Name: Grade 12 Advanced Functions | MHF4U | OSSD Online School | royalontarioacademy.com
Author: cherylrichardson250@gmail.com

Curriculum Coordinator and Learning Strategist

Cheryl Richardson

B.Sc., OCT

MHF4U

Grade 12

University Preparation

Advanced Functions

Find additional course details below, including delivery format, course availability, course duration, prerequisite, tuition fee, hardware/software requirements, etc.

Course Details

Course Code

MHF4U

Course Name

Advanced Functions

Grade

Grade 12

Course Type

University Preparation

Format

Asynchronous Delivery

Prerequisite

Functions, Grade 11, University Preparation, or Mathematics for College Technology, Grade 12, College Preparation

Tuition Fee

$500.00

Course Duration

At Your Own Pace (4 weeks to 12 months)

Credit Value

1.0

Availability

Start Anytime

Course Reviser/Developer

Dr. Karen McCloskey

Latest Revision Date

Feburary, 2025

Curriculum

MHF4U – The Ontario Curriculum, Mathematics, Grades 11 and 12, 2007 (revised)

Course Description, Unit Overview, Timeline

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.

Outlined below is a description of each unit, including what students will learn and the recommended hours for completion.

Unit Title & Description

Time Allocated

Unit 1: The Mathematics of Nature

Explore the role of logarithms and exponents in natural phenomena such as population growth and radioactive decay. Engage in H5P logarithm estimation exercises, Desmos graphing explorations, and problem-based learning scenarios. Assessments include an assignment focusing on conceptual understanding and a unit test.

12 Hours

Unit 2: Polynomial Functions in Engineering and Technology

Examine polynomial functions—linear, quadratic, and higher-degree—within engineering and technological contexts. Graph polynomial functions, solve equations, and analyze real-world applications such as bridge construction and robotics. Interactive elements include Desmos polynomial graphing, CloudLabs simulations, and algebraic problem-solving tasks.

12 Hours

Unit 3: Advanced Functions in Health & Medicine

Apply advanced functions to medical and health-related contexts, modeling patient data, disease spread, and biological processes using logarithmic, polynomial, and rational functions. Activities include modeling medication absorption rates, Desmos function explorations, and case studies.

14 Hours

Unit 4: Finance and Economics

Investigate logarithmic and exponential functions in financial modeling, including compound interest, inflation, and economic trends. Analyze function transformations and apply polynomial theorems to financial problem-solving. Activities include Desmos financial modeling, H5P mortgage simulations, and spreadsheet-based exponential growth explorations.

12 Hours

Unit 5: Polynomial and Rational Equations in Environmental Science

Connect polynomial and rational equations to environmental science, modeling pollution levels and population dynamics. Solve polynomial equations up to degree four, analyze roots, and apply factoring techniques. Activities include Desmos environmental data modeling, CloudLabs simulations, and inequality-solving tasks.

12 Hours

Unit 6: Waves, Pixels, and Angles: The Math Behind Digital Art and Media

Explore trigonometric properties, radian and degree measures, and function transformations within digital art and media applications. Create animations of circular motion and analyze sound waves. Interactive activities include Desmos sine wave visualizations, H5P trigonometric identity challenges, and transformation projects.

12 Hours

Unit 7: Robot Revolution: The Trigonometric Foundations of AI

Investigate advanced trigonometry concepts essential for artificial intelligence and robotics, including reciprocal trigonometric functions, transformations, and composite functions. Analyze robotic motion, programming logic, and AI-driven decision-making through GeoGebra robot path simulations and AI movement modeling.

14 Hours

Unit 8: Exploring Rates and Functions in Space Exploration

Apply calculus concepts such as instantaneous and average rates of change to space exploration. Analyze real NASA data, apply mathematical models to planetary motion, and solve composite and combined functions in astrophysics. Activities include Desmos space data modeling, real-world rate-of-change simulations, and function-solving tasks.

