Mathematics, Secondary 4 (Science)

Unit 1: Arithmetic

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)).

• Defines the concept absolute value in context (e.g. difference between two numbers, distance between two points)

Unit 2: Algebra

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)).

• Identifies the coefficient, degree, terms, constant term and like terms of an algebraic expression
• Interprets parameters (multiplicative or additive) and describes the effect of changing their values

• Manipulates algebraic expressions of the functions under study
• Analyzes second-degree polynomial functions of the form f(x) = ax² + bx + c, f(x) = a(b(x – h))² + k or f(x) = a(x – x₁)(x – x₂)

• Divides a polynomial by another polynomial (with or without a remainder)
• Validates the solution, with or without technological tools
• Constructs an algebraic expression using a register (type) of representation

• Factors polynomials by grouping (including decomposable second-degree trinomials)
• Factors by completing the square (switching from one type of notation to another)
• Factors trinomials of the form ax² + bx + c using formulas
• Factors by substituting second-degree algebraic identities (perfect square trinomial and difference of two squares)
• Interprets the solution or makes decisions if necessary, depending on the context
• Manipulates expressions involving multiplicative parameters
• Manipulates expressions involving additive parameters
• Determines values or data by solving equations and inequalities

• Recognizes or constructs equivalent algebraic expressions
• Interpolates and extrapolates data, if applicable

• Solves exponential, logarithmic and square root equations and inequalities using the properties of exponents, logarithms and radicals

• Solves a second-degree equation in two variables

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

• Analyzes a second-degree inequality in two variables

• Interprets solutions or makes decisions, if necessary, depending on the context

• Solves systems of first-degree equations in two variables
• Solves systems of second-degree equations in relation to conics, changing variables if applicable
• Represents and interprets the inverse of a function

• Analyzes a situation to be optimized 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)
• Models a situation verbally, algebraically, graphically, using a table of values or a scatter plot

• Analyzes step functions

• Analyzes greatest-integer functions of the form f(x) = a[b(x – h)] + k

Unit 3: Statistics

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)).

• Represents data using a scatter plot or a double-entry (two-variable) distribution table

• Models two-variable data using a first-degree polynomial function

• Describes and interprets the relationship between two variables, if any

• Gives a qualitative assessment of a linear correlation

• Approximates and interprets the linear correlation coefficient

• Represents a regression line algebraically or graphically

• Interpolates or extrapolates values using a regression line

• Compares two-variable distributions

Unit 4: Geometry

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)).

• Determines the minimum conditions required to conclude that triangles are congruent or similar
• Determines measures of segments or perimeters in equivalent figures
• Finds unknown measurements using metric or trigonometric relations

• Demonstrates the congruence or similarity between triangles or finds unknown measurements using minimum conditions
• Determines the area of equivalent figures
• Determines the volume of equivalent solids

• Recognizes equivalent figures (plane figures or solids)

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

• Finds unknown measurements using the trigonometric ratios sine, cosine and tangent
• Finds unknown measurements using the cosine law

• 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

Unit 5: Analytic Geometry

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 the distance between two points
• Calculates and interprets a slope

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

• Represents straight lines graphically and algebraically
• Represents a half-plane graphically and algebraically
• Represents parallel lines and perpendicular lines

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

• Determines the equation of a line parallel or perpendicular to another