Quebec
Skills available for Quebec grade 10 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 4 Quebec Progression of Learning: Secondary Cycle 2 Year 4
- Quebec Education Program: First Year of Cycle Two Quebec Education Program: First Year of Cycle Two
Actions
10-11.AR Arithmetic
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10-11.AR.1 Understanding real numbers
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10-11.AR.1.10 Defines the concept absolute value in context (e.g. difference between two numbers, distance between two points)
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10-11.AR.1.11 Represents and writes
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10-11.AR.1.11.g numbers using radicals or rational exponents
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10-11.AR.1.11.h numbers in logarithmic notation using the equivalence loga x = n <--> a to the n power = x, if necessary
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10-11.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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10-11.AR.3 Operations involving real numbers
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10-11.AR.3.14 Manipulates numerical expressions involving
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10-11.AR.3.14.b powers of bases (change of base), exponents, radicals (nth root), using their properties
- Evaluate expressions using properties of exponents (10-B.8)
- Identify equivalent expressions involving exponents (10-B.9)
- Multiply radical expressions (10-D.3)
- Add and subtract radical expressions (10-D.4)
- Simplify radical expressions using the distributive property (10-D.5)
- Simplify radical expressions: mixed review (10-D.6)
- Multiplication with rational exponents (10-E.2)
- Division with rational exponents (10-E.3)
- Power rule with rational exponents (10-E.4)
- Simplify expressions involving rational exponents I (10-E.5)
- Simplify expressions involving rational exponents II (10-E.6)
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10-11.AR.3.14.c logarithms
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10-11.AR.3.14.c.i definition and change of base
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10-11.AL Algebra
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10-11.AL.1 Understanding and manipulating algebraic expressions
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10-11.AL.1.A Algebraic expressions
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10-11.AL.1.A.4 Describes the role of components of algebraic expressions:
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10-11.AL.1.A.4.c parameter
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10-11.AL.1.B Manipulating algebraic expressions
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10-11.AL.1.B.4 Multiplies
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10-11.AL.1.B.4.b algebraic expressions
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10-11.AL.1.B.5 Divides
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10-11.AL.1.B.5.b a polynomial by a binomial (with or without a remainder)
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10-11.AL.1.B.5.c a polynomial by another polynomial (with or without a remainder)
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10-11.AL.1.B.6 Factors polynomials by
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10-11.AL.1.B.6.b factoring by grouping (polynomials including decomposable second-degree trinomials)
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10-11.AL.1.B.6.c completing the square (factoring and switching from one type of notation to another)
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10-11.AL.1.B.6.d using formulas for trinomials of the form ax² + bx + c:
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10-11.AL.1.B.6.d.i x1 = -b + √b² - 4ac/2a and x2 = -b - √b² - 4ac/2a
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10-11.AL.1.B.6.e substituting second-degree algebraic identities (perfect square trinomial and difference of two squares)
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10-11.AL.1.B.7 Manipulates rational expressions
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10-11.AL.1.C Analyzing situations using equations or inequalities
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10-11.AL.1.C.11 Solves the following types of equations or inequalities in one variable
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10-11.AL.1.C.11.a second-degree
- Solve a quadratic equation using square roots (10-Q.3)
- Solve a quadratic equation using the zero product property (10-Q.4)
- Solve a quadratic equation by factoring (10-Q.5)
- Solve a quadratic equation by completing the square (10-Q.7)
- Solve a quadratic equation using the quadratic formula (10-Q.8)
- Graph solutions to quadratic inequalities (11-C.9)
- Solve quadratic inequalities (11-C.10)
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10-11.AL.1.C.11.b exponential, logarithmic or square root, using the properties of exponents, logarithms and radicals
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10-11.AL.1.C.12 Solves a second-degree equation in two variables
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10-11.AL.1.C.14 Solves an inequality graphically and checks the feasible region of a
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10-11.AL.1.C.14.a first-degree inequality in two variables second-degree inequality in two variables
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10-11.AL.1.C.14.b second-degree inequality in two variables
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10-11.AL.1.D Analyzing situations using systems of equations or inequalities
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10-11.AL.1.D.3 Solves a system
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10-11.AL.1.D.3.b of first-degree equations in two variables
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10-11.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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10-11.AL.1.D.5 Validates the solution, with or without technological tools
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10-11.AL.1.D.6 Interprets the solution or makes decisions if necessary, depending on the context
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10-11.AL.2 Understanding dependency relationships
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10-11.AL.2.A Relations, functions and inverses
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10-11.AL.2.A.6 Describes, in the functions under study, the role of
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10-11.AL.2.A.6.a multiplicative parameters
