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Subject Mathematics

Course name: Calculus and Vectors Course code: (MCV4U)

Grade: 12
Type: University Preparation
Course description: This resource builds on Learners` previous experience with functions and their developing understanding of rates of change. Learners will solve problems involving geometric and algebraic representations of vectors and representations of lines and planes in three- dimensional space; broaden their understanding of rates of change to include the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions; and apply these concepts and skills to the modelling of real-world relationships. Learners will also refine their use of the mathematical processes necessary for success in senior mathematics. This resource is intended for Learners who choose to pursue careers in fields such as science, engineering, economics, and some areas of business, including those Learners who will be required to take a university-level calculus, linear algebra, or physics resource.
Grade: 12
Type: University Preparation
Prerequisites: None
Course description: This resource builds on Learners` previous experience with functions and their developing understanding of rates of change. Learners will solve problems involving geometric and algebraic representations of vectors and representations of lines and planes in three- dimensional space; broaden their understanding of rates of change to include the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions; and apply these concepts and skills to the modelling of real-world relationships. Learners will also refine their use of the mathematical processes necessary for success in senior mathematics. This resource is intended for Learners who choose to pursue careers in fields such as science, engineering, economics, and some areas of business, including those Learners who will be required to take a university-level calculus, linear algebra, or physics resource.
announcement

These learning resources support both Teacher led instruction and independent study.

For independent study, Learners may engage in active notebook reflection whenever prompted to participate in Discussions, Partner Activities, or Quizzes. No assignments can be submitted to TVO for grading or credit.

Educators may refer to the For Teachers page for extra information.

announcement

These learning resources support both Teacher led instruction and independent study.

For independent study, Learners may engage in active notebook reflection whenever prompted to participate in Discussions, Partner Activities, or Quizzes. No assignments can be submitted to TVO for grading or credit.

Educators may refer to the For Teachers page for extra information.

20 Lessons

4 Lessons

1.1   Reviewing prerequisite skills

1.2   Determining rates of change

1.3   Determining limits

1.4   Using first principles to determine the equation of a tangent

4 Lessons

2.1   Finding derivatives (part A)

2.2   Finding derivatives (part B)

2.3   Solving related rates problems

2.4   Investigating velocity, acceleration and second derivatives

4 Lessons

3.1   Exploring the first derivative

3.2   Exploring the second derivative

3.3   Sketching curves: Part A

3.4   Sketching curves: Part B

3 Lessons

4.1   Solving optimization problems

4.2   Working with sinusoidal functions

4.3   Working with exponential and logarithmic functions

5 Lessons

5.1   Using geometric vectors

5.2   Investigating Cartesian vectors

5.3   Exploring vectors in 3-space

5.4   Creating equations of vectors

5.5   Investigating lines and planes