Course Description
This course builds on students’ previous experience with functions and their developing understanding of rates of change. Students 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. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended for students who choose to pursue careers in fields such as science, engineering, economics, and some areas of business, including those students who will be required to take a university-level calculus, linear algebra, or physics course.
| MCV4U COURSE CONTENT | ||
| Unit # | Unit Name | Time Allocation |
| 1 | Introduction to Calculus - This unit continues on from the Rates of Change unit in Advanced Functions. | 13.5 |
| 2 | Derivatives - This unit will introduce student to shortcuts to taking derivatives, such as the product, quotient and chain rules. | 11.5 |
| 3 | Derivatives and their Applications - second derivatives will be discussed, as well as the real world and graphical applications of derivatives. | 13.5 |
| 4 | Increasing and Decreasing Functions -The concepts of instantaneous rate of change, tangent lines, and first principles will be discussed. | 11.5 |
| 5 | The Derivatives of Exponential Functions - The concept of the derivative function will be worked on and how first principles can be used to develop an equation that models the slope of the tangent. | 8.5 |
| 6 | Introduction to Vectors - Students will be introduced to vectors and various applications, such as the dot and cross product. Various forms of equations of lines and planes will be introduced to the student, and the advantages/disadvantages of each will be discussed. | 12.5 |
| 7 | Vectors as Force Velocity - Students will learn how to determine the nature of intersection between lines and planes in 3D. | 12.5 |
| 8 | Equations in R^2 and R^3 - Students will apply concepts from the previous unit to determine angles between planes, orthogonal solutions, and learn to solve and sketch systems of equations | 17.5 |
| Final Assignment: ISU & Final Exams (2) (30% of final mark) | 9 | |
| Total Hours | 110 |
Resources
- Calculus and Vectors, Nelson (2009)
- Calculus and Vectors 12, McGraw Hill Ryerson (2008)
- Moodle Website
FAQ
What is MCV4U?
MCV4U is a Grade 12 Calculus and Vectors course at a university preparation level.
What is the prerequisite course for MCV4U?
Proof of completion or enrollment of MHF4U
How long does it take to complete the MCV4U online course?
You can complete a grade 12 online high school credit courses as quickly as 4 weeks, or take as long as 5 months.