Calculus and Vectors, Grade 12, University Preparation (MCV4U)
Course Outline
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.
Prerequisite or Co-requisite: Advanced Functions (MHF4U)
Textbooks:
Geometry and Discrete Mathematics – Addison-Wesley
Calculus: A First Course – McGraw-Hill Ryerson
Topics and Overall Expectations –
Rate of Change
 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
 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
 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
 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
 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
 demonstrate an understanding of vectors in two-space and three-space by representing them algebraically and
geometrically and by recognizing their applications
 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
 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
 represent lines and planes using scalar, vector, and parametric equations, and solve problems involving distances
and intersections
Evaluation –
Report Card
November
January
April Interim
June
Term Work
December Exam
100%
70%
80%
60%
30%
20%
10%
Summative
Evaluation
30%
Total
100%
100%
100%
100%
Term work includes assignments, group work, quizzes and unit tests.
The four categories of Knowledge and Understanding, Inquiry, Communications, and Making Connections encompass the
curriculum expectations of all high school courses. Teaching, assessment, evaluation, feedback and the final grade will
be based on these four categories.
CLASSROOM EXPECTATIONS
ROSEDALE HEIGHTS SCHOOL OF THE ARTS
TEACHER: MS. MA
ROOM:
315
Evaluation and Grading –
Your grades in the class will come from assignments, homework, quizzes, tests and project(s).
Cheating will not be tolerated and will result in a grade of zero.
It is the student’s responsibility to seek assistance from the teacher when help is needed. It is not acceptable
to advise the teacher of difficulty on the day that an evaluation is due/taking place.
Assignments are due at the beginning of the period on the due date. Once the assignments are marked and
returned to students, missed assignments will receive a mark of zero.
If a test is missed, a note must be brought to the teacher on the first day back to school. This note should be
signed by a parent or guardian and should explain the absence and state that the parent or guardian is aware
that a test was missed.
Expectations –
Arrive to class on time and prepared. This means always bringing your textbook, notebook, calculator, pencil,
eraser and ruler with you.
Complete all assigned homework. At minimum, an attempt should be made for every question. Homework
should always be checked with answers in the back of the text. Any questions on the homework will be taken
up the next day.
Notebooks should be kept up-to-date and organized.
If you need help…ask! If you have any questions or concerns, please come and see me to schedule a time
and place we can meet. Before and after school I can usually be found in the Math Office (room 306B)