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.
Calculus and Vectors (MCV4U)
The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007 · 13 concepts
Strand A4
Rate of Change
Limits, the derivative and its rules.
- A1.1Coming soonLimits and continuityEvaluate limits numerically, graphically and algebraically, and describe continuity.
- A1.2Coming soonThe derivative from first principlesDefine the derivative as a limit of difference quotients and find it for simple functions.
- A2.1Coming soonDerivative rulesApply power, sum, product, quotient and chain rules.
- A3.1Coming soonDerivatives of exponential and trig functionsDifferentiate exponential, sine and cosine functions and their compositions.
Strand B3
Derivatives and Their Applications
Curve sketching and optimization.
- B1.1Coming soonCurve sketchingUse first and second derivatives to find extrema, intervals of increase and concavity, and sketch.
- B2.1Coming soonOptimizationModel a situation and use derivatives to find maximum or minimum values.
- B2.2Coming soonRelated rates and motionSolve related-rates problems and interpret velocity and acceleration as derivatives.
Strand C6
Geometry and Algebra of Vectors
Vectors in 2D and 3D, lines and planes.
- C1.1Coming soonVectors and operationsRepresent vectors geometrically and algebraically, and add, subtract and scale them.
- C1.2Coming soonDot and cross productsCompute dot and cross products and use them for angles, projections and areas.
- C2.1Coming soonApplications of vectorsSolve force and velocity problems with vectors.
- C3.1Coming soonLines in 2D and 3DWrite vector, parametric and scalar equations of lines.
- C3.2Coming soonPlanesWrite equations of planes and find intersections of lines and planes.
- C4.1Coming soonSystems of equationsSolve systems of linear equations and interpret them geometrically.