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Click on any standard to search for aligned resources. This data may be subject to copyright. You may download a CSV of the Quebec Education Program Progression of Learning if your intention constitutes fair use.

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Numbers in logarithmic notation using the equivalence (log)(a)x = n <=> a^n = x, if necessary

Numbers expressed in different ways (fractional, decimal, exponential [integral exponent], percentage, square root, scientific notation)

Establishes relationships between units of time: second, minute, hour, day, daily cycle, weekly cycle, yearly cycle

Describes the characteristics of different types of angles: complementary, supplementary, adjacent, vertically opposite, alternate interior, alternate exterior and corresponding

Determines measures of angles using the properties of the following angles: complementary, supplementary, vertically opposite, alternate interior, alternate exterior and corresponding

Finds unknown measurements using the properties of figures and relations

Justifies statements using definitions or properties associated with angles and their measures

Constructs relations that can be used to calculate the perimeter or circumference of figures

Finds the following unknown measurements, using properties of figures and relations

A segment in a plane figure, circumference, radius, diameter, length of an arc, a segment resulting from an isometry or a similarity transformation

Segments in a solid resulting from an isometry or a similarity transformation

Constructs relations that can be used to calculate the area of plane figures: quadrilateral, triangle, circle (sectors)

Uses relations that can be used to calculate the area of a right cone and a sphere

Finds unknown measurements, using properties of figures and relations

Area of figures that can be split into circles (sectors), triangles or quadrilaterals

Lateral or total area of right prisms, right cylinders and right pyramids

Lateral or total area of solids that can be split into right prisms, right cylinders or right pyramids

Area of a sphere, lateral or total area of right cones and decomposable solids

Constructs relations that can be used to calculate volumes: right cylinders, right pyramids, right cones and spheres

Finds unknown measurements using properties of figures and relations

Volume of right prisms, right cylinders, right pyramids, right cones and spheres

Volume of solids that can be split into right prisms, right cylinders, right pyramids, right cones and spheres

Volume solids resulting from an isometry or a similarity transformation

Justifies statements concerning measures of volume or capacity

Determines, through exploration or deduction, different metric relations associated with plane figures

In a circle: measure of arcs, chords, inscribed angles, interior angles and exterior angles

Proves trigonometric identities by using algebraic properties, definitions (sine, cosine, tangent, cosecant, secant, cotangent), Pythagorean identities, and the properties of periodicity and symmetry

Defines a vector: magnitude (length or norm), direction, sense

Represents a vector graphically (arrow in a plane or pair in a Cartesian plane)

Analyzes and models situations using vectors (e.g. displacements, forces, speeds or velocities)

Locates objects/numbers on an axis, based on the types of numbers studied

Locates points in a Cartesian plane, based on the types of numbers studied (x- and y-coordinates of a point)

Determine the coordinates of a point of division using a given ratio (including the coordinates of a midpoint)

Determines the relative position of two straight lines using their respective slope (intersecting at one point, perpendicular, non-intersecting parallel or coincident)

Models, with or without technological tools, a situation involving

Determines the equation of a line using the slope and a point or using two points

Analyzes and models situations using conics: describing the elements of a conic: radius, axes, directrix, vertices, foci, asymptotes, regions; graphing a conic and its internal and external region; constructing the rule of a conic based on its definition; finding the rule (standard form) of a conic and its internal and external region; validating and interpreting the solution, if necessary

Parabola centred at the origin and resulting from a translation

Establishes the relationship between trigonometric ratios and the standard unit circle (trigonometric ratios and lines)

Determines the coordinates of points associated with significant angles using metric relations in right triangles (Pythagorean relation, properties of angles: 30 degrees, 45 degrees, 60 degrees)

Analyzes and uses periodicity and symmetry to determine coordinates of points associated with significant angles in the standard unit circle

Describes the basic elements of graph theory: degree distance, path, circuit

Constructs graphs: directed graphs, weighted graphs, coloured graphs, trees

Determines elements of a situation associated with vertices and edges

Compares and interprets different voting procedures and their results

Powers of bases (change of base), exponents, radicals (nth root), using their properties

Uses, in different contexts, the properties of divisibility: 2, 3, 4, 5 and 10

Ratios and rates qualitatively (equivalent rates and ratios, unit rate)

Ratios and rates quantitatively (equivalent rates and ratios, unit rate)

Describes, using his/her own words and mathematical language, numerical patterns

Describes, using his/her own words and mathematical language, series of numbers and family of operations

Adds new terms to a series when the first three terms or more are given

Constructs an algebraic expression using a register (type) of representation

Performs the following operations on algebraic expressions, with or without objects or diagrams: addition and subtraction, multiplication and division by a constant, multiplication of first-degree monomials

Factors out the common factor in numerical expressions (distributive property of multiplication over addition or subtraction)

A polynomial by another polynomial (with or without a remainder)

Factoring by grouping (polynomials including decomposable second-degree trinomials)

Completing the square (factoring and switching from one type of notation to another)

Using formulas for trinomials of the form ax^2 + bx + c: x1 = (-b + or - square root (b^2-4ac)/2a)

