MHF4U: Advanced Functions

MHF4U: Advanced Functions


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.

Functions MCR3U or MCT4C – Mathematics for College Technology.

Course Preview



Exponential and Logarithmic Functions
EL1. Demonstrate an understanding of the relationship between exponential expressions and logarithmic expressions, evaluate logarithms, and apply the laws of logarithms to simplify numeric expressions;
EL2. 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;
EL3. Solve exponential and simple logarithmic equations in one variable algebraically, including those in problems arising from real-world applications.

Trigonometric Functions
TF1. Demonstrate an understanding of the meaning and application of radian measure;
TF2. 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;
TF3. Solve problems involving trigonometric equations and prove trigonometric identities.

Polynomial and Rational Functions
PR1. Identify and describe some key features of polynomial functions, and make connections between the numeric, graphical, and algebraic representations of polynomial functions;
PR2. Identify and describe some key features of the graphs of rational functions, and represent rational functions graphically;
PR3. Solve problems involving polynomial and simple rational equations graphically and algebraically;
PR4. Demonstrate an understanding of solving polynomial and simple rational inequalities

Characteristics of Functions
CF1. 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;
CF2. 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;
CF3. 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.


Unit Name of Unit Time Allocated in Hours
Unit 1 Polynomial and Rational Functions 40
Unit 2 Trigonometric Functions 30
Midterm Report Cards
Unit 3 Exponential and Logarithmic Functions 20
Unit 4 Characteristics of Functions 20
Final Examination
  Total 110 hours


A variety of teaching and learning strategies are used in this course to meet the needs of a diverse range of learners.

Articulate Learning Module
Computer Assisted Learning
Direct Instruction
Animated Games
Group Discussion
iSpring Presentation / Animation
Online Graphing Software
Problem-Based Learning
Work and Task Sheet
Interactive Online Activity
Decision Making
Independent Study
Model Analysis
Note Taking
Oral Explanation
Peer Assessment
Problem Solving
Reasoning and Proving


Assessment as Learning Assessment for Learning Assessment of Learning
Student Product
· Journals/Letters/Emails (checklist)
· Learning Logs (anecdotal)
· Peer Assessments
· Practice Worksheets
Student Product
· Check-up Time Assessments
· Journals/Letters/Emails (checklist)
· Pre-Skills Checks (scale)
· Quizzes (scale)
· Graphic organizers (scale)
· Peer feedback (anecdotal)
· Reports
· Rough drafts
· Practice Worksheets
Student Product
· Assignments
· Journals/Letters/Emails (checklist)
· Unit Tests (scale)
· Final Exam
· Case Studies
· Presentations
· Graphic organizers (scale)
· Whole class discussions (anecdotal)
· Self-proofreading (checklist)
· Class discussions (anecdotal)
· Problem Solving
· Presentations
· Student teacher conferences
· Small Group Discussions (checklist)
· Pair work (checklist)
· Skype meetings
· Student teacher conferences
· Small group discussions (checklist)
· Pair work (anecdotal)
· Peer-feedback (anecdotal)
· Peer-editing (anecdotal)
· Question and Answer Session (checklist)
· Oral tests (scale)
· Oral Presentation with question and answer session


The percentage grade represents the quality of the students’ overall achievement of the expectations for the course and reflects the corresponding achievement as described in the achievement chart for mathematics.

  1. 1. Term work will be 70% of the overall grade for the course;
  2. 2. The summative evaluations will be 30% of the overall grade, incorporating a final written examination.

Achievement Categories

Application 25% Knowledge and Understanding 25%
Communication 25% Thinking/Inquiry 25%

Achievement Chart
A Summary Description of Achievement in Each Percentage Grade Range And Corresponding Level of Achievement

Percentage Grade Range Achievement Level Summary Description
80–100% Level 4 A very high to outstanding level of achievement.  Achievement is above the provincial standard.
70–79% Level 3 A high level of achievement.  Achievement is at the provincial standard.
60–69% Level 2 Moderate level of achievement.  Achievement is below, but approaching the provincial standard.
50–59% Level 1 A passable level of achievement.  Achievement is below the provincial standard
Below 50% Level R Insufficient achievement of curriculum expectations.  A credit will not be granted


MHF4U Online Course of Study
Graphing calculator is highly recommended


Role of Technology in the Curriculum

Rosedale Academy courses leverage the power of information and communication technologies to provide rich, dynamic learning experiences.  Students explore, evaluate and create concepts and works using a wide array of digital tools.  They demonstrate their learning through text, video, voice and visual assignments that teach multi-literacy and media skills.  Students also enhance their computer and technology skills in ways that are useful for their future academic and personal pursuits.

