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Skills available for Saskatchewan grade 11 math curriculum

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11.P20.1 Demonstrate understanding of the absolute value of real numbers and equations and functions involving the absolute value of linear and quadratic functions.

  • 11.P20.1.a Provide examples relevant to one's life, family, or community that illustrate different situations in which quantities referenced are positive, negative, or an absolute value and justify.

  • 11.P20.1.b Determine the distance of two real numbers of the form ±a, a subset of R, from 0 on a number line, and relate this to the absolute value of a (|a|).

  • 11.P20.1.c Determine the absolute value of a real number.

  • 11.P20.1.d Order, with justification, a set of real numbers that includes the absolute value of one or more of the quantities.

  • 11.P20.1.e Explain, with the use of examples, how absolute value fits into the order of operations used on expressions involving real numbers.

  • 11.P20.1.f Determine the value of numerical expressions involving absolute value(s).

  • 11.P20.1.g Simplify expressions involving absolute value(s).

  • 11.P20.1.h Analyze, describe, and explain the relationship between the graph of y = f(x) and y = |f(x)|.

  • 11.P20.1.i Create a table of values for y = |f(x)| given y = f(x).

  • 11.P20.1.j Sketch the graph of y = |f(x)| given y = f(x) and explain the reasoning.

  • 11.P20.1.k Develop and apply strategies for determining the intercepts, domain, and range of y = |f(x)| given the equation of the function or its graph.

  • 11.P20.1.l Explain what the range of the function y = |f(x)| reveals about the graph of the function.

  • 11.P20.1.m Develop, generalize, explain, and apply strategies for graphically determining (with and without the use of technology) the solution set of an equation involving absolute values of algebraic expressions.

  • 11.P20.1.n Develop, generalize, explain, and apply strategies for algebraically determining the solution set of an equation involving absolute values of algebraic expressions.

  • 11.P20.1.o Analyze and generalize conclusions about absolute value inequalities of the form |f(x)| < 0.

  • 11.P20.1.p Identify and correct errors in a solution to an absolute value equation.

  • 11.P20.1.q Solve situational questions involving absolute value functions or equations.

  • 11.P20.1.r Analyze and generalize the relationship between |x| and the square root of x² and between |f(x)| and the square root of (f (x))².

11.P20.2 Expand and demonstrate understanding of radicals with numerical and variable radicands including: computations, solving equations (limited to square roots and one or two radicals).

11.P20.3 Expand and demonstrate understanding of rational expressions and equations (up to and including degree 2 numerators and denominators) including: equivalent forms of expressions, operations on expressions, solving equations that can be simplified to linear or quadratic equations.

11.P20.4 Expand and demonstrate understanding of the primary trigonometric ratios including the use of reference angles (0° ≤ θ ≤ 360°) and the determination of exact values for trigonometric ratios.

  • 11.P20.4.a Provide examples relevant to one's self, family, or community that illustrate the need to define a standard position for angles.

  • 11.P20.4.b Sketch an angle in standard position given the measure of the angle.

  • 11.P20.4.c Determine and justify, with or without sketching, the quadrant in which an angle in standard position terminates.

  • 11.P20.4.d Determine the reference angle for an angle in standard position.

  • 11.P20.4.e Analyze, describe, and generalize the relationship between the reference angles for angles (in standard positions) that are reflections of each other across both the x- and y-axes (e.g., 30° and 150°, or -60° and 60°).

  • 11.P20.4.f Sketch an angle in standard position given a point P(x, y) on the terminal arm of the angle.

  • 11.P20.4.g Develop, generalize, explain, and apply strategies for determining a point on the terminal arm of the angle in each quadrant that has the same reference angle as the angle with P(x, y) on its terminal arm.

  • 11.P20.4.h Develop, explain, and apply strategies for determining the distance between the origin and a point P(x, y) on the terminal arm of an angle.

  • 11.P20.4.i Develop, generalize, explain, and apply strategies for determining the value of sinθ, cosθ, and tanθ when given a point P(x, y) on the terminal arm of θ.

  • 11.P20.4.j Develop, generalize, explain, and apply strategies for determining sinθ, cosθ, and tanθ for quadrantal angles.

  • 11.P20.4.k Develop, generalize, explain, and apply strategies for determining the sign (without calculation or the use of technology) of sinθ, cosθ, or tanθ for a given value of θ.

  • 11.P20.4.l Develop, explain, and apply strategies for solving, for all values of θ, equations of the form sinθ = a or cosθ = a, where –1 ≤ a ≤ 1, and equations of the form tanθ = a, where a is a real number.

  • 11.P20.4.m Analyze 30°- 60°- 90° and 45°- 45°- 90° triangles to generalize about the relationship between pairs of sides in such triangles in relation to the angles.

  • 11.P20.4.n Develop, generalize, explain, and apply strategies for determining the exact value of the sine, cosine, or tangent (without the use of technology) of an angle with a reference angle of 30°, 45°, or 60°.

  • 11.P20.4.o Describe and generalize the relationships and patterns in and among the values of the sine, cosine, and tangent ratios for angles from 0° to 360°.

  • 11.P20.4.p Create and solve a situational question relevant to one's self, family, or community which involves a trigonometric ratio.

  • 11.P20.4.q Identify angles for which the tangent ratio does not exist and explain why.

11.P20.5 Demonstrate understanding of the cosine law and sine law, including the ambiguous case.

