MCV4U - Grade 12 Calculus and Vectors

Grade 12 Calculus and Vectors image
Course Code: MCV4U Course Type: University Preparation Format: Online School Course Prerequisite: Proof of completion or enrollment is MHF4U Co-requisite: MHF4U, Grade 12 Advanced Functions Tuition Fee (CAD): $574 Demo Lesson

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.

Summary Of Units And Timelines For Grade 12 Calculus and Vectors MCV4U

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 OrderUnit NameSuggested Time
Unit 0Prerequisite Review10 Hours
Unit 1Rates of Change14 Hours
Unit 2Derivatives15 Hours
Unit 3Curve Sketching and Optimization15 Hours
Mid Semester Point
Unit 4Trig & Exponential Functions18 Hours
Unit 5Geometric & Cartesian Vectors18 Hours
Unit 6Lines & Planes18 Hours
FINALFinal Exam2 Hours
View Sample Gradebook Total110 Hours

Please be aware that, as per Ministry guidelines, OVS has a mandatory minimum requirement of 14 days enrollment for students to be eligible for a midterm report card and 28 days enrollment to be eligible for a final report card.

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.

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

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 in their achievement of the curriculum expectations in each course.

This information also serves to guide teachers in adapting curriculum and instructional approaches to students’ needs and in assessing the overall effectiveness of programs and classroom practices. As part of assessment, teachers provide students with descriptive feedback that guides their efforts towards improvement. Evaluation refers to the process of judging the quality of student work on the basis of established criteria, and assigning a value to represent that quality. All curriculum expectations must be accounted for in instruction, but evaluation focuses on students’ achievement of the overall expectations.

A students’ achievement of the overall expectations is evaluated on the basis of his or her achievement of related specific expectations. Teachers will 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 necessarily evaluated. In order to ensure that assessment and evaluation are valid and reliable, and that they lead to the improvement of student learning, teachers must use assessment and evaluation strategies that:

  • Address both what students learn and how well they learn
  • Are based both on the categories of knowledge and skills and on the achievement level descriptions given in the achievement chart
  • Are varied in nature, administered over a period of 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 the use of samples of students’ work that provide evidence of 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. They include; knowledge and understanding, thinking, communication and application. Teachers will ensure that student work is assessed and/or evaluated in a balanced manner with respect to the four categories, and that achievement of particular expectations is considered within the appropriate categories. A final grade is recorded for this course, 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 will be based on evaluations conducted throughout the course. This portion of the grade should reflect 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 will be based on a final evaluation and administered towards the end of the course.

All students can succeed. Some students are able, with certain accommodations, to participate in the regular course curriculum and to demonstrate learning independently. 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 can be identified by the teacher, but 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 instruction focuses on the provision of accommodations to meet the diverse needs of learners.

Examples of accommodations (but not limited to) include:

  • Adjustment and or extension of time required to complete assignments or summative tasks
  • Providing alternative assignments or summative tasks
  • Use of scribes and/or other assistive technologies
  • Simplifying the language of instruction

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.

Reference: Mathematics, The Ontario Curriculum, Grades 11 and 12, 2007 (Revised) Ministry of Education of Ontario

Ontario Secondary School Diploma (OSSD) Requirements for all course.

Sample Lesson Video: Grade 12 Calculus and Vectors (MCV4U)


Frequently Asked Questions

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.

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.

Click here for more information on Course Coding System

Prerequisite: Proof of completion or enrollment is MHF4U

Click here for more information on Ontario secondary curriculum and their prerequisites

At Ontario Virtual School (OVS) you can complete an online highschool credit courses as quickly as 4 weeks, or take as long as 12 months.

Yes, we can send the marks for your online courses directly to OUAC, OCAS, your home, and to your day school.

Student & Parent Recommendations

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

Ontario Virtual School
4.9
Based on 1032 reviews
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Noura Elsabagh
I took MCV4U from the Ontario Virtual School, and it was a very good experience. It was very easy to register for the course online, and you are able to start the course within a week after you’ve registered! There were no extra fees after registering. It was easy for me to access the posted lectures, and assignments, my teacher was very quick to answer any of my questions, and when I completed an assignment or test, she marked it within 24 hours of me completing it. When I reached midterms, report card processing was quick and easy to request. I highly recommend this Virtual school as it was very professional and teachers were very helpful!
Noura Elsabagh image
Noura Elsabagh
I took MCV4U from the Ontario Virtual School, and it was a very good experience. It was very easy to register for the course online, and you are able to start the course within a week after you’ve registered! There were no extra fees after registering. It was easy for me to access the posted lectures, and assignments, my teacher was very quick to answer any of my questions, and when I completed an assignment or test, she marked it within 24 hours of me completing it. When I reached midterms, report card processing was quick and easy to request. I highly recommend this Virtual school as it was very professional and teachers were very helpful!
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Judha
My experience with OVS was very wonderful. I thoroughly enjoyed the course and experienced learning from a wonderful teacher that helped me when I needed it most. My grade 12 math course was well structured and I ended up learning the material well. This org is very good for students picking up credits outside of a typical school. Deadlines are mostly your own with a teacher to help you when you need it. 10/10 Virtual Class Experience.
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Angel Dasilva
I would very much recommend taking a course with OVS. The lessons are simple to understand, while covering everything needed. Teachers and support staff reply withing 24 hours. OVS allows you to take a test when you feel you're ready, which allows students to create a deeper understanding and perform exceptionally. I took Advanced functions with OVS and had a great experience, would recommend! Because of this great experience, I am currently enrolling into calculus at OVS as well.
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Justin Ariburnu
Ontario Virtual school was an amazing experience. They helped me earn a credit and achieve the grade I wanted. The teacher I had for my course (HFA4U) was extremely helpful and made it easy for me to understand the concepts taught in the course as the slideshows were easy to follow. The website was amazing and super easy to navigate through. It even allowed my parents to sign into my account as a "guardian" so they can look at my work and my sure I am on track. The lessons were super easy to follow as the slides shows were interactive and clear making it easy for the viewer to comprehend. There were no hidden fees at any given point during the corosue the expense was the flat fee (purchasing the course.) My work I submitted was always returned very quick and I was provided with feedback to always help me improve for the next assignment. When requesting my midterm and final report card the admin made it super easy as they processed it very quickly and sent it over to my school. Quick and simple! Overall Ontario Virtual School was an amazing experience as the admin and staff are all professionals and made it easy for me to gain my credit while at the same time teaching me a lot as I left the course (HFA4U) with lots of great knowledge.
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Naya Akkad
I took the MHF4U course at OVS, and the lessons were very descriptive and easy to understand. The tests were a good amount of difficulty, and you are given a more than reasonable amount of time to complete them. My teacher marked all my tests and final exam, in no more than a day, and was super helpful with any questions I had. My midterm and final marks were also uploaded to the OUAC in less than 2 days, and was a super easy process! I strongly recommend this course to anyone who's having a bit of trouble with how fast-paced their math class is at their day school, and wants to learn at their own comfortable speed.