MHF4U - Grade 12 Advanced Functions

Grade 12 Advanced Functions image
Course Code: MHF4U Course Type: University Preparation Format: Online School Course Prerequisite: MCR3U, Grade 11 Functions or MCT4C, Grade 12 Mathematics for College Technology Tuition Fee (CAD): $549 Demo Lesson

Course Description For MHF4U Grade 12 Advanced Functions Online Course

Grade 12 Advanced Functions (MHF4U) 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. **MHF4U 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.

Summary Of Units And Timelines For Grade 12 Advanced Functions MHF4U

Below is the suggested sequence of course unit delivery as well as the recommended number of hours to complete the respective unit. For complete details of targeted expectations within each unit and activity, please see each Unit Overview found in the MHF4U course profile.

Unit OrderUnit NameSuggested Time
Unit 1Polynomial Functions
Polynomial Equations and Inequalities
Rational Functions
30 Hours
Unit 2Trigonometry
Trigonometric Functions
26 Hours
Mid Semester Point
Unit 3Exponential and Logarithmic
Solving Exponential and Logarithmic
26 Hours
Unit 4Combining Functions26 Hours
FINALFinal Exam2 Hours
View Sample Gradebook Total110 Hours

Please be aware that, as per Ministry guidelines, OVS has a mandatory minimum requirement of 14 days enrollment for students to be eligible for a midterm report card and 28 days enrollment to be eligible for a final report card.

MHF4U 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.

The mathematical processes are to be integrated into student learning in all areas of this course. Throughout this course, students will:

  • Problem Solving – develop, select, apply, compare, and adapt a variety of problem-solving strategies as they pose and solve problems and conduct investigations, to help deepen their mathematical understanding
  • Reasoning and Proving – develop and apply reasoning skills (e.g., use of inductive reasoning, deductive
    reasoning, and counter-examples; construction of proofs) to make mathematical
    conjectures, assess conjectures, and justify conclusions, and plan and construct
    organized mathematical arguments;
  • Reflecting – demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by assessing the effectiveness of strategies and processes used, by proposing alternative approaches, by judging the reasonableness of results, by verifying solutions)
  • Selecting Tools and Computational Strategies – select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems
  • Connecting – make connections among mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, current events, art and culture, sports)
  • Representing – create a variety of representations of mathematical ideas (e.g., numeric, geometric, algebraic, graphical, pictorial representations; onscreen dynamic representations), connect and compare them, and select and apply the appropriate representations to solve problems
  • Communicating – communicate mathematical thinking orally, visually, and in writing, using precise mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions

As summarized in Growing Success 2010, the primary purpose of assessment and evaluation is to improve student learning. Information gathered through assessment helps teachers to determine students’ strengths and weaknesses in their achievement of the curriculum expectations in each course.

This information also serves to guide teachers in adapting curriculum and instructional approaches to students’ needs and in assessing the overall effectiveness of programs and classroom practices. As part of assessment, teachers provide students with descriptive feedback that guides their efforts towards improvement. Evaluation refers to the process of judging the quality of student work on the basis of established criteria, and assigning a value to represent that quality. All curriculum expectations must be accounted for in instruction, but evaluation focuses on students’ achievement of the overall expectations.

A students’ achievement of the overall expectations is evaluated on the basis of his or her achievement of related specific expectations. Teachers will use their professional judgement to determine which specific expectations should be used to evaluate achievement of overall expectations, and which ones will be covered in instruction and assessment but not necessarily evaluated. In order to ensure that assessment and evaluation are valid and reliable, and that they lead to the improvement of student learning, teachers must use assessment and evaluation strategies that:

  • Address both what students learn and how well they learn
  • Are based both on the categories of knowledge and skills and on the achievement level descriptions given in the achievement chart
  • Are varied in nature, administered over a period of time, and designed to provide opportunities for students to demonstrate the full range of their learning
  • Are appropriate for the learning activities used, the purposes of instruction, and the needs and experiences of the students
  • Are fair to all students
  • Accommodate students with special education needs, consistent with the strategies outlined in their Individual Education Plan
  • Accommodate the needs of students who are learning the language of instruction
  • Ensure that each student is given clear directions for improvement
  • Promote students’ ability to assess their own learning and to set specific goals
  • Include the use of samples of students’ work that provide evidence of their achievement
  • Are communicated clearly to students and parents at the beginning of the school year and at other appropriate points throughout the school year.

The achievement chart outlines four categories of knowledge and skills. They include; knowledge and understanding, thinking, communication and application. Teachers will ensure that student work is assessed and/or evaluated in a balanced manner with respect to the four categories, and that achievement of particular expectations is considered within the appropriate categories. A final grade is recorded for this course, and a credit is granted and recorded for this course if the student’s grade is 50% or higher. The final grade for this course will be determined as follows:

  • Seventy percent of the grade will be based on evaluations conducted throughout the course. This portion of the grade should reflect the student’s most consistent level of achievement throughout the course, although special consideration should be given to more recent evidence of achievement.
  • Thirty percent of the grade will be based on a final evaluation and administered towards the end of the course.

