Ethan Frome

Catholic District School Board of Eastern Ontario

Notre Dame Catholic High School

COURSE TITLE<= span lang=3DEN-GB style=3D'font-size:12.0pt;mso-bidi-font-size:10.0pt;mso-ansi-l= anguage: EN-GB'>: = ; &n= bsp; = ; &n= bsp; Advanced Functions

COURSE CODE= : &= nbsp; &nbs= p; &= nbsp; MHF 4U

LEVEL OF DIFFICULTY: = ; &n= bsp; University=

AREA OF STUDY: = &nb= sp; = MATHEMATICS

PREREQUISITE:= = &nb= sp; = Grade 11 Functions and Relations (MCR 3U)

NUMBER OF

SCHEDULED HOURS: = &nb= sp; 110

FACILITATOR(S): = &nb= sp; = Mark Melville, Cathy Wyatt

WRITER(S): &n= bsp; = ; &n= bsp; = ; Mark Melville

DATE OF PREPARATION: &= nbsp; &nbs= p; September 2007

UPDATED: = &nb= sp; = September 2010

MINISTRY GUIDELINES: = ; &n= bsp; Ontario Mathematics Curriculum, Grades 11 and 12

TEXTS: &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; Advanced Functions – Nelson

COURSE 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 faci= lity 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 variet= y of university programs.

STRANDS: &nbs= p; &= nbsp; &nbs= p; =

· Exponential and Logarithmic Functions

· Trigonometric Functions

· Polynomial and Rational Functions

· Characteristics of Functions<= /p>

LEARNING EXPECTATIONS

Learning Expectations describe in general terms the knowledge = and skills that students are expected to develop and demonstrate in their class work, tests and in various other activities.

By the end of this course, students will:

·         <= ![endif]>demonstrate an understanding of the relationship between ex= ponential expressions and logarithmic expressions, evaluate logarithms, and= apply the laws of logarithms to simplify numeric expressions; <= /span>
·         <= /span>identify and describe some key features of the graphs of lo= garithmic functions, make connections among the numeric, graphical, and alg= ebraic representations of logarithmic functions, and solve related problems= graphically;
·         <= /span>solve exponenti= al and simple logarithmic equations in one variable algebraically, includin= g those in problems arising from real-world applications.
·         <= ![endif]>demonstrate an understanding of the meaning and application= of radian measure;
·         <= ![endif]>make connections between trigonometric ratios and the graph= ical and algebraic representations of the corresponding trigonometric funct= ions and between trigonometric functions and their reciprocals, and use the= se connections to solve problems;

·         solve problems involving trigonometric equations and prove trigonometric identities.

·         <= ![endif]>identify and describe some key features of polynomial funct= ions, and make connections between the numeric, graphical, and algebraic re= presentations of polynomial functions;
·         <= ![endif]>identify and describe some key features of the graphs of ra= tional functions, and represent rational functions graphically; =
·         <= ![endif]>solve problems involving polynomial and simple rational equ= ations graphically and algebraically;
·         <= ![endif]>demonstrate an= understanding of solving polynomial and simple rational inequalities.
·         <= ![endif]>demonstrate an understanding of average and instantaneous r= ate of change, and determine, numerically and graphically, and interpret th= e average rate of change of a function over a given interval and the instan= taneous rate of change of a function at a given point;
·         <= ![endif]>determine functions that result from the addition, subtract= ion, multiplication, and division of two functions and from the composition= of two functions, describe some properties of the resulting functions, and= solve related problems;
·         <= /span>compare the chara= cteristics of functions, and solve problems by modelling and reasoning with functions, including pro= blems with solutions that are not accessible by standard algebraic techniqu= es.

