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Skills available for Saskatchewan grade 12 math curriculum

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12.PC30.1 Extend understanding of angles to angles in standard position, expressed in degrees and radians.

  • 12.PC30.1.a Sketch angles in standard position including positive and negative degrees.

  • 12.PC30.1.b Investigate and describe the relationship between different systems of angle measurements, with emphasis on radians and degrees.

  • 12.PC30.1.c Sketch, in standard position, an angle measuring 1 radian.

  • 12.PC30.1.d Sketch, in standard position, any angle measuring kπ radians where k∈Q.

  • 12.PC30.1.e Develop and apply strategies for converting between angle measures in degrees and radians (exact value or decimal approximation).

  • 12.PC30.1.f Develop and apply strategies for determining all angles that are coterminal to an angle within a specified domain (in degrees and radians).

  • 12.PC30.1.g Develop, explain, and apply strategies for determining the general form for all angles that are coterminal to a given angle (in degrees and radians).

  • 12.PC30.1.h Explain the relationship between the radian measure of an angle in standard position and the length of the arc cut on a circle of radius r, and solve situational questions based on that relationship.

12.PC30.2 Demonstrate understanding of the unit circle and its relationship to the six trigonometric ratios for any angle in standard position.

12.PC30.3 Demonstrate understanding of the graphs of the primary trigonometric functions.

12.PC30.4 Demonstrate understanding of first- and second-degree trigonometric equations.

  • 12.PC30.4.a Verify, with or without technology, whether or not a value is a solution to a particular trigonometric equation.

  • 12.PC30.4.b Develop and apply strategies for determining algebraically the exact form of the solution to a trigonometric equation.

  • 12.PC30.4.c Determine, using technology, the approximate solution in degrees and radians of a trigonometric equation in a restricted domain.

  • 12.PC30.4.d Explain the relationship between the general solution of trigonometric equations to the zeros of the related trigonometric functions limited to sine and cosine functions.

  • 12.PC30.4.e Determine, using technology, the general solutions for trigonometric equations.

  • 12.PC30.4.f Analyze solutions for given trigonometric equations to identify errors, and correct if necessary.

12.PC30.5 Demonstrate understanding of trigonometric identities including:

  • 12.PC30.5.1 reciprocal identities

  • 12.PC30.5.2 quotient identities

  • 12.PC30.5.3 Pythagorean identities

  • 12.PC30.5.4 sum or difference identities (restricted to sine, cosine, and tangent)

  • 12.PC30.5.5 double-angle identities (restricted to sine, cosine, and tangent)

  • 12.PC30.5.a Explain the difference between a trigonometric identity and a trigonometric equation.

  • 12.PC30.5.b Verify numerically (using degrees or radians) whether or not a trigonometric statement is a trigonometric identity.

  • 12.PC30.5.c Critique statements such as "If three different values verify a trigonometric identity, then the identity is valid".

  • 12.PC30.5.d Determine, with the use of graphing technology, the potential validity of a trigonometric identity.

  • 12.PC30.5.e Determine the non-permissible values of a trigonometric identity.

  • 12.PC30.5.f Develop, explain, and apply strategies for proving trigonometric identities algebraically.

  • 12.PC30.5.g Explain and apply strategies for determining the exact value of a trigonometric ratio by using sum, difference, and double-angle identities.

12.PC30.6 Demonstrate an understanding of operations on, and compositions of, functions.

  • 12.PC30.6.a Sketch the graph of a function that is the sum, difference, product, or quotient of two functions whose graphs are given.

  • 12.PC30.6.b Write the equation of a function that results from the sum, difference, product, or quotient of two or more functions.

  • 12.PC30.6.c Develop, generalize, explain, and apply strategies for determining the domain and range of a function that is the sum, difference, product, or quotient of two other functions.

  • 12.PC30.6.d Write a function as the sum, difference, product, or quotient (or some combination thereof) of two or more functions.

  • 12.PC30.6.e Develop, generalize, explain, and apply strategies for determining the composition of two functions:

  • 12.PC30.6.f Develop, generalize, explain, and apply strategies for evaluating a composition of functions at a particular point.

  • 12.PC30.6.g Develop, generalize, explain, and apply strategies for sketching the graph of composite functions in the form:

    • 12.PC30.6.g.1 f(f(x))

    • 12.PC30.6.g.2 f(g(x))

    • 12.PC30.6.g.3 g(f(x))

    • 12.PC30.6.g.4 where the equations or graphs of ƒ(x) and g(x) are given.

  • 12.PC30.6.h Write a function as a composition of two or more functions.

  • 12.PC30.6.i Write a function by combining two or more functions through operations on, and compositions of, functions.

12.PC30.7 Extend understanding of transformations to include functions (given in equation or graph form) in general, including horizontal and vertical translations, and horizontal and vertical stretches.

