MHF4U

 

ADE Schools

 

Grade 12 Advanced Functions Course Outline

 

 

 

School Name: ADE Schools 

 

Department: Department of Mathematics 

 

Curriculum policy document: The Ontario Curriculum, Grade 11 and 12,

 

Mathematics, 2007(Revised)

 

Course Developer: Department of Mathematics

 

Course Development Date: March 2011

 

Course Title: Advanced Functions  

 

Course Type: University Preparation

 

Course Level: Grade 12

 

Course Code: MHF4U

 

Credit Value: 1.0

 

Duration: 110 hours

 

 

 

Prerequisite: Functions, Grade 11, University Preparation, or

 

Mathematics for College Technology, Grade 12,

 

College Preparation

 

 

 

 

 

Course Origin: This course is developed at the ADE Schools’s department of Mathematics from the Ontario curriculum document:  “Ontario curriculum, mathematics Grades 11 and 12, 2007 (revised)”

 

Course Rational and Description:

 

This course extends students’ experience with functions. Students will investigate the properties of polynomial, rational, logarithmic, and trigonometric functions; develop techniques for combining functions; broaden their understanding of rates of change; and develop facility in applying these concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended both for students taking the Calculus and Vectors course as a prerequisite for a university program and for those wishing to consolidate their understanding of mathematics before proceeding to any one of a variety of university programs.

 

Prerequisite: Functions, Grade 11, University Preparation, or Mathematics for College

 

Technology, Grade 12, College Preparation

 

 

 

Strands:

 

The course consists of four strands, exponential and logarithmic functions, trigonometric functions, polynomial and rational functions and characteristics of functions.

 

 

 

Strand 1:                          EXPONENTIAL AND LOGARITHMIC FUNCTIONS

 

OVERALL EXPECTATIONS

 

By the end of this course, students will:

 

1.     Demonstrate an understanding of the relationship between exponential expressions and logarithmic expressions, evaluate logarithms, and apply the laws of logarithms to simplify numeric expressions;

 

2.     Identify and describe some key features of the graphs of logarithmic functions, make connections among the numeric, graphical, and algebraic representations of logarithmic functions, and solve related problems graphically;

 

3.     Solve exponential and simple logarithmic equations in one variable algebraically, including those in problems arising from real-world applications.

 

Strand 2:TRIGONOMETRIC FUNCTIONS

 

OVERALL EXPECTATIONS

 

By the end of this course, students will:

 

1.     Demonstrate an understanding of the meaning and application of radian measure;

 

2.     Make connections between trigonometric ratios and the graphical and algebraic representations of the corresponding trigonometric functions and between trigonometric functions and their reciprocals, and use these connections to solve problems;

 

3.     Solve problems involving trigonometric equations and prove trigonometric identities.

 

Strand 3:POLYNOMIAL AND RATIONAL FUNCTIONS

 

OVERALL EXPECTATIONS

 

 

 

By the end of this course, students will:

 

1.     Identify and describe some key features of polynomial functions, and make connections between the numeric, graphical, and algebraic representations of polynomial functions;

 

2.     Identify and describe some key features of the graphs of rational functions, and represent rational functions graphically;

 

3.     Solve problems involving polynomial and simple rational equations graphically and algebraically;

 

4.     Demonstrate an understanding of solving polynomial and simple rational inequalities

 

Strand 4:CHARACTERISTICS OF FUNCTIONS

 

OVERALL EXPECTATIONS

 

 

 

By the end of this course, students will:

 

1. demonstrate an understanding of average and instantaneous rate of change, and determine,
numerically and graphically, and interpret the average rate of change of a function over a given
interval and the instantaneous rate of change of a function at a given point;
2. determine functions that result from the addition, subtraction, multiplication, and division of two
functions and from the composition of two functions, describe some properties of the resulting
functions, and solve related problems;
3. compare the characteristics of functions, and solve problems by modelling and reasoning with
functions, including problems with solutions that are not accessible by standard algebraic techniques.

 

Course Content:

 

This course is clustered into four units of study relating directly to the four strands of the curriculum document. These units, sequenced in the order they are to be delivered, and not the order of their actual order, are as follows: (NB: the first strand or unit, Exponential and Logarithmic Functions is the last to be delivered)

 

 

 

Unit 3

Polynomial and Rational Functions (1st to be delivered)

28 hours

Unit 4

Characteristics of Functions( 2nd  to be delivered)

28  hours

Unit 2

Trigonometric Functions ( 3rd to be delivered) 

28  hours

Unit 1

Exponential and Logarithmic Functions (4th to be taught)

28  hours

 

Total Hours

112 hours

 

 

 

 

 

Teaching and Learning Strategies and Tools

 

Because the course the nature of the teaching strategies of the course is electronic and internet-based delivery, media for conveying learning will be either synchronous or asynchronous. Academy of Distance Education is dedicated to maximize possibility of establishing “comfort zone” for students while opportunities for learning successfully are continuously explored. For that reason, both of the mediums of electronic delivery mentioned above are equally utilized as per the need and suitability of each one in different situations.

