MHF4U

Grade 12, University Preparation
 * MHF4U - Advanced Functions**

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**Overall Course Description** Students will:
 * Investigate the properties of polynomial, rational, logarithmic and trigonometric functions;
 * Develop techniques for combining functions;
 * Broaden their understanding of rates of change;
 * Develop facility in applying these concepts and skills; and,
 * Refine their use of the mathematical processes necessary for success in senior mathematics.

=Prerequisites= Functions, Grade 11, University Preparation (MCR3U) Mathematics for College Technology, Grade 12, College Preparation (MCT4C)
 * Either of**:

=Units= These units are based on the Nelson Advanced Functions textbook. For a list of units from the McGraw-Hill Ryerson Advanced Functions 12 text, go to Other Outlines.

Unit 1 - Functions: Characteristics and Properties

 * Goals:**
 * Review and consolidate knowledge of the properties and characteristics of functions and their inverses
 * Review and consolidate knowledge of graphing functions using transformations
 * Investigate the characteristics of piecewise functions


 * Resources**:
 * Interactive notes and practice - [[file:Even and Odd Functions.doc]]
 * For many further lessons and practice problems, goto Mr. Jackson's SATEC class notes under Resources

Unit 2 - Functions: Understanding Rates of Change

 * Goals**:
 * Calculate an average rate of change of a function given a table of values, a graph, or an equation
 * Estimate the instantaneous rate of change of a function given a table of values, a graph, or an equation
 * Interpret the average rate of change of a function over a given interval
 * Interpret the instantaneous rate of change of a function at a given point
 * Solve problems that involve rate of change


 * Resources**:
 * TIPS4RM Unit outline (based on alternate TIPS4RM course outline). Days 1-4 include lesson plans for rates of change.
 * Changing Functions - Online activities, tasks, and exercise problems

Unit 3 - Polynomial Functions

 * Goals**:
 * Identify and describe key characteristics of polynomial functions
 * Divide one polynomial by another polynomial
 * Factor polynomial expressions
 * Solve problems that involve polynomial equations and inequalities graphically and algebraically


 * Resources**:
 * [|OAME Resources for this Unit] - Lesson Plans for selected days of unit including blackline masters
 * Geometer's sketchpad factored polynomials - [[file:MHF4U_Factored_Polynomials.gsp]]
 * TIPS4RM Unit Outline (based on alternate TIPS4RM course outline). Days 5-8 include lesson plans for polynomial functions
 * End behaviour, zeroes, graphing - purplemath

Unit 4 - Polynomial Equations and Inequalities

 * Goals**:
 * Determine the roots of polynomial equations, with and without technology
 * Solve polynomial inequalities, with and without technology
 * Solve problems involving polynomial function models


 * Resources**:
 * Powerpoint presentation on solving polynomial inequalities, with and without technology - [[file:MHF_U6L2_Inequalities.ppt]]
 * Construction inequalities - online activities, tools, and tasks

Unit 5 - Rational Functions, Equations and Inequalities

 * Goals**:
 * Determine the roots of polynomial equations, with and without technology
 * Solve polynomial inequalities, with and without technology
 * Solve problems involving polynomial function models


 * Resources**:
 * Unit outline based on TIPS4RM
 * [|OAME Resources for this Unit] - Lesson Plans for selected days of unit including blackline masters
 * Powerpoint presentation: "The Disappearing Asymptote" - [[file:MFH_U6L6_Asymptote.ppt]]
 * [[file:Key Features of Rational Functions (Practice&Solutions).doc]]
 * [[file:Rational Functions (Practice&Solutions).doc]]
 * [[file:Sketching Rational Functions (Practice & Solutions).doc]]

Unit 6 - Trigonometric Functions

 * Goals**:
 * Understand radian measure and its relationship to degree measure
 * Use radian measure with trigonometric functions
 * Make connections between trigonometric ratios and the graphs of the primary and reciprocal trigonometric functions
 * Pose, model, and solve problems that involve trigonometric functions
 * Solve problems that involve rates of change in trigonometric functions


 * Resources**:
 * [|OAME Resources for this Unit] - Lesson Plans for selected days of unit including blackline masters
 * [|Khan Academy Trigonometry] - Video Tutorials
 * [|Radian Measure of Angles for University Readiness] - Explanations & examples
 * [[file:ferriswheelmodelit.xls]]
 * Geometer's Sketchpad - [[file:Unit Circle Functions Present (draft).gsp]]
 * Geometer's Sketchpad - [[file:Toronto Temperature GSP file.gsp]]

Unit 7 - Trigonometric Identities and Equations

 * Goals**:
 * Recognize equivalent trigonometric relationships
 * Use compound angle formulas to determine the exact values of trigonometric ratios that involve sums, differences, and products of special angles
 * Prove trigonometric identities using a variety of strategies
 * Solve trigonometric equations using a variety of strategies