12 Hours

Culminating Task

Using mathematical models to investigate real-world problems. This summative assessment integrates key concepts from the course, requiring students to apply their understanding in a structured project.

8 Hours

Final Exam

Comprehensive assessment of all specific expectations covered in the course. Activities and Assessments: Cumulative final exam to assess overall understanding and application of course concepts.

2 Hours

Total Hours

110 Hours

Teaching and Learning Strategies

At Royal Ontario Academy, our asynchronous, self-paced courses are crafted to engage students actively, encouraging deep learning and self-reflection. Our online OSSD courses are normally divided into 8-10 smaller sections to help students learn content in manageable portions. Lessons connect concepts to practical, relatable social, environmental, and economic issues, fostering lifelong learning by helping students apply knowledge to real-life contexts.

Students are encouraged to explore, investigate, and think critically as they progress independently. This approach emphasizes problem-solving skills, guiding students to persist through challenges, reason through complex ideas, and explore alternative solutions on their own, building resilience and independence essential for success beyond the classroom.

Our virtual high school courses provide a variety of learning experiences through virtual labs, simulations, knowledge checks, reflections, and videos. Interactive activities and discussion forums are designed to draw on students prior knowledge, keeping them engaged and actively participating. These tools enable OSSD students to practice, reflect, and apply concepts flexibly at their own pace, creating a personalized learning journey tailored to each student’s interests and goals.

Assessment and Evaluation

A wide variety of assessment and evaluation tools will be used to earn credits towards the Ontario Secondary School Diploma at Royal Ontario Academy including quizzes, tests, projects, essays, journals, and final assessments.

The final exam is a closed book, online test that is proctored and has a time limit. Students may also be required to appear on video for other assessments in certain courses.

All OSSD courses follow a simple evaluation breakdown at our virtual high school:
70% of the grade will be based on evaluations conducted throughout the online course. The remaining 30% of the grade will be based on a final evaluation or exam. This may be a final exam, a final project/report, or a combination of both an exam and a project.

Students will receive two reports per course:

First Mid Term Report: Reflects achievement and development after the first 4 Units.

Final Report: Reflects overall achievement and development for the entire course.

According to Growing Success First Edition, Grades 1 to 12, 2010, the primary purpose of assessment and evaluation is to improve student learning. To ensure that assessment, evaluation, and reporting are valid and reliable, and that they lead to the improvement of learning for all students, Royal Ontario Academy teachers use practices and procedures that:

are fair, transparent, and equitable for all students;
support all students, including those with special education needs, those who are learning the language of instruction (English or French), and those who are First Nation, Métis, or Inuit;
are carefully planned to relate to the curriculum expectations and learning goals and, as much as possible, to the interests, learning styles and preferences, needs, and experiences of all students;
are communicated clearly to students and parents at the beginning of the school year or course and at other appropriate points throughout the school year or course;
are ongoing, varied in nature, and administered over a period of time to provide multiple opportunities for students to demonstrate the full range of their learning;
provide ongoing descriptive feedback that is clear, specific, meaningful, and timely to support improved learning and achievement;
develop students’ self-assessment skills to enable them to assess their own learning, set specific goals, and plan next steps for their learning.

Accommodations and IEP for Students

At Royal Ontario Academy, we believe that all OSSD students can benefit from a more accommodating online learning experience Accommodations allow for increased access to the course, without any changes to the knowledge and skills the student is expected to demonstrate.

An Individual Education Plan (IEP)is a personalized document that outlines a student’s learning needs, as well as the accommodations or services they require to succeed in their courses. At Royal Ontario Academy, our flexible online learning environment already addresses many common accommodation needs, but if a student requires additional support, our Principal is ready to help you!

– Students with Existing IEP: If a student has an existing IEP from another elementary or secondary school, Royal Ontario Academy can implement the listed accommodations, provided they are applicable within our online learning environment. To do so, a copy of the student’s IEP must be submitted to our Principal for review.

– Students Without IEP: If a student requires accommodations but does not currently have an IEP, our Principal will work with the student to assess their learning needs and develop a path forward. In this case, students will need to submit supporting documentation to help determine the appropriate accommodations.

