Mathematics, Secondary 5 (Cultural, Social and Technical)

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

I can switch between exponential and logarithmic notation and evaluate a logarithm in any base with a calculator.

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

I can use the laws of exponents to simplify numerical expressions and rewrite powers in a common base so their exponents can be compared.

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

I can solve exponential and logarithmic equations and inequalities with the definition of a logarithm and the change of base, and interpret the answer in a real situation.

Analyzes a first-degree inequality in two variables

I can graph a first-degree inequality in two variables as a half-plane and decide which points satisfy it.

Determines whether a situation can be translated by a system of inequalities

I can recognize the conditions of a situation that call for inequalities, translate each one, and tell when the whole situation is a system of inequalities.

Models a situation verbally, algebraically, graphically, using a table of values or a scatter plot

I can model a situation in the form that answers its question: an exponential rule, a system of constraints with a function to optimize, or a table of values.

Translates a situation algebraically or graphically using a system of inequalities

I can translate a situation with several constraints into a system of inequalities, both algebraically and as a graph of the region that satisfies them all, and read a system back from its graph.

Optimizes a situation under constraints and makes decisions

I can find the optimal solution of a linear programming situation, interpret and justify it, and show how changing a condition changes the best choice.

Finds the rule of a function or its inverse, depending on the context

I can find the rule of a function from a situation or its data, and the rule of its inverse when the question asks for the input instead of the output.

Solves systems of first-degree inequalities in two variables

I can solve a system of first-degree inequalities in two variables by graphing the region where all of them hold and finding its vertices.

Interprets parameters (multiplicative or additive) and describes the effect of changing their values

I can interpret the parameters of a rule in its situation and describe what happens to the graph and the results when one of them changes.

Distinguishes between dependent and independent events and quantifies probabilities using fractions, decimals or percentages

I can tell whether two events are dependent or independent and express their probabilities as fractions, decimals or percentages.

Calculates mathematical expectation

I can calculate the mathematical expectation of a game or a decision by adding each gain multiplied by its probability.

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

I can tell whether a probability is theoretical, experimental or subjective, and judge how far to trust it.

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

I can explain what odds for and odds against mean and convert between odds and probabilities.

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

I can explain mathematical expectation as the long-run average result of a random situation and connect it with a weighted mean.

Calculates probabilities, including geometric probabilities, in measurement contexts

I can calculate a probability from lengths, areas or volumes when the outcomes are spread over a measure instead of counted.

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

I can determine the odds for or against an event in a situation, by counting outcomes or from a probability.

Interprets and makes decisions with respect to the odds obtained

I can use odds to compare options and make a reasoned decision, including judging whether a payout is fair.

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

I can change a prize, a cost or a probability so that a game becomes fair or reaches a goal, and check the result with the expectation.

Interprets the resulting mathematical expectation and makes appropriate decisions

I can interpret an expectation in a real decision, such as a warranty, insurance or a game, and justify a choice with it and with what it leaves out.

Calculates the probability of outcomes of random experiments related to situations involving arrangements, permutations or combinations

I can count the outcomes of situations with order, repetition or selection by reasoning with trees and the multiplication principle, and use the counts to find probabilities.

Recognizes equivalent figures (plane figures or solids)

I can recognize equivalent figures, plane figures with the same area or solids with the same volume, even when their shapes differ.

Determines measures of segments or perimeters in equivalent figures

I can find an unknown length or perimeter in a figure that must be equivalent to another, and compare the perimeters of equivalent figures.

Determines the area of equivalent figures

I can compare the total areas of equivalent solids and use them to choose the most economical shape for a container.

Determines the volume of equivalent solids

I can find an unknown dimension of a solid equivalent to another, and compare the volumes that solids can hold for the same amount of material.

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

I can explore a relation between lengths or areas in a plane figure on several cases, state it, and justify it with known properties.

Finds unknown measurements using the cosine law

I can use the cosine law to find a side or an angle in any triangle, and choose between the cosine law and the sine law.

Represents a half-plane graphically and algebraically

I can model one condition of a situation as a half-plane, writing the inequality from a graph and drawing the graph from the inequality.

Describes the basic elements of graph theory: degree, distance, path, circuit

I can describe a graph with the right words: vertices, edges, the degree of a vertex, a path, a circuit and the distance between two vertices.

Determines elements of a situation associated with vertices and edges

I can decide which elements of a situation become vertices and which become edges when I model it with a graph.

Counts and enumerates possibilities

I can count and list the possible preference rankings or ballots in a vote, and organize the voters' choices in a preference table.

Compares and interprets different voting procedures and their results

I can apply different voting procedures to the same preferences, compare the winners they produce, and explain why the choice of procedure matters.

Recognizes Euler paths or circuits and Hamiltonian paths or circuits

I can recognize whether a graph has an Euler path or circuit, which uses every edge once, or a Hamiltonian path or circuit, which visits every vertex once.

Represents a situation using a graph

I can draw the graph that represents a situation from a description, a map or a table, with the right kind of edges.

Constructs graphs: directed graphs, weighted graphs, coloured graphs, trees

I can construct directed graphs, weighted graphs, coloured graphs and trees to fit what a situation needs.

Compares graphs, if necessary

I can compare two graphs of a situation by their vertices, edges, degrees, weights or structure, to decide which one fits the situation or which option is better.

Identifies properties of graphs

I can identify and use properties of graphs, such as the sum of the degrees, the number of odd vertices, the edges of a tree and the regions of a planar graph, to check and reason about a graph.

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

I can find the route or structure a situation needs in a graph: an Euler or Hamiltonian route, the critical path, the shortest path, a tree of minimum value or a colouring with the chromatic number.

Value acquired by capital compounded over multiple periods

I can calculate the value acquired by a capital compounded over many periods, including when the rate changes along the way, and find how many periods a goal needs.

Comparing interest rates to make informed decisions

I can compare interest rates with different compounding periods by their effective annual rates, and choose the best offer for saving or for borrowing.

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

I can calculate income from a salary, an hourly wage with overtime, a commission, a contract and gratuities, and compare job offers that pay in different ways.

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

I can calculate income tax with a bracket table, the deductions at source on a pay cheque and the property tax on an assessed value, and explain how each affects a budget.

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

I can compare ways of financing a purchase, such as cash, instalments, a personal loan, a lease or a mortgage, by their total cost and their cost in today's dollars, and choose one with reasons.