 

Examples E- Teaching/ E-Learning Strategies in the course/courses:

 

  • Lectures/handouts/note taking (through on-line vehicles both synchronously and asynchronously)

  • Case Studies (both synchronously and asynchronously)

  • Brainstorming (in virtual class discussions as well as in face book or other social sites used for the purpose of e-learning and e-teaching)

  • Writing (research, essays, poems)

  • Homework, class work, assignments

  • Labs and demonstrations (mainly computer simulations to accommodate distance learning)

 

  • Small/large group discussions (virtual classes or one-on-one virtual situations)

  • Multimedia presentations (all on-line)

  • Guest speeches

    Teaching/Learning Tools: (all designed to meet the requirements of e-schooling)

 

  • Textbook

 

  • Overhead projector, screen, electronic writing devices like the electronic pen pad and transparencies

  • Online software, CDs, DVDs, videos/films

 

  • Chart paper,

  • Posters

  • Online educational activities and games

  • Relevant scientific sites & magazines & articles

    Assessment & Evaluation;

    Note:

    Academy of Distance Education has in place a policy that requires students to write an obligatory supervised final evaluation worth 30 % of the overall grade of each course as well as an obligatory supervised midterm worth 20% of the overall grades which takes place midway through the course.

    At ADE, Assessment and Evaluation is done in such a way that for each course, every other unit test is written at the ADE site with full supervision to allow for a maximum control on the fairness of reporting student achievement of curricular expectations and performance standards. The proportion of the final evaluation that the supervised, on-site tests cover are clearly mentioned within the breakdown (along the different units) of the 70% of the overall grade section of the course outline.  The final Examination (or the exam and another assessment instrument) worth 30% will also be written at the ADE office in a supervised environment. This mechanism will leave at least 50% of the final overall grade to have resulted from assessments conducted directly at on-site supervised settings.

    ADE also assures students teacher-led session, fully executed through virtual, synchronous settings that allow for maximum student-teacher interaction and information-sharing through live sessions. Students will have the opportunity to ask questions before the teacher goes to the next section or topic and not wait until time interval has lapsed. This will assure students that delivery of learning requirements will be similar to the physical class settings except that the challenges of space, time and schedule limitations have all been erased.

    Assessment and Evaluation processes completed at ADE heavily rely on the newly legislated Ontario dual standard system (Growing Success) where content standards and performance standards are assessed and linked properly; content standards being the curricular expectations from the discipline documents and performance standards coming from the achievement chart categories and the levels that reflect how effectively such categories are linked. Each assessment will clearly mention how the interconnection and inter=relations of the assessment components and types take place.

    Assessment and evaluation at the Academy of Distance Education is based heavily on dividing the assessment strategies equally between comprehensive, on-site and supervised assessments and assessments conducted by the student alone and sent electronically or through other means by the student. The latter will include instances where the student does access-controlled on-line testing and quizzing where possibilities of extra-personal efforts are eliminated completely making sure that the student does the work. Other opportunities will allow for students meeting assessment requirements while seeking help from any source but making sure knowledge has been gained by the student through the help provided to him/her. All these systems are designed the benefits of e-learning and e-teaching are maximized and not diminished by factors that could be brought forth by the introduction of non-traditional classrooms.

    In general, Assessment is a continuous process of gathering evidence to facilitate and enhance student learning, provide feedback, and improve instructional strategies. Evaluation is the process of judging the quality of student work in an assessment, on the basis of established criteria, and the assigning of a value to represent that quality. The purpose of evaluation is to summarize student progress at a given point in time.

     

    In the 2010/2011 and beyond, Numerous and varied assessment opportunities will be given to students and various strategies and tools will be employed throughout the course in order to achieve maximum precision and fairness in assessing how well students learned the curricular expectations of each strand and the course. This will be an attempt meet ministry of education guidelines introduced for the 2010 and effective successive years until further notice of change.   Diagnostic assessments will be used to determine prior learning, students’ strengths and for planning purposes and therefore will not be used to determine term or final grades for report card. Formative assessments will be used regularly as a learning tool and feedback mechanism to improve student learning and instructional strategies. Summative assessments will be used to provide final professional judgment and evaluation of student learning of curricular expectations and therefore will be used to evaluate term work and the final assessment for reporting purposes. When planning assessments, the curricular expectations will be reviewed and linked to the achievement categories to which they relate. This is to ensure that all the expectations are accounted for in instruction, and that achievement of the expectations is assessed within the appropriate categories. All three types of assessments are still further regrouped into three parts: assessment for learning, feedback mechanisms meant to enhance student learning (formative and diagnostic); assessment as learning, self assessment and  peer assessment tools done led and /or teachers in which students learn how to independently assess the level of their own learning (diagnostic , formative)’ and assessment of learning (summative only), which is led by the teacher alone and is used for purposes of evaluation and reporting of student achievement to parents and other stake holders.

