Mathematics, Secondary 5 (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")).

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

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

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

• Analyzes a first-degree inequality in two variables

• Solves inequalities when analyzing a situation to be optimized
• Models a situation verbally, algebraically, graphically, using a table of values or a scatter plot

• Uses inequalities when optimizing a situation
• 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
• Finds the rule of a function or its inverse, depending on the context

• Solves systems of first-degree inequalities in two variables
• Interprets parameters (multiplicative or additive) and describes the effect of changing their values

Unit 3: Probability

The PDA Probability 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")).

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

• 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

• 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: 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")).

• Recognizes equivalent figures (plane figures or solids)

• Determines measures of segments or perimeters in equivalent figures

• Determines the area of equivalent figures
• Determines the volume of equivalent solids

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

• Finds unknown measurements using the cosine law

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")).

• Represents a half-plane graphically and algebraically

Unit 6: Discrete Mathematics

The PDA Discrete Mathematics 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")).

• Describes the basic elements of graph theory: degree, distance, path, circuit
• Determines elements of a situation associated with vertices and edges
• Counts and enumerates possibilities
• Compares and interprets different voting procedures and their results

• Recognizes Euler paths or circuits and Hamiltonian paths or circuits
• Represents a situation using a graph

• Constructs graphs: directed graphs, weighted graphs, coloured graphs, trees
• Compares graphs, if necessary

• Identifies properties of graphs
• Finds Euler and Hamiltonian paths and circuits, the critical path, the shortest path, the tree of minimum or maximum values or the chromatic number, depending on the situation

Unit 7: 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.

• Value acquired by capital compounded over multiple periods

• Comparing interest rates to make informed decisions

• Types of income (salary, commission, contract, gratuities)

• Types of taxation (income tax, property tax, source deductions)

• Types of financing (purchase options, loans, mortgages, costs)