Mathematics

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

Grade: 12

Type: University Preparation

Language of Study: English

Prerequisites: MHF4U

This course builds on your previous experience with functions and your developing understanding of rates of change. You will solve problems involving geometric and algebraic representations of vectors and representations of lines and planes in three-dimensional space; broaden your 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.

You will also refine your use of the mathematical processes necessary for success in senior mathematics. This course prepares you for careers in fields such as science, engineering, economics, and some areas of business. It will prepare you for university-level calculus, linear algebra, or physics courses.

Grade: 12

Type: University Preparation

Language of Study: English

Prerequisites: MHF4U

This course builds on your previous experience with functions and your developing understanding of rates of change. You will solve problems involving geometric and algebraic representations of vectors and representations of lines and planes in three-dimensional space; broaden your 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.

You will also refine your use of the mathematical processes necessary for success in senior mathematics. This course prepares you for careers in fields such as science, engineering, economics, and some areas of business. It will prepare you for university-level calculus, linear algebra, or physics courses.

Course Lessons

This course is designed for independent study.

TVO Learn supports families and educators with curriculum-aligned resources, some
of which are being upgraded for content and accessibility. Thank you for your patience.

This course is designed for independent study. To review the lessons, please visit this page with a computer or tablet.

20 Lessons

4 Lessons

1.1 Reviewing prerequisite skills

1.2 Determining rates of change

1.3 Determining limits

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

Course 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

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

Course Lessons

Unit 1 : Rates of change 4 Lessons .chain-link{fill:#3d4649;} .icon-circle{fill:#e6e6e6;}

1.1 Reviewing prerequisite skills 1.1 Reviewing prerequisite skills

1.2 Determining rates of change 1.2 Determining rates of change

1.3 Determining limits 1.3 Determining limits

1.4 Using first principles to determine the equation of a tangent 1.4 Using first principles to determine the equation of a tangent

Unit 2 : Derivatives 4 Lessons .chain-link{fill:#3d4649;} .icon-circle{fill:#e6e6e6;}

2.1 Finding derivatives (part A) 2.1 Finding derivatives (part A)

2.2 Finding derivatives (part B) 2.2 Finding derivatives (part B)

2.3 Solving related rates problems 2.3 Solving related rates problems

2.4 Investigating velocity, acceleration and second derivatives 2.4 Investigating velocity, acceleration and second derivatives

Unit 3 : Curve Sketching 4 Lessons .chain-link{fill:#3d4649;} .icon-circle{fill:#e6e6e6;}

3.1 Exploring the first derivative 3.1 Exploring the first derivative

3.2 Exploring the second derivative 3.2 Exploring the second derivative

3.3 Sketching curves part A 3.3 Sketching curves part A

3.4 Sketching curves part B 3.4 Sketching curves part B

Unit 4 : Extensions 3 Lessons .chain-link{fill:#3d4649;} .icon-circle{fill:#e6e6e6;}

4.1 Solving optimization problems 4.1 Solving optimization problems

4.2 Working with sinusoidal functions 4.2 Working with sinusoidal functions

4.3 Working with exponential and logarithmic functions 4.3 Working with exponential and logarithmic functions

Unit 5 : Vectors 5 Lessons .chain-link{fill:#3d4649;} .icon-circle{fill:#e6e6e6;}

5.1 Using geometric vectors 5.1 Using geometric vectors

5.2 Investigating Cartesian vectors 5.2 Investigating Cartesian vectors

5.3 Exploring vectors in 3-space 5.3 Exploring vectors in 3-space

5.4 Creating equations of vectors 5.4 Creating equations of vectors

5.5 Investigating lines and planes 5.5 Investigating lines and planes

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