Substituting second-degree algebraic identities (perfect square trinomial and difference of two squares)

Solves the following types of equations or an inequalities in one variable

Exponential, logarithmic or square root, using the properties of exponents, logarithms and radicals

First-degree trigonometric involving a sine, cosine or tangent expression

Trigonometric that can be expressed as a sine, cosine or tangent function

Validates a solution, with or without technological tools, by substitution

Solves an inequality graphically and checks the feasible region of a

Inequality relations and first-degree inequalities in one variable

An equation using another register (type) of representation, if necessary

An inequality using another register (type) of representation, if necessary

Determines the missing term in an equation (relations between operations) :1 a + b = , a + = c, + b = c, a b = , a = c, b = c, a b = , a = c, b = c, a b = , a = c, b = c

Transforms arithmetic equalities and equations to maintain equivalence (properties and rules for transforming equalities) and justifies the steps followed, if necessary

Transforms inequalities to maintain equivalence (properties and rules for transforming inequalities) and justifies the steps followed, if necessary

Uses different methods to solve first-degree equations with one unknown of the form ax + b = cx + d : trial and error, drawings, arithmetic methods (inverse or equivalent operations), algebraic methods (balancing equations or hidden terms)

Determines whether a situation may be translated by a system of

Translates a situation algebraically or graphically using a system of

Of first-degree equations in two variables of the form y = ax + b by using tables of values, graphically or algebraically (by comparison), with or without technological tools

Composed of a first-degree equation in two variables and a second-degree equation in two variables

Involving various functional models (mostly graphical solutions)

Involving various functional models (mostly graphical solutions)

Interprets the solution or makes decisions if necessary, depending on the context

Mathematizing the situation using a system of first-degree inequalities in two variables

Drawing a bounded or unbounded polygon of constraints to represent the situation

Determining the coordinates of the vertices of the bounded polygon (feasible region)

Optimizes a situation by taking into account different constraints and makes decisions with respect to this situation

Determining the best solution(s) for a particular situation, given a set of possibilities

Validating and interpreting the optimal solution, depending on the context

Changing certain conditions associated with the situation to provide a more optimal solution, if necessary

Analyzes situations using different registers (types) of representation

f(x) = ax^2+ bx + c, f(x) = a(b(x - h))^2 + k, f(x) = a(x - x1)(x - x2)

f(x) = k/x or xy = k where k is an element of the set of positive rational numbers.

Modelling periodic occurences (e.g. natural phenomena such as tides or sound, medical or electrical phenomena)

Sinusoidal : f(x) = a sin b(x - h) + k, f(x) = a cos b(x - h) + k

Models a situation verbally, algebraically, graphically, using a table of values or a scatter plot

Finds the rule of a function or its inverse, depending on the context

Interprets parameters (multiplicative or additive) and describes the effect of changing their value, if necessary

Describes the properties of real functions: domain, range, interval within which the function is increasing or decreasing, sign, extrema, x-intercept and y-intercept

Determines values or data by solving equations and inequalities

Recognizes certain, probable, impossible, simple, complementary, compatible, incompatible, dependent, independents events

Distinguishes between mutually exclusive and non-mutually exclusive, and between dependent and independent events

Uses fractions, decimals or percentages to quantify a probability

Represents an event using different registers (types of representation))

Chooses and applies the concept of odds/chance (odds for and odds against) or probability, depending on the context

Interprets and makes decisions with respect to the odds obtained

Interprets the resulting mathematical expectation and makes appropriate decisions

Calculates the probability of outcomes of random experiments related to situations involving arrangements, permutations or combinations

Associates the type of probability to a situation: experimental, theoretical, subjective

Collects, describes and organizes data (classifies or categorizes) using tables

Chooses the appropriate statistical measures for a given situation

Interprets data presented in a table or a bar graph, a pictograph, a broken-line graph or a circle graph

Distinguishes different types of statistical variables: qualitative, discrete or continuous quantitative

Chooses appropriate register(s) (types) of representation to organize, interpret and present data

Describes the concept of arithmetic mean (levelling or balance point)

Associates the most appropriate functional model with a scatter plot :

Justifies statements using definitions or properties of plane figures

Decomposes plane figures into circles (sectors), triangles or quadrilaterals

Diagonal, altitude, median, perpendicular bisector, bisector, apothem, radius, diameter, chord

Identifies the properties of plane figures using geometric transformations and constructions

Represents three-dimensional figures in the plane, using different procedures:

Projection and perspective (e.g. orthogonal projections [different views], parallel projections [cavalier and axonometric perspectives] or central projections [with one or two vanishing points])

Identifies properties and invariants resulting from geometric constructions and transformations

Constructs the image of a figure under a translation, rotation and reflection

Constructs the image of a figure under a dilatation with a positive scale factor

Determines the properties and invariants of congruent or similar figures

Determines the minimum conditions required to conclude that triangles are congruent or similar

Demonstrates the congruence or similarity between triangles or finds unknown measurements using minimum conditions

Justifies statements using definitions or properties of congruent, similar or equivalent figures, depending on the cycle and year

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