Mathematics, Secondary 4 (Cultural, Social and Technical)

Unit 1: Arithmetic

The PDA Arithmetic branch, taught in the Cultural, Social and Technical sequence register (mathematics for informed social, consumer and financial decisions (Quebec CST program: "purchasing goods and balancing their budget")).

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

• 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)

Unit 2: Algebra

The PDA Algebra branch, taught in the Cultural, Social and Technical sequence register (mathematics for informed social, consumer and financial decisions (Quebec CST program: "purchasing goods and balancing their budget")).

• Solves systems of first-degree equations in two variables
• Represents and interprets the inverse of a function

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

• Interprets the solution or makes decisions if necessary, depending on the context
• Determines values or data by solving equations and inequalities

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

• Analyzes piecewise functions

• Analyzes step functions

Unit 3: Statistics

The PDA Statistics branch, taught in the Cultural, Social and Technical sequence register (mathematics for informed social, consumer and financial decisions (Quebec CST program: "purchasing goods and balancing their budget")).

• Constructs and interprets a stem-and-leaf diagram
• Approximates and interprets the linear correlation coefficient

• Calculates and interprets the mean deviation
• Determines and interprets percentiles

• 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

• Draws a curve associated with the chosen model

• Interpolates or extrapolates values using a regression line

• Compares two-variable distributions

Unit 4: Geometry

The PDA Geometry branch, taught in the Cultural, Social and Technical sequence register (mathematics for informed social, consumer and financial decisions (Quebec CST program: "purchasing goods and balancing their budget")).

• 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 using Hero’s formula

• 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 Cultural, Social and Technical sequence register (mathematics for informed social, consumer and financial decisions (Quebec CST program: "purchasing goods and balancing their budget")).

• 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 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

Unit 6: Financial mathematics

The Cultural, Social and Technical option's own financial mathematics (Quebec Cycle Two program) — interest, present/future value and personal-finance decisions. This is the CST-distinctive strand, absent from the PDA progression and mined from the program document.

• Simple and compound interest

• Interest period

• Discounting (present value)

• Compounding (future value)

• Calculating, interpreting and analyzing financial situations