Calculus and Vectors

The course combines the study of rate of

The course combines the study of rate of change, derivatives, and curve sketching with an in-depth look at vectors and their geometric applications

• Students learn to apply calculus to motion
• Optimization
• Modeling problems
• While exploring vectors in two
• Three dimensions

The course emphasizes both conceptual understanding and analytical problem-solving

Unit 1: Rates of Change and Limits
Students explore foundational concepts in differential calculus.
Lessons include:

• Limits and Continuity
• Average and Instantaneous Rates of Change
• The Slope of the Tangent
• Introduction to Derivatives and Notation

Unit 2: Derivatives and Applications
This unit introduces differentiation rules and real-world applications.
Lessons include:

• Chain Rule and Product/Quotient Rules
• Derivatives of Trigonometric and Exponential Functions
• Higher-Order Derivatives
• Derivatives in Motion and Business Contexts

Unit 3: Curve Sketching and Optimization
Students apply calculus to graphing and problem-solving
Lessons include:

• Finding Extrema and Points of Inflection
• Optimization Problems
• Analyzing Concavity
• Complete Curve Sketching Using Calculus

Unit 4: Vectors in Geometry and Algebra
This unit focuses on organizational planning and strategic tools for decision-making.
Lessons include:

• Geometric and Algebraic Vectors
• Vector Operations and Equations
• The Dot and Cross Product
• Equations of Lines and Planes
• Applications of Vectors in Physics and Geometry

Unit 5: Final Evaluation
Students demonstrate mastery through comprehensive assessments.
Lessons include:

• Culminating Project (e.g., Real-World Optimization or 3D Vector Model)
• Final Exam

• 70% of the final grade is based on coursework, including:
  • Calculus and vector problem sets
  • Application tasks and optimization models
  • Curve sketching projects and unit quizzes
  • Discussions on motion, rates of change, and 3D space
• 30% of the final grade is based on final evaluations:
  • 10% Culminating strategic leadership project
  • 20% Final exam on management theory, planning, and leadership practices

All assessments follow Ontario curriculum standards and are designed to build essential analytical, modeling, and theoretical skills required for success in STEM-related postsecondary programs