Quebec
Skills available for Quebec grade 12 math curriculum
Objectives are in black and IXL math skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practise that skill.
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- Quebec Progression of Learning: Secondary Cycle 2 Year 5 Quebec Progression of Learning: Secondary Cycle 2 Year 5
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11-12.AR Arithmetic
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11-12.AR.1 Understanding real numbers
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11-12.AR.1.11 Represents and writes
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11-12.AR.1.11.g numbers using radicals or rational exponents
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11-12.AR.1.11.h numbers in logarithmic notation using the equivalence loga x= n <-> an = x, if necessary
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11-12.AR.1.12 Estimates the value of the power of an exponential expression with respect to its components: base (between 0 and 1, greater than 1), exponent (positive or negative, integral or fractional)
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11-12.AR.3 Operations involving real numbers
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11-12.AR.3.14 Manipulates numerical expressions involving
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11-12.AR.3.14.b powers of bases (change of base), exponents, radicals (nth root), using their properties
- Multiply radical expressions (11-K.7)
- Divide radical expressions (11-K.8)
- Add and subtract radical expressions (11-K.9)
- Simplify radical expressions using the distributive property (11-K.10)
- Simplify radical expressions using conjugates (11-K.11)
- Multiplication with rational exponents (11-L.2)
- Division with rational exponents (11-L.3)
- Power rule (11-L.4)
- Simplify expressions involving rational exponents I (11-L.5)
- Simplify expressions involving rational exponents II (11-L.6)
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11-12.AR.3.14.c logarithms
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11-12.AR.3.14.c.i definition and change of base
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11-12.AR.3.14.c.ii properties
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11-12.AR.3.14.d absolute values
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11-12.AL Algebra
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11-12.AL.1 Understanding and manipulating algebraic expressions
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11-12.AL.1.A Algebraic expressions
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11-12.AL.1.A.4 Describes the role of components of algebraic expressions:
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11-12.AL.1.A.4.c parameter
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11-12.AL.1.B Manipulating algebraic expressions
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11-12.AL.1.B.6 Factors polynomials by
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11-12.AL.1.B.6.c completing the square (factoring and switching from one type of notation to another)
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11-12.AL.1.B.6.d using formulas for trinomials of the form ax + bx + c: x1 = -b + √b² - 4ac and x2 = -b - √b² - 4ac/2a
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11-12.AL.1.C Analyzing situations using equations or inequalities
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11-12.AL.1.C.11 Solves the following types of equations or an inequalities in one variable
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11-12.AL.1.C.11.a second-degree
- Graph solutions to quadratic inequalities (11-C.9)
- Solve quadratic inequalities (11-C.10)
- Solve a quadratic equation using square roots (11-H.6)
- Solve a quadratic equation using the zero product property (11-H.7)
- Solve a quadratic equation by factoring (11-H.8)
- Solve a quadratic equation using the quadratic formula (11-H.11)
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11-12.AL.1.C.11.b exponential, logarithmic or square root, using the properties of exponents, logarithms and radicals
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11-12.AL.1.C.11.c rational
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11-12.AL.1.C.11.d absolute value
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11-12.AL.1.C.11.e first-degree trigonometric involving a sine, cosine or tangent expression
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11-12.AL.1.C.11.f trigonometric that can be expressed as a sine, cosine or tangent function
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11-12.AL.1.C.12 Solves a second-degree equation in two variables
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11-12.AL.1.C.14 Solves an inequality graphically and checks the feasible region of a
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11-12.AL.1.C.14.a first-degree inequality in two variables
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11-12.AL.1.C.14.b second-degree inequality in two variables
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11-12.AL.1.D Analyzing situations using systems of equations or inequalities
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11-12.AL.1.D.1 Determines whether a situation may be translated by a system of
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11-12.AL.1.D.1.b inequalities
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11-12.AL.1.D.2 Translates a situation algebraically or graphically using a system of
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11-12.AL.1.D.2.b inequalities
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11-12.AL.1.D.3 Solves a system
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11-12.AL.1.D.3.c composed of a first-degree equation in two variables and a second-degree equation in two variables
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11-12.AL.1.D.3.d of second-degree equations in relation to conics using changing variables, if applicable
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11-12.AL.1.D.3.e involving various functional models (mostly graphical solutions)
- Solve a system of equations by graphing (11-E.2)
- Solve a system of equations by graphing: word problems (11-E.3)
- Solve a system of equations using substitution (11-E.6)
- Solve a system of equations using substitution: word problems (11-E.7)
- Solve a system of equations using elimination (11-E.8)
- Solve a system of equations using elimination: word problems (11-E.9)