  • 11.P20.5.a Provide a diagram or picture to illustrate a situation relevant to one's self, family, or community that involves a triangle without a right angle.

  • 11.P20.5.b Develop, explain, and apply strategies for solving a non-right angle triangle using the primary trigonometric ratios.

  • 11.P20.5.c Derive and explain a proof of the sine law or cosine law.

  • 11.P20.5.d Provide an example of a situation relevant to one's self, family, or community that involves the need to consider the ambiguous case and provide a diagram or picture to illustrate the situation and explain why the ambiguous case needs to be considered.

  • 11.P20.5.e Apply the sine law and/or cosine law to solve situational questions.

  • 11.P20.5.f Critique the statement "For every possible pair of angles (whose sum is less than 180°) and line segment, a triangle can be constructed".

  • 11.P20.5.g Critique the statement "The sine law and the cosine law only apply to non-right triangle."

11.P20.6 Expand and demonstrate understanding of factoring polynomial expressions including those of the form: a²x² - b²y², a ≠ 0, b ≠ 0; a(f(x))² - b(f(x)) + c, a ≠ 0; a²(f(x))² - b²(g(y))², a ≠ 0, b ≠ 0 where a, b, and c are rational numbers.

  • 11.P20.6.a Develop, generalize, explain, and apply strategies for factoring polynomial expressions of the form:

    • 11.P20.6.a.1 a²x² - b²y², a ≠ 0, b ≠ 0, a and b are real numbers

    • 11.P20.6.a.2 ca²x² - cb²y², a ≠ 0, b ≠ 0, a, b, and c are real numbers

    • 11.P20.6.a.3 a(f(x))² - b(f(x)) + c, a ≠ 0, a, b, and c are real numbers

    • 11.P20.6.a.4 da(f(x))² - db(f(x)) + dc, a ≠ 0, a, b, c, and d are real numbers

    • 11.P20.6.a.5 a²(f(x))² - b²(g(y))², a ≠ 0, b ≠ 0, a and b are real numbers

    • 11.P20.6.a.6 da²(f(x))² - db²(g(y))², a ≠ 0, b ≠ 0, a, b, and d are real numbers

  • 11.P20.6.b Verify, with explanation, whether or not a given binomial is a factor for a given polynomial.

11.P20.7 Demonstrate understanding of quadratic functions of the form y = ax² + bx + c and of their graphs, including: vertex, domain and range, direction of opening, axis of symmetry, x- and y-intercepts.

11.P20.8 Demonstrate understanding of quadratic equations including the solution of: single variable equations, systems of linear-quadratic and quadratic-quadratic equations in two variables.

  • 11.P20.8.a Explain, using examples, the relationship among the roots of a quadratic equation, the zeros of the corresponding quadratic function and the x-intercepts of the graph of the quadratic function.

  • 11.P20.8.b Derive the quadratic formula, using deductive reasoning.

  • 11.P20.8.c Apply strategies for solving quadratic equations of the form ax² + bx + c = 0 including:

  • 11.P20.8.d Explain different strategies for verifying the solution to a quadratic equation.

  • 11.P20.8.e Explain, using examples, how the discriminant may be used to determine whether a quadratic equation has two, one, or no real roots; and relate this knowledge to the number of zeros that the corresponding quadratic function will have.

  • 11.P20.8.f Apply knowledge of quadratic equations and functions to identify and correct any errors within a solution to a quadratic equation.

  • 11.P20.8.g Solve situational questions involving the writing and solving of quadratic equations.

  • 11.P20.8.h Match systems of linear-quadratic and quadratic-quadratic functions to situations.

  • 11.P20.8.i Develop, generalize, explain, and apply strategies for solving systems of linear-quadratic and quadratic-quadratic functions, including:

  • 11.P20.8.j Explain the meaning of the intersection point of a system of linear-quadratic or quadratic-quadratic equations in terms of the situation being modeled.

  • 11.P20.8.k Illustrate and explain how a system of linear-quadratic or quadratic-quadratic equations may have zero, one, two, or an infinite number of solutions.

  • 11.P20.8.l Solve situational questions by using systems of linear-quadratic or quadratic-quadratic equations.

11.P20.9 Expand and demonstrate understanding of inequalities including: one-variable quadratic inequalities, two-variable linear and quadratic inequalities.

11.P20.10 Demonstrate understanding of arithmetic and geometric (finite and infinite) sequences and series.

11.P20.11 Demonstrate understanding of reciprocal functions of: linear functions, quadratic functions.

  • 11.P20.11.a Describe the relationship between a function and its reciprocal.

  • 11.P20.11.b Apply knowledge of rational expressions to determine nonpermissible values for reciprocal functions.

  • 11.P20.11.c Analyze and describe the relationship between vertical asymptotes and non-permissible values.

  • 11.P20.11.d Develop, explain, and apply strategies for graphing (with or without the use of technology) y = f(x) given either the graph or equation for y = 1/f(x) where f(x) is a polynomial of degree ≤ 2.

  • 11.P20.11.e Develop, explain, and apply strategies for graphing (with or without the use of technology) y = f(x) given either the graph or equation for y = 1/f(x) where f(x) is a polynomial of degree ≤ 2.

  • 11.P20.11.f Sketch the graph of a function in the form y = 1/f(x).

  • 11.P20.11.g Analyze reciprocal functions to describe the end behaviour of the functions.