This course enables students to extend their knowledge of functions. Students will investigate and apply properties of polynomial, exponential, and trigonometric functions; continue to represent functions numerically, graphically, and algebraically; develop facility in simplifying expressions and solving equations; and solve problems that address applications of algebra, trigonometry, vectors, and geometry. Students will reason mathematically and communicate their thinking as they solve multi-step problems. This course prepares students for a variety of college technology programs
Prerequisite: : Functions and Applications, Grade 11, University/College Preparation, or Functions, Grade 11, University Preparation
COURSES DETAILS
Type
College Preparation
Credit Value
1.0
Curriculum Policy
https://www.edu.gov.on.ca/eng/curriculum/secondary/2009science11_12.pdf#page=120
OVERALL CURRICULUM EXPECTATIONS
A. EXPONENTIAL FUNCTIONS
A1. solve problems involving exponential equations graphically, including problems arising from real-world applications;
A2. solve problems involving exponential equations algebraically using common bases and logarithms, including problems arising from real-world applications.
B. POLYNOMIAL FUNCTIONS
B1. recognize and evaluate polynomial functions, describe key features of their graphs, and solve problems using graphs of polynomial functions;
B2. make connections between the numeric, graphical, and algebraic representations of polynomial functions;
B3. solve polynomial equations by factoring, make connections between functions and formulas, and solve problems involving polynomial expressions arising from a variety of applications.
C. TRIGONOMETRIC FUNCTIONS
C1. determine the values of the trigonometric ratios for angles less than 360º, and solve problems using the primary trigonometric ratios, the sine law, and the cosine law;
C2. make connections between the numeric, graphical, and algebraic representations of sinusoidal functions;
C3. demonstrate an understanding that sinusoidal functions can be used to model some periodic phenomena, and solve related problems, including those arising from real-world applications.
D. APPLICATIONS OF GEOMETRY
D1. represent vectors, add and subtract vectors, and solve problems using vector models, including those arising from real-world applications;
D2. solve problems involving two-dimensional shapes and three-dimensional figures and arising from real-world applications;
D3. determine circle properties and solve related problems, including those arising from real-world applications.
TEACHING AND LEARNING STRATEGIES
Teachers will bring enthusiasm and varied teaching and assessment approaches to the classroom, addressing individual students’ needs and ensuring sound learning opportunities for every student. The activities offered should enable students to relate and apply these concepts to the social, environmental, and economical conditions and concerns of the world in which they live. Opportunities to relate knowledge and skills to these wider contexts will motivate students to learn in a meaningful way and to become life-long learners. Teachers will help students understand that problem solving of any kind often requires a considerable expenditure of time and energy and a good deal of perseverance. Teachers also will encourage students to investigate, to reason, to explore alternative solutions and to take the risks necessary to become successful problem solvers. Effective instructional approaches and learning activities draw on students’ prior knowledge, capture their interest, and encourage meaningful practise both inside and outside the classroom. Students will be engaged when they are able to see the connection between the scientific concepts they are learning and their application in the world around them and in real-life situations. Due to its importance, students will have opportunities to learn in a variety of ways- individually, cooperatively, independently, with teacher direction, through hands-on experiences, and through examples followed by practice. The approaches and strategies teachers use will vary according to both the object of the learning and the needs of the students. Teachers will accomplish this in online environment with the use of: virtual labs, online simulations, animations, videos, discussion forums, live chat and other interactive objects.
ASSESSMENT AND EVALUATION
As summarized in Growing Success 2010, the primary purpose of assessment and evaluation is to improve student learning.
The seven fundamental principles given below lay the foundation for rich and challenging practice. When these principles are fully understood and observed by all teachers, they will guide the collection of meaningful information that will help inform instructional decisions, promote student engagement, and 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, teachers use practices and procedures that:
- are fair, transparent, and equitable;
- support all students;
- 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.
Seventy per cent of the final grade (a percentage mark) in a course will be based on evaluation conducted throughout the course. This portion of the grade should reflect the student’s most consistent level of achievement, with special consideration given to more recent evidence. Thirty per cent will be based on a final evaluation administered at or towards the end of the course.
ACCOMMODATIONS FOR STUDENTS
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
THE FINAL GRADES
The final Grades
The evaluation for this course is based on the student’s achievement of curriculum expectations and the demonstrated skills required for effective learning. The final percentage grade represents the quality of the student’s overall achievement of the expectations for the course and reflects the corresponding level of achievement as described in the achievement chart for the discipline. A credit is granted and recorded for this course if the student’s grade is 50% or higher. The final grade will be determined as follows:
- 70% of the grade will be based upon evaluations conducted throughout the course. This portion of the grade will reflect the student’s most consistent level of achievement throughout the course, although special consideration will be given to more recent evidence of achievement.
- 30% of the grade will be based on final evaluations administered at the end of the course. The final assessment may be a final exam, a final project, or a combination of both an exam and a project.
THE REPORT CARDS
Two official report cards are issued – midterm and final. Each report card will focus on two distinct but related aspects of student achievement. First, the achievement of curriculum expectations is reported as a percentage grade. Additionally, the course median is reported as a percentage. The teacher will also provide written comments concerning the student’s strengths, areas for improvement and next steps. Second, the learning skills are reported as a letter grade, representing one of four levels of accomplishment. The report cards contain separate sections for the reporting of these two aspects. The report card also indicates whether an OSSD credit has been earned.