 * Resources**:
 * [|Khan Academy Trigonometry] - Video Tutorials
 * [|Trig Functions for University Readiness] - Explanations & examples

Unit 8 - Exponential and Logarithmic Functions

 * Goals**:
 * Relate logarithmic functions to exponential functions
 * Describe the characteristics of logarithmic functions and their graphs
 * Evaluate logarithms and simplify logarithmic expressions
 * Solve exponential and logarithmic equations
 * Use exponential and logarithmic functions to solve problems involving exponential growth and decay, and applications of logarithmic scales


 * Resources**:
 * [|OAME Resources for this Unit] - Lesson Plans for selected days of unit including blackline masters
 * [|Exponents and Exponential Functions for University Readiness] - Explanations & examples
 * [|Logarithms for University Readiness] - Explanations & examples
 * Unit outline based on TIPS4RM
 * Geometer's sketchpad logarithmic functions investigation - [[file:MHF4U_Log_Investigation.gsp]]

Unit 9 - Combination of Functions

 * Goals**:
 * Consolidate your understanding of the characteristics of functions
 * Create new functions by adding, subtracting, multiplying, and dividing functions
 * Investigate the creation of composite functions numerically, graphically, and algebraically
 * Determine key characteristics of these new functions
 * Solve problems using a variety of function models


 * Resources**:
 * Unit outline based on TIPS4RM
 * Geometer's sketchpad function models - [[file:MHF_U6L1_Under_Pressure.gsp]] [[file:MHF_U6L3_The_Chipmunk_Problem.gsp]]
 * Connecting Compositions with transformations using Winplot - [[file:MHF_Unit6L7_8_9.wp2]]
 * Solving problems using a model - modeling a ferris wheel with demo video (Look for "7. Ferris Wheel" mid-way down webpage)
 * Enveloping Functions Lesson - Investigating products of functions, and how separate factors help determine product function
 * [|Addition and Subtraction of functions] - online lessons, interactive tools, activities, and practice problems

**Exam Review**

 * [[file:MHF 4U EXAM REVIEW.doc]] [[file:MHF4U Exam Review Answers.doc]]
 * [[file:Formula Sheet-2.doc]]

Other Outlines
From McGraw-Hill Ryerson //Advanced Functions 12//:
 * Unit 1: Polynomial Functions
 * Unit 2: Polynomial Equations and Inequalities
 * Unit 3: Rational Functions
 * Unit 4: Trigonometry
 * Unit 5: Trigonometric Functions
 * Unit 6: Exponential and Logarithmic Functions
 * Unit 7: Tools and Strategies for Solving Exponential and Logarithmic Functions
 * Unit 8: Combining Functions

TIPS4RM Course Outline including content and reporting targets.

=Resources=

Online Resources
__OAME Online Resources__: The OAME Resources include Ontario Resources, Learning Resources, and Virtual Resources

__Exercised in Math Readiness__: EMR is a collection of exercises that we at the Department of Mathematics and Statistics at the University of Saskatchewan have put together on those high school mathematics topics that seem to be most important for university study in mathematics, the other sciences, engineering, and commerce. This website is free for individual use. For more details, please read the copyright and usage notice.

[|EDU GAINS] is an ever-changing Ontario website with fresh content "establishing communities of practice at every level".

[|Ontario Ministry of Education]

Mr. Jackson's SATEC MHF4U Advanced Functions Class notes & practice problems

Israeli "Visual Math: Functions" website by Michal Yershalmy, Haggai Katriel, and Beba Sternberg

Video Tutorials
__Khan Academy__: “The Khan Academy is a not-for-profit organization with the mission of providing a high quality education to anyone, anywhere. We have 1000+ videos on YouTube covering everything from basic arithmetic and algebra to differential equations, physics, chemistry, biology and finance which have been recorded by [|Salman Khan].”
 * YouTube Channel

'AIRichards314' has posted many videos relating to MHF4U on YouTube. Here is a link to his 'Solving trigonometric equations Part I':
 * AI Richards' YouTube Videos

Texts
Kirkpatrick, C. (2009). //Advanced Functions 12//. Nelson Education Ltd. Erdman, W., Lenjosek, A., Meisel, R., & Speijer, J. (2008). //Advanced Functions 12.// McGraw-Hill Ryerson.
 * Course Texts**:

Zimmer, D., Kirkpatrick, C., et al. (2002). //Advanced Functions and Introductory Calculus//. Nelson Education Ltd. Dearling, C., D'Agostino, S., Erdman, W., & Ferneyhough, F. (2002). //Calculus and Advanced Functions//. McGraw-Hill Ryerson. Malinowski, R., Murray, D., Shifrin, J., Wilson, L. (2002). //Harcourt Advanced Functions and Introductory Calculus 12//. Nelson Education Ltd.
 * Supplementary Texts**: