top of page

About the course

This course introduces basic features of the function by extending students’ experiences with quadratic relations. It focuses on quadratic, trigonometric, and exponential functions and their use in modelling real-world situations. Students will represent functions numerically, graphically, and algebraically; simplify expressions; solve equations; and solve problems relating to applications. Students will reason mathematically and communicate their thinking as they solve multi-step problems.

Functions and Applications

Course Credit

1

Course Price

$ 550.00

Course Developer

My Learning Oasis

Prerequisite(s) (Text)

Principles of Mathematics, Grade 10, Academic,(MPM2D)

Course Code

Department Head & Contact Information

MCF3M

Course Type

University/College

Grade Level

Grade 11

Course Development Date

June 10th, 2021

Course Outline

Quadratic Functions

Students will expand and simplify quadratic expressions, solve quadratic equations, and relate the roots of a quadratic equation to the corresponding graph. They will further demonstrate an understanding of functions, and make connections between the numeric, graphical, and algebraic representations of quadratic functions. This unit will conclude with students solving problems involving quadratic functions, including problems arising from real-world applications.

Expected Hours of Instruction: 37 Hours

Exponential Functions

Students will look at different rules and techniques to simplify and evaluate numerical expressions involving exponents, and make connections between the numeric, graphical, and algebraic representations of exponential functions. They will represent real-life situations using exponential functions and solve for simple cases. The concept of compound interest will be introduced and related problems with simple annuities will be analyzed. Students will look at the concept of exponential growth and exponentiation. Real-life situations like bacterial growth and how scientists determine the epi-center of a viral infection. The exponential function will be used to determine infection rates. If time permits, students will look at the importance of safely disposing of nuclear waste. A study of the exponential decay of such waste will be analyzed.

Expected Hours of Instruction: 35 Hours

Trigonometric Functions

In this unit, the trigonometric ratios are introduced and they will be used to solve problems involving trigonometry in acute triangles using the sine law and the cosine law, including problems arising from real-world applications. Periodicity of the trigonometric ratios will be introduced and connections are made between the numeric, graphical, and algebraic representations of sine functions.

Expected Hours of Instruction: 36 Hours

Exam

This is a proctored exam worth 30% of your final grade.

Expected Hours of Instruction: 2 Hours

Total: 110 Hours

Resources

All notes and assignments will be provided by the teacher.

The students are responsible to have:

● A non-programmable, non-graphing, scientific calculator.

● A note taking device for online students

● Internet connection for online students

Overall Curriculum Expectations

A. Quadratic Functions

A1: expand and simplify quadratic expresratic equations, and relate the roots of a quadratic equation to the corresponding graph;
A2: demonstrate an understanding of functions, and make connections between the numeric, graphical, and algebraic representations of quadratic functions;
A3: solve problems involving quadratic functions, including problems arising from real-world applications.

B. Exponential Functions

B1: simplify and evaluate numerical expressions involving exponents, and make connections between the numeric, graphical, and algebraic representations of exponential functions;
B2: identify and represent exponential functions, and solve problems involving exponential functions, including problems arising from real-world applications;
B3: demonstrate an understanding of compound interest and annuities, and solve related problems.

C. Trigonometric Functions

C1: solve problems involving trigonometry in acute triangles using the sine law and the cosine law, including problems arising from real-world applications;
C2: demonstrate an understanding of periodic relationships and the sine function, and make connections between the numeric, graphical, and algebraic representations of sine functions;
C3: identify and represent sine functions, and solve problems involving sine functions, including problems arising from real-world applications

Special Accommodations

Only Some students are able, with accommodations, to be part of a regular course curriculum and to demonstrate independent learning. These accommodations allow access to the course without any dilution of the knowledge and skills the student is expected to demonstrate. These required accommodations to facilitate the student’s learning will be identified in his or her IEP (see IEP Standards, 2000, page 11*). It is likely that IEP for many or all courses will reflect the same accommodations. The instructions and accommodations are geared to meet the diverse needs of learners.

The three types of accommodations that are going to be used are:

i) Instructional accommodations - changes in teaching/learning strategies facilitated by different styles of presentation; methods of organization; the use of technology and multimedia.
ii) Environmental accommodations - Certain classroom settings and preferential seating may benefit these students.
iii) Assessment: assessment procedures that enable the student to demonstrate his or her learning, such as Multiple Intelligence Theory, giving more time to complete tasks (see page 29 of the IEP Resource Guide, 2004, for more examples).

