MCV4U - Grade 12 Calculus and Vectors Online

Course Description For MCV4U Grade 12 Calculus and Vectors Online Course
Grade 12 Calculus & Vectors (MCV4U) 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.
MCV4U Course Outline and Timeline
Below is the suggested sequence of course unit delivery as well as the recommended number of hours to complete the respective unit. For complete details of targeted expectations within each unit and activity, please see each Unit Overview found in the MCV4U course profile.
Unit Order | Unit Name | Suggested Time |
---|---|---|
Unit 0 | Prerequisite Review | 10 Hours |
Unit 1 | Rates of Change | 14 Hours |
Unit 2 | Derivatives | 15 Hours |
Unit 3 | Curve Sketching and Optimization | 15 Hours |
Mid Semester Point | ||
Unit 4 | Trig & Exponential Functions | 18 Hours |
Unit 5 | Geometric & Cartesian Vectors | 18 Hours |
Unit 6 | Lines & Planes | 18 Hours |
FINAL | Final Exam | 2 Hours |
View Sample Gradebook Total | 110 Hours |
Please note, as per Ministry guidelines, OVS has a mandatory 14 day minimum requirement for student enrollment to be eligible for a midterm report card and 28 days enrollment to be eligible for a final report card.
Fundamental Concepts Covered in Mathematics Grade 12 Online Course
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.
Online Teaching and Learning Strategies
The mathematical processes are to be integrated into student learning in all areas of this course. Throughout this course, students will:
- Problem Solving – develop, select, apply, compare, and adapt a variety of problem-solving strategies as they pose and solve problems and conduct investigations, to help deepen their mathematical understanding
- Reasoning and Proving – develop and apply reasoning skills (e.g., use of inductive reasoning, deductive reasoning, and counter-examples; construction of proofs) to make mathematical conjectures, assess conjectures, and justify conclusions, and plan and construct organized mathematical arguments;
- Reflecting – demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by assessing the effectiveness of strategies and processes used, by proposing alternative approaches, by judging the reasonableness of results, by verifying solutions)
- Selecting Tools and Computational Strategies – select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems
- Connecting – make connections among mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, current events, art and culture, sports)
- Representing – create a variety of representations of mathematical ideas (e.g., numeric, geometric, algebraic, graphical, pictorial representations; onscreen dynamic representations), connect and compare them, and select and apply the appropriate representations to solve problems
- Communicating – communicate mathematical thinking orally, visually, and in writing, using precise mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions
Assessment & Evaluation
As summarized in Growing Success 2010, the primary purpose of assessment and evaluation is to improve student learning. Information gathered through assessment helps teachers to determine students’ strengths and weaknesses and adapt curriculum and instructional approaches accordingly.
As part of assessment, teachers provide students with descriptive feedback to help guide their learning Evaluation refers to the process of measuring the quality of work against an established criteria, and assigning a value representative of work quality. All curriculum expectations must be accounted for in instruction, but evaluation focuses on students’ achievement of the overall expectations.
A students’ achievement is evaluated in relation to specific expectations. Teachers use their professional judgement to determine which specific expectations should be used to evaluate achievement of overall expectations, and which ones will be covered in instruction and assessment but not used as an evaluation benchmark. To ensure assessment and evaluation are valid and fair teachers use assessment and evaluation strategies that:
- Address both what students learn and how well they learn
- Are based on the achievement level descriptions given in the achievement chart
- Are varied in nature, administered over time, and designed to provide opportunities for students to demonstrate the full range of their learning
- Are appropriate for the learning activities used, the purposes of instruction, and the needs and experiences of the students
- Are fair to all students
- Accommodate students with special education needs, consistent with the strategies outlined in their Individual Education Plan
- Accommodate the needs of students who are learning the language of instruction
- Ensure that each student is given clear directions for improvement
- Promote students’ ability to assess their own learning and to set specific goals
- Include student work samples as evidence their achievement
- Are communicated clearly to students and parents at the beginning of the school year and at other appropriate points throughout the school year.
The achievement chart outlines four categories of knowledge and skills:
- Knowledge and understanding
- Critical thinking
- Communication
- Application
Teachers assess and/or evaluate work in a balanced manner with respect to the four categories. A final grade is recorded, and a credit is granted and recorded for this course if the student’s grade is 50% or higher. The final grade for this course will be determined as follows:
Seventy percent of the grade is based on evaluations conducted throughout the course. This portion of the grade reflects the student’s most consistent level of achievement throughout the course, although special consideration should be given to more recent evidence of achievement.
Thirty percent of the grade is based on a final evaluation and administered towards the end of the course.
Special Accommodations for Students with an IEP
Every single student is capable of success. Some students are able, with certain accommodations, to participate in the regular course curriculum and demonstrate independent learning.
Accommodations allow access to the course without any changes to the knowledge and skills the student is expected to demonstrate. The accommodations required to facilitate the student’s learning are identified by the teacher. Recommendations from a School Board generated Individual Education Plan (IEP) if available can also be consulted. Instruction based on principles of universal design and differentiated make it possible to meet the diverse needs of all learners.
Examples of accommodations (but not limited to) include:
- Adjusting or extending assessment deadlines
- Providing alternative assignments or summative tasks
- Use of scribes and/or other assistive technologies
- Simplifying the language of instruction
Resources
Teachers will bring additional resources and teaching materials that provide a rich and diverse learning environment. Units in this course profile make specific reference to the intended textbook for this course but can be substituted for any relevant and approved text.
- Erdman, Wayne. McGraw-Hill Ryerson Calculus and Vectors 12. Toronto: McGraw-Hill Ryerson, 2008.
- D’Agostino, Santo. McGraw-Hill Ryerson Calculus & Advanced Functions. [Whitby, Ont.]: McGraw-Hill Ryerson, 2002.
- Calculus.org – The Calculus Page. Web.
Ontario Secondary School Diploma (OSSD) Requirements for all course.
Sample Lesson Video: Grade 12 Calculus and Vectors (MCV4U)
Frequently Asked Questions
What is MCV4U?
MCV4U is a Grade 12 Calculus and Vectors course at a University preparation level. MCV4U is a required prerequisite course for most business, mathematics, science and engineering university programs.
What are 4U courses?
4U refers to the Grade level of the courses and the pathway. 4 means it is a grade 12 course and U means it is a university preparation course.
What is the Prerequisite Course for MCV4U?
Prerequisite: Proof of completion or enrollment is MHF4U
Click here for more information on Ontario secondary curriculum and their prerequisites
How Long Does it take to Complete the MCV4U Online Course?
At Ontario Virtual School (OVS) you can complete an online high school credit courses as quickly as 4 weeks, or take as long as 12 months. Self-paced learning is one of the many benefits of the Ontario Virtual School.
Will my Marks be Sent Directly to OUAC or OCAS?
Student & Parent Recommendations
Testimonials for MCV4U - Grade 12 Calculus and Vectors
I took grade 12 Calculus and Vectors and the lesson quality was so much better than you would expect for an online course. I honestly preferred this course to many courses I have taken in-person. The teacher was extremely kind, professional and understanding. No hidden fees. Fast report card processing. Totally love the OVS team and would 10/10 recommend this course. AMAZING!Amy D.L
I took MCV4U from Ontario Virtual School. The teacher and administration were very helpful and responded promptly to all of my concerns. I am very pleased with my experience and the overall structure of the online course.Devon Jarovi
Google Reviews for MCV4U - Grade 12 Calculus and Vectors

