MATHEMATICS
Notre Dame Catholic Secondary School
Course Code: MCR3U1-05
Course Name: Functions
Level:
Grade 11, University Preparation
Prerequisite:
Principles of Mathematics, Grade 10
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The Ontario Curriculum Grades 11 and 12, 2007
Course Overview:
This course introduces some financial applications of mathematics, extends students’ experience
with functions and introduces second-degree relations. Students will solve problems in personal
finance involving application of sequences and series; investigate properties and applications of
trigonometric functions; develop facility in operating with polynomials, rational expressions and
exponential expressions, develop an understanding of inverses and transformations of functions; and
develop facility in using function notation and in communicating mathematical reasoning. Students
will also investigate loci and the properties and applications of conics.
THE OVERALL AND SPECIFIC EXPECTATIONS INCLUDE:
CHARACTERISTICS OF FUNCTIONS
• demonstrate an understanding of functions, their representations, and their inverses, and make connections between the algebraic
and graphical representations of functions using transformations;
• determine the zeros and the maximum or minimum of a quadratic function, and solve problems involving quadratic functions,
including problems arising from real-world applications;
• demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions.
EXPONENTIAL FUNCTIONS
• evaluate powers with rational exponents, simplify expressions containing exponents, and describe properties of exponential
functions represented in a variety of ways;
• identify and represent exponential functions, and solve problems involving exponential functions, including problems arising from
real-world applications.
TRIGONOMETRIC FUNCTIONS
• determine the values of the trigonometric ratios for angles less than 360o; prove simple trigonometric identities; and
solve problems using the primary trigonometric ratios, the sine law, and the cosine law;
• demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the
numeric, graphical, and algebraic representations of sinusoidal functions;
• identify and represent sinusoidal functions, and solve problems involving sinusoidal functions, including problems
arising from real-world applications.
DISCRETE FUNCTIONS
• demonstrate an understanding of recursive sequences, represent recursive sequences in a variety of ways, and make
connections to Pascal’s triangle;
• demonstrate an understanding of the relationships involved in arithmetic and geometric sequences and series, and
solve related problems;
• make connections between sequences, series, and financial applications, and solve problems involving
compound interest and ordinary annuities.
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INVESTIGATING LOCI AND CONICS
1. Representing loci
Course Breakdown
Resources:
Chapter 1 – Introduction to Functions
Chapter 2 – Equivalent Algebraic Expressions
Chapter 3 – Quadratic Functions
Chapter 4 – Exponential Functions
Chapter 5 – Trigonometric Ratios
Chapter 6 – Sinusoidal Functions
Chapter 7 – Discrete Functions:
Sequences and Series
Chapter 8 – Discrete Functions:
Financial Applications
The course will use a variety of resources including
video, CD-ROM, Internet Applications and a variety of
print sources. The textbook, Functions 11, 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 $100.00.
Evaluation Structure::
Knowledge/Understanding
Thinking/Inquiry
Communication
Application
30
20
20
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 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
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.
CULMINATING ACTIVITIES These activities will be due toward the end of the course. They are valued between 5 and 15 per cent of the
final mark and will reflect course material and competencies not otherwise reflected on the final exam.
Plagiarism in any form reflects academic dishonesty and will result in a mark of zero for the assignment in question.