# MCV4U: Calculus & Vectors

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, rational, exponential, and sinusoidal 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 plan to study mathematics in university and who may choose to pursue careers in fields such as physics and engineering. Note: The new Advanced Functions must be taken concurrently with or must precede Calculus and Vectors.

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, rational, exponential, and sinusoidal 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 plan to study mathematics in university and who may choose to pursue careers in fields such as physics and engineering. Note: The new Advanced Functions must be taken concurrently with or must precede Calculus and Vectors.

Level: University Prep

Credit Value: 1

Course Forum

Welcome to Grade 12 Calculus and Vectors! In this course, you will engage in a broad spectrum of learning opportunities. 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 three-dimensional 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. Throughout this course, you will make connections among mathematical concepts and procedures and relate mathematical ideas to situations or phenomena drawn from real world contexts.

In this course, you will be invited to be an active participant in your learning. You will often be asked to reflect on your learning, and to think about strategies to continue your growth as a learner.

Unit 1: Rates of Change

Lesson 1: Reviewing prerequisite skills

Lesson 2: Determining rates of change

Lesson 3: Determining limits

Lesson 4: Using first principles to determine the equation of a tangent

Unit 2: Derivatives

Lesson 1: Finding derivatives, Part A

Lesson 2: Finding derivatives, Part B

Lesson 3: Solving related rates problems

Lesson 4: Investigating velocity, acceleration, and second derivatives

Unit 3: Curve Sketching

Lesson 1: Exploring the first derivative

Lesson 2: Exploring the second derivative

Lesson 3: Sketching curves Part A

Lesson 4: Sketching curves Part B

Unit 4: Extensions

Lesson1: Solving optimization problems

Lesson 2: Working with sinusoidal functions

Lesson 3: Working with exponential and logarithmic functions

Unit 5: Vectors

Lesson 1: Using geometric vectors

Lesson 2: Investigating Cartesian vectors

Lesson 3: Exploring vectors in 3-space

Lesson 4: Creating equations of vectors

Lesson 5: Investigating lines and planes

# How will I be assessed?

Assessment invites you to actively engage in your learning journey and collaborate within our course community. Throughout the course, various assessment methods will facilitate your learning process.

Self-assessment serves as a valuable tool for fostering self-awareness and aiding in your strategic planning for future learning endeavors. Engaging in self-checks and reflections is crucial as they gauge your comprehension of the material and prepare you for forthcoming tasks.

Peer assessment and discussions enrich the learning experience by fostering dynamic conversations and idea exchanges within the CIL community. Feedback from peers and instructors will further reinforce your grasp of course material and foster connections among classmates.

Assessment opportunities will offer personalized feedback from your instructor, highlighting your strengths, areas for improvement, and guiding your next steps. There are numerous opportunities for you to submit work for a grade and/or feedback in this course. Review specific instructions given by your teacher about each assessment and participate in co-constructing success criteria, where possible.

For each lesson, participate in assessments AS, FOR, and OF learning:

Assessment AS Learning

This part:

• Has to be submitted by the student for feedback but will not be marked
• will be highlighted in GREEN colour
• will include Practice Questions

Assessment FOR Learning

This part:

• Has to be submitted by the student for feedback but will not be marked
• This part will be highlighted in GREY colour
• Will include Self-assessments and Self Reflections

Assessment OF Learning

This part:

• Has to be submitted by the student and will be marked
• It includes Discussions, Quizzes, Projects, Student-teacher Interviews after each unit (Observations and Conversations), Assignments, Labs (for Science courses), Peer Assessments, Culminating Project, Final Exam

The final grade will be determined in accordance with Ministry of Education standards.

 Course Evaluation % Course Work 70% Culminating Project and or Final Test 30%

### Reporting on Demonstrated Learning Skills and Work Habits

There are six categories in which the secondary provincial report cards record learning skills and work habits established by students.

 Learning Skills Sample Behaviours for students Responsibility ·       Fulfill responsibilities and commitments within the learning environment Completes and submits class work, homework, and assignments according to the agreed-upon timelines ·       Take responsibility for and manage own behavior. Organization ·       Devices and follows a plan and process for completing work and tasks ·       Establishes priorities and manages time to complete tasks and achieve goals ·       Identifies, gathers, evaluates, and uses information, technology, and resources to complete tasks. Independent Work ·       Independently monitors, assesses, and revises plans to complete tasks and meet goals ·       Uses class time appropriately to complete tasks; ·       Follows instructions with minimal supervision Collaboration ·       Accepts various roles and an equitable share of work in a group ·       Responds positively to the ideas, opinions, values, and traditions of others ·       Builds healthy peer-to-peer relationships through personal and media-assist interactions ·       Works with others to resolve conflicts and build consensus to achieve goals ·       Share information, resources, and expertise and promote critical thinking to solve problems and make decisions Initiative ·       Looks for and acts on new ideas and opportunities for learning ·       Demonstrates the capacity for innovation and a willingness to take risks

## Course Content

### Course Outline

Unit 1: Rates of Change
Lesson Content
Unit 2 : Derivatives
Lesson Content
Unit 3 : Curve Sketching
Unit 4 : Extensions
Lesson Content
Unit 5 : Vectors
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Not Enrolled

• 21 Lessons
• 20 Quizzes