Mathematics, Secondary 5 (Science)

Writes numbers using radicals or rational exponents

I can rewrite numbers using radicals or rational exponents — in Science (Natural Science) 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 Science (Natural Science) contexts.

Estimates the order of magnitude of a real number using scientific notation

I can estimate the order of magnitude of a real number using scientific notation — in Science (Natural Science) 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 Science (Natural Science) contexts.

Manipulates numerical expressions involving logarithms

Manipulates numerical expressions involving absolute values

I can define absolute values — in Science (Natural Science) contexts.

Factors trinomials of the form ax² + bx + c using formulas

Determines values or data by solving equations and inequalities

I can determine values or data by solving equations and inequalities — in Science (Natural Science) contexts.

Solves rational equations and inequalities in one variable

Solves absolute value equations and inequalities in one variable

I can define absolute value — in Science (Natural Science) contexts.

Solves trigonometric equations that can be expressed as a sine, cosine or tangent function

I can use trigonometric that can be expressed as a sine, cosine or tangent function — in Science (Natural Science) contexts.

Solves inequalities when analyzing a situation to be optimized

I can solve inequalities — in Science (Natural Science) 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 Science (Natural Science) contexts.

Uses inequalities when optimizing a situation

I can solve inequalities — in Science (Natural Science) 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 Science (Natural Science) 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 Science (Natural Science) contexts.

Solves systems of second-degree equations in relation to conics, changing variables if applicable

Represents and interprets the inverse of a function

I can represent and interprets the inverse — in Science (Natural Science) contexts.

Solves systems of first-degree inequalities in two variables

I can analyze of first-degree inequalities in two variables — in Science (Natural Science) contexts.

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 Science (Natural Science) contexts.

Performs operations on functions (including composition)

I can perform operations on functions (including composition) — in Science (Natural Science) contexts.

Interpolates and extrapolates data, if applicable

I can interpolate and extrapolates data, if applicable — in Science (Natural Science) contexts.

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 Science (Natural Science) contexts.

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

Analyzes piecewise functions

Analyzes absolute value 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 Science (Natural Science) 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 Science (Natural Science) 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 Science (Natural Science) contexts.

Defines the concept of radian

I can define the concept of radian — in Science (Natural Science) contexts.

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 Science (Natural Science) contexts.

Determines the correspondence between degrees and radians

I can determine the correspondence between degrees and radians — in Science (Natural Science) 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 Science (Natural Science) contexts.

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 Science (Natural Science) 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

Expresses a vector as a linear combination of vectors

Applies the Chasles relation to vectors

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 Science (Natural Science) contexts.

Identifies properties of vectors

I can identifie properties of vectors — in Science (Natural Science) contexts.

Justifies statements using properties associated with vectors

I can justifie statements using properties associated with vectors — in Science (Natural Science) contexts.

Calculates and interprets a slope

I can work in coordinate geometry with calculate and interpret a slope — in Science (Natural Science) 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 Science (Natural Science) 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 Science (Natural Science) 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

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 Science (Natural Science) contexts.

Finds the points of intersection between a line and a conic

Finds the points of intersection between two conics (a parabola and a conic)

Proves Pythagorean identities

I can prove Pythagorean identities — in Science (Natural Science) contexts.