# Course Information

## Calculus and Vectors - MCV4U

ILC Course Code: MCV4U-B

Grade 12, University Preparation, 1.0 credit

**Prerequisites**

Advanced Functions (MHF4U-C)

**Course Description**

In this course, you will build 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 threedimensional 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.

**Online Submission**

Online submission of course work is required for this course using *Microsoft Word* © or *OpenOffice Writer*.

**Unit 1: Rates of change and derivatives (Part A)**

Lesson 1: Rates of change

Lesson 2: Limits

**Unit 2: Rates of change and derivatives (Part B)**

Lesson 3: Introduction to curve sketching

Lesson 4: Derivatives

Lesson 5: The rules of derivatives

**Unit 3: Exploring derivatives (Part A)**

Lesson 6: Exponential functions and their derivatives

Lesson 7: Derivatives of sinusoidal, radical, and rational functions

Lesson 8: The second derivative: A graphical look

**Unit 4: Exploring derivatives (Part B)**

Lesson 9: Curve sketching: Polynomial functions

Lesson 10: Curve sketching: Rational functions

**Unit 5: Applying derivatives and introduction to vectors**

Lesson 11: Real-world applications of derivatives

Lesson 12: Optimization Problems

Lesson 13: Introduction to vectors

Lesson 14: Three-dimensional vectors and operations on vectors

Lesson 15: Properties of vectors and scalar multiplication

**Unit 6: Lines and planes (Part A)**

Lesson 16: Dot product and cross product of two vectors

Lesson 17: Applications of vector multiplication

**Unit 7: Lines and planes (Part B)**

Lesson 18: Lines and planes

Lesson 19: Scalar, vector, and parametric equations

Lesson 20: Intersections of lines and planes in 3-space

#### This is the English version of the course.

Click here to view the French version of the course.