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The official Quebec Mathematics, Secondary 5 (Science) curriculum
Quebec defines Mathematics, Secondary 5 (Science) by strands and outcomes. MapleMind teaches the same curriculum reorganized for one-skill-at-a-time tutoring — the table shows exactly where every official strand lands, and the ministry's own wording is quoted under each unit below.
Official source Québec's official education programRead it on the government site — quebec.ca ↗| Official strand | Outcomes | Where MapleMind teaches it |
|---|---|---|
| Strand A | 6 | Arithmetic |
| Strand B | 24 | Algebra |
| Strand D | 1 | Statistics |
| Strand E | 14 | Geometry |
| Strand F | 9 | Analytic Geometry |
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How MapleMind teaches Mathematics, Secondary 5 (Science) — every unit, lesson, and skill
Every skill below runs as a short session: a plain-words lesson, a worked example, solving it together, then a five-question skill check that earns up to three stars. Guided Mode keeps it teaching instead of answer-handing — turning it off needs a parent's password.
Unit 1ArithmeticOfficial strand · Strand A
The PDA Arithmetic branch, taught in the Science (Natural Science) sequence register (formal mathematics as the object of study (Quebec Science program: "develop formal proofs... to confirm a truth", properties of mathematical objects, abstract thinking)).
Writes numbers using radicals or rational exponents
- Writes numbers using radicals or rational exponentsARITH.N11.g — The student carries out: numbers using radicals or rational exponents — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
Estimates the value of the power of an exponential expression
- 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)ARITH.N12 — The student carries out: 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) — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
Estimates the order of magnitude of a real number using scientific notation
- Estimates the order of magnitude of a real number using scientific notationARITH.N13 — The student carries out: Estimates the order of magnitude of a real number using scientific notation — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
Manipulates numerical expressions: powers, radicals, logarithms, absolute values
- Manipulates numerical expressions involving powers (change of base), exponents and radicals (nth root), using their propertiesARITH.N14.b — The student carries out: powers of bases (change of base), exponents, radicals (nth root), using their properties — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
- Manipulates numerical expressions involving logarithmsARITH.N14.c.ii — The student carries out: logarithms — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
- Manipulates numerical expressions involving absolute valuesARITH.N14.d — The student carries out: absolute values — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
The official wording — 6 outcomes in this unit
- ARITH.N11.g
numbers using radicals or rational exponents
- ARITH.N12
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)
- ARITH.N13
Estimates the order of magnitude of a real number using scientific notation
- ARITH.N14.b
powers of bases (change of base), exponents, radicals (nth root), using their properties
- ARITH.N14.c.ii
logarithms
- ARITH.N14.d
absolute values
Unit 2AlgebraOfficial strand · Strand B
The PDA Algebra branch, taught in the Science (Natural Science) sequence register (formal mathematics as the object of study (Quebec Science program: "develop formal proofs... to confirm a truth", properties of mathematical objects, abstract thinking)).
Factors trinomials of the form ax² + bx + c using formulas
- Factors trinomials of the form ax² + bx + c using formulasALG.N6.d — The student carries out: using formulas for trinomials of the form ax2 + bx + c : — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
- Determines values or data by solving equations and inequalitiesALG.N6.4 — The student carries out: Determines values or data by solving equations and inequalities — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
Solves equations and inequalities in one variable
- Solves rational equations and inequalities in one variableALG.N11.c — The student carries out: rational — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
- Solves absolute value equations and inequalities in one variableALG.N11.d — The student carries out: absolute value — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
- Solves trigonometric equations that can be expressed as a sine, cosine or tangent functionALG.N11.f — The student carries out: trigonometric that can be expressed as a sine, cosine or tangent function — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
Analyzes and models situations to be optimized
- Solves inequalities when analyzing a situation to be optimizedALG.N1.b.2 — The student carries out: inequalities — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
- Models a situation verbally, algebraically, graphically, using a table of values or a scatter plotALG.N1.5 — The student carries out: Models a situation verbally, algebraically, graphically, using a table of values or a scatter — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
Optimizes a situation under constraints
- Uses inequalities when optimizing a situationALG.N2.b — The student carries out: inequalities — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
