ADE Schools 

Grade 12 Calculus and Vectors Course Outline


School Name: ADE Schools

Department: Department of Mathematics

Curriculum policy document: The Ontario Curriculum, Grade 11 and 12, Mathematics, 2007(Revised)

Course Development Date: August 6, 2007
Course Developer:     Department of Mathematics
Course Revision Date: August 30, 2010
Course Title: Calculus and Vectors  
Course Type: University Preparation
Course Level: Grade 12
Course Code: MCV4U
Credit Value: 1.0
Duration: 110 hours
Prerequisite: Functions, Grade 11, University Preparation, or

Mathematics for College Technology, Grade 12,

College Preparation

Course Origin: This course is developed at the ADE Schools departments of Mathematics from the Ontario curriculum document:  “Ontario curriculum, mathematics Grades 11 and 12, 2000. 2007 (revised).”

Course Rationale and Description: 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 modeling 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.

Prerequisite: Functions, Grade 11, University Preparation, or Mathematics for College

Technology, Grade 12, College Preparation


The course consists of three strands, rate of change, derivatives and their applications and geometry and algebra of vectors.


Overall Expectations

By the end of this course, students will:

 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.

 4. Demonstrate an understanding of solving polynomial and simple rational inequalities.




By the end of this course, students will:

 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.



By the end of this course, students will:

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.

 Course Content:

This course is clustered into four units of study relating directly to the four strands of the curriculum document. These units, sequenced in the order they are to be delivered are as follows:

Unit 1: Rate Of Change 38_ hours

Unit 2: Derivatives and their Applications 34_ hours

Unit 3: Geometry and Algebra Of Vectors 38_ hours

Total Hours 110 hours


Teaching and Learning Strategies and Tools

Because the course the nature of the teaching strategies of the course is electronic delivery, media for conveying learning will be either synchronous or asynchronous. Academy of Distance Education is dedicated to maximize possibility of establishing “comfort zone” for students while opportunities for learning successfully are continuously explored. For that reason, both of the mediums of electronic delivery mentioned above are equally utilized as per the need and suitability of each one in different situations.

Examples E- Teaching/ E-Learning Strategies in the course/courses:


  • Lectures/handouts/note taking (through on-line vehicles both synchronously and asynchronously)

  • Case Studies (both synchronously and asynchronously)

  • Brainstorming (in virtual class discussions as well as in face book or other social sites used for the purpose of e-learning and e-teaching)

  • Writing (research, essays, poems)

  • Homework, class work, assignments

  • Labs and demonstrations (mainly computer simulations to accommodate distance learning)


  • Small/large group discussions (virtual classes or one-on-one virtual situations)

  • Multimedia presentations (all on-line)

  • Guest speeches


    Teaching/Learning Tools: (all designed to meet the requirements of e-schooling

  • Textbook

  • Overhead projector, screen, electronic writing devices like the electronic pen pad and transparencies

  • Online software, CDs, DVDs, videos/films 

  • Chart paper,

  • Posters

  • Online educational activities and games

  • Relevant scientific sites & magazines & articles


    Assessment & Evaluation;

    Assessment and evaluation at the ADE Schools is based heavily on dividing the assessment strategies equally between comprehensive, on-site and supervised assessments and assessments conducted by the student alone and sent electronically or through other means by the student. The latter will include instances where the student does access-controlled on-line testing and quizzing where possibilities of extra-personal efforts are eliminated completely making sure that the student does the work. Other opportunities will allow for students meeting assessment requirements while seeking help from any source but making sure knowledge has been gained by the student through the help provided to him/her. All these systems are designed the benefits of e-learning and e-teaching are maximized and not diminished by factors that could be brought forth by the introduction of non-traditional classrooms.

    In general, Assessment is a continuous process of gathering evidence to facilitate and enhance student learning, provide feedback, and improve instructional strategies. Evaluation is the process of judging the quality of student work in an assessment, on the basis of established criteria, and the assigning of a value to represent that quality. The purpose of evaluation is to summarize student progress at a given point in time.


