MCV4U - Grade 12 Calculus and Vectors

Grade 12 Calculus and Vectors image
Course Code: MCV4U Course Type: University Preparation Format: Online School Course Prerequisite: MCR3U, Grade 11 Functions Co-requisite: MHF4U, Grade 12 Advanced Functions Tuition Fee (CAD): $549 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
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

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 296 reviews
powered by Google
Anthony Truong image
Anthony Truong
My experience taking an online course from OVS was excellent! Very helpful and friendly teachers who replies quickly to your emails/questions. Would definitely recommend to those who are looking to get their high school credits!
nikki chalhoub image
nikki chalhoub
I took the grade 12 Calculus and Vectors course (MCV4U-06) through Ontario Virtual School. I would 100% recommend taking courses with them because of how amazing the experience was. I took the course during the summertime and was able to work at my own pace. This also allowed me to work ahead or take more time on lessons I was having any difficulties with. The lessons they provided were helpful since they included both lecture style as well as some videos going further into depth. The teacher I had was super helpful and replied to emails right away. She also marked my tests extremely fast, which I was super impressed by! This course is definitely worth taking, whether you just need the credit or want to prepare for university/college. When taking a course like math, it's extremely important to understand how to solve the equations/problems. That's why I would recommend taking them through this school.
Qusay Ali image
Qusay Ali
The ontario virtual school is a very good school because of it’s fast and flexible contact with admins and teachers and they are very helpful thank you ovs
sasha samaroo image
sasha samaroo
Ontario Virtual School provided clear and understanding lessons and also gave me the perfect opportunity to complete my course at a steady pace. Highly recommended
Detective image
Detective
I was initially skeptical of online learning, especially after not being in high school for so long. However I was pleasantly surprised by how well the course delivered its content as I felt the combination of slides, recordings, quizzes, and embedded videos really kept me engaged. The only shortcoming personally was the assigned readings that followed the lessons as I felt it was relatively easy to get distracted in a home environment. I do however believe this is less the fault of the course and more of a personal issue for myself. The quality of the labs and tests were definitely well thought out and I had no issues with them. I'd also like to thank my instructor for being a very helpful during this course, being there to help and answer my questions and even going as far as to let me have the opportunity to redo a lab I had botched.
Mihailo image
Mihailo
My experience with Ontario Virtual High school was great. The lessons were well designed and easy to follow. I liked how I was able to work at my own pace. The teacher I had was very helpful and quickly responded to my emails. Overall this course is very well organized and I would 100% recommend it.