Introduction
This is a credit course for University-bound students. This course builds on students' previous experience with functions and their developing understanding of rates of change. Students will solve problems involving geometric and algebraic representations of vectors and representations of lines and planes in three dimensional space; broaden their understanding of rates of change to include the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions; and apply these concepts and skills to the modelling of real-world relationships. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended for students who choose to pursue careers in fields such as science, engineering, economics, and some areas of business, including those students who will be required to take a university-level calculus, linear algebra, or physics course.
Throughout this course, students will learn the following:
- Problem Solving: 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
- Reasoning and Proving 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
- Reflecting: 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)
- Selecting Tools and Computational Strategies: Select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems
- Connecting: 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)
- Representing: 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;
- Communicating: 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:
- The Ontario Curriculum, Grades 11 and 12 Mathematics, Revised 2007
- Growing Success: Assessment, Evaluation, and Reporting in Ontario Schools (2010)
Major Units and Allocated Time
| Unit | Suggested Time |
|---|---|
| Unit 1 | 10.5 hours |
| Unit 2 | 10.1 hours |
| Unit 3 | 12.4 hours |
| Unit 4 | 11.3 hours |
| Mid Term Point | |
| Unit 5 | 11.6 hours |
| Unit 6 | 15.5 hours |
| Unit 7 | 17.1 hours |
| Unit 8 | 13.4 hours |
| Unit 9 | 11.1 hours |
| Final Assessments | |
| Final Exam Practice 1 | 2 hours |
| Final Exam Practice 2 | 2 hours |
| Final Examination | 3 hours |
| Total | 126 hours |
Curriculum Expectations
| A Rate of Change | |
| A1 | demonstrate an understanding of rate of change by making connections between average rate of change over an interval and instantaneous rate of change at a point, using the slopes of secants and tangents and the concept of the limit; |
| A2 | graph the derivatives of polynomial, sinusoidal, and exponential functions, and make connections between the numeric, graphical, and algebraic representations of a function and its derivative; |
| A3 | verify graphically and algebraically the rules for determining derivatives; apply these rules to determine the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions, and simple combinations of functions; and solve related problems. |
| B Derivatives and their Applications | |
| B1 | make connections, graphically and algebraically, between the key features of a function and its first and second derivatives, and use the connections in curve sketching; |
| B2 | solve problems, including optimization problems, that require the use of the concepts and procedures associated with the derivative, including problems arising from real-world applications and involving the development of mathematical models. |
| C Geometry and Algebra of Vectors | |
| C1 | demonstrate an understanding of vectors in two-space and three-space by representing them algebraically and geometrically and by recognizing their applications; |
| C2 | perform operations on vectors in two-space and three-space, and use the properties of these operations to solve problems, including those arising from real-world applications; |
| C3 | distinguish between the geometric representations of a single linear equation or a system of two linear equations in two-space and three-space, and determine different geometric configurations of lines and planes in three-space; |
| C4 | represent lines and planes using scalar, vector, and parametric equations, and solve problems involving distances and intersections. |
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.