MCV4U – Calculus and Vectors (Grade 12 University)

By Dr. M Categories: Mathmatics, MCV4U, Grade 12
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About Course

Comprehensive review course for Ontario MCV4U (Grade 12 University Calculus and Vectors). Master the complete curriculum through structured lessons, worked examples, and self-assessment quizzes.

What you’ll learn:
– Rates of Change — limits, derivatives, and applications
– Derivatives of Polynomial, Rational, Exponential, Logarithmic, and Trigonometric Functions
– Curve Sketching — critical points, concavity, optimization
– Geometric Vectors — vector operations, dot and cross products
– Algebraic Vectors — vectors in R² and R³
– Lines and Planes — equations of lines and planes in 3D
– Intersections of Lines and Planes
– Applications to Physics, Engineering, and Computer Graphics

This course is designed for students preparing for:
– Final MCV4U exam
– University programs in Engineering, Computer Science, Physics, Mathematics, and Economics
– AP Calculus AB/BC preparation

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What Will You Learn?

  • Compute limits and apply the formal definition of the derivative
  • Master differentiation rules — power, product, quotient, and chain rules
  • Differentiate exponential, logarithmic, and trigonometric functions
  • Apply derivatives to optimization, related rates, and motion problems
  • Sketch curves using calculus — critical points, concavity, asymptotes
  • Perform vector operations in 2D and 3D — addition, scalar multiplication
  • Compute and apply the dot product, cross product, and scalar projections
  • Write equations of lines and planes in vector, parametric, and scalar forms
  • Solve intersection problems involving lines and planes in R³
  • Calculate distances from points to lines and planes
  • Prepare confidently for the MCV4U final exam and university-level calculus

Course Content

1: Introduction to Calculus — Rates of Change
Foundations of calculus through rates of change, slopes of tangent lines, and limits. Sets up the derivative concept.

  • 1.1 The Slope of a Tangent

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