# MCV4U Calculus and Vectors Grade 12 University Preparation

```MATHEMATICS DEPARTMENT
Course Code: MCV4U
Course Name: Calculus and Vectors
Instructor:
Period:
Room Number:
Course Overview:
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.
Connection to our Catholic Faith:
Specific
Strands
of to
Study
Expectations
include:
Students
will apply
Catholic values
pose andand
solve problems,
to make logical
decisions, and to become critical thinkers who share their
abilities for the benefit of all in their classroom and school community. A supportive mathematics classroom provides a caring and
sensitive environment where the dignity and value of all students is respected and affirmed as they grow in confidence in their
mathematical abilities. Mathematical investigations will promote a respect for God’s creation and an understanding of the need to use
resources wisely. A student will become self-directed, responsible and life-long learner in the mathematics classroom.
Specific Strands of Study and Expectations include:
Rate of Change:
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.
Derivatives and Their Applications:
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.
Geometry and Algebra of Vectors:
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.
Efforts will be made to meet the individual learning needs of students in order to ensure
these expectations are being met.
Course Breakdown
Resources: The course will use a variety of resources including video, CD-
to ensure
these
Chapter
1:
Introduction to Calculus
Chapter 2:
Chapter 3:
Chapter 4:
Chapter 5:
Chapter 6:
Chapter 7:
Chapter 8:
Chapter 9:
Derivatives
Derivatives and Their Applications
Curve Sketching
Derivatives of Exponential And
Trigonometric Functions
An Introduction to Vectors
Applications of Vectors
Equations of Lines and Planes
Relationships between Points,
Lines and Planes
ROM, Internet Applications and a variety of print sources. The textbook,
Nelson, Calculus and Vectors, will be distributed to students during the first
week of the course. The text and all other resources assigned to students are
the responsibility of the student. Any damage incurred will result in payment
for replacement (\$90.00).
Evaluation Structure:
Knowledge/Understanding
30 %
Application
30 %
Communication
20 %
Thinking
20 %
The above is reflected both in the term work (worth 70% of the final mark) and
the Final Exam (30%).
Evaluation Policy Students will be assessed & evaluated according to the work produced & skills displayed. Methods of providing
feedback will include assessing work in process & evaluating completed assignments, tests, co-operative learning activities, simulations
and presentations. Peer & self-evaluations will also be utilized. Student marks will be determined by evaluating process & product
according to 4 categories & 4 levels. Please see the chart below for specific skills and key words used to determine student competency
in the different categories.
Level
Level 1:
Level 2:
Level 3:
Level 4:
Category
50-59%
60-69%
70-79%
80-100%
Knowledge/Understanding
-Limited display
-Some success
-Considerable
-Thorough
of
knowledge,
in
displaying
display
of
understanding of
 Knowledge of facts & terms
skills
and
ability
knowledge,
knowledge
skills
concepts and
 Understanding of concepts & relationships
to
apply
skills
and
and
ability
to
apply
ability to
Thinking/Inquiry
concepts
application
of
concepts
communicate,
 Critical thinking skills
concepts
think creatively
 Creative thinking skills
and apply concepts
 Inquiry Skills
Communication
 Communication of ideas and information
 Use of symbols & visuals
 Oral & written communication
Application
 Applications in familiar contexts
 Transfer of concepts to new contexts
 Making logical conclusions and predictions
 Use of technology
 Making connections
Feedback will also be provided for student learning skills. Skills such as responsibility, organization, independent work, collaboration, initiative and self
regulation are assessed independently student achievement and will be conducted through the use of a rubric indicating specific criteria to be
E –Excellent
G – Good
S – Satisfactory
N - Needs Improvement
Other Evaluation Issues




LATE ASSIGNMENTS. Assignments submitted after the Primary Due Date established by the teacher will be accepted with a penalty
of 5% off for the first day late and 2% for subsequent days to a maximum of 10%. This four day Penalty Zone is the maximum time
allowed for submissions. The fourth day after the assignment is due is considered the Closure Date upon which no further
assignments will be accepted. If the teacher returns the marked assignments within the four day penalty zone, the date of return is
considered the closure date. Repeated lateness in submissions indicates poor organization skills and will result in parental contact
and will be reflected in the learning skills section of the report card.
INCOMPLETE ASSSIGNMENTS Assignments will be graded according to the extent with which they meet the criteria established in
the rubric or evaluation structure.
MISSED TESTS Tests missed with a legitimate reason will be written within a few days of the student returning from the absence.
Student eligibility to write the test and the date of writing will be at the discretion of the teacher in consultation with the