COURSE OUTLINE OF MHF4U

Course Development: Lighthouse Academy Canada
Department: Mathematics and Computer Science
Teacher: Ms. Farzana Akhter
Course Development Date: Jan. 10, 2020
Course Reviser: None
Course Revision Date: Not Applicable
Course Title: Advanced Functions, Grade 12
Course Code: MHF4U
Grade: 12
Course Type:  University Preparation
Credit Value: 1
Prerequisite: Functions, Grade 11, University Preparation, or Mathematics for College Technology, Grade 12, College Preparation

Name of Ministry Curriculum Policy Document(s):

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.

Overall Expectations

  1. Demonstrate an understanding of the relationship between exponential expressions and logarithmic expressions, evaluate logarithms, and apply the laws of logarithms to simplify numeric expressions;
  2. 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;
  3. Solve exponential and simple logarithmic equations in one variable algebraically, including those in problems arising from real-world applications.
  1. Demonstrate an understanding of the meaning and application of radian measure;
  2. 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;
  3. Solve problems involving trigonometric equations and prove trigonometric identities.
  1. Identify and describe some key features of polynomial functions, and make connections between the numeric, graphical, and algebraic representations of polynomial functions;
  2. Identify and describe some key features of the graphs of rational functions, and represent rational functions graphically;
  3. Solve problems involving polynomial and simple rational equations graphically and algebraically;
  4. demonstrate an understanding of solving polynomial and simple rational inequalities.
  1. 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;
  2. 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;
  3. 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.

Units: Titles and Hours

Unit

Titles and Descriptions

Hours

Unit 1

Polynomial Functions

24

Unit 2

Rational Functions

15

Unit 3

Trigonometric Functions

24

Unit 4

Exponential and Logarithmic Functions

21

Unit 5

Rate of Change and Combinations of Functions

18

Review for Final Exam

6

Final Exam

2

Total

110

Learning Skills

The following learning skills will be taught and assessed throughout the course and will be shown on the report card. Students’ performance in these skill areas will not be included in the final numeric mark. It is important to remember, however, that the development and consistent practice of these skills will influence academic achievement. These skills include:

Responsibility

Organization

Independent Work

Collaboration

Initiative

Self-regulation

Teaching Strategies

  • Brain storming
  • Problem solving
  • Independent Study
  • Review
  • Group Discussion
  • Presentation
  • Class discussion (teacher facilitated)
  • Lecture
  • Interviews/Questions
  • Learn by Practice
  • Student teacher conference/ conversation
  • Individual work (Teacher facilitation)

Assessment and Evaluation Guidelines

Assessment and evaluation are based on the provincial expectations and levels of achievement outlined in the provincial curriculum document for each subject in secondary school. A wide range of assessment and evaluation opportunities allows students to demonstrate their learning in a variety of ways. This information provides the basis for reporting student grades on the Provincial Report Card. Achievement (reflected in a final mark) will be calculated using the following categories:

Communication

Knowledge/Understanding

Thinking

Application

25 %

25 %

25 %

25 %

The student’s grade for the term marks will be based on the most consistent achievement with emphasis on the most recent within each category.

Students will also receive descriptive feedback as part of the learning process which may not be assigned a mark.

Final Mark = 70% Term + 30% Final Evaluation

Achievement Level Chart

Grade Range (%)

Achievement Level

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

A moderate level of achievement.  Achievement is below, but approaching the provincial standard.

70-79

Level 1

A passable level of achievement.  Achievement is below the provincial standard.

<50

Insufficient achievement, a credit will not be granted.

Considerations for Program Planning

In order to achieve the curriculum expectations, the program is planned to conduct a variety of activities considering the following but not limited to:

  • The teacher will provide with new learning based on the knowledge and skills that the students acquired in the previous years
  • The students will have opportunities to learn in a variety of ways such as individually, cooperatively, independently with the teacher’s direction through investigation involving kinds on experience and through practice examples.
  • The learning/teaching approaches and strategies will vary according to the learning goals and student’s needs in order to help students achieve the curriculum expectations.
  • The teacher will provide with the instructional and learning strategies best suited to the particular learning goal so that the students can learn concepts, acquire procedures and skills and apply the knowledge.
  • The students will learn the concepts in a variety of representations such as algebraic, graphical and in tabular form.
  • The students will also be engaged in learning the concepts, skills and applications by using different technologies such as graphing calculator, online graphing calculator etc.
  • The students will be provided with the opportunities to participate in the group discussion to share ideas and thinking in order to achieve a common goal of learning.
  • The teacher will provide with interesting examples and explanations to enhance the student’s interest in learning Mathematics and to apply the knowledge in various fields.
  • The teacher will encourage students to explore alternate solutions in order to help students become successful problem solvers and develop confidence.
  • The teacher will incorporate appropriate adaptations in instructions and assessments to facilitate the success of English language learners such as using more visual materials, using simple English, offering extra instruction time, granting extra time for assessments etc.

Accommodations

Accommodations will be based on meeting with parent, teachers, administration and external educational assessment report. The following three types of accommodations may be provided:

  • Instructional accommodations: such as changes in teaching strategies, including styles of presentation, methods of organization, or use of technology and multimedia.
  • Environmental accommodations: such as preferential seating or special lighting.
  • Assessment accommodations: such as allowing additional time to complete tests or assignments or permitting oral responses to test questions.

Other examples of modifications and aids, which may be used in this course, are:

  • Provide step-by-step instructions.
  • Help students create organizers for planning writing tasks.
  • Record key words on the board or overhead when students are expected to make their own notes.
  • Allow students to report verbally to a scribe (teacher/ student) who can help in note taking.
  • Permit students a range of options for reading and writing tasks.
  • Where an activity requires reading, provide it in advance.
  • Provide opportunities for enrichment.

Teaching/Learning Resources

  • Growing Success Document, Ministry of Education, 2010.
  • The Ontario Curriculum, Grades 11 and 12 mathematics, Revised 2007
  • Textbook: Advanced Functions, Grade 12, McGraw-Hill Ryerson
  • Textbook: Advanced Functions, Grade 12, Nelson
  • Lecture notes/slides on LMS

Teaching/Learning Materials

Desmos Graphing Calculator, Pen Pencil, Graph paper, White Paper, LMS, Video Conferencing Tool etc.

Additional Information

Behavior

Every student is expected to respect other students’ right to a safe and supportive learning environment. Students are expected to behave in a considerate and reasonable manner at all times. A “zero tolerance” policy with respect to bullying, threatening, harassment, abusive language, spam, disruptive behavior and lack of respect is in effect and misbehavior may result in your removal from the course.

Academic Integrity

Students are expected to submit original work. Students who seek to attain academic advantage or help someone else obtain such advantage through cheating will receive a grade of zero. Any assignments submitted that are not original will receive a mark of zero. Students who persist in submitting un-cited or improperly cited assignments may be suspended or withdrawn from the course.

Homework

In this course, students are expected to spend approximately 25 hours per week on homework. The deadlines of homework are realistic in the normal working life outside of the school setting. Deadlines are also set as a reasonable management strategy for teachers so that workloads can be varied and balanced. We also set deadlines as a way of bringing closure to one unit of work and moving ahead to another.

Missed Assessment

To earn a credit, students have a responsibility to submit sufficient evidence of understanding within established deadlines. It is in the student’s best interest to submit evidence of learning at every opportunity that is provided, so that his/her grade accurately reflects what was learned. In the event that a student produces insufficient evidence in the key understandings for the course, as deemed by the teacher, the entire credit is at stake