Grade 12 Advanced Functions University Preparation MHF4U Course Outline

Basic Information

Department: Math | Course Developer: Canada Online School | Credit value: 1.0 | Credit Hours: 110

Development Date: April 2018 | Revision Date: N/A

Ministry Document: Mathematics, The Ontario Curriculum, Grades 11 and 12, 2007

Prerequisite(s): MCR3U OR MCT4C

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.

Course Units

Teaching & Learning Strategies

Students will explore mathematical concepts through theoretical frameworks and follow specific examples. They will practice abstract math questions and solve complex problems that require the use of these concepts or apply the theory to a real-world application. They will complete exercises and review against correct solutions. They will do assignments, quizzes, and tests.

Textbooks and other required resources

• Nelson Advanced Functions ISBN: 9780176374433 (Provided by COS)
• A non-programmable scientific calculator
• An Internet connection and a device with basic web browsing capabilities (see System Requirements in Course Calendar)

Assessment & Evaluation

Assessment & evaluation is based on the Ministry of Education’s Growing Success (click to access) guidelines. Students are evaluated on:

Strands and Overall Expectations

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.

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.

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.

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 modelling and reasoning with functions, including problems with solutions that are not accessible by standard algebraic techniques.

Special Program Planning Considerations

COS develops its programs with consideration for Ontario Ministry of Education policies and initiatives. Many areas of special consideration are embedded naturally within course content. These include but are not limited to the following:

• Students with special education needs: Our courses and teachers will strive to equitably accommodate exceptional students with support and/or modified expectations they may need as per their Individual Education Plan (IEP). The modified expectations or support may take the form of altered assignments, differently formatted tests/exams, the use of special technological tools, etc. Special education accommodations are only implemented to provide fair treatment to students who have a demonstrated and documented need.
• English language learners: COS has strategies in place to support students who are learning English as a second language. Teachers are made aware which students are in or were in ESL programs and will make appropriate accommodations or provide resources to help them gain more proficiency.
• Environmental protection: Whenever possible, issues in environmental protection are highlighted, provided as extra interest topics, or used as examples during courses.
• Healthy Relationships: Every student is entitled to a safe environment based on mutual respect. Our courses use online discussions, case studies, role play, etc, to encourage cooperation and constructive comments. Students also learn about building healthy relationships through course content that highlights inclusive values.
• Equity and inclusive education: Diversity is valued at COS and we encourage students to share their unique life experiences and perspective while respecting others’ different values or viewpoints. Learning activities and the curriculum reflect the multicultural nature of Canada and the importance of equitable and inclusive treatment of all others.
• Financial literacy: Students must learn to make informed financial decisions and understand economic forces to be effective members of society. COS and the Ministry are working to embed financial literacy skills and knowledge in courses as appropriate.
• Critical thinking, literacy, numeracy and inquiry: Literacy is more than reading and writing. Its definition is constantly evolving and by today’s standard increasingly needs more sophisticated skills. It is the entire set of skills that allow a person to critically comprehend, analyze, generate and process information in all its forms, and then communicate it meaningfully to others. Every subject is responsible for enhancing students’ literacy, including mathematical literacy (numeracy). Students learn to inquiry deeply and think critically at all times, use relevant terminology, and conduct their own research. They will form opinions backed by logical evidence, detect bias, uncover implied meanings, and take big picture perspectives. With numeracy, students learn to not only perform mathematical operations but also understand their significance, application, and hidden biases.
• School library: A library provides access to resources and also allows students to develop skills in research. COS does not have a library in the conventional sense but we do provide information to students on how to access information they need, find useful texts or other media, and use electronic tools of research. In general, this information is made publicly available through our website.
• Information and communications technology (ICT): By use the COS online learning platform, students will naturally develop transferable skills relating to ICT. Students will learn to use various electronic tools to communicate, cooperate, and conduct research. Students will also be made aware of pitfalls and potential abuse in using the Internet or other electronic tools.
• The Ontario Skills Passport: This is a free bilingual web-based resource to help students understand what are Essential Skills needed for success in school, work, and life. We encourage students to review their learning and see how they develop such skills. For more information, visit http://www.skills.edu.gov.on.ca.
• Education and career/life planning: As students progress through their courses, they will be provided opportunities to learn about future opportunities and how to make career choices. Teachers are available to guide students through their planning and COS provides resources for students to research these opportunities on their own, using the Individual Pathways Plan process.
• Cooperative education and experiential learning: COS does not have a co-op program but we recognize the value of experiential learning and will direct students to information regarding Ministry programs and opportunities when needed.
• Ethics: As part of the process of forming opinions and thinking critically, students will learn to develop their sense of ethics as it relates to both society and private decision making. As an academic institution, COS also requires students to understand ethical conduct in their academic work. Students learn about the consequences of plagiarism both dishonest and negligent, as well as the accepted conventions for citing the work of others properly.