Ontario, Canada · Curriculum spine

Grade 12

13 concepts across 1 subject. Codes follow the ministry's own expectation numbers; where a course is broken into bites (chapter.bite), each bite names the expectations it covers.

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Calculus and Vectors (MCV4U)

The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007 · 13 concepts
Strand A

Rate of Change

Limits, the derivative and its rules.

4
  1. A1.1
    Limits and continuity
    Evaluate limits numerically, graphically and algebraically, and describe continuity.
    function grapher
    Coming to Studio
  2. A1.2
    The derivative from first principles
    Define the derivative as a limit of difference quotients and find it for simple functions.
    After A1.1function grapher
    Coming to Studio
  3. A2.1
    Derivative rules
    Apply power, sum, product, quotient and chain rules.
    After A1.2balance
    Coming to Studio
  4. A3.1
    Derivatives of exponential and trig functions
    Differentiate exponential, sine and cosine functions and their compositions.
    After A2.1function grapher
    Coming to Studio
Strand B

Derivatives and Their Applications

Curve sketching and optimization.

3
  1. B1.1
    Curve sketching
    Use first and second derivatives to find extrema, intervals of increase and concavity, and sketch.
    After A2.1function grapher
    Coming to Studio
  2. B2.1
    Optimization
    Model a situation and use derivatives to find maximum or minimum values.
    After B1.1modelling canvas
    Coming to Studio
  3. B2.2
    Related rates and motion
    Solve related-rates problems and interpret velocity and acceleration as derivatives.
    After A2.1function grapher
    Coming to Studio
Strand C

Geometry and Algebra of Vectors

Vectors in 2D and 3D, lines and planes.

6
  1. C1.1
    Vectors and operations
    Represent vectors geometrically and algebraically, and add, subtract and scale them.
    vector grid
    Coming to Studio
  2. C1.2
    Dot and cross products
    Compute dot and cross products and use them for angles, projections and areas.
    After C1.1vector grid
    Coming to Studio
  3. C2.1
    Applications of vectors
    Solve force and velocity problems with vectors.
    After C1.2vector grid
    Coming to Studio
  4. C3.1
    Lines in 2D and 3D
    Write vector, parametric and scalar equations of lines.
    After C1.1vector grid
    Coming to Studio
  5. C3.2
    Planes
    Write equations of planes and find intersections of lines and planes.
    After C3.1vector grid
    Coming to Studio
  6. C4.1
    Systems of equations
    Solve systems of linear equations and interpret them geometrically.
    After C3.2balance
    Coming to Studio