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10-11.AL.2.A.6.b additive parameters
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10-11.AL.2.B Analyzing situations using real functions
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10-11.AL.2.B.1 Models a situation verbally, algebraically, graphically, using a table of values or a scatter plot
- Slope-intercept form: graph an equation (10-L.6)
- Complete a table and graph a linear function (10-L.12)
- Standard form: graph an equation (10-L.16)
- Graph a horizontal or vertical line (10-L.18)
- Point-slope form: graph an equation (10-L.19)
- Complete a function table: quadratic functions (10-Q.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)
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10-11.AL.2.B.2 Finds the rule of a function or its inverse, depending on the context
- Slope-intercept form: write an equation from a graph (10-L.7)
- Slope-intercept form: write an equation (10-L.8)
- Slope-intercept form: write an equation from a table (10-L.9)
- Slope-intercept form: write an equation from a word problem (10-L.10)
- Write equations in standard form (10-L.14)
- Equations of horizontal and vertical lines (10-L.17)
- Point-slope form: write an equation (10-L.20)
- Point-slope form: write an equation from a graph (10-L.21)
- Write linear, quadratic and exponential functions (10-S.3)
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10-11.AL.2.B.3 Represents and interprets the inverse
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10-11.AL.2.B.4 Interprets parameters (multiplicative or additive) and describes the effect of changing their value, if necessary
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10-11.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
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10-11.AL.2.B.6 Determines values or data by solving equations and inequalities
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10-11.AL.2.B.7 Interpolates and extrapolates data, if applicable
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10-11.AL.2.B.8 Compares situations or graphical representations
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10-11.AL.2.B.9 Makes decisions, if necessary, depending on the context
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10-11.P Probability
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10-11.P.1 Understanding data from random experiments
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10-11.P.1.A Processing data from random experiments
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10-11.P.1.A.12 Distinguishes between mutually exclusive and non-mutually exclusive, and between dependent and independent events
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10-11.P.1.A.16 Uses factorial notation, if necessary
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10-11.P.1.A.17 Recognizes, depending on the context, different types of probabilities: experimental, theoretical, subjective
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10-11.P.1.A.18 Defines or interprets the concept of odds/chance (odds for and odds against) (e.g. makes connections between odds and probabilities)
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10-11.P.1.A.19 Defines or interprets the concept of mathematical expectation (e.g. makes connections between mathematical expectation and weighted mean)
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10-11.P.1.B Analyzing probability situations
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10-11.P.1.B.6 Associates the type of probability to a situation: experimental, theoretical, subjective
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10-11.P.1.B.8 Calculates conditional probabilities
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10-11.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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10-11.P.1.B.11 Determines the odds for or odds against
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10-11.P.1.B.12 Interprets and makes decisions with respect to the odds obtained
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10-11.P.1.B.13 Calculates mathematical expectation
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10-11.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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10-11.P.1.B.15 Interprets the resulting mathematical expectation and makes appropriate decisions
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10-11.S Statistics
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10-11.S.1 Analyzing and making decisions about one- or two-variable distributions, using statistical tools
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10-11.S.1.A One-variable distributions
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10-11.S.1.A.6 Organizes and presents data using
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10-11.S.1.A.6.d a stem-and-leaf diagram
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10-11.S.1.A.11 Determines and interprets
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10-11.S.1.A.11.b measures of dispersion:
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10-11.S.1.A.11.b.iii mean deviation
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10-11.S.1.A.11.b.iv standard deviation
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10-11.S.1.A.11.c measures of position:
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10-11.S.1.A.11.c.ii percentile
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10-11.S.1.B Two-variable distributions
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10-11.S.1.B.2 Represents data using a scatter plot or a double-entry (two-variable) distribution table
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10-11.S.1.B.3 Associates the most appropriate functional model with a scatter plot:
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10-11.S.1.B.3.a first-degree polynomial function
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10-11.S.1.B.3.b functions under study
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10-11.S.1.B.4 Describes and interprets the relationship between two variables, if any
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10-11.S.1.B.5 Gives a qualitative assessment of a linear correlation
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10-11.S.1.B.6 Approximates and interprets the linear correlation coefficient
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10-11.S.1.B.7 Draws a curve associated with the chosen model
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10-11.S.1.B.8 Represents a regression line algebraically or graphically
