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MCV4U-A  Calculus and Vectors

Course Code: MCV4U-A

Grade 12, University Preparation, 1.0 credit

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.


Ordering by Unit

Course units can be purchased individually.

Unit 1: Lessons 1-5

Lesson 1:
Rates of Change
Lesson 2:
Lesson 3:
Intervals of Increase and Decrease
Lesson 4:
Derivative of a Polynomial Function
Lesson 5:
Properties of the Derivative

Unit 2: Lessons 6-10

Lesson 6:
Exploring Exponential Functions and Their Derivatives
Lesson 7:
The Derivatives of Sinusoidal and Rational Functions
Lesson 8:
The Second Derivative: A Graphical Look
Lesson 9:
Applications of the Derivative: Key Features of a Polynomial Function
Lesson 10:
Sketching Functions

Unit 3: Lessons 11-15

Lesson 11:
Real-Life Applications
Lesson 12:
Optimization Problems
Lesson 13:
Introduction to Vectors
Lesson 14:
Vectors in Three-Space, Addition and Subtraction
Lesson 15:
Properties of Vectors and Scalar Multiplication

Unit 4: Lessons 16-20

Lesson 16:
The Dot and Cross Product of Two Vectors
Lesson 17:
Properties and Applications of Dot and Cross Products
Lesson 18:
Lines and Planes Using Linear Equations
Lesson 19:
Lines and Planes Using Scalar, Vector, and Parametric Equations
Lesson 20:
This course has no additional items.
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