- 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 justifying the solution(s) chosen changing certain conditions associated with the situation to provide a more optimal solution, if necessaryALG.N2.3 — The student carries out: 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 justifying the solution(s) chosen changing certain conditions associated with the situation to provide a more optimal solution, if necessary — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
- Finds the rule of a function or its inverse, depending on the contextALG.N2.5 — The student carries out: Finds the rule of a function or its inverse, depending on the context — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
Solves systems of second-degree equations in relation to conics
- Solves systems of second-degree equations in relation to conics, changing variables if applicableALG.N3.d — The student carries out: of second-degree equations in relation to conics using changing variables, if applicable — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
- Represents and interprets the inverse of a functionALG.N3.5 — The student carries out: Represents and interprets the inverse — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
Solves systems of inequalities and interprets parameters
- Solves systems of first-degree inequalities in two variablesALG.N4.a.4 — The student carries out: of first-degree inequalities in two variables — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
- Interprets parameters (multiplicative or additive) and describes the effect of changing their valuesALG.N4.2 — The student carries out: Interprets parameters (multiplicative or additive) and describes the effect of changing — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
Performs operations on functions (including composition)
- Performs operations on functions (including composition)ALG.N7.4 — The student carries out: Performs operations on functions (including composition) — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
- Interpolates and extrapolates data, if applicableALG.N7.5 — The student carries out: Interpolates and extrapolates data, if applicable — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
Analyzes square root functions of the form f(x) = a√b(x – h) + k
- Analyzes square root functions of the form f(x) = a√b(x – h) + kALG.c.ii — The student carries out: f(x) = a b(x – h)+ k — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
Analyzes rational functions of the form f(x) = (ax + b)/(cx + d)
- Analyzes rational functions of the form f(x) = (ax + b)/(cx + d)ALG.d.ii — The student carries out: ax + b — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
Analyzes exponential functions of the form f(x) = a·c^(b(x – h)) + k
- Analyzes exponential functions of the form f(x) = a·c^(b(x – h)) + kALG.e.iii — The student carries out: f(x) = acb(x – h) + k — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
Analyzes logarithmic functions of the form f(x) = a log_c b(x – h) + k
- Analyzes logarithmic functions of the form f(x) = a log_c b(x – h) + kALG.f.iii — The student carries out: f(x) = a logc b(x – h) + k — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
Analyzes piecewise functions
- Analyzes piecewise functionsALG.g — The student carries out: Piecewise functions — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
Analyzes absolute value functions of the form f(x) = a|b(x – h)| + k
- Analyzes absolute value functions of the form f(x) = a|b(x – h)| + kALG.h — The student carries out: Absolute value functions : f(x) = a|b(x – h)| + k — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
Analyzes sinusoidal and tangent functions
- Analyzes sinusoidal functions of the form f(x) = a sin b(x – h) + k or f(x) = a cos b(x – h) + kALG.k.ii — The student carries out: sinusoidal : f(x) = a sin b(x – h) + k, f(x) = a cos b(x – h) + k — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
- Analyzes tangent functions of the form f(x) = a tan b(x – h) + kALG.k.iii — The student carries out: tangent : f(x) = a tan b(x – h) + k — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
The official wording — 24 outcomes in this unit
- ALG.N6.d
using formulas for trinomials of the form ax2 + bx + c :
- ALG.N6.4
Determines values or data by solving equations and inequalities
- ALG.N11.c
rational
- ALG.N11.d
absolute value
- ALG.N11.f
trigonometric that can be expressed as a sine, cosine or tangent function
- ALG.N1.b.2
inequalities
- ALG.N1.5
Models a situation verbally, algebraically, graphically, using a table of values or a scatter
- ALG.N2.b
inequalities
- ALG.N2.3
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 justifying the solution(s) chosen changing certain conditions associated with the situation to provide a more optimal solution, if necessary
- ALG.N2.5
Finds the rule of a function or its inverse, depending on the context
- ALG.N3.d
of second-degree equations in relation to conics using changing variables, if applicable
- ALG.N3.5
Represents and interprets the inverse
- ALG.N4.a.4
of first-degree inequalities in two variables
- ALG.N4.2
Interprets parameters (multiplicative or additive) and describes the effect of changing
- ALG.N7.4
Performs operations on functions (including composition)
- ALG.N7.5
Interpolates and extrapolates data, if applicable
- ALG.c.ii
f(x) = a b(x – h)+ k
- ALG.d.ii
ax + b
- ALG.e.iii
f(x) = acb(x – h) + k
- ALG.f.iii
f(x) = a logc b(x – h) + k
- ALG.g
Piecewise functions
- ALG.h
Absolute value functions : f(x) = a|b(x – h)| + k
- ALG.k.ii
sinusoidal : f(x) = a sin b(x – h) + k, f(x) = a cos b(x – h) + k
- ALG.k.iii
tangent : f(x) = a tan b(x – h) + k
Unit 3StatisticsOfficial strand · Strand D
The PDA Statistics branch, taught in the Science (Natural Science) sequence register (formal mathematics as the object of study (Quebec Science program: "develop formal proofs... to confirm a truth", properties of mathematical objects, abstract thinking)).
