- 1. Demonstrate an understanding of rate of change by making connections between average rate of change over an interval and instantaneous rate of change at a point, using the slopes of secants and tangents and the concept of the limit.
- 2. Graph the derivatives of polynomial, sinusoidal, and exponential functions, and make connections between the numeric, graphical, and algebraic representations of a function and its derivative.
- 3. Verify graphically and algebraically the rules for determining derivatives; apply these rules to determine the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions, and simple combinations of functions; and solve related problems.
MCV4U | Grade 12 Calculus & Vectors Course | OSSD Credit Online
Prerequisite: MHF4U which must be taken prior to or concurrently
Ontario Ministry of Education Inspected Private School BSID #882250
Recognized by Canadian and Global Universities.
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Course Enrollments
Course Details
- Course Title: Calculus and Vectors
- Grade Level: 12
- Ministry Course Code: MCV4U
- Course Type: Academic
- Credit Value: 1.0 Credit
- Prerequisite: Advanced Functions (MHF4U), which must be taken prior to or concurrently
- Curriculum Policy Document: Mathematics, The Ontario Curriculum, Grades 11 and 12, 2007 (Revised)
Course Description
This Grade 12 Calculus and Vectors (MCV4U) course prepares students for success in university programs and careers in engineering, science, business, and mathematics. Following the Ontario Curriculum standards, it offers a deep exploration of key mathematical concepts, including rates of change, derivatives, and vector geometry in two- and three-dimensional spaces.
Students will develop problem-solving skills as they learn to represent and analyze real-world relationships through polynomial, sinusoidal, exponential, and rational functions. The course fosters critical thinking by introducing vector applications in fields like physics and engineering, enabling students to model systems involving velocity, forces, and displacement.
Skills gained in this course translate directly to real-world applications. For example, mastering derivatives can help students optimize business processes, predict trends in economics, and analyze scientific data. Understanding vectors equips learners to design and troubleshoot in physics and engineering contexts.
MCV4U is ideal for students aiming to build a strong foundation in mathematics while enhancing analytical abilities critical for STEM fields. By completing this course, students gain not only the academic credit but also practical, transferable skills that prepare them for academic excellence and career readiness.
Outline of Course Content
| Unit | Unit Description | Time Frame |
|---|---|---|
| 1. |
Rates of Change In this unit, students will notice a shift in content as we move from the vectors portion of the course to the calculus portion. Students will be introduced to the idea of a rate of change. This is one of the most important concepts needed to understand calculus and will be used often throughout the course. |
36 hrs |
| 2. |
Derivatives & Their Applications In this unit, students will be introduced to one of the most fundamental operations in the study of calculus – the derivative! Understanding the derivative will require the use of the understandings students developed throughout the first unit. A concrete understanding of the derivative is necessary to understand the remaining units in this course. |
36 hrs |
| 3. |
Geometry & Algebra of Vectors In this unit, students will be studying a quantity known as a vector. It is simply your typical line segment with a direction, but what is surprising is the number of applications that make use of it. For example, in the field of physics there is position, displacement, velocity, acceleration, forces, momentum, fields, and so on. Students will look at some vector applications and solve related problems both geometrically and algebraically by performing operations on vectors. |
35 hrs |
| 4. | Culminating Project | 1 hr |
| 5. | Final Exam | 2 hrs |
| Total | 110 hrs | |
Resources
While the course does not include physical textbooks, students will have access to:
- Interactive digital tools and learning modules.
- The “Nelson Calculus and Vectors 12” eTextbook.
- Supplementary problem sets and visual aids to support independent and guided learning.
Overall Curriculum Expectation
Rate of Change
Derivatives & Their Applications
- 1. Make connections, graphically and algebraically, between the key features of a function and its first and second derivatives, and use the connections in curve sketching.
- 2. Solve problems, including optimization problems, that require the use of the concepts and procedures associated with the derivative, including problems arising from real-world applications and involving the development of mathematical models.