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10-11.S.1.B.9 Interpolates or extrapolates values using
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10-11.S.1.B.9.a a regression line
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10-11.S.1.B.9.b the functional model best suited to the situation
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10-11.S.1.B.10 Compares two-variable distributions
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10-11.G Geometry
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10-11.G.1 Spatial sense and analyzing situations involving geometric figures
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10-11.G.1.D Congruent, similar or equivalent figures
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10-11.G.1.D.5 Determines the minimum conditions required to conclude that triangles are congruent or similar
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10-11.G.1.D.6 Demonstrates the congruence or similarity between triangles or finds unknown measurements using minimum conditions
- SSS and SAS Theorems (10-AA.5)
- ASA and AAS Theorems (10-AA.6)
- SSS, SAS, ASA and AAS Theorems (10-AA.7)
- SSS Theorem in the coordinate plane (10-AA.8)
- Hypotenuse-Leg Theorem (10-AA.10)
- Side lengths and angle measures in similar figures (10-CC.4)
- Similar triangles and indirect measurement (10-CC.5)
- Similarity rules for triangles (10-CC.7)
- Similar triangles and similarity transformations (10-CC.8)
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10-11.G.1.D.7 Recognizes equivalent figures (plane figures or solids)
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10-11.G.2 Analyzing situations involving measurements
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10-11.G.2.D Length
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10-11.G.2.D.5 Finds the following unknown measurements, using properties of figures and relations
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10-11.G.2.D.5.d segments or perimeters resulting from equivalent figures
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10-11.G.2.E Area
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10-11.G.2.E.6 Finds unknown measurements, using properties of figures and relations
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10-11.G.2.E.6.h area of equivalent figures
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10-11.G.2.F Volume
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10-11.G.2.F.6 Finds unknown measurements using properties of figures and relations
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10-11.G.2.F.6.d volume of equivalent solids
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10-11.G.2.G Metric or trigonometric relations
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10-11.G.2.G.1 Determines, through exploration or deduction, different metric relations associated with plane figures
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10-11.G.2.G.2 Finds unknown measurements in various situations
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10-11.G.2.G.2.a in a right triangle rectangle using
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10-11.G.2.G.2.a.ii the following metric relations
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10-11.G.2.G.2.a.ii.1 The length of a leg of a right triangle is the geometric mean between the length of its projection on the hypotenuse and the length of the hypotenuse.
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10-11.G.2.G.2.a.ii.2 The length of the altitude to the hypotenuse of a right triangle is the geometric mean between the lengths of the segments of the hypotenuse.
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10-11.G.2.G.2.a.ii.3 The product of the lengths of the legs of a right triangle is equal to the product of the length of the hypotenuse and the length of the altitude to the hypotenuse.
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10-11.G.2.G.2.a.iii trigonometric ratios: sine, cosine, tangent
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10-11.G.2.G.2.b in any triangle using
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10-11.G.2.G.2.b.i sine law
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10-11.G.2.G.2.b.ii cosine law
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10-11.G.2.G.2.b.iii Hero's formula
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10-11.G.2.G.2.c in a circle: measure of arcs, chords, inscribed angles, interior angles and exterior angles
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10-11.G.2.G.3 Calculates the area of a triangle given the measure of an angle and the lengths of two sides or given the measures of two angles and the length of one side
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10-11.G.2.G.5 Justifies statements concerning
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10-11.G.2.G.5.b metric or trigonometric relations
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10-11.AG Analytic Geometry
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10-11.AG.1 Analyzing situations using analytic geometry
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10-11.AG.1.B Straight lines and half-planes
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10-11.AG.1.B.1 Uses the concept of change to
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10-11.AG.1.B.1.a calculate the distance between two points
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10-11.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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10-11.AG.1.B.1.c calculate and interpret a slope
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10-11.AG.1.B.2 Determines the relative position of two straight lines using their respective slope (intersecting at one point, perpendicular, non-intersecting parallel or coincident)
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10-11.AG.1.B.3 Models, with or without technological tools, a situation involving
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10-11.AG.1.B.3.a straight lines: graphically and algebraically
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10-11.AG.1.B.3.b a half-plane: graphically and algebraically
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10-11.AG.1.B.3.c parallel lines and perpendicular lines
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10-11.AG.1.B.4 Determines the equation of a line using the slope and a point or using two points
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10-11.AG.1.B.5 Determines the equation of a line parallel or perpendicular to another
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