Grade 12 Functions
Course outline:

CanterburyHigh School
Advanced Functions, Grade 12
University Preparation MHF4U

This course extends students’ experience with functions. Students will investigate the properties of polynomials, 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 considered a prerequisite for Calculus and Vectors as well as for those wishing to consolidate their understanding of the mathematics before proceeding to any of the university programs.

Prerequisite: MCR3U

The Term work will be worth 70% . The methods of evaluation will include tests, quizzes, and in class tasks.

The topics to be studied and evaluated in this course are:

A. EXPONENTIAL AND LOGARITHMIC FUNCTIONS
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.

B. TRIGONOMETRIC FUNCTIONS
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.

C. POLYNOMIAL AND RATIONAL FUNCTIONS
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.

D. CHARACTERISTICS OF FUNCTIONS
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.


The Final Evaluation will be worth 30% of the course.


Required materials

All students are required to have a scientific calculator, pencils, pens, an eraser, paper, graph paper, and a ruler for each class. Borrowing from other students in class during tests, exams, and quizzes is not permitted. Please come to class prepared.

Textbook cost


The textbook for this course costs $95. A textbook will be loaned to you. If you lose or damage the textbook you will be required to pay for it.

Teacher: Mr. Hughson e-mail: darrin.hughson@ocdsb.ca

Website: hughsonmath.wikispaces.com

WolframAlpha: http://www.wolframalpha.com/
University of waterloo video lessons and exercises with solutions:http://courseware.cemc.uwaterloo.ca/8?gid=122
videos: Go to the second page of this link to start seeing lessons for this course http://www.yourepeat.com/g/MHF4U

Textbook Homework

Ch 3
Page
Numbers
136
1,3,5,6,10,11
146
1,2,4,6,8,9,12,14
169
1,2,3,4,5,6,8,10,12,18
176
1,2,3,4,5,6,7,10,11,12
182
2,4,5,6,8

Ch 4
Page
Numbers
204
2,4,7,9,10,11,14,15
213
16
1,2,3,4,6,7,10,15
3 to 10
225
1,2,3,5,6,7,8,10

Ch 5
Page
Numbers
285
2,3,5,6,7,11,13,15
296
2,3,4,5
254
1,2,5,6,8,9,11
273
1,2,3,4,5,6,8,13,14

Ch 6
Page
Numbers
320
1,2,3,4,5,6,7,8,9,11,12
330
1,2,3,4,5,6,7,8,9,10,11,13,17
336
3,5
343
1,2,3,4,5,8,9,10,11,12
353
5,7
361
6,7,8

Ch 7
Page
Numbers
392
6,7
400
1,2,3,4,5,6,7,8,9,10,11,12
407
1,2,3,5,7,11,12,13,15
418
3,4,8,9,10,11
426
1,3,5,6,8,10,11,12
437
1,3,4,5,6,7,8,9,13,14

Ch 8
Page
Numbers
451
1,2,3,4,5,6,7,8,9
457
1,2,3,4,5,8,9
466
1,2,3,4,5,6,7,8,9,10
475
1,2,3,4,5,6,7,8,9,10,11,12,13
485
1,2,3,5,6,7,8,12,14,15
491
1,2,4,5,6,7,8,10,11,12,18

Ch 2
Page
Numbers
76
1,4
85
1,4
111
2,3,4,5
236
10
304
8,9,10
371
5,6,7,12
507
6,9

Chs 1 and 9
Page
Numbers


43
3,4,13
51
1,3,5,8,9,14
528
1,2,3,5,9
537
1,3,4,5
542
1,2
552
1,2,3,5,7,10




Trig identities
http://www.oame.on.ca/main/files/Gr12-2007/MHF4U/MHF4U-unit4.doc

Tuesday, September 01, 2009

Wednesday, September 02, 2009
Page. 2 #'s 2,3,5
Page. 11 #'s 1,3,4,5
Thursday, September 03, 2009

Friday, September 04, 2009
Page. 16 #'s 1 to 8
Monday, September 07, 2009

Tuesday, September 08, 2009
Page. 25 # 12
Page. 24 #'s 8,9
Wednesday, September 09, 2009
Page. 24 # 10
Thursday, September 10, 2009

Friday, September 11, 2009
Page. 43 #'s 1 to 4
Page. 35 #'s 1,2,4,5,9,14
Monday, September 14, 2009
Page. 60 #'s 1 to 13
Tuesday, September 15, 2009
Page 51 #'s 1,3,8,9
Wednesday, September 16, 2009
Page 56 #'s 1 to 4a, 5ac
Page 76 #'s 1ac,2,8
Thursday, September 17, 2009

Friday, September 18, 2009
Page 85 #'s 3
Monday, September 21, 2009
Page 87 #'s 7
Page 112 #'s 5ac,6ace,10
Tuesday, September 22, 2009

