MCV4U - Grade 12 Calculus and Vectors (Upgrade)

Grade 12 Calculus and Vectors (Upgrade) image
Course Code: MCV4U Course Type: University Preparation Format: Online School Course Prerequisite: Documentation showing you have successfully passed this course before Tuition Fee (CAD): $549 Demo Lesson

Course Description For MCV4U Grade 12 Calculus and Vectors (Upgrade) 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 (Upgrade) 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 Change15 Hours
Unit 2Derivatives15 Hours
Unit 3Curve Sketching and Optimization15 Hours
Mid Semester Point
Unit 4Trig & Exponential Functions20 Hours
Unit 5Geometric & Cartesian Vectors20 Hours
Unit 6Lines & Planes20 Hours
FINALFinal Exam2 Hours
Total117 Hours

Please be aware that, as per Ministry guidelines, OVS has a mandatory minimum requirement of 11 days enrollment for students to be eligible for a midterm report card and 21 days enrollment to be eligible for a final report card in repeat/upgrade courses.

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 (Upgrade) (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: Documentation showing you have successfully passed this course before

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.

Student & Parent Recommendations

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

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

Ontario Virtual School
4.9
Based on 296 reviews
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Austin Sung
I had a hard trouble catching up with the coursework at my day school because I had a really mean teacher. This is when I decided to take my courses online. I was really happy with the supportive teachers and ended up with an excellent mark!
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Lisa Marie Dugec
I was having difficulty at school with my time management of schoolwork and my responsibilities outside of school such as sports. My mom and I decided to switch to online schooling through this program and I was able to finish courses with even higher averages because the time I could study and do tests was very flexible. You can go at your own pace and the teachers offer a lot of help, and reply to you very quickly with the best answers to any of your questions. I highly recommend doing your schooling through Ontario Virtual School, I recommended it to my friend and she is doing great in her functions course as well! I’d recommend it to any athletes or anyone that has certain responsibilities outside of school because you can accommodate it to your schedule, and you have a longer time period to finish the course!
AN – 12EA – Jean Augustine SS (2612) image
AN – 12EA – Jean Augustine SS (2612)
OVS was a great experience. I was able to work at my own pace, so I was not rushing to complete assignments, and the teachers replied quickly and gave constructive feedback! Being able to work freely, anywhere, and anytime made my hefty workload a little more manageable. I would 10/10 recommend.
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Alex Taylor
I have taken several courses through OVS and each time it has been a very positive experience. The teachers and administrative support staff are always very quick to respond to any emails. The courses themselves are of the highest quality and the site is very user-friendly. I highly recommend OVS to anyone considering taking courses online.
Vivek B image
Vivek B
Was very satisfied with my experience on OVS as I learned a lot more at my own pace than having the pressure of learning in school. A huge thanks to my teacher for having my tests marked on time and marking accurately.
Kurtis George-Wegner image
Kurtis George-Wegner
My Ontario Virtual School Experience was fantastic! My teacher was very knowledgeable on the subject as one would expect and was always willing to help out. The marking was extremely fast and I usually had my results the same day I submitted them! I would highly recommend the Ontario Virtual School as a great place to upgrade a mark or to finish a high school diploma. Overall great job!!