Geometry & Algebra of Vectors
- 1. Demonstrate an understanding of vectors in two-space and three-space by representing them algebraically and geometrically and by recognizing their applications.
- 2. Perform operations on vectors in two-space and three-space, and use the properties of these operations to solve problems, including those arising from real-world applications.
- 3. Distinguish between the geometric representations of a single linear equation or a system of two linear equations in two-space and three-space, and determine different geometric configurations of lines and planes in three-space.
- 4. Represent lines and planes using scalar, vector, and parametric equations, and solve problems involving distances and intersections.
Teaching and Learning Strategies
At Canadian Virtual School (CVS), our teaching approach is designed to engage students in meaningful, interactive, and skill-building learning experiences. This course empowers students to master their skills through a variety of dynamic assignments and creative projects, all tailored to align with Ontario’s curriculum standards.
Key Strategies Include:
Diverse Assignments for Holistic Skill Development: Students undertake a wide array of tasks, including descriptive and personal writing, oral presentations, opinion pieces, multi-genre projects, and formal essays. These assignments encourage various modalities such as speaking, presenting, creative representation (e.g., visual art, poetry, music), and structured academic writing.
Mastering Note-Taking Techniques: Students explore different note-taking strategies to determine the most effective method for analyzing novels, short stories, and poetry. This skill ensures their ability to synthesize and retain critical information across texts.
Video Analysis for Presentation Skills: Students view curated video presentations to critique delivery techniques, identifying strengths and weaknesses. These insights help students refine their own oral presentation skills for maximum impact.
Interactive and Scaffolding Tools for Writing Excellence:
- Teaching videos on literary devices, MLA formatting, and personal essay analysis provide foundational knowledge.
- Interactive tools and quizzes challenge students to apply their learning while deepening their understanding of course material.
- Longer writing assignments are broken into manageable steps, allowing students to work through the entire writing process. With teacher feedback at every stage, students improve both their content and writing style.
Engaging Multimedia Resources:
- Oral readings accompany poetry and prose excerpts, enhancing the auditory appreciation of literature.
- Interactive videos guide students through self-directed learning, with built-in assessments to check comprehension and progress.
Critical Reading and Discussions: Reading Guides for novels encourage deep engagement, prompting students to ask thoughtful questions, interpret texts critically, and consider multiple perspectives. Close readings of texts are further supported by interactive discussion posts and one-on-one communication with teachers, allowing for personalized feedback and collaboration.
Frequent Self-Assessment: Students reflect on their learning journey at the end of each unit, identifying areas for growth and setting actionable goals for future improvement.
Real-Time Feedback and Support: Throughout the course, students receive continuous feedback from certified teachers, ensuring a personalized learning experience that adapts to individual needs.
At CVS, we prioritize building confident, independent learners who are equipped with the skills needed to excel academically and beyond. By leveraging a blend of innovative teaching techniques and interactive tools, students are empowered to take charge of their learning while staying connected to expert guidance.
Assessment and Evaluation
At Canadian Virtual School (CVS), our approach to assessment and evaluation is rooted in the Ministry of Education’s Growing Success document, ensuring that students receive a fair, transparent, and meaningful evaluation process that supports their individual learning journey. Our philosophy prioritizes the best interests of students by designing assessments that not only measure achievement but also actively promote growth, understanding, and self-reflection.
Our Key Principles:
Multiple Pathways to Show Learning: We believe in creating diverse and inclusive assessments that allow students to demonstrate their knowledge, skills, and understanding in ways that align with their strengths. Whether through written assignments, oral presentations, multimedia projects, or creative expressions, CVS assessments provide varied opportunities for success.
Gradual Release of Responsibility: Assessments at CVS are designed to empower students to take ownership of their learning. Through guided practice, feedback, and reflection, students gradually build the confidence and skills needed to succeed independently in their evaluations.
Feedback-Driven Growth: Detailed and actionable feedback is a cornerstone of our assessment process. By providing regular insights into student performance, we help them reflect on their strengths, address areas for improvement, and refine their strategies for success.
