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Skills available for Saskatchewan grade 12 math curriculum

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12.A Introduction

12.B Functions

12.C Limits and Continuity

12.D Differentiation

12.E Applications of Derivatives to Curve Sketching

  • 12.E.1 To find the second derivative of a function.

  • 12.E.2 To determine the absolute extrema and relative extrema of a continuous function on a closed interval.

    • 12.E.2.a To make and justify decisions based upon understanding of calculus concepts (CCT).

  • 12.E.3 To determine the interval(s) in which a function is increasing or decreasing and to use the first derivative test to determine local extrema.

    • 12.E.3.a To listen, read and view ideas and concepts analytically and critically (CCT).

    • 12.E.3.b To further develop their ability to read graphs and functions for information in order to understand and analyze (NUM).

  • 12.E.4 To determine the concavity and points of inflection of a function and to apply the second derivative test to determine local extrema.

    • 12.E.4.a To represent understandings through a variety of communication modes (COM).

    • 12.E.4.b To engage in activities that require exploration and manipulation in order to develop understandings of a concept (CCT).

    • 12.E.4.c To use language as a tool for learning and communicating (COM).

    • 12.E.4.d To make and justify decisions based upon understanding of calculus concepts (CCT).

  • 12.E.5 To determine the asymptotes (vertical, horizontal) of a function.

  • 12.E.6 To sketch the graph of a function by analyzing the first and second derivatives, the asymptotes, and the intercepts of the function.

  • 12.E.2B To understand and apply Rolle's Theorem and the Mean Value Theorem.

    • 12.E.2B.a To consider various points of view and alternative perspectives (CCT).

  • 12.E.7 To find the x -intercept(s) of a function using Newton's Method.

12.F Practical Applications of Derivatives

  • 12.F.1 To solve problems that involve rates of change.

  • 12.F.2 To solve a wide variety of optimization problems.

    • 12.F.2.a To pose questions and seek clarification from peers, the teacher, and other sources (CCT).

  • 12.F.3 To determine the instantaneous velocity and acceleration of a particle given the function for its position.

  • 12.F.4 To solve related rate problems.

    • 12.F.4.a To represent problems and understandings through a variety of communication modes (COM).

    • 12.F.4.b To find alternate solutions and interpretations (CCT).

    • 12.F.4.c To engage in activities that require exploration and manipulation in order to develop understandings related to rate of change (CCT).

  • 12.F.5 To use differentials to approximate values of functions.

    • 12.F.5.a If y = f(x) was a curve in a highway, and P(x, f(x)) if at you left the curve following the tangent line, then after travelling dx horizontal units, you would be off the highway by delta y - dy units.

12.G Derivatives of the Transcendental Functions

12.H Integration

  • 12.H.1 To integrate functions by sight.

  • 12.H.2 To integrate functions using u substitution.

  • 12.H.3 To perform definite integration.

    • 12.H.3.a To use language as a tool for learning and communicating (COM).

    • 12.H.3.b To develop and demonstrate the abilities to communicate in ways that support social harmony (PSVS).

12.I The Fundamental Theorem of Calculus

  • 12.I.1 To use the Fundamental Theorem of Calculus to determine the area bounded by a function above, the x -axis below, and the vertical lines x = a and x = b.

    • 12.I.1.a To represent problems and understandings through a variety of communication modes (COM).

  • 12.I.2 To determine the area bounded by the x -axis above, a function below, and the vertical lines x = a and x = b.

    • 12.I.2.a To represent problems and understandings through a variety of communication modes (COM).

  • 12.I.3 To determine the area of the region bounded by the continuous functions y = f(x) above, y = g(x) below, and the vertical lines x = a and x = b.

    • 12.I.3.a To represent problems and understandings through a variety of communication modes (COM).