Advanced Functions, Grade 12, University Preparation (MHF4U). Credit value: ...
Students will investigate the properties of polynomial, rational, logarithmic, and ...
Advanced Functions, Grade 12, University Preparation (MHF4U) Credit value: Prerequisite:
1.0 Credits Functions, Grade 11, University Preparation (MCR3U)
Teachers:
Trevor Armstrong
[email protected] http://tpsMHF4U.wikispaces.com
Steve Kinnear
[email protected] http://tpsadvancedfunctions12.wikispaces.com
Textbook:
Advanced Functions 12. W. Erdman et. al. McGraw-Hill Ryerson, 2008.
Course Description: This course extends students’ experience with functions. Students will investigate the properties of polynomial, rational, logarithmic, and trigonometric functions; develop techniques for combining functions; broaden their understanding of rates of change; and develop facility in applying these concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended both for students taking the Calculus and Vectors course as a prerequisite for a university program and for those wishing to consolidate their understanding of mathematics before proceeding to any one of a variety of university programs. Overall Expectations: A. Exponential and Logarithmic Functions demonstrate an understanding of the relationship between exponential expressions and logarithmic expressions, evaluate logarithms, and apply the laws of logarithms to simplify numeric expressions; identify and describe some key features of the graphs of logarithmic functions, make connections among the numeric, graphical, and algebraic representations of logarithmic functions, and solve related problems graphically; solve exponential and simple logarithmic equations in one variable algebraically, including those in problems arising from real-world applications. B. Trigonometric Functions demonstrate an understanding of the meaning and application of radian measure; make connections between trigonometric ratios and the graphical and algebraic representations of the corresponding trigonometric functions and between trigonometric functions and their reciprocals, and use these connections to solve problems; solve problems involving trigonometric equations and prove trigonometric identities. C. Polynomial and Rational Functions identify and describe some key features of polynomial functions, and make connections between the numeric, graphical, and algebraic representations of polynomial functions; identify and describe some key features of the graphs of rational functions, and represent rational functions graphically; solve problems involving polynomial and simple rational equations graphically and algebraically; demonstrate an understanding of solving polynomial and simple rational inequalities. D. Characteristics of Functions demonstrate an understanding of average and instantaneous rate of change, and determine, numerically and graphically, and interpret the average rate of change of a function over a given interval and the instantaneous rate of change of a function at a given point; determine functions that result from the addition, subtraction, multiplication, and division of two functions and from the composition of two functions, describe some properties of the resulting functions, and solve related problems; compare the characteristics of functions, and solve problems by modeling and reasoning with functions, including problems with solutions that are not accessible by standard algebraic techniques.
Evaluation:
Your Final Mark will include:
70% 30%
Course Work (assignments, quizzes, and tests) Final Exam
Your Course Work and Final Exam will each reflect four categories: 35% 30% 20% 15%
Knowledge/Understanding Application Thinking Communication
Unit
Time
Polynomial Functions Students investigate the properties of polynomial functions including x-intercepts and end behaviour. They extend their knowledge of factoring to include the factor theorem and remainder theorem. They solve polynomial inequalities and communicate their results algebraically and graphically. Students also investigate and make connections between average and instantaneous rates of change and solve related problems. They determine the slopes of secants and tangents from the equations and graphs of functions. They graph combinations of functions and solve related problems.
30 h
Rational Functions Students investigate rational functions as combinations of functions. They make connections between the algebraic and graphical representations of rational functions including horizontal and vertical asymptotes. They solve problems and inequalities involving rational equations and communicate their results algebraically and graphically. Students also determine the slopes of secants and tangents and solve related problems.
25 h
Trigonometric Functions Students work with angles in radian measure to graph the primary and reciprocal trigonometric functions and use the trigonometric ratios to determine angles. They explore and apply compound angle formulas, solve trigonometric equations, and prove trigonometric identities. They pose and solve problems based on applications involving trigonometric functions. Students also make connections between trigonometric functions and compositions of functions.
30 h
Exponential and Logarithmic Functions Students develop an understanding of the relationship between logarithms and exponents, evaluate logarithmic expressions, and make connections between the laws of exponents and the laws of logarithms. They graph logarithmic functions and apply transformations to the graphs. They pose and solve problems based on applications involving exponential and logarithmic functions. Students also make connections between exponential/logarithmic functions and compositions of functions.
25 h
Total
110 h
Required Materials:
Textbook, binder, paper, pencil, eraser, ruler, scientific calculator, ¼ inch graph paper.
Extra Help:
Extra help is available Monday to Friday 9:00–9:55 AM and after school by appointment.
ACADEMIC DUE DATE POLICY All assignments and projects will have a due date. The due date is the beginning of the period for that given class. For example if a project is due for the period one class it must be submitted at 10:00 AM, if it is due for the period four class on a Wednesday, then it is due at 2:49 PM. The due date represents the date in which the assignment/project is due. Students should submit the assignment/project to their subject teacher on the due date. If a student does not submit the task on the due date the subject teacher will contact the parents/guardian to notify them of the outstanding work that day. The subject teacher will not provide support after the due date has passed. Late marks will be deducted on late assignments. This strategy is in keeping with the Ministry’s policy document “Growing Success”. Late projects/assignments will be assessed at a reduction of 5% per day for the first two days and 10% per day after that to a maximum of 50%. Each project will be assessed for the 100% of its original value, and late marks will be clearly stated on the final evaluation. After 6 school days, a student will receive a zero. Students are strongly encouraged to still hand in late projects for assessment and written feedback. A Saturday Club inclusion will be made within the 6 days. Projects/assignments turned into the teacher after they have been marked and returned to students, will not be awarded a grade if the project/assignment is one the teacher believes can be copied from peers (at teacher’s discretion), however, written feedback on the assignment will be given. (For example: journals, reflection pieces, etc.) Extension Request Form There is a procedure for students to seek relief from a due date and extend a deadline without academic penalty. In extraordinary circumstances, extensions may be granted, if an Extension Request Form is filled out by the student and signed by a parent and approved by the teacher at least one day before the due date. It is up to the discretion of the teacher and the school administration whether or not to accept the Extension Request. A student may request an extension to the maximum of 2 times in each course and for no more than 3 days. After the allotted time has passed and the assignment has not been submitted then late marks will be assigned. Our policy recognizes that extenuating circumstances may legitimately prevent a student from meeting a due date. The Extension Request Form may be garnered from the principal or vice-principal. Illness/Doctor’s Notes If a student is absent on the due date, a doctor’s note (or parental note in case of a family emergency) must be provided to the subject teacher in order for the student to submit the assignment. The assignment must be submitted upon the first day the student returns. Parental Communication Parents will be contacted if the assignment/project is not submitted on the due date. Email receipt of Assignments Since weekend days will be included in the late policy, the submitted time and date will be based on the time that the assignment arrives in the teacher’s email in-box.