Alignment with Growing Success: The Growing Success framework defines seven core principles for effective assessment and evaluation. These principles guide our practices to ensure that every assessment is:
- are fair, transparent, and equitable for all students;
- support all students, including those with special education needs, those who are learning the language of instruction (English or French), and those who are First Nation, Métis, or Inuit;
- are carefully planned to relate to the curriculum expectations and learning goals and, as much as possible, to the interests, learning styles and preferences, needs, and experiences of all students;
- are communicated clearly to students and parents at the beginning of the course and at other points throughout the school year or course;
- are ongoing, varied in nature, and administered over a period of time to provide multiple opportunities for students to demonstrate the full range of their learning;
- provide ongoing descriptive feedback that is clear, specific, meaningful, and timely to support improved learning and achievement;
- develop students’ self-assessment skills to enable them to assess their own learning, set specific goals, and plan next steps for their learning.
At CVS, we view assessment not as a final judgment of performance but as an ongoing process that supports learning and growth. By integrating innovative evaluation techniques with the principles outlined in Growing Success, we ensure that students are prepared not only for academic success but also for lifelong learning.
Final Grade
At Canadian Virtual School (CVS), the evaluation process is designed to accurately reflect each student’s mastery of curriculum expectations and essential skills for effective learning. The final grade represents the quality and consistency of a student’s overall achievement throughout the course and aligns with the achievement chart provided by the Ontario Ministry of Education.
Credit Requirements:
A credit for this course will be granted if the student achieves a final grade of 50% or higher. The grade reflects the student’s demonstrated knowledge, skills, and understanding of the course expectations.
Grade Breakdown:
70% Ongoing Assessment:
This portion of the grade is based on evaluations conducted throughout the course. It reflects the student’s most consistent level of achievement, with special consideration given to more recent evidence of learning. Students will engage in a variety of assignments, quizzes, and activities that demonstrate their progress across multiple competencies.30% Final Evaluation:
This portion of the grade is determined by a comprehensive final evaluation administered at the end of the course. The final evaluation may take the form of:- A final exam
- A culminating task
- A combination of both an exam and a culminating task
At CVS, we are committed to ensuring that assessments are not only fair and transparent but also empower students to showcase their knowledge and skills in meaningful ways. By combining consistent, ongoing evaluations with a final summative assessment, we provide a holistic view of each student’s growth and achievement throughout their learning journey.
Report Card
At Canadian Virtual School (CVS), we are committed to keeping students and parents informed about academic progress through formal and detailed report cards. These report cards provide a comprehensive view of student achievement and offer actionable insights for continuous improvement.
Report Card Delivery:
- Report cards are issued twice during the course: once at the midterm and again upon course completion.
- Students will receive their report cards directly via email.
Key Features of the Report Card:
Academic Achievement:
- Curriculum expectations are evaluated and reported as a percentage grade, reflecting the student’s overall performance in the course.
- The course median is also reported to provide context for the student’s performance relative to the class.
- Teachers include personalized comments highlighting the student’s strengths, areas for improvement, and actionable next steps for continued success.
Learning Skills and Work Habits:
- Learning skills such as responsibility, collaboration, and initiative are assessed and reported as a letter grade (E – Excellent, G – Good, S – Satisfactory, N – Needs Improvement). These grades represent one of four levels of accomplishment and provide valuable feedback on the student’s approach to learning.
Credit Completion:
- Upon course completion, the report card will indicate whether the student has earned an Ontario Secondary School Diploma (OSSD) credit for the course.
Official Transcript Management:
- For students attending school in Ontario, a copy of the final report card will be sent to the student’s main school. The school will then add the completed course to the student’s official Ontario Student Transcript (OST).
At CVS, our report cards go beyond grades. They serve as a vital tool for reflection, growth, and achievement, ensuring students and their families have a clear understanding of their academic progress and accomplishments.
Considerations
At Canadian Virtual School (CVS), our teachers carefully design programs that reflect the highest standards of education, aligning with the Ontario Ministry of Education’s policies and the following initiatives.