- Solve a system of equations using any method (11-E.10)
- Solve a system of equations using any method: word problems (11-E.11)
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11-12.AL.1.D.4 Solves a system
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11-12.AL.1.D.4.a of first-degree inequalities in two variables
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11-12.AL.1.D.4.b involving various functional models (mostly graphical solutions)
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11-12.AL.1.E Linear programming
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11-12.AL.1.E.1 Analyzes a situation to be optimized
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11-12.AL.1.E.1.a mathematizing the situation using a system of first-degree inequalities in two variables
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11-12.AL.1.E.1.b drawing a bounded or unbounded polygon of constraints to represent the situation
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11-12.AL.1.E.1.c determining the coordinates of the vertices of the bounded polygon (feasible region)
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11-12.AL.1.E.1.d recognizing and defining the function to be optimized
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11-12.AL.1.E.2 Optimizes a situation by taking into account different constraints and makes decisions with respect to this situation
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11-12.AL.1.E.2.a determining the best solution(s) for a particular situation, given a set of possibilities
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11-12.AL.1.E.2.b validating and interpreting the optimal solution, depending on the context
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11-12.AL.1.E.2.c justifying the solution(s) chosen
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11-12.AL.1.E.2.d changing certain conditions associated with the situation to provide a more optimal solution, if necessary
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11-12.AL.2 Understanding dependency relationships
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11-12.AL.2.A Relations, functions and inverses
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11-12.AL.2.A.6 Describes, in the functions under study, the role of
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11-12.AL.2.A.6.b additive parameters
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11-12.AL.2.A.7 Performs operations on functions (including composition)
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11-12.AL.2.B Analyzing situations using real functions
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11-12.AL.2.B.1 Models a situation verbally, algebraically, graphically, using a table of values or a scatter plot
- Complete a function table: absolute value functions (11-D.10)
- Graph an absolute value function (11-D.11)
- Complete a function table: quadratic functions (11-H.2)
- Graph quadratic functions in vertex form (11-H.4)
- Match quadratic functions and graphs (11-H.5)
- Match exponential functions and graphs II (11-N.2)
- Graph sine functions (12-O.4)
- Graph cosine functions (12-O.8)
- Graph sine and cosine functions (12-O.9)
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11-12.AL.2.B.2 Finds the rule of a function or its inverse, depending on the context
- Find a quadratic function (11-H.3)
- Find inverse functions and relations (12-A.15)
- Write equations of sine functions from graphs (12-O.2)
- Write equations of sine functions using properties (12-O.3)
- Write equations of cosine functions from graphs (12-O.6)
- Write equations of cosine functions using properties (12-O.7)
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11-12.AL.2.B.3 Represents and interprets the inverse
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11-12.AL.2.B.4 Interprets parameters (multiplicative or additive) and describes the effect of changing their value, if necessary
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11-12.AL.2.B.5 Describes the properties of real functions: domain, range, interval within which the function is increasing or decreasing, sign, extrema, x-intercept and y-intercept
- Characteristics of quadratic functions (11-H.1)
- Domain and range of radical functions (11-K.12)
- Rational functions: asymptotes and excluded values (11-M.1)
- Identify linear and exponential functions (11-N.4)
- Exponential functions over unit intervals (11-N.5)
- Describe linear and exponential growth and decay (11-N.6)
- Domain and range of exponential and logarithmic functions (12-G.1)
- Find properties of sine functions (12-O.1)
- Find properties of cosine functions (12-O.5)
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11-12.AL.2.B.6 Determines values or data by solving equations and inequalities
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11-12.AL.2.B.7 Interpolates and extrapolates data, if applicable
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11-12.AL.2.B.8 Compares situations or graphical representations
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11-12.AL.2.B.9 Makes decisions, if necessary, depending on the context
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11-12.P Probability
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11-12.P.1 Understanding data from random experiments
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11-12.P.1.A Processing data from random experiments
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11-12.P.1.A.12 Distinguishes between mutually exclusive and non-mutually exclusive, and between dependent and independent events
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11-12.P.1.B Analyzing probability situations
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11-12.P.1.B.6 Associates the type of probability to a situation: experimental, theoretical, subjective
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11-12.P.1.B.8 Calculates conditional probabilities
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11-12.P.1.B.10 Chooses and applies the concept of odds/chance (odds for and odds against) or probability, depending on the context
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11-12.P.1.B.11 Determines the odds for or odds against
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11-12.P.1.B.12 Interprets and makes decisions with respect to the odds obtained
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11-12.P.1.B.13 Calculates mathematical expectation
