Newfoundland and Labrador

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Skills available for Newfoundland and Labrador grade 12 math curriculum

Objectives are in black and IXL math skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practise that skill.

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Pre-Calculus

  • Develop algebraic and graphical reasoning through the study of relations.

    • 12.RF1 Demonstrate an understanding of operations on, and compositions of, functions.

      • 12.RF1.1 Write a function h(x) as the sum, difference, product or quotient of two or more functions.

      • 12.RF1.2 Sketch the graph of a function that is the sum, difference, product or quotient of two functions, given their graphs.

      • 12.RF1.3 Determine the domain and range of a function that is the sum, difference, product or quotient of two functions.

      • 12.RF1.4 Determine the value of the composition of functions when evaluated at a point, including:

        • 12.RF1.4.a f(f(a))

        • 12.RF1.4.b f(g(a))

        • 12.RF1.4.c g(f(a)).

      • 12.RF1.5 Determine the equation of the composite function given the equations of two functions f(x) and g(x):

      • 12.RF1.6 Sketch the graph of the composite function given the equations of two functions f(x) and g(x) and determine the domain and range.

      • 12.RF1.7 Determine the original functions from a composition.

Limits and Continuity

Rational Functions

  • Develop algebraic and graphical reasoning through the study of relations.

    • 12.RF2 Graph and analyze rational functions (limited to numerators and denominators that are monomials, binomials or trinomials).

      • 12.RF2.1 Explain the behaviour of the graph of a rational function for values of the variable near a non-permissible value.

      • 12.RF2.2 Determine if the graph of a rational function will have an asymptote or a hole for a nonpermissible value.

      • 12.RF2.3 Sketch the graph of a rational function.

Derivative

Applications of Derivatives

  • Develop introductory calculus reasoning.

    • 12.C6 Use derivatives to sketch the graph of a polynomial function.

      • 12.C6.1 Use f'(x) to identify the critical numbers, relative and absolute extrema and intervals of increase and decrease.

      • 12.C6.2 Use f"(x) to identify the hypercritical numbers, points of inflection and intervals of concavity.

      • 12.C6.3 Sketch the graph of f(x) using information obtained from the function and its derivatives.

      • 12.C6.4 Use the given function f(x) to determine its features such as intercepts and the domain.

    • 12.C7 Use derivatives to sketch the graph of a rational function.

      • 12.C7.1 Use f'(x) to identify the critical numbers, relative and absolute extrema and intervals of increase and decrease.

      • 12.C7.2 Use f"(x) to identify the hypercritical numbers, points of inflection and intervals of concavity.

      • 12.C7.3 Sketch the graph of f(x) using information obtained from the function and its derivatives.

      • 12.C7.4 Use the given function f(x) to determine its features such as intercepts, asymptotes, points of discontinuity and the domain.

    • 12.C8 Use calculus techniques to solve and interpret related rates problems.

      • 12.C8.1 Solve a problem involving related rates drawn from a variety of applications.

      • 12.C8.2 Interpret the solution to a related rates problem.

    • 12.C9 Use calculus techniques to solve optimization problems.

      • 12.C9.1 Determine the equation of the function to be optimized in an optimization problem.

      • 12.C9.2 Determine the equations of any parameters necessary in an optimization problem.

      • 12.C9.3 Solve an optimization problem drawn from a variety of applications, using calculus techniques.

      • 12.C9.4 Interpret the solution(s) to an optimization problem.

Calculus of Trigonometry

Anti-differentiation and Integration

  • Develop introductory calculus reasoning.

    • 12.C13 Determine the indefinite integral of polynomial and radical functions.

      • 12.C13.1 Explain the meaning of the phrase "F(x) is an antiderivative of f(x)".

      • 12.C13.2 Determine the general antiderivative of functions.

      • 12.C13.3 Use antiderivatives notation appropriately (i.e., Γ f(x)dx for the antiderivative of f(x)).

      • 12.C13.4 Identify the properties of antidifferentiation.

      • 12.C13.5 Determine the indefinite integral of a function given extra conditions.

      • 12.C13.6 Use antidifferentiation to solve problems about motion of a particle along a line that involves:

        • 12.C13.6.a computing the position given the initial position and velocity as a function of time

        • 12.C13.6.b computing velocity and/or position given the suitable initial conditions and acceleration as a function of time.

    • 12.C14 Determine the definite integral of a polynomial function.

      • 12.C14.1 Estimate an area using a finite sum.

      • 12.C14.2 Determine the area using the infinite Riemann sum.

      • 12.C14.3 Convert a Riemann sum to a definite integral.

      • 12.C14.4 Using definite integrals, determine the area under a polynomial function from x = a to x = b.

      • 12.C14.5 Calculate the definite integral of a function over an interval [a, b].

      • 12.C14.6 Determine the area between two polynomial functions.

Calculus of Exponential and Logarithmic Functions

  • Develop introductory calculus reasoning.

    • 12.C15 Determine the limit and derivative of exponential and logarithmic functions.

      • 12.C15.1 Graph and analyze exponential and logarithmic functions y = e to the × power and y = ln x.

      • 12.C15.2 Establish the exponential limit h→0 eh-1/h=1 using informal methods.

      • 12.C15.3 Derive the derivatives of the exponential functions e to the x power and a to the x power, and the logarithmic functions ln x and logax.

      • 12.C15.4 Determine the derivative of an exponential function.

      • 12.C15.5 Solve problems involving the derivative of an exponential or a logarithmic function.

      • 12.C15.6 Determine the derivative of a logarithmic function.

      • 12.C15.7 Determine the derivative of a function using logarithmic differentiation.