CATHOLIC GRADUATE EXPECTATIONS

·      an effective communicator

·      a reflective and creative thinker

·      a self-directed, responsible, life long learner
·      a collaborative contributor

·      a caring family member

·      a responsible citizen

COURSE EVALUATION

&nb= sp;

Course Assessment

=

Student achievement will b= e based on the achievement chart categories outlined below and individual demonstra= tion of the specific expectations. Achievement chart categories will be posted in the classroom and distributed to students for greater awareness and understanding of assessment. All major assignments will be evaluated by lev= els. Grades will be determined using the students’ most consistent and most recent levels of achievements. For purposes of reporting, the percentage gr= ade range will correspond to the following levels as defined by the board:

Level

Mark/Code

Level

Mark/Code

Level

Mark/Code

Level

Mark/Code

4++

98/100

4+

94

3+

79

2+

69

1+

59

4

86/90

3

75

2

65

1

55

4-

82

3-

72

2-

62

1-

52

=

The Achievement Chart for Mathematics

=

The ac= hievement chart is the fundamental tool of evaluating the progress of students. The c= hart identifies four categories of knowledge and skills in Mathematics: Knowledg= e, Thinking and Inquiry/Problem Solving, Communication and Application. The achievement chart provides a standard province-wide method for teachers to use in assessing and evaluati= ng their students’ achievement. Each achievement chart has descriptions of the levels of achievement= for each of the four categories of knowledge and skills. Level 3 is the provincial standard; level 4 indicates a level of achievement beyond the standard; level 2 indic= ates the student is slightly below provincial standard; and level 1 indicates limited understanding of the material.&nbs= p; The achievement chart helps determine, throughout the course, the student’s most consistent level of achievement of the curriculum expe= ctations as reflected in his or her course work.

Achievement Chart Category Descriptions

Knowledge and Understanding – the degree to which the student demonstrates understanding of the concepts.

Thinking and Inquiry = 211; the student utilizes proper problem solving techniques, strategies, resources, technology and tools.<= /p>
Communication – the student represents information properly: written, graphical, cha= rt, numerical and symbolic forms. Effective communication implies timeliness, presentation and completeness.

Application – the student will apply proper mathematical concepts and procedures relating to familiar and unfamiliar settings.

Course Evaluation

&nb= sp;

Summative Evaluation (= 70%)

  &nbs= p;         Knowledge and Understanding     &= nbsp;           &nbs= p;

  &nbs= p;         Problem Solving, Thinking, and Inquiry  &= nbsp;

  &nbs= p;         Application        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;

  &nbs= p;         Communication        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;

       &= nbsp;    Final Assessment (30%)=

  &nbs= p;         Final Exam   &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;             = 20%.

Culminating Activity <= span style=3D'mso-tab-count:4'>        &= nbsp;           &nbs= p;            &= nbsp;   10%

            =             *= *Students must write the final exam to pass the course

COURSE EXPECTATIONS:

Each student in this math course is expected to:
1.     This is a senior Mathema= tics class, appropriate behaviour and regular attenda= nce are expected.

2.     Everyone has the right to silence while writing the test. There will be no talking during a = quiz or test until everyone has finished. Cheating will not be tolerated. The Academic Dishonesty Policy will be i= n full effect.

3.     Students are expected to= be present for all their tests. Should a student be involved in a school appro= ved extra-curricular activity on the day of the test, it becomes the responsibility of the student to = inform the teacher well in advance so= that arrangements may be made for a make-up test. Ask for help when experiencing any difficulty. I will willingly = help you. I have scheduled times available for extra help.

4. &= nbsp;   Since each learning acti= vity and evaluation tool measures specific expectations, it is necessary for students to be present for all tests and to submit all assignments on the scheduled due date. Summative Assignments that are not submitted on the given due date are subject to the Notre Dame Late Policy.

5.     Any missing assignment m= ay affect your overall level of achievement.

6.     Students may, for legiti= mate reasons, negotiate an extension or due date change with the teacher prior to the original due date. Approval for such a change will be at the discretion= of the teacher. It must be put in writing with teacher and student signature. Computer printing problems will not be accepted as legitimate reasons for l= ate assignments. If such a situation should occur the student must either prese= nt a hand written assignment or a computer disc that the teacher can read on a computer compatible with the Notre Dame computer system. This must be done on = the day the assigment is due.

*** The above expectations will be continually monitored throughout the course.

Level	Mark/Code	Level	Mark/Code	Level	Mark/Code	Level	Mark/Code
4++	98/100
4+	94	3+	79	2+	69	1+	59
4	86/90	3	75	2	65	1	55
4-	82	3-	72	2-	62	1-	52