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11-12.P.1.B.14 Modifies, if necessary, the parameters of a situation in order to make it fair, attain an objective or optimize a gain or loss
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11-12.P.1.B.15 Interprets the resulting mathematical expectation and makes appropriate decisions
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11-12.S Statistics
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11-12.S.1 Analyzing and making decisions about one- or two-variable distributions, using statistical tools
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11-12.S.1.B Two-variable distributions
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11-12.S.1.B.9 Interpolates or extrapolates values using
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11-12.S.1.B.9.b the functional model best suited to the situation
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11-12.G Geometry
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11-12.G.1 Spatial sense and analyzing situations involving geometric figures
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11-12.G.1.D Congruent, similar or equivalent figures
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11-12.G.1.D.7 Recognizes equivalent figures (plane figures or solids)
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11-12.G.2 Analyzing situations involving measurements
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11-12.G.2.C Angles
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11-12.G.2.C.6 Defines the concept of radian
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11-12.G.2.C.7 Determines the correspondence between degrees and radians
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11-12.G.2.D Length
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11-12.G.2.D.5 Finds the following unknown measurements, using properties of figures and relations
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11-12.G.2.D.5.d segments or perimeters resulting from equivalent figures
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11-12.G.2.E Area
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11-12.G.2.E.6 Finds unknown measurements, using properties of figures and relations
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11-12.G.2.E.6.h area of equivalent figures
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11-12.G.2.F Volume
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11-12.G.2.F.6 Finds unknown measurements using properties of figures and relations
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11-12.G.2.F.6.d volume of equivalent solids
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11-12.G.2.G Metric or trigonometric relations
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11-12.G.2.G.1 Determines, through exploration or deduction, different metric relations associated with plane figures
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11-12.G.2.G.2 Finds unknown measurements in various situations
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11-12.G.2.G.2.b in any triangle using
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11-12.G.2.G.2.b.i sine law
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11-12.G.2.G.2.b.ii cosine law
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11-12.G.2.G.2.c in a circle: measure of arcs, chords, inscribed angles, interior angles and exterior angles
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11-12.G.2.G.4 Proves trigonometric identities by using algebraic properties, definitions (sine, cosine, tangent, cosecant, secant, cotangent), Pythagorean identities, and the properties of periodicity and symmetry
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11-12.G.2.H Vectors in the Cartesian or Euclidian plane
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11-12.G.2.H.1 Defines a vector: magnitude (length or norm), direction, sense
- Find the magnitude of a vector (12-U.1)
- Find the direction angle of a vector (12-U.2)
- Find the component form of a vector (12-U.3)
- Find the component form of a vector from its magnitude and direction angle (12-U.4)
- Find the magnitude of a three-dimensional vector (12-V.1)
- Find the component form of a three-dimensional vector (12-V.2)
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11-12.G.2.H.2 Represents a vector graphically (arrow in a plane or pair in a Cartesian plane)
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11-12.G.2.H.3 Identifies properties of vectors
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11-12.G.2.H.4 Performs operations on vectors
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11-12.G.2.H.4.a determination of the resultant or projection of a vector
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11-12.G.2.H.4.b addition and subtraction of vectors
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11-12.G.2.H.4.c multiplication of a vector by a scalar
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11-12.G.2.H.4.d scalar product of two vectors
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11-12.G.2.H.4.e linear combination of vectors
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11-12.G.2.H.4.f application of Chasles relation
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11-12.G.2.H.5 Justifies statements using properties associated with vectors
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11-12.G.2.H.6 Analyzes and models situations using vectors (e.g. displacements, forces, speeds or velocities)
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11-12.AG Analytic Geometry
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11-12.AG.1 Analyzing situations using analytic geometry
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11-12.AG.1.B Straight lines and half-planes
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11-12.AG.1.B.1 Uses the concept of change to
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11-12.AG.1.B.1.b determine the coordinates of a point of division using a given ratio (including the coordinates of a midpoint)
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11-12.AG.1.B.3 Models, with or without technological tools, a situation involving
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11-12.AG.1.B.3.b a half-plane: graphically and algebraically
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11-12.AG.1.B.3.c parallel lines and perpendicular lines