Interpolates or extrapolates values using the best-suited functional model
- Interpolates or extrapolates values using the functional model best suited to the situationSTAT.N9.b — The student carries out: the functional model best suited to the situation — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
The official wording — 1 outcome in this unit
- STAT.N9.b
the functional model best suited to the situation
Unit 4GeometryOfficial strand · Strand E
The PDA Geometry branch, taught in the Science (Natural Science) sequence register (formal mathematics as the object of study (Quebec Science program: "develop formal proofs... to confirm a truth", properties of mathematical objects, abstract thinking)).
Defines the concept of radian
- Defines the concept of radianGEOM.N6.4 — The student carries out: Defines the concept of radian — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
- Analyzes and models situations using vectors (e.g. displacements, forces, speeds or velocities)GEOM.N6.6 — The student carries out: Analyzes and models situations using vectors (e.g. displacements, forces, speeds or velocities) — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
Determines the correspondence between degrees and radians
- Determines the correspondence between degrees and radiansGEOM.N7.4 — The student carries out: Determines the correspondence between degrees and radians — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
Determines metric relations associated with plane figures
- Determines, through exploration or deduction, different metric relations associated with plane figuresGEOM.N1.11 — The student carries out: Determines, through exploration or deduction, different metric relations associated with plane figures — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
Proves trigonometric identities and performs vector operations
- Proves trigonometric identities by using algebraic properties, definitions (sine, cosine, tangent, cosecant, secant, cotangent), Pythagorean identities, and the properties of periodicity and symmetryGEOM.N4.8 — The student carries out: Proves trigonometric identities by using algebraic properties, definitions (sine, cosine, tangent, cosecant, secant, cotangent), Pythagorean identities, and the properties of periodicity and symmetry — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
- Determines the resultant or projection of a vectorGEOM.N4.a.3 — The student carries out: determination of the resultant or projection of a vector — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
- Adds and subtracts vectorsGEOM.N4.b.3 — The student carries out: addition and subtraction of vectors — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
- Multiplies a vector by a scalarGEOM.N4.c.2 — The student carries out: multiplication of a vector by a scalar — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
- Calculates the scalar product of two vectorsGEOM.N4.d — The student carries out: scalar product of two vectors — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
- Expresses a vector as a linear combination of vectorsGEOM.N4.e — The student carries out: linear combination of vectors — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
- Applies the Chasles relation to vectorsGEOM.N4.f — The student carries out: application of Chasles relation — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
Represents a vector graphically
- Represents a vector graphically (arrow in a plane or pair in a Cartesian plane)GEOM.N2.11 — The student carries out: Represents a vector graphically (arrow in a plane or pair in a Cartesian plane) — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
Identifies properties of vectors
- Identifies properties of vectorsGEOM.N3.11 — The student carries out: Identifies properties of vectors — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
Justifies statements using properties associated with vectors
- Justifies statements using properties associated with vectorsGEOM.N5.7 — The student carries out: Justifies statements using properties associated with vectors — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
The official wording — 14 outcomes in this unit
- GEOM.N6.4
Defines the concept of radian
- GEOM.N6.6
Analyzes and models situations using vectors (e.g. displacements, forces, speeds or velocities)
- GEOM.N7.4
Determines the correspondence between degrees and radians
- GEOM.N1.11
Determines, through exploration or deduction, different metric relations associated with plane figures
- GEOM.N4.8
Proves trigonometric identities by using algebraic properties, definitions (sine, cosine, tangent, cosecant, secant, cotangent), Pythagorean identities, and the properties of periodicity and symmetry
- GEOM.N4.a.3
determination of the resultant or projection of a vector
- GEOM.N4.b.3
addition and subtraction of vectors
- GEOM.N4.c.2
multiplication of a vector by a scalar
- GEOM.N4.d
scalar product of two vectors
- GEOM.N4.e
linear combination of vectors
- GEOM.N4.f
application of Chasles relation
- GEOM.N2.11
Represents a vector graphically (arrow in a plane or pair in a Cartesian plane)
- GEOM.N3.11
Identifies properties of vectors
- GEOM.N5.7
Justifies statements using properties associated with vectors
Unit 5Analytic GeometryOfficial strand · Strand F
The PDA Analytic Geometry branch, taught in the Science (Natural Science) sequence register (formal mathematics as the object of study (Quebec Science program: "develop formal proofs... to confirm a truth", properties of mathematical objects, abstract thinking)).
