Mathematics, Secondary 4 (Technical and Scientific)

Unit 1: Arithmetic

The PDA Arithmetic branch, taught in the Technical and Scientific sequence register (mathematics tied to technical instruments, measurement and case studies (Quebec TS program: "design, operation or use of certain technical instruments", identifying errors and anomalies)).

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

• Writes numbers using radicals or rational exponents
• Writes numbers in logarithmic notation using the equivalence log_a x = n ⇔ a^n = x

• 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)

• Manipulates numerical expressions involving powers (change of base), exponents and radicals (nth root), using their properties
• Manipulates numerical expressions involving logarithms

Unit 2: Algebra

The PDA Algebra branch, taught in the Technical and Scientific sequence register (mathematics tied to technical instruments, measurement and case studies (Quebec TS program: "design, operation or use of certain technical instruments", identifying errors and anomalies)).

• Interprets the role of a parameter in 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) = (bx)² or f(x) = a(bx)²

• Divides a polynomial by a binomial (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 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
• Determines values or data by solving equations and inequalities

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

• Solves second-degree equations and inequalities in one variable
• 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

• Analyzes a first-degree inequality in two variables
• Analyzes a second-degree inequality in two variables

• Solves systems of first-degree equations in two variables
• 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 square root functions of the form f(x) = a√b(x – h) + k

• Analyzes exponential functions of the form f(x) = a·c^(bx)

• Analyzes logarithmic functions of the form f(x) = a log_c bx

• Analyzes piecewise functions

• Analyzes step functions

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

• Analyzes sinusoidal functions of the form f(x) = a sin b(x – h) + k or f(x) = a cos b(x – h) + k

Unit 3: Probability

The PDA Probability branch, taught in the Technical and Scientific sequence register (mathematics tied to technical instruments, measurement and case studies (Quebec TS program: "design, operation or use of certain technical instruments", identifying errors and anomalies)).

• Distinguishes between dependent and independent events and quantifies probabilities using fractions, decimals or percentages
• Calculates mathematical expectation

• Uses factorial notation, if necessary

• Recognizes, depending on the context, different types of probabilities: experimental, theoretical, subjective

• Defines or interprets the concept of odds/chance (odds for and odds against) (e.g. makes connections between odds and probabilities)

• Defines or interprets the concept of mathematical expectation (e.g. makes connections between mathematical expectation and weighted mean)

• Calculates probabilities, including geometric probabilities, in measurement contexts

• Interprets probabilities and makes appropriate decisions

• Determines the odds for or odds against, depending on the context

• Interprets and makes decisions with respect to the odds obtained

• Modifies, if necessary, the parameters of a situation to make it fair, attain an objective or optimize a gain or loss

• 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

Unit 4: Statistics

The PDA Statistics branch, taught in the Technical and Scientific sequence register (mathematics tied to technical instruments, measurement and case studies (Quebec TS program: "design, operation or use of certain technical instruments", identifying errors and anomalies)).

• Calculates and interprets the mean deviation
• Calculates and interprets the standard deviation

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

• Models two-variable data using a first-degree polynomial function
• Models two-variable data using the functions under study

• 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

• Draws a curve associated with the chosen model

• Interpolates or extrapolates values using a regression line
• Interpolates or extrapolates values using the functional model best suited to the situation

• Compares two-variable distributions

Unit 5: Geometry

The PDA Geometry branch, taught in the Technical and Scientific sequence register (mathematics tied to technical instruments, measurement and case studies (Quebec TS program: "design, operation or use of certain technical instruments", identifying errors and anomalies)).

• Determines the minimum conditions required to conclude that triangles are congruent or similar
• Finds unknown measurements using metric or trigonometric relations

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

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

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

• 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 6: Analytic Geometry

The PDA Analytic Geometry branch, taught in the Technical and Scientific sequence register (mathematics tied to technical instruments, measurement and case studies (Quebec TS program: "design, operation or use of certain technical instruments", identifying errors and anomalies)).

• Calculates the distance between two points
• Determines the coordinates of a point of division using a given ratio (including the coordinates of a midpoint)
• 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