Advance Functions Grade 12

Outline of Course Content

Unit 1: Polynomial and Rational Functions

In this unit, students will focus on key features of graphs of polynomial functions, such as power functions, and their transformations. Students will also be introduced to the concepts of average and instantaneous rate of change. Rational functions take the form of f(x) = P(x) / Q(x), where P(x) and Q(x) are both polynomial functions and Q(x) is not equal to 0. Students will investigate these rational functions, their graphs, and their rates of change and apply them to such fields as business, medicine, environmental studies, and electronics.

Unit 2: Trigonometric Functions

In this unit, students will investigate another method of measuring angles known as radian measure. They will extend the use of radian measure to trigonometric ratios and gain an appreciation for the simpler representations that occur when using radian measure. They will develop trigonometric formulas for compound angles and investigate equivalent trigonometric expressions using a variety of approaches. Students will develop techniques for identifying and proving trigonometric identities. Also in this unit, students will extend their knowledge of trigonometric ratios to develop trigonometric functions expressed in radian measure. They will investigate the properties of the sine, cosine, tangent, cosecant, secant, and cotangent functions.

Unit 3: Exponential and Logarithmic Functions

In this unit, students will explore a variety of situations that can be modeled with an exponential function or its inverse, the logarithmic function. They will learn a variety of strategies for solving exponential and logarithmic equations, and apply modeling strategies to solve a variety of problems involving data that can be modeled by exponential and other types of curves.

Unit 4: Characteristics of Functions

In this unit, students will learn techniques to analyse various combinations of functions and solve real-world problems requiring these techniques. Students will determine functions that result from the addition, subtraction, multiplication, and divisions of two functions and from the composition of two functions, describes some properties of the resulting functions, and solve related problems.

Unit 5:Course Review, Summative ISU, Final Exam

Students will be given time near the end of the course to review all the concepts they have learned throughout the course in preparation for the final exam. Included in this unit, students will also be able to apply their knowledge on a summative ISU which is a case study that covers all overall expectations.

Resources required by the student:

· A scanner, smart phone camera, or similar device to digitize handwritten or hand-drawn work,

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

· Spreadsheet software (e.g. Microsoft Excel^TM, Mac Numbers^TM, or equivalent)

· Word processing software (e.g. Microsoft Word^TM, Mac Pages^TM, or equivalent)

· Microphone and audio recording software

· Graphing Software. For Windows users, a link to free graphing software will be provided in the course. For Mac users, we recommend using the Grapher^TM software that s pre-installed

Types of Assessment

Assessmentsforandaslearning will have a diagnostic and formative purpose; their role is to check for students’ understanding. Assessments that serve this purpose will usually manifest themselves in the form of short, daily quizzes, teacher checking of homework, and conversations about progress. The purpose these quizzes serve is to encourage students to review daily and to alert students when there is a specific expectation they have not yet achieved. Quizzes are effective simply because they provide immediate feedback for the student.

Assessmentsoflearning have a summative purpose and are given at strategic instances- for example, after a critical body of information/set of overall or specific expectations has been covered. “This type of assessment collects evidence for evaluating the student’s achievement of the curriculum expectations and for reporting to students and parents/guardians” (Growing Success- assessment, evaluation, and reporting: improving student learning, pg. 1-ii). Assessmentsof learning consider product, observation, and conversation as sources of evidence.

Final Mark Calculation

Calculation of the Term Mark will be based upon theCategories of theAchievement Chart. This chart is meant to assist teachers in planning instruction and learning activities for the achievement of the curriculum expectations. It is also used in designing assessment and evaluation tasks and tools and in providing feedback to students. Each mathematical topic will contain each category in the chart due to the integrated nature of the discipline in mathematics. Final marks will be calculated as follows:

Term Work: 70%Final Summative Evaluation: 30%

CategoryWeightTaskWeight

Knowledge and Understanding: 25%

Thinking and Inquiry: 25% Final Exam 30%

Application: 25%

Communication: 25%

Final Summative Evaluation: 30%

CategoryWeight

Knowledge and Understanding: 25%

Thinking and Inquiry: 25%

Application: 25%

Communication: 25%

The Final Summative Evaluation will take the form of a proctored 3 hours exam worth 30% of the students final mark. It is important to note that the Final Summative Evaluation will share the same weighting for each category of the achievement chart as the term work. This means that K/T/A/C will have a 25%/25%/25%/25% split on the final examination in accordance with the rest of the term work.

Teaching and Learning Strategies:

The over-riding aim of this course is to help students use the language of mathematics skillfully, confidently and flexibly, a wide variety of instructional strategies are used to provide learning opportunities to accommodate a variety of learning styles, interests and ability levels. The following mathematical processes will form the heart of the teaching and learning strategies used:

Communicating: This course offers students many opportunities to share their understanding both in oral as well as written form. Students will discuss concepts they have learned through discussion boards, write reports which relate concepts taught to real-world applications, and create presentations to demonstrate understanding of some concepts.

Problem solving: This course scaffolds student learning by building on prior knowledge and skills. Students will have the opportunity to review prior concepts and will be presented with problems that require them to apply their skills in new ways to solve problems related to real-world applications.

Reflecting: This course models the reflective process. Through the use of examples and practice exercises, the course demonstrates proper communication to explain intermediate steps and reflect on solutions to determine if they make sense in the given context.

Selecting Tools and Computational Strategies: This course models the use of graphing software to help solve problems and to familiarize students with technologies that can help make solving problems faster and more accurate.

Connecting: Students will connect the concepts taught in the course to real-world applications (e.g. concepts related to polynomial functions will be connected to applications in engineering). Students will have opportunities to connect previous concepts to new concepts through posed problems, investigations, and enrichment activities.

Self-Assessment: Through the use of interactive activities (e.g. multiple choice quizzes, and drag-and-drop activities) students receive instantaneous feedback and are able to self-assess their understanding of concepts.