Introduction
This course introduces the mathematical concept of the function by extending students' experiences with linear and quadratic relations. Students will investigate properties of discrete and continuous functions, including trigonometric and exponential functions; represent functions numerically, algebraically, and graphically; solve problems involving applications of functions; investigate inverse functions; and develop facility in determining equivalent algebraic expressions. Students will reason mathematically and communicate their thinking as they solve multi-step problems.
Throughout this course, students will:
- 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;
- 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;
- 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);
- select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems;
- 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);
- 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;
- communicate mathematical thinking orally, visually, and in writing, using precise mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions.
Strictly follows Ministry of Education curriculum
This is an OSSD credit course. It has been developed based on the following Ontario Ministry of Education documents:
- Mathematics, The Ontario Curriculum, Grades 11 and 12, 2007 (Revised)
- Growing Success: Assessment, Evaluation, and Reporting in Ontario Schools (2010)
Curriculum Expectations
| A Characteristics of Functions | |
| A1 | demonstrate an understanding of functions, their representations, and their inverses, and make connections between the algebraic and graphical representations of functions using transformations; |
| A2 | determine the zeros and the maximum or minimum of a quadratic function, and solve problems involving quadratic functions, including problems arising from real-world applications; |
| A3 | demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions. |
| B Exponential Functions | |
| B1 | evaluate powers with rational exponents, simplify expressions containing exponents, and describe properties of exponential functions represented in a variety of ways; |
| B2 | make connections between the numeric, graphical, and algebraic representations of exponential functions; |
| B3 | identify and represent exponential functions, and solve problems involving exponential functions, including problems arising from real-world applications. |
| C Discrete Functions | |
| C1 | demonstrate an understanding of recursive sequences, represent recursive sequences in a variety of ways, and make connections to Pascal's triangle; |
| C2 | demonstrate an understanding of the relationships involved in arithmetic and geometric sequences and series, and solve related problems; |
| C3 | make connections between sequences, series, and financial applications, and solve problems involving compound interest and ordinary annuities. |
| D Trigonometric Functions | |
| D1 | determine the values of the trigonometric ratios for angles less than 360º; prove simple trigonometric identities; and solve problems using the primary trigonometric ratios, the sine law, and the cosine law; |
| D2 | demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the numeric, graphical, and algebraic representations of sinusoidal functions; |
| D3 | identify and represent sinusoidal functions, and solve problems involving sinusoidal functions, including problems arising from real-world applications. |
How you are assessed in this course
At Agile Preparatory Academy, tests and assignments are carefully crafted to promote understanding of course content and help students achieve academic success. This success translates to high grades achieved by our students, which reflect a thorough understanding of concepts covered in the course as well as meeting and exceeding curriculum expectations.
Assessment FOR / AS / OF learning
Our teachers champion the idea that the primary purpose of assessment and evaluation is to improve student learning. Our teachers monitor student progression through the course and provide reflection and feedback that guides students towards improvement. The assessment and evaluation strategies of our school follow the Ministry of Education's policies and curriculum requirements. Our teachers use the following types of assessments to improve student learning:
Assessment for learning – These assessments include practice questions which do not contribute significantly (or at all) to the final grade. These assessments give students opportunities to practice their skills and test their knowledge prior to attempting assessments that affect their final grade. It also gives students and teachers opportunities to identify gaps in understanding and discover concepts that have been misunderstood. Here, our teacher gives students descriptive feedback and coaching for improvement.
Assessment as learning – These assessments include self reflections. The purpose of these assessments is to help students develop their capacity to be independent and autonomous learners who are able to set their own goals, monitor their own progress, determine next steps, and reflect on their thinking and learning. These tasks allow students to identify areas of strengths and weaknesses and allow them to advocate for their own learning.
Assessment of learning – These assessments contribute to the final mark of the course. Our teachers ensure that these assessments are ongoing, varied in nature, and administered over a period of time to give multiple opportunities to our students to demonstrate the full range of their learning. It allows our teachers to judge the quality of student learning with respect to curriculum expectations and assign a percentage grade to represent that quality. These assessments are designed to be fair, transparent, and equitable for of our students.
The Final Grade
The overall grade of the course is composed of:
- 70% from course work
- 30% from final evaluation
Most of the overall grade, 70%, is based on course work done prior to the final evaluation. This portion of the grade reflects the student's most consistent level of achievement in the course, with special consideration given to more recent evidence of achievement. Here, our teachers gather evidence of learning from assignments, projects, presentations, and tests throughout the course (Assessment of Learning), giving students multiple opportunities to perform well.
The balance, only 30% of the overall grade, is gathered from 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 OSSD credit
A credit is granted and recorded when the final percentage mark in this course is 50 per cent or higher.
Agile Prep Academy is a high school through which a student can earn credits towards the Ontario Secondary School Diploma (OSSD) high school diploma. We are in compliance with Ontario Ministry of Education policies, and are assessed and authorized by the Ministry to grant the OSSD diploma as well as OSSD credits.
Our courses are taught online, which allows our students to meet and exceed the online credit requirements needed for graduation. For further high school graduation requirements, including the Online learning graduation requirement, please visit the Ministry’s website.