For students who require accommodations for only the mathematics courses, the assessment and evaluation of their achievement will be based on the appropriate course curriculum expectations and the achievement levels outlined in this document. The IEP box on the students’ Provincial Report Cards will not be checked, and no information on the provision of accommodations will be included.

* Taken from: Ministry of Education, Ontario. Extracted from The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007; (Pg:- 28-30) Date of extraction: Sunday, March 14, 2021

Program Considerations For English Language Learners

Students from a variety of cultural and linguistic backgrounds. For many of these students, English is not their spoken language. They may be coming from highly sophisticated educational systems, while others may have come from regions where access to formal schooling was limited. These students offer a rich addition to the classroom experience by way of their background knowledge and experience. All teachers will assist with their English- language development. In mathematics the teachers will include appropriate adaptations and strategies in their instructions and assessments to facilitate the success of the English language learners in their classrooms. Some of these strategies and adaptations are: modification of some or all of the course expectations so that they are challenging but attainable for the learner at his or her present level of English proficiency, given the necessary support from the teacher.

Teaching/Learning Strategy

The key learning strategy at My Learning Oasis Elite Private School is Constructivism. This format facilitates learning by many techniques, most or all of which will be adopted in the classroom. The most dominant of these is group learning. The facilitator places students of different backgrounds in the same group so that they can feed off each other. Each may bring to the table a different reasoning strategy to facilitate problem-solving. Now, each student becomes a learner and a teacher at the same time, as he/she has to communicate his/her solution. This builds the students' knowledge base and by default, increases their confidence to speak in a crowd, albeit a small group at the beginning. The famous educationalist, Vygotsky, proved that by placing students in a group they function at the upper level of their zone of proximal development, each one scaffolding the other.

This strategy is further enhanced by the teacher asking leading questions as opposed to giving the answer outright, then allowing for group discussion. The students are encouraged to make connections between what they have learnt and their life experiences, then share with the group. The effect of this strategy is intrinsic motivation and learning. Each student develops an expanded appreciation of the topic at hand by seeing how it applies in different settings around the world by way of listening to their group members.

This Constructivist approach will be further accentuated by implementing “fish-bowling”. There are many ways to implement this technique. The one that will mostly be used will be by dividing up the larger problem (technical, mathematics, science, or otherwise) into smaller bits and have each student thoughtfully master one part. That student then teaches the group and facilitates a discussion reflection about the strategy (computational or otherwise) used in the solution. Each student in turn does this.

The above techniques enable students to reflect on the material learnt, make real life connections, and develop problem solving skills. One important by-product of the technique of Constructivism is that each student develops an appreciation of each other’s culture. This cultivates healthy people’s skill, which is not only important for the professional world but for life itself.

Constructivism lends itself well to students whose first language is not the language of instruction and who is new to the class. While other strategies will be used for students having difficulty with the English Language, this technique will definitely be used to enhance their English skill.

Assessment And Evaluation

At My Learning Oasis, course facilitators do not wait for a quiz or exam to determine how well a student is doing. Here, evaluation is an on-going exercise. The pedagogical techniques (refer to Teaching and Learning Strategies) used at My learning Oasis are perhaps the best techniques suited for on-going assessment, hence, they being an integral part of our delivery methodologies.

Concrete assessments are made through projects and assignments. However, the evaluation is based on “our flavor” of the Mastery Teaching technique. This ensures that the emphasis is on the quality of learning and NOT grading. Students' projects and homework will continuously be evaluated and re-evaluated with appropriate guidance to meet the school’s and Ministry’s expectations. At My Learning Oasis, we will work with the students until the projects meet a minimum of a B-grade, unless in extreme circumstances where the willful negligence of the students force lower grades. While this is a lot more taxing on the facilitator, it does not matter because My Learning Oasis is a Learner-centered institution NOT a Grade-Centered nor a Teacher-Centered institution.

Four categories of knowledge and skills are outlined in the achievement chart - knowledge and understanding, thinking, communication, and application. Student’s work is assessed and evaluated with respect to these categories, and that achievement of particular expectations is considered within the appropriate categories. A final grade will then be recorded for this course and if that grade is 50% or higher, a credit is granted to the student and recorded for this course. The final grade for this course will be determined as follows:

● For material evaluated throughout the course, seventy percent of the grade will be assigned. This portion of the grade should reflect the student's consistency in his/her 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, which is administered towards the end of the course.

Final Exam: 30%
Grading for all course work, projects, presentation, participation, interim quizzes and exam: 70%

Course Summary
Couse Outline
Earn Bonus

Do you like rewards? Knowledge grows when you share, so does our benefits when you refer a friend.

bottom of page