Mathematics, Secondary 4 (Technical and Scientific)

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

I can define the concept absolute value in context (e.g. difference between two numbers, distance between two points) — in Technical and Scientific contexts.

Writes numbers using radicals or rational exponents

I can rewrite numbers using radicals or rational exponents — in Technical and Scientific contexts.

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

I can convert numbers in logarithmic notation using the equivalence loga x = n an = x, if necessary — in Technical and Scientific contexts.

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)

I can estimate 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) — in Technical and Scientific contexts.

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

I can estimate powers of bases (change of base), exponents, radicals (nth root), using their properties — in Technical and Scientific contexts.

Manipulates numerical expressions involving logarithms

Interprets the role of a parameter in an algebraic expression

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

I can interpret parameters (multiplicative or additive) and describes the effect of changing — in Technical and Scientific contexts.

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

I can validate the solution, with or without technological tools — in Technical and Scientific contexts.

Constructs an algebraic expression using a register (type) of representation

I can construct an algebraic expression using a register (type) of representation — in Technical and Scientific contexts.

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

I can interpret the solution or makes decisions if necessary, depending on the context — in Technical and Scientific contexts.

Manipulates expressions involving multiplicative parameters

Determines values or data by solving equations and inequalities

I can determine values or data by solving equations and inequalities — in Technical and Scientific contexts.

Recognizes or constructs equivalent algebraic expressions

I can recognize or constructs equivalent algebraic expressions — in Technical and Scientific contexts.

Interpolates and extrapolates data, if applicable

I can interpolate and extrapolates data, if applicable — in Technical and Scientific contexts.

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

I can rewrite exponential, logarithmic or square root, using the properties of exponents, logarithms and radicals — in Technical and Scientific contexts.

Solves a second-degree equation in two variables

I can solve a second-degree equation in two variables — in Technical and Scientific contexts.

Analyzes a first-degree inequality in two variables

I can analyze first-degree inequality in two variables — in Technical and Scientific contexts.

Analyzes a second-degree inequality in two variables

Solves systems of first-degree equations in two variables

I can solve of first-degree equations in two variables — in Technical and Scientific contexts.

Represents and interprets the inverse of a function

I can represent and interprets the inverse — in Technical and Scientific contexts.

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)

I can analyze 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) — in Technical and Scientific contexts.

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

I can model a situation verbally, algebraically, graphically, using a table of values or a scatter — in Technical and Scientific contexts.

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)

I can model with f(x) = acbx — in Technical and Scientific contexts.

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

I can graph sinusoidal : f(x) = a sin b(x – h) + k, f(x) = a cos b(x – h) + k — in Technical and Scientific contexts.

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

Calculates mathematical expectation

I can calculate mathematical expectation — in Technical and Scientific contexts.

Uses factorial notation, if necessary

I can use factorial notation, if necessary — in Technical and Scientific contexts.

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

I can recognize , depending on the context, different types of probabilities: experimental, theoretical, subjective — in Technical and Scientific contexts.

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

I can define or interprets the concept of odds/chance (odds for and odds against) (e.g. makes connections between odds and probabilities) — in Technical and Scientific contexts.

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

I can define or interprets the concept of mathematical expectation (e.g. makes connections between mathematical expectation and weighted mean) — in Technical and Scientific contexts.

Calculates probabilities, including geometric probabilities, in measurement contexts

Interprets probabilities and makes appropriate decisions

I can interpret probabilities and makes appropriate decisions — in Technical and Scientific contexts.

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

Interprets and makes decisions with respect to the odds obtained

I can interpret and makes decisions with respect to the odds obtained — in Technical and Scientific contexts.

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

I can modifie , if necessary, the parameters of a situation in order to make it fair, attain — in Technical and Scientific contexts.

Interprets the resulting mathematical expectation and makes appropriate decisions

I can optimize an objective or optimize a gain or loss Interprets the resulting mathematical expectation and makes appropriate decisions — in Technical and Scientific contexts.

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

I can calculate the probability of outcomes of random experiments related to situations involving arrangements, permutations or combinations — in Technical and Scientific contexts.

Calculates and interprets the mean deviation

I can compute mean deviation — in Technical and Scientific contexts.

Calculates and interprets the standard deviation

I can compute standard deviation — in Technical and Scientific contexts.

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

I can represent data using a scatter plot or a double-entry (two-variable) distribution table — in Technical and Scientific contexts.

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

I can analyze first-degree polynomial function — in Technical and Scientific contexts.

Models two-variable data using the functions under study

Describes and interprets the relationship between two variables, if any

I can describe and interprets the relationship between two variables, if any — in Technical and Scientific contexts.

Gives a qualitative assessment of a linear correlation

I can give a qualitative assessment of a linear correlation — in Technical and Scientific contexts.

Approximates and interprets the linear correlation coefficient

I can approximate and interprets the linear correlation coefficient — in Technical and Scientific contexts.

Draws a curve associated with the chosen model

I can draw a curve associated with the chosen model — in Technical and Scientific contexts.

Interpolates or extrapolates values using a regression line

I can analyze a regression line — in Technical and Scientific contexts.

Interpolates or extrapolates values using the functional model best suited to the situation

I can analyze the functional model best suited to the situation — in Technical and Scientific contexts.

Compares two-variable distributions

I can compare two-variable distributions — in Technical and Scientific contexts.

Determines the minimum conditions required to conclude that triangles are congruent or similar

I can determine the minimum conditions required to conclude that triangles are congruent or similar — in Technical and Scientific contexts.

Finds unknown measurements using metric or trigonometric relations

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

I can demonstrate the congruence or similarity between triangles or finds unknown measurements using minimum conditions — in Technical and Scientific contexts.

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

I can determine , through exploration or deduction, different metric relations associated with plane figures — in Technical and Scientific contexts.

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

I can use trigonometric ratios: sine, cosine, tangent — in Technical and Scientific contexts.

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

I can calculate 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 — in Technical and Scientific contexts.

Calculates the distance between two points

I can work in coordinate geometry with calculate the distance between two points — in Technical and Scientific contexts.

Determines the coordinates of a point of division using a given ratio (including the coordinates of a midpoint)

I can work in coordinate geometry with determine the coordinates of a point of division using a given ratio (including the coordinates of a midpoint) — in Technical and Scientific contexts.

Calculates and interprets a slope

I can work in coordinate geometry with calculate and interpret a slope — in Technical and Scientific contexts.

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

I can determine the relative position of two straight lines using their respective slope (intersecting at one point, perpendicular, non-intersecting parallel or coincident) — in Technical and Scientific contexts.

Represents straight lines graphically and algebraically

Represents a half-plane graphically and algebraically

I can solve a half-plane: graphically and algebraically — in Technical and Scientific contexts.

Represents parallel lines and perpendicular lines

I can work in coordinate geometry with parallel lines and perpendicular lines — in Technical and Scientific contexts.

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

I can determine the equation of a line using the slope and a point or using two points — in Technical and Scientific contexts.

Determines the equation of a line parallel or perpendicular to another

I can determine the equation of a line parallel or perpendicular to another — in Technical and Scientific contexts.