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11-12.AG.1.C Geometric transformations
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11-12.AG.1.C.1 Identifies, through observation, the characteristics of geometric transformations in the Cartesian plane: translations, rotations centred at the origin, reflections with respect to the x-axis and y-axis, dilatations centred at the origin, scaling (expansions and contractions)
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11-12.AG.1.C.2 Defines algebraically the rule for a geometric transformation
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11-12.AG.1.C.3 Constructs, in the Cartesian plane, the image of a figure using a transformation rule
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11-12.AG.1.C.4 Anticipates the effect of a geometric transformation on a figure
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11-12.AG.1.D Geometric loci
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11-12.AG.1.D.1 Describes, represents and constructs geometric loci in the Euclidian and Cartesian planes, with or without technological tools
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11-12.AG.1.D.2 Analyzes and models situations involving geometric loci in the in the Euclidian and Cartesian planes
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11-12.AG.1.D.3 Analyzes and models situations using conics
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11-12.AG.1.D.3.a describing the elements of a conic: radius, axes, directrix, vertices, foci, asymptotes, regions
- Identify the direction a parabola opens (11-I.1)
- Find the vertex of a parabola (11-I.2)
- Find the axis of symmetry of a parabola (11-I.3)
- Find properties of circles (12-Q.4)
- Find properties of ellipses (12-Q.7)
- Find the eccentricity of an ellipse (12-Q.8)
- Find properties of hyperbolas (12-Q.10)
- Find the eccentricity of a hyperbola (12-Q.11)
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11-12.AG.1.D.3.b graphing a conic and its internal and external region
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11-12.AG.1.D.3.c constructing the rule of a conic based on its definition
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11-12.AG.1.D.3.d finding the rule (standard form) of a conic and its internal and external region
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11-12.AG.1.D.3.e validating and interpreting the solution, if necessary
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11-12.AG.1.D.3.f parabola centered at the origin and resulting from a translation
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11-12.AG.1.D.3.g circle, ellipse and hyperbola centered at the origin
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11-12.AG.1.D.3.h circle, ellipse and hyperbola resulting from a translation
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11-12.AG.1.D.4 Determines the coordinates of points of intersection between
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11-12.AG.1.D.4.a a line and a conic
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11-12.AG.1.D.4.b two conics (a parabola and a conic)
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11-12.AG.1.E Standard unit circle
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11-12.AG.1.E.1 Establishes the relationship between trigonometric ratios and the standard unit circle (trigonometric ratios and lines)
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11-12.AG.1.E.2 Determines the coordinates of points associated with significant angles using metric relations in right triangles (Pythagorean relation, properties of angles: 30°, 45°, 60°)
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11-12.AG.1.E.3 Analyzes and uses periodicity and symmetry to determine coordinates of points associated with significant angles in the standard unit circle
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11-12.AG.1.E.4 Proves Pythagorean identities
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11-12.DM Discrete Mathematics
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11-12.DM.1 Introduction to graph theory
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11-12.DM.1.A Concepts associated with graph theory
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11-12.DM.1.A.1 Describes the basic elements of graph theory: degree distance, path, circuit
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11-12.DM.1.A.2 Recognizes Euler paths or circuits and Hamiltonian paths or circuits
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11-12.DM.1.A.3 Constructs graphs: directed graphs, weighted graphs, coloured graphs, trees
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11-12.DM.1.A.4 Identifies properties of graphs
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11-12.DM.1.B Situation analysis, optimization and decision making
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11-12.DM.1.B.1 Determines elements of a situation associated with vertices and edges
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11-12.DM.1.B.2 Represents a situation using a graph
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11-12.DM.1.B.3 Compares graphs, if necessary
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11-12.DM.1.B.4 Finds Euler and Hamiltonian paths and circuits, the critical path, the shortest path, the tree of minimum or maximum values or the chromatic number, depending on the situation
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11-12.DM.2 Introduction to social choice theory
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11-12.DM.2.1 Makes decisions concerning social choices
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11-12.DM.2.1.a Counts and enumerates possibilities
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11-12.DM.2.1.b Compares and interprets different voting procedures and their results
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11-12.DM.3 Introduction to matrices
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11-12.DM.3.2 Represents, interprets data using matrices
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11-12.DM.3.3 Performs operations on matrices: addition and subtraction, multiplication with a scalar and with another matrix
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11-12.DM.3.4 Performs geometric transformations (transformation matrices)
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11-12.DM.3.5 Solves systems of equations (augmented matrix)
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