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Skills available for Ontario 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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12.A Exponential Functions

12.B Polynomial Functions

  • 12.B.1 recognize and evaluate polynomial functions, describe key features of their graphs, and solve problems using graphs of polynomial functions;

    • 12.B.1.1 recognize a polynomial expression (i.e., a series of terms where each term is the product of a constant and a power of x with a nonnegative integral exponent, such as x³ – 5x² + 2x – 1); recognize the equation of a polynomial function and give reasons why it is a function, and identify linear and quadratic functions as examples of polynomial functions

    • 12.B.1.2 compare, through investigation using graphing technology, the graphical and algebraic representations of polynomial (i.e., linear, quadratic, cubic, quartic) functions (e.g., investigate the effect of the degree of a polynomial function on the shape of its graph and the maximum number of x-intercepts; investigate the effect of varying the sign of the leading coefficient on the end behaviour of the function for very large positive or negative x-values)

    • 12.B.1.3 describe key features of the graphs of polynomial functions (e.g., the domain and range, the shape of the graphs, the end behaviour of the functions for very large positive or negative x-values)

    • 12.B.1.4 distinguish polynomial functions from sinusoidal and exponential functions [e.g., f(x) = sin x, f(x) = 2 to the x power)], and compare and contrast the graphs of various polynomial functions with the graphs of other types of functions

    • 12.B.1.5 substitute into and evaluate polynomial functions expressed in function notation, including functions arising from real-world applications

    • 12.B.1.6 pose problems based on real-world applications that can be modelled with polynomial functions, and solve these and other such problems by using a given graph or a graph generated with technology from a table of values or from its equation

    • 12.B.1.7 recognize, using graphs, the limitations of modelling a real-world relationship using a polynomial function, and identify and explain any restrictions on the domain and range (e.g., restrictions on the height and time for a polynomial function that models the relationship between height above the ground and time for a falling object)

  • 12.B.2 make connections between the numeric, graphical, and algebraic representations of polynomial functions;

  • 12.B.3 solve polynomial equations by factoring, make connections between functions and formulas, and solve problems involving polynomial expressions arising from a variety of applications.

12.C Trigonometric Functions

12.D Applications of Geometry

  • 12.D.1 represent vectors, add and subtract vectors, and solve problems using vector models, including those arising from real-world applications;

  • 12.D.2 solve problems involving two-dimensional shapes and three-dimensional figures and arising from real-world applications;

    • 12.D.2.1 gather and interpret information about real-world applications of geometric shapes and figures in a variety of contexts in technology-related fields (e.g., product design, architecture), and explain these applications (e.g., one reason that sewer covers are round is to prevent them from falling into the sewer during removal and replacement)

    • 12.D.2.2 perform required conversions between the imperial system and the metric system using a variety of tools (e.g., tables, calculators, online conversion tools), as necessary within applications

    • 12.D.2.3 solve problems involving the areas of rectangles, parallelograms, trapezoids, triangles, and circles, and of related composite shapes, in situations arising from real-world applications

    • 12.D.2.4 solve problems involving the volumes and surface areas of spheres, right prisms, and cylinders, and of related composite figures, in situations arising from real-world applications

  • 12.D.3 determine circle properties and solve related problems, including those arising from real-world applications.

    • 12.D.3.1 recognize and describe (i.e., using diagrams and words) arcs, tangents, secants, chords, segments, sectors, central angles, and inscribed angles of circles, and some of their real-world applications (e.g., construction of a medicine wheel)

    • 12.D.3.2 determine the length of an arc and the area of a sector or segment of a circle, and solve related problems

    • 12.D.3.3 determine, through investigation using a variety of tools (e.g., dynamic geometry software), properties of the circle associated with chords, central angles, inscribed angles, and tangents (e.g., equal chords or equal arcs subtend equal central angles and equal inscribed angles; a radius is perpendicular to a tangent at the point of tangency defined by the radius, and to a chord that the radius bisects)

    • 12.D.3.4 solve problems involving properties of circles, including problems arising from real-world applications