Teachers at Rosedale Academy get to know their learners, provide rich, descriptive feedback and assess student contributions and products AS, FOR and OF learning through digital technologies.  They enable rapid feedback and communication at any time without borders in our global community.

Tool Use Benefit
Discussion forums Whole class discussion (written) Creates a record of each student’s contributions.
Group activities Small group collaboration and discussions. (written) Encourages student participation; creates a record
Live Skype sessions Teacher leads the lesson with students as a class Observations of whole class and individual students
Workshop Students submit work for peer assessment to Moodle. Peers assess each other’s work based on rubrics, etc. Promotes assessment as learning
Peer Teaching Students research a given topic and share their findings and opinions with other students. Fosters discussion between students and allows for content to be learned and expressed from a student perspective
Journals Small group discussions using problem solving Improves students’ critical inquiry, and reflective thinking skills about the concepts learned within the course
Learning Modules Students explore content in an interactive manner with built-in assessments as they progress. Students can navigate content at their own pace and assess their own learning along the way.
Computer Simulations Individual or class exploration and visualization of concepts relating to the curriculum. Allows hands-on exploration and investigation as an alternative learning strategy.

English as a Second Language

Rosedale Academy provides students with comprehensive ESL support to enhance their proficiency with the English language.

  • All Rosedale Academy instructional materials and resources are designed with English Language Learners in mind. Online and face-to-face instructional resources make use of differentiated learning methods and carefully structured language. These resources support English language development as students are taking credit courses in all academic fields.
  • The self-paced delivery method of this course allows students to take the time that they require to engage in meaningful participation while still enjoying the enriching experience of working in an online global classroom.
  • The self-paced delivery method of this course allows students to take the time that they require to engage in meaningful participation while still enjoying the enriching experience of working in an online global classroom.
  • All teachers at Rosedale Academy are responsible for helping students to develop their ability to use English in academic courses.

Career Education

This course promotes skills effective for a variety of careers and informs students of some of the career opportunities where oral and written communication is considerable assets. Students will learn how to use English to inform audiences about ideas, persuade audiences to change their opinion or buy a product, and to formulate ideas. Students will also understand the importance of social media in their search for future education and career opportunities. Finally, this course also helps to prepare students for university application by providing a unit that helps them write a persuasive application essay.  Beyond the immediate needs of the student, this also course focuses on demonstrating the value of English in jobs like business where clear communication is highly valued.

Academic Integrity

Students are expected to maintain high standards of honesty and academic integrity throughout their participation in all courses. This includes avoiding any instance of fraud, plagiarism and cheating.  Rosedale Academy takes the following steps to ensure academic integrity:

  • Students provide photo identification
  • Course assignments include audio and video components
  • Teachers Skype weekly with their classes
  • Students are encouraged and supported to develop original work
  • Exams are proctored by adults in trusted positions

When a teacher has reasonable grounds to believe that a student has violated these standards, the school principal will review the incident and, if needed, enforce disciplinary procedures. More information about Academic Honesty may be found in section 5.3 of the school calendar.

Late and Missed Assignment

Rosedale Academy provides a flexible, self-paced learning opportunity, which allows students to proceed through each course at their own speed.  Students may submit any assignment from any unit while he or she is enrolled in this course.  Assignments will not be accepted once the student’s enrolment period has ended. Students must complete and submit all course requirements prior to booking their final exam. Course requirements include but are not limited to: assignments, tests, and learning log.

SKU: MHF4U-2017-03 Category: Tag:

Additional information

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I am an ONTARIO student with an OEN ($590.00 CAD), I am an INTERNATIONAL student without an OEN ($680.00 CAD)