Calculates and interprets a slope
- Calculates and interprets a slopeANGEO.N1.c — The student carries out: calculate and interpret a slope — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
Analyzes and models situations involving geometric loci
- Analyzes and models situations involving geometric loci in the Euclidian and Cartesian planesANGEO.N2.4 — The student carries out: Analyzes and models situations involving geometric loci in the in the Euclidian and Cartesian planes — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
- Determines the coordinates of points associated with significant angles using metric relations in right triangles (Pythagorean relation, properties of angles: 30°, 45°, 60°)ANGEO.N2.5 — The student carries out: Determines the coordinates of points associated with significant angles using metric relations in right triangles (Pythagorean relation, properties of angles: 30°, 45°, 60°) — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
Describes and represents conics in the Cartesian plane
- Describes and represents a parabola centred at the origin or resulting from a translationANGEO.N3.a.2 — The student carries out: parabola centred at the origin and resulting from a translation — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
- Describes and represents the circle, ellipse and hyperbola centred at the originANGEO.N3.b.2 — The student carries out: circle, ellipse and hyperbola centred at the origin — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
- Analyzes and uses periodicity and symmetry to determine coordinates of points associated with significant angles in the standard unit circleANGEO.N3.2 — The student carries out: Analyzes and uses periodicity and symmetry to determine coordinates of points associated with significant angles in the standard unit circle — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
Finds points of intersection between lines and conics
- Finds the points of intersection between a line and a conicANGEO.N4.a — The student carries out: a line and a conic — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
- Finds the points of intersection between two conics (a parabola and a conic)ANGEO.N4.b — The student carries out: two conics (a parabola and a conic) — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
- Proves Pythagorean identitiesANGEO.N4.3 — The student carries out: Proves Pythagorean identities — in Science (Natural Science) contexts (state the general result and prove/justify it formally, not just compute a case).
The official wording — 9 outcomes in this unit
- ANGEO.N1.c
calculate and interpret a slope
- ANGEO.N2.4
Analyzes and models situations involving geometric loci in the in the Euclidian and Cartesian planes
- ANGEO.N2.5
Determines the coordinates of points associated with significant angles using metric relations in right triangles (Pythagorean relation, properties of angles: 30°, 45°, 60°)
- ANGEO.N3.a.2
parabola centred at the origin and resulting from a translation
- ANGEO.N3.b.2
circle, ellipse and hyperbola centred at the origin
- ANGEO.N3.2
Analyzes and uses periodicity and symmetry to determine coordinates of points associated with significant angles in the standard unit circle
- ANGEO.N4.a
a line and a conic
- ANGEO.N4.b
two conics (a parabola and a conic)
- ANGEO.N4.3
Proves Pythagorean identities
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Yes. Every skill in this course maps to an official outcome code from Quebec's Grade 11 Mathematics curriculum, and the ministry's own wording is quoted under each unit on this page — with the official government source linked so you can check it yourself.
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Where can I see the official Quebec curriculum for Mathematics, Secondary 5 (Science)?
The official source is linked on this page — Québec's official education program. The outline here follows it: every MapleMind skill carries its official outcome code, and the ministry's own wording is quoted under each unit.
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