12.PC30.8 Demonstrate understanding of functions, relations, inverses and their related equations resulting from reflections through the:

  • 12.PC30.8.1 x-axis

  • 12.PC30.8.2 y-axis

  • 12.PC30.8.3 line y = x.

  • 12.PC30.8.a Generalize and apply the relationship between the coordinates of an ordered pair and the coordinates of the corresponding ordered pair that results from a reflection through the x-axis, the y-axis, or the line y = x.

  • 12.PC30.8.b Develop and apply strategies for sketching the reflection of a function y = f(x) through the x-axis, the y-axis, or the line y = x when the graph of f(x) is given but the equation is not.

  • 12.PC30.8.c Develop and apply strategies for sketching the graphs of y = -f(x), y = f(-x), and x = -f(y) when the graph of f(x) is given and the equation is not.

  • 12.PC30.8.d Develop and apply strategies for writing the equation of a function that is the reflection of the function f(x) through the x-axis, y-axis, or line y = x.

  • 12.PC30.8.e Develop and apply strategies for sketching the inverse of a relation, including reflection across the line y = x and the transformation (x,y)⇒(y,x).

  • 12.PC30.8.f Sketch the graph of the inverse relation, given the graph of the relation.

  • 12.PC30.8.g Develop, generalize, explain, and apply strategies for determining if one or both of a relation and its inverse are functions.

  • 12.PC30.8.h Determine what restrictions must be placed on the domain of a function for its inverse to be a function.

  • 12.PC30.8.i Critique statements such as "If a relation is not a function, then its inverse also will not be a function".

  • 12.PC30.8.j Determine the equation and sketch the graph of the inverse relation, given the equation of a linear or quadratic relation.

  • 12.PC30.8.k Explain the relationship between the domains and ranges of a relation and its inverse.

  • 12.PC30.8.l Develop and apply numeric, algebraic, and graphic strategies to determine if two relations are inverses of each other.

12.PC30.9 Demonstrate an understanding of logarithms including:

12.PC30.10 Demonstrate understanding of polynomials and polynomial functions of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).

12.PC30.11 Demonstrate understanding of radical and rational functions with restrictions on the domain.

  • 12.PC30.11.a Sketch the graph of the function y = square root of x using a table of values, and state the domain and range of the function.

  • 12.PC30.11.b Develop, generalize, explain, and apply transformations to the function y = square root of x to sketch the graph of y - k = a square root of b(x - h).

  • 12.PC30.11.c Sketch the graph of the function y = square root of f(x) given the graph of the function y = f(x), and compare the domains and ranges of the two functions.

  • 12.PC30.11.d Describe the relationship between the roots of a radical equation and the x-intercepts of the graph of the corresponding radical function.

  • 12.PC30.11.e Determine, graphically, the approximate solutions to radical equations.

  • 12.PC30.11.f Sketch rational functions, with and without the use of technology.

  • 12.PC30.11.g Explain the behaviour (shape and location) of the graphs of rational functions for values of the dependent variable close to the location of a vertical asymptote.

  • 12.PC30.11.h Analyze the equation of a rational function to determine where the graph of the rational function has an asymptote or a hole, and explain why.

  • 12.PC30.11.i Match a set of equations for rational and radical functions to their corresponding graphs.

  • 12.PC30.11.j Describe the relationship between the roots of a rational equation and the x-intercepts of the graph of the corresponding rational function.

  • 12.PC30.11.k Determine graphically an approximate solution to a rational equation.

  • 12.PC30.11.l Critique statements such as "Any value that makes the denominator of a rational function equal to zero will result in a vertical asymptote on the graph of the rational function".

12.PC30.12 Demonstrate understanding of permutations, including the fundamental counting principle.

  • 12.PC30.12.a Develop and apply strategies, such as lists or tree diagrams, to determine the total number of choices or arrangements possible in a situation.

  • 12.PC30.12.b Explain why the total number of possible choices is found by multiplying rather than adding the number of ways that individual choices can be made.

  • 12.PC30.12.c Provide examples of situations relevant to self, family, and community where the fundamental counting principle can be applied to determine the number of possible choices or arrangements.

  • 12.PC30.12.d Create and solve situational questions that involve the application of the fundamental counting principle.

  • 12.PC30.12.e Count, using graphic organizers, the number of ways to arrange the elements of a set in a row.

  • 12.PC30.12.f Develop, generalize, explain, and apply strategies, including the use of factorial notation, to determine the number of permutations possible if n different elements are taken n or r at a time.

  • 12.PC30.12.g Explain why n must be greater than or equal to r in the notation nPr.

  • 12.PC30.12.h Solve equations that involve nPr notation such as nP2=30.

  • 12.PC30.12.i Develop, generalize, explain, and apply strategies for determining the number of permutations possible when two or more elements in the set are identical (non-distinguishable).

12.PC30.13 Demonstrate understanding of combinations of elements, including the application to the binomial theorem.