Below are five reimagined focus areas where CVS stands out, delivering a transformative online education experience tailored to meet diverse student needs.
Fostering Diversity and Belonging
At CVS, we embrace the unique backgrounds and experiences of every student to create an inclusive and equitable learning environment. Our approach includes:
- Embedding diverse perspectives and voices into our curriculum to reflect the multicultural world we live in.
- Ensuring every student has access to the resources and opportunities needed to succeed, regardless of background.
- Addressing global and societal issues through critical discussions and assignments, empowering students to advocate for fairness and equity.
By celebrating diversity and promoting belonging, CVS equips students with the tools to contribute meaningfully to their communities and the world.
Building Foundational Academic and Life Skills
At CVS, we focus on developing essential literacy, numeracy, and inquiry skills that serve as the foundation for academic and personal success. Key initiatives include:
- Integrating reading, writing, and numeracy exercises across all subjects to build critical thinking and analytical abilities.
- Encouraging real-world applications of knowledge, such as problem-solving and data analysis.
- Promoting inquiry-based learning, where students ask questions, research answers, and engage with multiple viewpoints.
Our goal is to prepare students with the skills they need to navigate both academic and real-world challenges confidently.
Developing Critical and Analytical Mindsets
At CVS, we empower students to become thoughtful, independent thinkers who can navigate a complex and fast-paced world. Our focus includes:
- Teaching students to critically evaluate information, from traditional texts to modern media, to identify bias, credibility, and intent.
- Fostering discussions and debates on societal and global issues to help students develop well-rounded perspectives.
- Encouraging students to tackle complex problems through innovative thinking and data-driven analysis.
This emphasis on critical and analytical skills ensures that students leave CVS ready to make informed decisions and solve meaningful problems.
Advancing Digital Competencies for a Tech-Driven World
As an online school, CVS prioritizes teaching students the skills they need to thrive in an increasingly digital world. This includes:
- Utilizing cutting-edge platforms and tools, such as Moodle and multimedia resources, to deliver interactive and engaging content.
- Equipping students with digital literacy skills, including responsible technology use and effective online communication.
- Offering personalized online support and collaboration opportunities through virtual forums and teacher feedback.
CVS ensures students graduate with the tech skills necessary to succeed in higher education and their future careers.
Preparing Students for Academic and Career Success
At CVS, we connect classroom learning to real-world goals by helping students identify their strengths, interests, and aspirations. Our efforts include:
- Guiding students to set achievable academic and career goals that align with their skills and passions.
- Providing resources and tools to explore diverse career paths and post-secondary opportunities.
- Helping students develop leadership, communication, and organizational skills that are valuable for any profession.
Through personalized planning and support, CVS ensures students are prepared not just for academic success but also for thriving careers and fulfilling lives.
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Tip: Add a Fast Track course to your cart by selecting the Fast Track toggle on any course page.
How Does It Work?
At Canadian Virtual School, we recognize that no two learners are the same. That’s why students at VHS get to choose when and where to study, when to submit assignments, and when to write their final exams. With certified teachers, interactive course content, free online tutoring, dedicated student support teams, and an outstanding administrative staff, we stay focused on meeting the needs of each student to deliver the best in online secondary education.
Frequently Asked Questions
What is MCV4U, and who is it for?
MCV4U, or Grade 12 Calculus and Vectors, is an advanced academic course designed for students aiming to pursue university programs in fields such as engineering, science, mathematics, or business. It is essential for students needing a strong foundation in calculus for their academic and career paths.
How is the course delivered, and what resources will I need?
The ENG4U course is delivered through our interactive Learning Management System (LMS), offering engaging modules and assessments. Students will need a reliable internet connection and a device like a laptop or tablet. All materials are provided digitally, ensuring seamless access to course content.
How will I be assessed, and will I receive an OSSD credit?
Assessment is based on a combination of ongoing evaluations (70%) and a final exam or project (30%). Students who achieve a grade of 50% or higher will receive an official OSSD credit, and a report card will be sent to their primary school (if applicable) for transcript inclusion.
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