Wednesday, September 23, 2009

Thursday, September 24, 2009

Friday, September 25, 2009

Monday, September 28, 2009

Tuesday, September 29, 2009
Page 122 #'s 1 to 8
Wednesday, September 30, 2009
Page 136 #'s 1 to 7
Page 146 #'s 1 to 8, 12, 13
Thursday, October 01, 2009

Friday, October 02, 2009

Monday, October 05, 2009
Page 168 #'s 1 to 3
Tuesday, October 06, 2009
Page 168 #'s 5 to 14, 18
Wednesday, October 07, 2009

Thursday, October 08, 2009

Friday, October 09, 2009

Monday, October 12, 2009

Tuesday, October 13, 2009
Page 176. #'s 1, 2, 4, 5
Wednesday, October 14, 2009
Ch 1 & 2 test

Thursday, October 15, 2009
Page 176. #'s 3, 6 to 13
Friday, October 16, 2009
Work period
Monday, October 19, 2009
factor difference and sum of cubes
Tuesday, October 20, 2009
Page 182. #'s 1 to 5, 8
Wednesday, October 21, 2009
Page 187. Chapter task
Page 204. #'s 1 to 9
Thursday, October 22, 2009
Study for quiz
Friday, October 23, 2009
Ch. 3 Quiz
Monday, October 26, 2009
Page 206 #16
Page 213 #1 to 7,9, 11
Tuesday, October 27, 2009
Page 215 #'s 15, 19
Wednesday, October 28, 2009
Page 225 #'s 1 to 10, 13,14
Thursday, October 29, 2009

Friday, October 30, 2009

Monday, November 02, 2009
Teacher away.
Ch 4 Quiz postponed until tuesday.
Do Numbers 1 to 14 and 16 on Page 235.
Tuesday, November 03, 2009
Ch 4 Quiz
Wednesday, November 04, 2009
Page 254. #'s 1 to 8
Thursday, November 05, 2009

Friday, November 06, 2009

Monday, November 09, 2009

Tuesday, November 10, 2009
Page 257. #'s 12, 13
Wednesday, November 11, 2009

Thursday, November 12, 2009
Sketching 3 rational functions given in class.
Friday, November 13, 2009

Monday, November 16, 2009
Page 272. #'s 1 to 8, 13,14.
Tuesday, November 17, 2009

Wednesday, November 18, 2009
Page 285. #'s 1 to 7, 10, 12, 15
Page 295. #'s 1 to 7, 9, 11, 13
Thursday, November 19, 2009

Friday, November 20, 2009
Page 320. #'s 1 to 5, 7 to 9, 11 to 13.
Monday, November 23, 2009
Page 330. #'s 1 to 8.
Tuesday, November 24, 2009

Wednesday, November 25, 2009
Ch 5 test
Thursday, November 26, 2009

Friday, November 27, 2009

Monday, November 30, 2009
Page 336 #2(c)
Page 353 #'s 1,2,3,5,6,7
Page 343 # 1(graph each function)
Tuesday, December 01, 2009
Page 345 #'s 6,7,8(c)(f), 10,11,12
Wednesday, December 02, 2009
Page 360 #'s 1,2,4,5,7,8,9
Thursday, December 03, 2009
Page 392 #'s 5,6,7
Friday, December 04, 2009
Page 401 #'s 1 to 13
Monday, December 07, 2009
Page 407 #'s 1 to 5
Tuesday, December 08, 2009

Wednesday, December 09, 2009
Page 407 #'s 6 to 13
Thursday, December 10, 2009
Page 417 #'s 8 to 11
Friday, December 11, 2009

Monday, December 14, 2009
Page 426 #'s 3,4,5
Tuesday, December 15, 2009
Page 428 #'s 6 to 10, 12, 13
Page 435 # 1
Wednesday, December 16, 2009
Page 436 #'s 2 to 9
Thursday, December 17, 2009

Friday, December 18, 2009

Monday, January 04, 2010
Page 451 #'s 2(ii), 6,8,9
Page 466 #'s 1,2,3
Tuesday, January 05, 2010
Page 466 #'s 4 to 10, 12, 14, 18
Wednesday, January 06, 2010
Trig test
Thursday, January 07, 2010

Friday, January 08, 2010
Page 457 #'s 1 to 7
Page 475 #'s 1 to 13
Monday, January 11, 2010
Page 485 #'s 1 to 8, 10
Tuesday, January 12, 2010
Page 491 #'s 1 to 7odd
Wednesday, January 13, 2010

Thursday, January 14, 2010

Friday, January 15, 2010

Monday, January 18, 2010

Tuesday, January 19, 2010
Summative
Wednesday, January 20, 2010

Thursday, January 21, 2010

Friday, January 22, 2010

Monday, January 25, 2010
Exam
Tuesday, January 26, 2010

Wednesday, January 27, 2010

Thursday, January 28, 2010

Friday, January 29, 2010