– English Language Learners:– English Language Learners: Students who enroll at Royal Ontario Academy can provide information about their English language proficiency during the registration process. This information helps our teachers and Principal to tailor their teaching strategies and implement accommodations that support English language learners effectively.

For students and parents wishing to submit IEP documentation or request accommodations, please contact our Principal at info@royalontarioacademy.com

Resources Required by the Student

Students should have the following minimum hardware and software requirements to access the Advanced Functions

Minimum Technical Specifications

Hardware

A PC running Windows XP or higher or
A Mac running OS X or
A Chromebook running Chrome OS
2GB of RAM
High speed internet connection
A sound card with speakers or headphones
A functional webcam and microphone

Software

Adobe Reader
Java
A typical Office Suite including a word processor application, equation editor and spreadsheets

Browser

Mozilla Firefox4 or higher or
Internet Explorer 7 or higher or
Safari 5 or higher or
Google Chrome 11 or higher
In some cases, a scanner or phone/camera may be used to submit handwritten assignments.

Do students need any additional resources (i.e. textbooks)?

Every student in a virtual high school needs access to a desktop computer or laptop with high-speed internet and word processing software.

Any additional course-specific resources (i.e., calculators, software downloads, etc.) are listed on the individual course outline pages on our website.

All Royal Ontario Academy online course content is contained within our moodle learning management system, so no textbooks are required. For English courses and some social science/humanities courses, students may be required to locate copies of novels and plays that are readily available at public libraries or bookstores.

Frequently Asked Questions (FAQs)

1. What is MHF4U?
MHF4U is a Grade 12 Advanced Functions course at University Preparation level.

2. What are 4U – (eg: 3M in AWQ3M (MHF4U))
4U for the MHF4U refers to the grade level and the course type. 4 refers to the 12th Grade and the second digit refers to the University Preparation course type.

3. What is the prerequisite for MHF4U?
The prerequisite for Advanced Functions is Any Functions, Grade 11, University Preparation, or Mathematics for College Technology, Grade 12, College Preparation

4. How long does it take to complete the MHF4U online course?
The completion of the MHF4U course varies depending on the availability and pace of each student. However, the course can be completed in minimum of 4 weeks to maximum of 12 months.

5. Will my marks be sent directly to OUAC or OCAS?
Yes. We can send your MHF4U online course marks to OUAC (Ontario University’ Application Centre) or OCAS (Ontario College Application Service).

6. How lessons are delivered for the MHF4U?
At Royal Ontario Academy, course learning is asynchronously delivered for the MHF4U in various formats such as videos, question and answers, interactive tools, written notes, simulations, presentations, and external websites/links depending on the subject material of the course.

7. What is the withdrawal policy?
For students registered in Grade 9 and 10 courses, withdrawals can be made at any time and are not recorded on the Ontario Student Transcript (OST).

For students registered in Grade 11 and 12 courses, withdrawals made within 5 days of the issuance of the first (mid-term) report card from Royal Ontario Academy will result in the mark not being recorded on the Ontario Student Transcript (OST). Withdrawals after 5 days of the issuance of the first (mid term) report card will result in a “W” being entered in the “Credit” column of the OST, along with the mark at the time of withdrawal.

8. What is the due date of my course?
Since your course is self-paced, there are no set due dates, allowing you to progress at your own speed. However, please be mindful of any deadlines for university or college applications.

9. Can I earn my OSSD (Ontario secondary school diploma) credits through online courses?
Yes, you can earn your Ontario Secondary School Diploma (OSSD) credits fully online through Royal Ontario Academy. To earn OSSD credits, you will need to complete 30 credits (18 compulsory and 12 optional), pass the Ontario Secondary School Literacy Test, and fulfill 40 hours of community involvement.

Price Detail

$500

/ 1 Course

$800

/ 2 Course

$1050

/ 3 Course

Start your learning journey with us.

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Advanced Functions

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