MATHEMATICS
Notre Dame Catholic Secondary School
Course Code: MCV4U1
Course Name: Calculus and Vectors
Level:
Grade 12, University
Prerequisite: Grade 12 Advanced Functions, MHF4U1, University
must be taken prior to or concurrently with Calculus and Vectors.
The Ontario Curriculum Grades 11 and 12, 2007
3.0 y
2.0
1.0
-p -p/2
-1.0
-2.0
-3.0
x
p/2 p 3p/2
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 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.
Note: The new Advanced Functions course (MHF4U) must be taken prior to or concurrently with
THE
OVERALL
SPECIFIC EXPECTATIONS INCLUDE:
Calculus
and VectorsAND
(MCV4U).
A. RATE OF CHANGE
1. Demonstrate an understanding of rate of change.
2. Graph the derivatives of polynomial, sinusoidal, and exponential functions.
3. Verify graphically and algebraically the rules for determining derivatives.
B. 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.
C. 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.
4. Represent lines and planes using scalar, vector, and parametric equations, and solve problems
involving distances and intersections.
Resources:
Course Breakdown
Chapter
Chapter
Chapter
Chapter
Chapter
1
2
3
4
5
Chapter
Chapter
Chapter
Chapter
6
7
8
9
-
Introduction to Calculus
Derivatives
Derivatives and their Applications
Curve Sketching
Derivatives of Exponential and
Trigonometric Functions
- An Introduction to Vectors
– Applications on Vectors
– Equations of Lines and Planes
- Relationships between Points,
Lines and Planes
The course will use a variety of resources including
video, CD-ROM, Internet Applications and a variety
of print sources. The Nelson’s textbook, 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. Replacement cost for the
text is $100.
Evaluation Structure:
Knowledge/Understanding
30 %
Thinking
20 %
Communication
20 %
Application
30 %
The above is reflected both in the term work (worth
70% of the final mark) and the summative work
(worth 30% of the final mark). Summative work
consists of a 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
Category
Knowledge/Understanding
Knowledge of facts & terms
Understanding of concepts & relationships
•
•
Thinking/Inquiry
Critical thinking skills
Creative thinking skills
Inquiry Skills
•
•
•
Communication
Communication of ideas and information
Use of symbols & visuals
Oral & written communication
•
•
•
Level 1:
50-59%
Level 2:
60-69%
Level 3:
70-79%
Level 4:
80-100%
-Limited
display of
knowledge,
skills and
ability to
apply
concepts
-Some
success in
displaying
knowledge,
skills and
application
of concepts
-Considerable
display of
knowledge
skills and
ability to apply
concepts
-Thorough
understanding
of concepts
and ability to
communicate,
think
creatively and
apply concepts
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 like working independently, team work, organization,
work habits and homework, and initiative are assessed independently student achievement and will be conducted through
the use of a rubric indicating specific criteria to be achieved to receive each of the following letter grades:
E –Excellent
G – Good
S – Satisfactory
N - Needs Improvement
Other Evaluation Issues
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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 department head.
Plagiarism in any form reflects academic dishonesty and will result in a mark of zero for the assignment in question.