes based on the number of tests: If the values are grouped into classes and represented by a histogram, we can find a frequency polygon by joining the [...]

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Weight

Vertical force exerted on a body due to gravity. This force attracts objects toward the ground. The greater the mass, the greater this force. This force is less on the Moon than on Earth, so we would feel lighter on the Moon. It is probably greater on Saturn than on Earth, so we would feel [...]

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Loss

Difference between the sale price and the cost price when the sale price is less than the cost price. A loss provides the opposite effect of a profit or gain. Examples If we sell a piece of furniture for $450 and it cost $500, we have a loss of $50. If we sell a piece [...]

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Greatest Common Divisor

If m and n are integers, the greatest divisor shared by m and n is the greatest positive integer that divides both m and n. Notation We use the expression GCD(a, b, c) to refer to the greatest common divisor of the numbers a, b and c. Properties The GCD is always a positive integer. The [...]

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permutation

Bijection of a set in itself. A permutation of the n objects of a set E is all ordered combinations of these n elements. Therefore, a permutation of n objects in a set E of n elements is an n-tuple formed by these elements. If E \(= \left\{0, 1, 2, 3\right\}\), then a permutation of E could be represented [...]

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Three-Point Perspective

Means of representing a solid using a central projection with three fixed points. Property In three-point perspective, the parallelism of the segments is not preserved. Example

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Period of a Rational Number

When writing a rational number in decimal notation, a group of digits that repeats in the decimal part of the number. Symbol In the decimal notation of a rational number, the notation of the period p consists of drawing a line over the sequence of numbers that repeats. In the decimal notation of the rational number \(\dfrac [...]

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Part

In the most general sense, a portion of a whole. Depending on the context, the term part can also refer to a component of a number or a figure or even a component of the representation of a number. See also : Aliquant part of an integer Aliquot part of a a whole Part of [...]

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Parameter

In an algebraic expression or an equation, a letter other than the variable for which we can set the numerical value at will. A parameter is one of the variable elements that figures in an algebraic expression or in a relation (equation, function, etc.) and for which we are interested in the characteristics that are [...]

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Pentahedron

Polyhedron with five faces. The three main pentahedra are: A pyramid with a rectangular base; A truncated pyramid with a triangular base; A prism with a triangular base. Examples Here is a pyramid with a rectangular base: Here is a prism with a triangular base:

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Pair

Set that includes two distinct elements. It’s important to distinguish between a pair of elements like {3, 6}, and an ordered pair of elements like (3, 6). Notation The elements in a pair are written between braces and we do not consider the order in which the elements are written, because it is a set. [...]

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Parabola

The site of points equidistant from a fixed line called the directrix and a fixed point called the focus. The line that is perpendicular to the directrix and passes through the focus is the line of symmetry of the parabola.

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Ascending Order

To arrange numbers in ascending order consists of putting them in order from the least value to the greatest value. Examples In each of these lists of numbers, the numbers are arranged in ascending order: 1, 2, 3, 4, 5, 6, 7, 8, 9 3, 5, 7, 9, 9, 12, 15, 15, 23, 45 30, [...]

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Descending Order

To arrange numbers in descending order consists of putting them in order from greatest to least. Examples In each of these lists of numbers, the numbers are arranged in descending order: 9 , 8 , 7 , 6 , 5 , 4 , 3 , 2 , 1 45 , 23 , 15 , 12 [...]

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Order of Operations

Synonym of priority of operations.

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Origin

One of the extremities of a ray, an axis, a directed segment, a directed arc, etc., randomly taken as the first element of this object or as the point of departure. Examples Point O is the origin of this axis:   Point A is the origin of the directed segment AB and point B is [...]

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ordinal

See ordinal number.

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Put in Order

To arrange in ascending order or descending order.

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Y-Intercept

The y-intercept of a graph of a function f represented on a Cartesian plane is the y-coordinate of the point at the coordinates (0, f(0)), or the point where the line intersects with the y-axis. The y-intercept of a function f is therefore the value of f when the independent variable x is zero, or [...]

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Operand

A name sometimes given to the data that is part of an operation. The term operand is generally used in a logical operation. Examples In the addition operation 12 + 45 = 57, the operands are the terms 12 and 45. In the multiplication operation 12 × 7 = 84, he operands are the factors [...]

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Operator

Symbol that defines a mathematical operation used to solve it. This term also refers to an element in a set of real numbers used in an external composition law. Operators with effects that cancel each other out are called inverse operators. Example In this diagram, +5 and –5 are inverse operators:

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Scatter Plot

In a Cartesian plane, the representation of a distribution with one or more qualitative statistical attributes in which each element is represented individually by a point. The scatter plot is sometimes called a scatter graph. A scatter plot can reveal a group or cluster of the most significant data, any gaps, or inconsistent data in [...]

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Numerator

First term in a fraction or a fractional expression. Examples In the fraction \(\dfrac{4}{5}\), the numerator is 4. In the fractional expression \(\dfrac{3x\space +\space 5}{4x\space–\space3}\), the numerator is 3x + 5.

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Octahedron

Polyhedron with eight faces. A regular octahedron is a regular convex polyhedron in which all of its faces are isometric equilateral triangles. It is one of the five Platonic solids. It has 6 vertices, 12 edges, and 8 faces. Formulas Based on the length \(a\) of the edge, we can calculate the area A and [...]

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Norm of a Vector

Positive real number that characterizes the size of a vector. In a Euclidean vector space, the norm of a vector \(\overline{v}\), noted as \(\parallel \overline{v}\parallel\), corresponds to its measure.

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Numbers

Comparing numbers to one another often shows relationships that are interesting enough that we believe it is useful to name them. Here are a few cases: Amicable numbers Congruent numbers modulo n Twin primes Opposite numbers Relatively prime numbers (or coprime numbers)

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Amicable Numbers

A pair (p, q) of numbers for which the sum of the proper divisors of p is equal to q and the sum of the proper divisors of q is equal to p. Amicable numbers are sometimes called sociable numbers. There do not seem to be any amicable numbers formed by an even number and an odd number. Examples Here [...]

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Equivalent Decimal Numbers

Decimal numbers that represent the same rational number. Theoretically, there are an infinite number of ways to write the same decimal number. Each of these ways corresponds to a decimal fraction that is equivalent to the initial decimal number. Examples 235.78 = 235.780 = 235.7800 = ... Because \(\dfrac{6}{10} = \dfrac{60}{100} = \dfrac{600}{1000} = ... [...]

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Twin Primes

Pair (p, q) of prime numbers where q = p + 2. We call them twin primes because, except for the case of 2 and 3, the least difference between two prime numbers is 2. Examples The numbers 11 and 13 are twin primes because they are two prime numbers with a difference of 2. [...]

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Opposite Numbers

Pair of numbers x and y that verify the relationship x + y = 0. The opposite of the number 0 is the number 0. Two opposite numbers are two numbers with the same absolute value and opposite signs. Example The numbers 7 and –7 are opposite numbers.

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Relatively Prime Numbers

Integers for which the greatest common divisor is 1. We also say that two relatively prime numbers are coprime. The concept of relatively prime numbers is used when verifying that a fraction cannot be further simplified. So, the fraction \(\frac{9}{64}\) cannot be further simplified, because the numbers 9 and 64 are relatively prime. Examples The numbers [...]

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