All students can succeed. Some students are able, with certain accommodations, to participate in the regular course curriculum and to demonstrate learning independently. Accommodations allow access to the course without any changes to the knowledge and skills the student is expected to demonstrate. The accommodations required to facilitate the student’s learning can be identified by the teacher, but recommendations from a School Board generated Individual Education Plan (IEP) if available can also be consulted. Instruction based on principles of universal design and differentiated instruction focuses on the provision of accommodations to meet the diverse needs of learners.

Examples of accommodations (but not limited to) include:

  • Adjustment and or extension of time required to complete assignments or summative tasks
  • Providing alternative assignments or summative tasks
  • Use of scribes and/or other assistive technologies
  • Simplifying the language of instruction

Teachers will bring additional resources and teaching materials that provide a rich and diverse learning environment. Units in this course profile make specific reference to the intended textbook for this course but can be substituted for any relevant and approved text.

  • Speijer, Jacob et al. McGraw-Hill Ryerson Advanced Functions 12. Toronto: McGraw-Hill Ryerson, 2008.
  • Small, Marian. Nelson Advanced Functions 12. Toronto: Nelson Education, 2008.

Reference: Mathematics, The Ontario Curriculum, Grades 11 and 12, 2007 (Revised) Ministry of Education of Ontario

Ontario Secondary School Diploma (OSSD) Requirements for all course.


Frequently Asked Questions

MHF4U is a Grade 12 Advanced Functions course at a University preparation level.

4U refers to the Grade level of the courses and the pathway. 4 means it is a grade 12 course and U means it is a university preparation course.

Click here for more information on Course Coding System

At Ontario Virtual School (OVS) you can complete an online highschool credit courses as quickly as 4 weeks, or take as long as 12 months.

Yes, we can send the marks for your online courses directly to OUAC, OCAS, your home, and to your day school.

Student & Parent Recommendations

Ontario Virtual School
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Pasha Radmanesh
I had an amazing experience with Ontario virtual school, was a bit hesitant going in since I've never been in a private school before but the teachers and admin at Ontario virtual school were amazing. There were no hidden fees included and I got my test marks back within 24 hours. The best thing about my advanced functions course was that the admin were able to send my report card mark to OUAC so fast. It took them last than a day to submit. Highly recommend this private school to others.
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Mélanie Barré
My experience taking online courses with OVS was phenomenal! I took grade 12 Advanced Functions MHF4U and my teacher was Mr. Currie. He was extremely quick with responding to any of my questions and marking my tests, discussion posts and lab simulations. The corrections were always sent to me within 24h, even on the weekends! The course lessons were easy to follow and were delivered in an organized fashion. Doing the course at my own pace allowed me to achieve unmatched success. I would highly recommend OVS to any students interested in following the Ontario curriculum who are looking to "reach ahead" in their high school studies.
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Layan Shaltaf
I took grade 12 advanced functions at Ontario Virtual School. The website was easily accessible and navigating around it was simple as well. The teachers reply fairly quickly to any questions or concerns. The tests were very similar to the practice questions and the lessons were easy to understand. The good thing about this school is that it is self paced so you aren't in a rush to finish things like other schools. -Layan
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Sahil k
I had a great experience with OVS during my MHF4U course.The quality of lessons were high and a variety of questions were solved and the homework was of a good level.There were no hidden fees as well.On top of that there were a variety of assessments and exams having different kinds of questions.The report card processing took very less amount of time and the replies were prompt from the teacher Ms.Lai which I really appreciate. All of my work was returned and marked within 1-2 working days. Overall my experience with OVS was splendid and enjoyable.
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Naya Akkad
I took the MHF4U course at OVS, and the lessons were very descriptive and easy to understand. The tests were a good amount of difficulty, and you are given a more than reasonable amount of time to complete them. My teacher marked all my tests and final exam, in no more than a day, and was super helpful with any questions I had. My midterm and final marks were also uploaded to the OUAC in less than 2 days, and was a super easy process! I strongly recommend this course to anyone who's having a bit of trouble with how fast-paced their math class is at their day school, and wants to learn at their own comfortable speed.
Sharon Elsa image
Sharon Elsa
I have just finished Grade 2 Advance Functions course -MHF4U course with OVS. Course material was well laid out and very much helpful for my preparation. Admission process was very fast and the whole team was very supportive. My teacher Mr. Currie, Michael was extremely knowledgeable, passionate and supportive through out the course. Teacher was very prompt in replying to e-mail communications and clearing my doubts. Overall, I enjoyed the course with OVS and I highly recommend to any one to take it with confidence. Thank you.