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.
Prerequisite: Advanced Functions (MHF4U) must be taken prior to or concurrently with Calculus and Vectors (MCV4U).
Course Outline
| Unit | Unit Name | Unit Description | Time Allocated |
|---|---|---|---|
| 1 | Geometry and Algebra of Vectors | Students work with vectors in 2D and 3D, including operations, magnitude, direction, and applications to geometry and physics. | 21 Hours |
| 2 | Equations of Lines and Planes | Students represent and analyze lines and planes using vector, parametric, and Cartesian equations, including intersections, angles, and distances. | 20 Hours |
| — | Midterm Exam | Assessment of Units 1–2. | 2 Hours |
| 3 | Rates of Change | Students explore average and instantaneous rates of change and develop an introduction to limits and derivatives. | 20 Hours |
| 4 | Derivatives and Applications | Students apply differentiation rules to polynomial, rational, exponential, and trigonometric functions, including motion, optimization, and related rates. | 25 Hours |
| 5 | Curve Sketching | Students use first and second derivatives to analyze function behaviour, including intervals, concavity, inflection points, asymptotes, and intercepts. | 20 Hours |
| — | Final Exam | Assessment of all course content. | 2 Hours |
| Total Instructional Time | 110 Hours | ||
Overall Curriculum Expectations
By the end of this course, students will have explored the following topics and learning expectations:
A. Geometry and Algebra of Vectors
A1. Introduction to Vectors
A2. Operations with Geometric Vectors
A3. Algebraic (Cartesian) Vectors
A4. Dot Product
A5. Cross Product
A6. Properties of Vectors
A7. Applications of Vector
A8. Practice Test
B. Equations of Lines and Planes
B1. Equations of Lines in 2-Space
B2. Equations of Lines in 3-Space
B3. Vector and Parametric Equations of a Plane
B4. Scalar Equation of a Plane
B5. Investigation of the Intersection of Planes
B6. Intersections of Lines and Planes
B7. Unit Review
C. Rates of Change
C1. Rates of Change
C2. Slope and Limits
C3. Maximums and Minimums
C4. Graphs of the Derivative
C5. Derivatives
C6. Practice Test
D. Derivatives and Their Applications
D1. Graphing Derivatives of Exponential Functions
D2. Special Exponential Function
D3. Applications
D4. Graphing of Derivatives
D5. Trig Functions
D6. Practice Test
E. Curve Sketching
E1. Characteristics of a Function given its Derivative
E2. Graphs of Functions and their Derivatives
E3. Transformations and Graphs of Derivative Functions
E4. Concavity, Points of Inflection and Rate of Change of the Dependent Variable
E5. Inflection Points and the Second Derivative
E6. Sketching Graphs of Polynomial and Rational Functions
E7. Applications of Curve Sketching
E8. Unit Review
Teaching and Learning Strategies
Students will engage in a variety of learning activities designed to develop knowledge, skills, critical thinking, communication, and problem-solving.
Multimedia Lessons: Videos, presentations, examples, practice questions, simulations, quizzes, and other digital resources support different learning styles.
Teacher–Student Discussions: Video conferencing, discussions, and instructor demonstrations provide opportunities to ask questions, clarify concepts, and receive feedback.
Discussion Forums: Students share ideas, explain concepts, and provide constructive peer feedback.
Reflection: Students connect course concepts to real-world situations, personal experiences, and prior learning.
Individual Activities and Assessments: Students complete assignments and practice activities at their own pace to reinforce and demonstrate learning. Teachers provide ongoing written and verbal feedback.
Visual Learning: Diagrams, graphics, charts, and tables help students organize information, identify relationships, and interpret data.
Practice Problems: Students apply concepts and skills to mathematical and real-world problems to strengthen understanding and problem-solving.
Design and Application Projects: Students apply their learning to practical problems and develop solutions using research, critical thinking, and problem-solving skills.
Assessment Strategies
Students will be provided with numerous and varied opportunities to demonstrate the full extent of their achievement of the curriculum expectations, across all four categories of the Achievement Chart.
Progress will be monitored on an ongoing basis using a variety of assessment tools, including written work, formal testing, quizzes, teacher-student communication, discussion boards, and chat rooms.
Assessment Activities
- Discussion Forums
- Tests and Quizzes
- Reflections
- Graphing, Plotting, and Data Analysis
- Problem-Solving Calculations
- Lab Reports
- Simulation, Lab, and Case Study Worksheets
- Research Projects and Reports
- Design Projects and Reports
- End-of-Unit Conversations (Google Meet)
Final Grade
The final grade will be determined as follows (in accordance with Ministry of Education standards):
| Component | Percentage |
|---|---|
|
Term Work Based on evaluations conducted throughout the course. |
65% |
|
Final Evaluation A final evaluation in the form of a written exam. |
25% |
| Attendance and Participation | 10% |
Final Examination Breakdown
25% written exam.
Attendance Policy
Regular attendance and active engagement are important for student success. Attendance and participation are monitored through the school’s Learning Management System (LMS).
All online credit courses at ICE are designed to meet or exceed the minimum 110 hours of instructional time required for a credit course.
Online instructional time and engagement are monitored through:
LMS Engagement: Students are expected to log in regularly and actively participate in online learning activities. LMS activity records are used to monitor engagement.
Biweekly Check-Ins: Students complete a brief check-in every two weeks to review their progress and engagement. Additional support may be provided when concerns are identified.