    Assessment Methods: The means through which student learning may be assessed (i.e., written, spoken, or done). In this course, students will use all three methods to demonstrate their learning: oral work (debates, discussions, presentations, skits), written work (tests, quizzes, reports, essays), and performances (labs, models, pamphlets, charts). Both synchronous and asynchronous opportunities are made available.

    Assessment Strategies: The actual assessment instruments used as the  process used for assessing student learning and the level of their achievement of meeting curricular expectations (e.g. journal). ADE will use conduct assessments both synchronously and asynchronously throughout the course. Below is a list of the most commonly used assessment strategies for this course:

 

  • Tests/Quizzes (done both on-line and a designated site with supervision)

  • Interviews/Conferences  (Virtual class discussions)

  • Examinations (done only comprehensively at a site with supervision)

  • Multimedia Presentations (virtual class presentation synchronously

  • Assignments, Research Projects/Reports (on-line)

    Assessment Tools: An instrument that is used to initiate or guide the assessment strategy or to track, monitor or record the assessment data (e.g. rubric). Below is a list of the most commonly used assessment tools for this course:

 

  • Check lists (learning skills, homework check, completion of a task, basically to check absence or presence of a concept, process, skill, or attitude)

  • Marking Scheme (tests/quizzes, assignments, worksheets, to quantify student response; value based tasks)

  • Rating Scales (to assess frequency of achieving a task or quality of task)

  • Rubrics  (performances, written reports, presentations, labs, complex projects/tasks)

  • Anecdotal Comments (learning skills, group work, independent work, presentations,

    Evaluation:

    Two parts make up the evaluation of student achievement through the different assessment strategies mentioned above.

    a)      The term work accounts for 70% of the overall grade for the course. Assessment for this portion is spread through out the course up until six weeks before the end of the study term.

    b)      The final evaluation will account for 30% of the final overall grade for the course.  Its assessment takes place during the last 6 weeks of the study term and will in the form of a final examination more than two thirds of which comes from material covered after November 15, 2008.

    Evaluation

    Breakdown of the 70% course evaluation among the units

    This unit’s work will account for 18% of the 70 marks for coursework.

    Unit 4: CHARACTERISTICS OF FUNCTIONS

    Tests                                                10% (2 tests)

    Quizzes                                              5%

    Assignments                                  2.5%

    ______________________________________

    Total Unit 1 Evaluation                 17.5%

    This unit’s work will account for 17.5% of the 70 marks for coursework.

    Unit  2: EXPONENTIAL ANDLOGARITHMIC FUNCTIONS

    Tests                                    10%

    Quizzes                                  5%

    Assignments                      2.5%

    ______________________________________

    Total Unit 2 Evaluation       17.5%

    This unit’s work will account for 18% of the 70 marks for coursework.

    Unit 3: TRIGONOMETRIC FUNCTIONS

    Tests                                                10% (2 tests)

    Quizzes                                             5%

    Assignments                                 2.5%

    ____________________________________

    Total Unit 3 Evaluation                  17.5%

    This unit’s work will account for 17.5% of the 70 marks for coursework.

    Unit 4: POLYNOMIAL AND RATIONAL FUNCTIONS

    Tests                                                10% (2 tests)

    Quizzes                                              5%

    Assignments                                   2.5%

    ______________________________________

    Total Unit 4 Evaluation                   17.5%

    This unit’s work will account for 17.5% of the 70 marks for coursework

    The final assessment covers what students have been learning the length of the course with more emphasis on the more recent parts.  It will be managed within the last 6 Weeks in full course (through the year) and the last three weeks in half credit course (Sep to Jan) and accounts for 30% of the overall grades that will appear in the “final” box of the report card.  The final evaluation will be administered as follows:

     

 

Final Examination 

20%

Performance task  

10%

Total for final evaluation 

30%

Overall Grade mark 

70+30 = 100%

 

 

 

 

 

Main Resources:

 

Main Textbook:  Nelson Mathematics: Advanced Functions , grade 12, University Preparation (MHF4U)

 

1.     Internet

 

2.     Public Library