```CHARLES P. ALLEN HIGH SCHOOL ∞ MATHEMATICS DEPARTMENT ∞
MATH 12 PRECALCULUS COURSE OUTLINE
Teaching Staff 2014 – 2015:
 M. Andrecyk
 J. Murphy
[email protected]
[email protected]
Room 335
Room 332
Prerequisite: Successful completion of Advanced Mathematics 11 and Advanced Mathematics 12 OR
Successful completion of Mathematics 11 and Mathematics 12 AND demonstrated very good to outstanding
performance in relation to the curriculum outcomes prescribed for Mathematics 11 and Mathematics 12
Textbook: Mathematical Modeling , Book 4 (Thomson Nelson 2002)
Course Outline:
Sequences and Series
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Functions - a new Perspective
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Assessment: 25%
Combine functions using addition, subtraction, and/or multiplication. Interpret and analyze
these combined functions and use their graphs to solve problems.
Apply transformations to functions
Find the equations of combined functions from graphs
Solve polynomial equations and inequalities
Form, interpret, and analyze composite functions. Use graphs of composite functions to solve problems.
Interpret slope to find average and instantaneous rate of change
Find the slope of the tangent to a graph at a point using a derivative
Compare the graph of a function to the corresponding graph of the slope of the tangent
Find the equation of a polynomial function from given points and/or intercepts
Use the power rule to find the derivative of a polynomial function
Sketch the graph of polynomial functions using intercepts and critical points
Solve maximum/minimum problems using a derivative
Functions, Part II
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Assessment: 20%
Demonstrate an understanding of recursive formulas
Represent sequences graphically
Develop, analyze and apply procedures to describe sequences algebraically
Develop, analyze and apply procedures to evaluate the sums of series
Develop proofs of mathematical statements using mathematical induction
Demonstrate an understanding of the concept of limit in the context of sequences and series
Demonstrate an understanding of the concepts of convergence and divergence
Apply convergence in a variety of contexts
Demonstrate an understanding of how to find the area of a region under a curve
Assessment: 25%
Plot the graphs of the functions in the transformational form and use these functions to model real-world phenomena.
Identify the zeros, the vertical, horizontal, and oblique asymptotes, and the points of discontinuity of rational functions, and sketch the
graphs of these functions.
Simplify rational expressions and complex fractions
Solve problems that involve rational equations
Analyze the effect of taking the square root of polynomial and rational functions, plot the graphs of irrational functions, and use these
functions to model real world phenomena.
Analyze the effect of taking the absolute value of polynomial, rational, and irrational functions, determine the domain and range of
these absolute-value functions, and plot their graphs.
Analyze and plot the graphs of piecewise functions.
Review exponential and logarithmic functions and use these functions to model real-world phenomena.
Determine the value of e, plot the graph of ex, and use this natural exponential function to model real-world phenomena.
Analyze and plot the graph of y = ln x, and use this natural logarithmic function to model real-world phenomena.
Solve inequalities involving rational expressions and absolute values.
Trigonometry
 Express angle measures in terms of arc length
 Model periodic behaviour and solve problems using periodic functions
 Identify equivalent trigonometric relations
 Describe transformations of periodic functions to model situations
 Combine trigonometric functions to create models
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Use matrix multiplication to rotate images
Prove trigonometric identities
Solve trigonometric equations
Identify the graphs of the reciprocal trigonometric functions
Use reciprocal and inverse trigonometric functions and their graphs to solve problems
Complex Numbers
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Assessment: 25%
Assessment: 5%
Explain the connections between real numbers and complex numbers
Represent complex numbers in a variety of ways
Construct and examine graphs in the complex and polar planes
Develop and evaluate mathematical arguments and proofs
Apply operations on complex numbers in both rectangular and polar forms
Translate between polar and rectangular representations, and investigate the relationships in the operations using graphs
Apply De Moivre's Theorem
Assessment:
Mathematics courses require commitment and students must take responsibility for achieving the outcomes. Students need to make sure that
they keep up with the work and seek help early if they encounter difficulties before they become insurmountable. Extra help is available at lunch
hour.
Unit assessments will consist of multiple opportunities for a student to demonstrate their understanding of the outcomes. Such opportunities
include (but are not limited to) tests, quizzes, in-class assignments, portfolios, comprehension questions, and projects. Teachers will employ both
formative and summative assessments in gathering information to determine a student grade. No one method of assessment will be worth more
than 50% of the unit.
Throughout the semester, students may feel that they have not successfully demonstrated their understanding of particular outcomes and would
like another opportunity to demonstrate that they now “Get It”. Please refer to the “I Get It” document on teacher/school website for more
details. As per HRSB Assessment Policy; grades will be derived from a student’s most recent assessment.
Students are NOT permitted to exempt the final exam.
Final Assessment:
80% Course Outline
20% Final Exam
Continuous School Improvement (CSI):
Literacy Goal:
Students will develop their critical thinking skills.
Math Goal: Students will develop their mathematical critical thinking skills with a focus on improving achievement on Analysis questions (formerly
called level three questions).
Levels of cognitive demand include Knowledge, Application and Analysis. Analysis, a level 3 question, is one in which students have the necessary
skills/tools to solve a problem which is unfamiliar. This requires higher order thinking skills and problem solving techniques. Throughout the course
of this year, as part of our CSI goal, teachers in the math department will expose their students to these types of problems and give them strategies
that will help refine their critical thinking skills.
Communication of Student Achievement:
A collaborative effort of all stakeholders (student / parent/ teacher) is important to ensure student academic success. In an effort to maintain
communications, a number of avenues are available.
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Class Web sites are updated daily
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Marks and attendance can be checked at any time on the Parent/ Student Portal of Powerschool. (If you do not have a password for the
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The Auto-dialer calls home regarding unexcused absences and upcoming events.
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Parents and students are encouraged to contact the teacher via email if they have any concerns regarding academic progress.
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Important dates include:
o Curriculum night:
September 16, 2014
o Parent/teacher interviews:
November 17 , 2014
o “ I Get It” / multiple opportunity testing:
Jan 6 - 16, 2015
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