Post-Unit Quizzes: Short formative quizzes are completed at the end of each unit to monitor student progress and pacing.
Discussion Forums: Students participate in required unit discussions and peer activities. Participation is monitored based on completion and engagement.
Instructional Records: The school maintains records of instructional time, attendance, and student engagement.
Students are responsible for maintaining regular participation and completing required learning activities within the course schedule.
Evaluation Model – 10% Total Attendance and Engagement Weight
| Component | Weight | Quantifiable Metric | Criteria |
|---|---|---|---|
| Biweekly Check-In | 3% | Completed every two weeks | Students complete the required check-in within the scheduled time frame. |
| Post-Unit Formative Quiz | 4% | Completed after each unit | Students complete the formative quiz by the assigned deadline. |
| Discussion Forum Participation | 3% | Required posts and responses | Students submit the required original response and complete assigned peer responses. |
Considerations for Program Planning
Planning Programs for Students with Special Education Needs
Students are supported through Universal Design for Learning, differentiated instruction, and accommodations identified in their IEPs. The asynchronous format provides flexibility through extended time, breaks, assistive technology, and opportunities to review lessons and examples as needed.
Program Considerations for English Language Learners
ELL students are supported through clear instructional language, visual and multimedia resources, opportunities to review lessons, additional time where appropriate, and teacher feedback. Bilingual dictionaries may be permitted when appropriate.
Environmental Education
Environmental education is integrated through mathematical applications involving real-world data, including resource use, climate trends, and population growth. The online format also supports paperless learning.
Equity and Inclusive Education
Learning materials and assessments reflect diverse perspectives and experiences. Students participate in a respectful, inclusive, and supportive online learning environment.
Financial Literacy Education
Students apply mathematics to financial situations such as budgeting, saving, interest, taxes, credit, and comparing costs to support informed financial decisions.
First Nations, Métis, and Inuit Education
Where appropriate to course expectations, students explore Indigenous perspectives, histories, cultures, contributions, and contemporary issues using accurate and respectful resources.
The Role of Information and Communications Technology
ICT supports asynchronous instruction, assessment, communication, and mathematical learning. Students use digital tools such as calculators, spreadsheets, graphing tools, simulations, and other mathematical technologies to collect, analyze, represent, and communicate information. Digital citizenship, academic integrity, and responsible technology use are emphasized.
Career Education
Students develop problem-solving, reasoning, quantitative, and technology skills applicable to careers in mathematics, technology, engineering, finance, data analysis, skilled trades, and related fields.
Cooperative Education and Experiential Learning
Where appropriate, students may connect mathematical learning to workplace experiences, job-shadowing, cooperative education, and other experiential learning opportunities.
Health and Safety
Students are encouraged to maintain healthy online learning practices, including proper ergonomics, balanced screen time, regular breaks, and strategies that support well-being. A safe and respectful virtual learning environment is maintained.
Accommodations
Accommodations are provided based on IEPs and appropriate educational documentation. These may include step-by-step instructions, additional time, assistive technology, alternative response formats, planning organizers, advance access to materials, and enrichment opportunities.
Course Materials – MCV4U
Required Textbooks and Resources
Mathematics textbooks covering vectors, equations of lines and planes, rates of change, derivatives, curve sketching, and applications of calculus.
Supplementary resources such as online tutorials, instructional videos, interactive graphing tools, and problem-solving guides related to calculus and vectors.
Teacher-provided worksheets, practice problems, investigations, and problem-based learning tasks.
Digital Resources and Software
Google Drive – storing, sharing, and submitting assignments and assessments.
Internet access for research, graphing tools, and mathematical reference resources.
Microsoft Office Suite (Word, Excel, PowerPoint) or equivalent software for written solutions, data tables, graphs, and presentations.
Graphing technology (e.g., Desmos, GeoGebra, or graphing calculators) for visualization and analysis.
Teacher Considerations
Assistive technology (text-to-speech, speech-to-text, screen readers) may be used to support diverse learning needs.
Flexibility in submission formats (Google Docs, PDFs, spreadsheets, slides, or handwritten work submitted digitally).
Guided notes, worked examples, and scaffolded instruction to support understanding of complex calculus and vector concepts.
Tips for Success – MCV4U
Welcome to MCV4U: Grade 12 Calculus and Vectors – University Preparation!
Check announcements and course messages daily to stay updated on lessons, assignments, and deadlines.
Stay Organized
Review the course calendar regularly and complete all assignments, problem sets, and quizzes on time.
Carefully read instructions and rubrics; use checklists to ensure all steps, calculations, and representations are correct.
Engage Actively
Participate in discussions, problem-solving activities, and collaborative work to deepen understanding of vectors, derivatives, and calculus applications.
Ask for Help
For technical issues, contact the Help Desk.
For course-related questions, email your teacher; expect a response within 24 hours. Mark emails as “URGENT” if needed.
Key Elements to Success
Time Commitment: Plan for 1–2 hours of focused study each day, plus additional time for problem-solving and practice exercises.
Communication: Maintain regular contact with your teacher for guidance, clarification, and feedback.
Engagement: Stay curious, persistent, and attentive. Active participation and practice are essential for mastering complex calculus and vector concepts.
Remember
This course is designed to help you understand how calculus and vector concepts are applied to real-world problems in science, engineering, and technology. Approach all activities thoughtfully and accurately while developing critical thinking, problem-solving, and analytical skills.
