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.
Pre-requisite(s): • Grade 12 Advanced Functions, University preparation (MHF4U-C), must be taken prior to or concurrently with Calculus and Vectors.
Course Syllabus
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
