Subject
Mathematics
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.
Course Lessons
This course is designed for independent study.
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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.
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20 Lessons
4 Lessons
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
4 Lessons
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
4 Lessons
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
3 Lessons
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
5 Lessons
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
