MCV4U

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Calculus and Vectors, Grade 12, University Preparation
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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.

Unit 1:
Introduction to Calculus

This unit begins with students developing a better understanding of these essential concepts. Students will then deal with rates of change problems and the limit concept. 

Unit 2:
Derivatives

This unit begins by examining those rules including: the power rule, the product rule, the quotient rule and the chain rule followed by a study of the derivatives of composite functions.

Unit 3: Derivatives of Exponential, Logarithmic&Trigonometric Functions 

In this unit, students will learn about the rates of change of exponents and Logarithms. Students will cover derivatives of exponential functions and its applications. 

Unit 4:
Curve Sketching 

This unit will help you understand the fundamentals of using calculus to help us sketch curves, and solve some basic optimization problems. 

Unit 5: Derivative Applications and Related Rates 

In this unit, will explore about how to calculate Implicit and Logarithmic differentiation, sketch the velocity-time and acceleration-time graph, and solve related real world problems.

Unit 6:
Introduction to Vectors 

In this unit, students will learn to define a vector as a quantity with both magnitude and direction; distinguish between a scalar quantity and vector quantity; 

Unit 7: 
Vector Applications 

Applications involving work and torque are used to introduce and lend context to the dot and cross products of Cartesian vectors. The vector and scalar projections of Cartesian vectors are written in terms of the dot product. 

Unit 8: Lines in Three-Space 

 A variety of types of problems exist in this unit and are generally grouped into the following categories: Pythagorean Theorem Problems, Volume Problems, Trough Problems, Shadow problems and General Rate Problems. 

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