    In the 2010/2011 and beyond, Numerous and varied assessment opportunities will be given to students and various strategies and tools will be employed throughout the course in order to achieve maximum precision and fairness in assessing how well students learned the curricular expectations of each strand and the course. This will be an attempt meet ministry of education guidelines introduced for the 2010 and effective successive years until further notice of change.   Diagnostic assessments will be used to determine prior learning, students’ strengths and for planning purposes and therefore will not be used to determine term or final grades for report cards.Formative assessments will be used regularly as a learning tool and feedback mechanism to improve student learning and instructional strategies. Summative assessments will be used to provide final professional judgment and evaluation of student learning of curricular expectations and therefore will be used to evaluate term work and the final assessment for reporting purposes. When planning assessments, the curricular expectations will be reviewed and linked to the achievement categories to which they relate. This is to ensure that all the expectations are accounted for in instruction, and that achievement of the expectations is assessed within the appropriate categories. All three types of assessments are still further regrouped into three parts:assessment for learning, feedback mechanisms meant to enhance student learning (formative and diagnostic); assessment as learning, self assessment and  peer assessment tools done led and /or teachers in which students learn how to independently assess the level of their own learning (diagnostic , formative)’ and assessment of learning (summative only), which is led by the teacher alone and is used for purposes of evaluation and reporting of student achievement to parents and other stake holders.


    Assessment Methods: The means through which student learning may be assessed (i.e., written, spoken, or done). In this course, students will use all three methods to demonstrate their learning: oral work (debates, discussions, presentations, skits), written work (tests, quizzes, reports, essays), and performances (labs, models, pamphlets, charts). Both synchronous and asynchronous opportunities are made available.


    Assessment Strategies: The actual assessment instruments used as the  process used for assessing student learning and the level of their achievement of meeting curricular expectations (e.g. journal). ADE will use conduct assessments both synchronously and asynchronously throughout the course. Below is a list of the most commonly used assessment strategies for this course: 

  • Tests/Quizzes (done both on-line and a designated site with supervision)

  • Interviews/Conferences  (Virtual class discussions)

  • Examinations (done only comprehensively at a site with supervision)

  • Multimedia Presentations (virtual class presentation synchronously

  • Assignments, Research Projects/Reports (on-line)

    Assessment Tools: An instrument that is used to initiate or guide the assessment strategy or to track, monitor or record the assessment data (e.g. rubric). Below is a list of the most commonly used assessment tools for this course:


  • Check lists (learning skills, homework check, completion of a task, basically to check absence or presence of a concept, process, skill, or attitude)

  • Marking Scheme (tests/quizzes, assignments, worksheets, to quantify student response; value based tasks)

  • Rating Scales (to assess frequency of achieving a task or quality of task)

  • Rubrics  (performances, written reports, presentations, labs, complex projects/tasks)

  • Anecdotal Comments (learning skills, group work, independent work, presentations,


    Two parts make up the evaluation of student achievement through the different assessment strategies mentioned above.

    a)      The term work accounts for 70% of the overall grade for the course. Assessment for this portion is spread through out the course up until six weeks before the end of the study term.

    b)      The final evaluation will account for 30% of the final overall grade for the course.  Its assessment takes place during the last 6 weeks of the study term and will in the form of a final examination more than two thirds of which comes from material covered after November 15, 2008.


    Breakdown of the 70% course evaluation among the units

    This unit’s work will account for 25% of the 70 marks for coursework.

    Unit 1: RATE OF CHANGE

    Tests                                    15%

    Quizzes                                10%

    Assignments                         5%

    Total Unit 1 Evaluation       25%

    This unit’s work will account for 25% of the 70 marks for coursework.


    Tests                                  15%

    Quizzes                              10%

    Assignments                       5%


    Total Unit 2 Evaluation      25%

    This unit’s work will account for 25% of the 70 marks for coursework.


    Tests                                  15%

    Quizzes                              10%

    Assignments                       5%
    Total Unit 3 Evaluation      25%

    This unit’s work will account for 25% of the 70 marks for coursework.

    The final assessment covers what students have been learning the length of the course with more emphasis on the more recent parts.  It will be managed within the last 6 Weeks in full course (through the year) and the last three weeks in half credit course (Sept. to Jan.) and accounts for 30% of the overall grades that will appear in the “final” box of the report card.  The final evaluation will be administered as follows:

    Final Examination                                                                                                     20%

    Performance task                                                                                                     10%

    Total for final evaluation                                                                                          30%

    Overall Grade mark                                                                                   70+30 = 100%

    Main Resources:

    Main Textbook:  Calculus and Vectors, grade 12, University Preparation (MCV4U).

1.     Internet

2.     Ottawa Public Library

3.     Carleton University 

4.     Ottawa University