Calculus and Vectors – MCV4U

Description

This Grade 12 university preparation course builds on students’ experience with functions and rates of change. Students develop differential-calculus concepts, solve problems involving derivatives and optimization, and study geometric and Cartesian vectors, lines and planes in three-dimensional space. The course is intended for students pursuing university programs requiring calculus, linear algebra or physics.

What You’ll Learn

• Analyze average and instantaneous rates of change and develop the concept of the derivative.
• Differentiate polynomial, sinusoidal, exponential, rational and radical functions as appropriate to the course.
• Use derivatives to analyze curve behaviour and solve optimization and modelling problems.
• Work with geometric vectors and operations in two and three dimensions.
• Use Cartesian vectors to solve problems involving vector equations and relationships.
• Represent and analyze lines and planes in three-dimensional space.

Skills You’ll Develop

• Calculus and derivative techniques
• Rates of change and optimization
• Geometric and Cartesian vectors
• Three-dimensional analytic geometry
• Advanced problem solving, modelling and mathematical communication

Learning Outcomes

• Demonstrate understanding of rate of change and derivative concepts.
• Determine derivatives and use them to analyze functions and solve problems.
• Apply derivatives to curve sketching, optimization and real-world modelling.
• Perform operations with geometric and Cartesian vectors.
• Solve problems involving dot products, projections and vector relationships as addressed in the course.
• Represent and analyze lines and planes in three-dimensional space.
• Use mathematical processes to reason, justify, model and communicate solutions.