Mathematics, Secondary 5 (Technical and Scientific)

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.

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

Solves systems of first-degree inequalities in two variables

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

Solves inequalities involving various functional models (mostly graphical solutions)

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.

Factors by completing the square (switching from one type of notation to another)

Manipulates expressions involving additive 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.

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 rational equations and inequalities in one variable

Solves first-degree trigonometric equations involving a sine, cosine or tangent expression

I can use first-degree trigonometric involving a sine, cosine or tangent expression — 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 second-degree inequality in two variables

Solves inequalities when analyzing a situation to be optimized

I can solve inequalities — 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.

Uses inequalities when optimizing a situation

I can solve inequalities — in Technical and Scientific contexts.

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

I can optimize 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 — in Technical and Scientific contexts.

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

I can find the rule of a function or its inverse, depending on the context — in Technical and Scientific contexts.

Solves systems composed of a first-degree equation and a second-degree equation in two variables

Solves systems involving various functional models (mostly graphical solutions)

Represents and interprets the inverse of a function

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

Performs operations on functions (including composition)

I can perform operations on functions (including composition) — in Technical and Scientific contexts.

Interpolates and extrapolates data, if applicable

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

Analyzes second-degree polynomial functions of the form f(x) = ax² + bx + c, f(x) = a(b(x – h))² + k or f(x) = a(x – x₁)(x – x₂)

Analyzes square root functions of the form f(x) = a√b(x – h) + k

Analyzes rational functions of the form f(x) = (ax + b)/(cx + d)

Analyzes exponential functions of the form f(x) = a·c^(b(x – h)) + k

I can model with f(x) = acb(x – h) + k — in Technical and Scientific contexts.

Analyzes logarithmic functions of the form f(x) = a log_c b(x – h) + k

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.

Analyzes tangent functions of the form f(x) = a tan b(x – h) + k

I can use tangent : f(x) = a tan b(x – h) + k — in Technical and Scientific contexts.

Recognizes equivalent figures (plane figures or solids)

I can recognize equivalent figures (plane figures or solids) — in Technical and Scientific contexts.

Determines the correspondence between degrees and radians

I can determine the correspondence between degrees and radians — in Technical and Scientific contexts.

Defines the concept of radian

I can define the concept of radian — in Technical and Scientific contexts.

Determines the area of equivalent figures

Determines the volume of equivalent solids

Analyzes and models situations using vectors (e.g. displacements, forces, speeds or velocities)

I can analyze and models situations using vectors (e.g. displacements, forces, speeds or velocities) — in Technical and Scientific contexts.

Determines measures of segments or perimeters in equivalent figures

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.

Defines a vector: magnitude (length or norm), direction, sense

I can define a vector: magnitude (length or norm), direction, sense — in Technical and Scientific contexts.

Finds unknown measurements using the cosine law

Represents a vector graphically (arrow in a plane or pair in a Cartesian plane)

I can represent a vector graphically (arrow in a plane or pair in a Cartesian plane) — in Technical and Scientific contexts.

Determines measures in a circle: arcs, chords, inscribed angles, interior angles and exterior angles

Proves trigonometric identities by using algebraic properties, definitions (sine, cosine, tangent, cosecant, secant, cotangent), Pythagorean identities, and the properties of periodicity and symmetry

I can prove trigonometric identities by using algebraic properties, definitions (sine, cosine, tangent, cosecant, secant, cotangent), Pythagorean identities, and the properties of periodicity and symmetry — in Technical and Scientific contexts.

Determines the resultant or projection of a vector

Adds and subtracts vectors

Multiplies a vector by a scalar

Calculates the scalar product of two vectors

Identifies properties of vectors

I can identifie properties of vectors — in Technical and Scientific contexts.

Identifies, through observation, the characteristics of geometric transformations in the Cartesian plane: translations, rotations centred at the origin, reflections with respect to the x-axis and y-axis, dilatations centred at the origin, scaling (expansions and contractions)

I can identifie , through observation, the characteristics of geometric transformations in the Cartesian plane: translations, rotations centred at the origin, reflections with respect to the x-axis and y-axis, dilatations centred at the origin, scaling (expansions and contractions) — in Technical and Scientific contexts.

Describes, represents and constructs geometric loci in the Euclidian and Cartesian planes, with or without technological tools

I can describe , represents and constructs geometric loci in the Euclidian and Cartesian planes, with or without technological tools — in Technical and Scientific contexts.

Establishes the relationship between trigonometric ratios and the standard unit circle (trigonometric ratios and lines)

I can establishe the relationship between trigonometric ratios and the standard unit circle (trigonometric ratios and lines) — in Technical and Scientific contexts.

Defines algebraically the rule for a geometric transformation

I can define algebraically the rule for a geometric transformation — in Technical and Scientific contexts.

Analyzes and models situations involving geometric loci in the Euclidian and Cartesian planes

I can analyze and models situations involving geometric loci in the in the Euclidian and Cartesian planes — in Technical and Scientific contexts.

Determines the coordinates of points associated with significant angles using metric relations in right triangles (Pythagorean relation, properties of angles: 30°, 45°, 60°)

I can determine the coordinates of points associated with significant angles using metric relations in right triangles (Pythagorean relation, properties of angles: 30°, 45°, 60°) — in Technical and Scientific contexts.

Constructs, in the Cartesian plane, the image of a figure using a transformation rule

I can construct , in the Cartesian plane, the image of a figure using a transformation rule — in Technical and Scientific contexts.

Describes and represents a parabola centred at the origin or resulting from a translation

Describes and represents the circle, ellipse and hyperbola centred at the origin

Describes and represents the circle, ellipse and hyperbola resulting from a translation

Analyzes and uses periodicity and symmetry to determine coordinates of points associated with significant angles in the standard unit circle

I can analyze and uses periodicity and symmetry to determine coordinates of points associated with significant angles in the standard unit circle — in Technical and Scientific contexts.

Anticipates the effect of a geometric transformation on a figure

I can anticipate the effect of a geometric transformation on a figure — in Technical and Scientific contexts.

Finds the points of intersection between a line and a conic

Proves Pythagorean identities

I can prove Pythagorean identities — in Technical and Scientific contexts.

Represents, interprets data using matrices

I can represent , interprets data using matrices — in Technical and Scientific contexts.

Performs operations on matrices: addition and subtraction, multiplication with a scalar and with another matrix

I can perform operations on matrices: addition and subtraction, multiplication with a scalar and with another matrix — in Technical and Scientific contexts.

Performs geometric transformations (transformation matrices)

I can perform geometric transformations (transformation matrices) — in Technical and Scientific contexts.

Solves systems of equations (augmented matrix)

I can solve systems of equations (augmented matrix) — in Technical and Scientific contexts.