| 
  • If you are citizen of an European Union member nation, you may not use this service unless you are at least 16 years old.

  • Files spread between Dropbox, Google Drive, Gmail, Slack, and more? Dokkio, a new product from the PBworks team, integrates and organizes them for you. Try it for free today.

View
 

MHF4U 2016-2017 Semester 1

Page history last edited by Steve Sweeney 2 years, 5 months ago

MHF4U - Advanced Functions (University Preparation)

 

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.


Prerequisites:

  1. Functions, Grade 11, University Preparation; or
  2. Mathematics for College Technology, Grade 12, College Preparation

 

This page will have a daily breakdown of the course.  Most recent classes are at the top of the page, while the older classes get pushed to the bottom.

 

The beginning of each unit will be marked in blue.

Evaluations (e.g., tests, assignments, quizzes) will be marked in red.

 

University of Waterloo CEMC Courseware for MHF4U & MCV4U

Corrections to MHF4U Textbook Answer Section

 

Date Topic / Lesson

Extra Resources

Assigned Work

Fri

J27

Final Exam Carleton Exam Prep Tutoring  
  Review

Review # 1 (w/ answers)

Review # 2

Review # 3 (w/ answers)

p.188 #1,2,4,6,8-11,14,15,20,22,23,24,26-30

p.380 #1,2,4,5,6,8-25,27

p.580 #1-6,8,9,11,12,14,16,18,19,21,22,26,29,31,32,34

  Test: Combinations of Functions
   
J10
Review - Combinations of Functions extra review solutions
p.576 # 2, 4, 5, 6bcd, 7cd, 8, 9, 11, 12d
D22

Solving Equations & Inequalities

note

  p.560 # 1, 3, 4, 5ef, 6ace, 9bdf
D21

Composition of Functions

note

video lesson

  p.552 # 1, 2abf, 3, 5aef, 6def, 7cf, 10, 13
D20

Dividing Functions

note

video lesson

 

p.542 # 1, 2, 3

p.544 # 3, 4, 6

D19

Multiplying Functions

note

video lesson

  p.537 # 1ae, 3, 4bef, 5bef, 8ad, 11, 12
D14

Adding & Subtracting Functions

note

video lesson

  p.528 # 1ace, 2, 3, 5, 7, 9acef, 10, 11, 13
D13 Exploring Combinations of Functions

Handout

Video - Sound of Adding Sine Waves

p.520 # 1, 2
D16 Test: Logarithmic Functions    
D15 Review Questions from Other Texts

*** look at all notes & homework ***

p.510 # 1, 2, 3, 6a, 7, 8, 10, 11bc, 13,

14ac, 15bd, 17, 19, 22, 23


D12

Rates of Change

note

no video lesson

   
D09

Solving Exp & Log Problems

note

video lesson

  p.499 # 1, 2, 3, 5a, 6a, 11, 13, 15
D08 work period    
D07

Solving Exp & Log Equations

note

video lesson

 

p.485 # 2, 8, 10, 17

p.491 # 4, 5, 7, 12

D06

Laws of Logarithms

note

video lesson

 

p.475 # 5, 6, 7, 9ace, 10ace, 11bde, 17

D05

Evaluating Logarithms

note

video lesson

VT - Changing Base of Logs
.466 # 3 (using rule 1 or 2),

# 5 (using 1 or 2), 8 (using 4), 6, 9, 12, 17

D02

Graphs & Transformations of Log Functions

note

video lesson

  p.456 # 1-3 (basics), 4, 5, 8, 9, 11
N28

Introduction to Logarithmic Functions

video lesson

note

Handout - Graphs of Exp & Log Functions
p.451 # 4 - 9
 

Unit 6:

Exponential & Logarithmic Functions

   
D01
Test - Trigonometric Identities & Equations    
N30
Review   p.440 # 1, 2, 3ac, 4, 5, 6, 7, 8, 9, 10, 11b, 12bcd, 13
N29 Work Period   focus on solving quadratics, then general review

N25

 

Solving Quadratic Trig Equations

note

video lesson

 

p.436 # 1, 3, 6ac, 7bd, 8ad, 9ac, 11, 14, 18

  • work period next class
  • before, complete: 1, 3, 6a, 7b, 8a, 9a
  • ­day of, complete: 6c, 7d, 8d, 9c, 11, 14
N24

Solving Linear Trig Equations

note

video lesson

Sample Quiz Solutions - Compound & Double Angles

(potential test questions)

p.426 # 1bdf, 2bdf, 5, 6bdf, 8, 10bef, 11, 

18

N23

Work Period

Practice Quiz: Evaluate Trig Ratios (no calculators)

Worksheet: RAA, CAST, Trig Ratios

(practice problems similar to quiz)

 

N22

 

Trigonometric Identities

note

video lesson

MCR3U: WS 3.3 Trig Identities(solutions)

Trig Identity Solver

p.416 # 5, 8, (9, 10, 11)(odd), 17
N21

Double Angle Formulas

note

video lesson

  p.407 # 1­-3, 5, 6, 8, 9 (see p.406), 13
N17 work period    
N16

Compound Angle Formulas

note

video lesson

(Addition & Subtraction Identities)

  p.400 # 1-­4, 5acf, 6cde, 8, 9ade, 10, 13
N07

Equivalent Trigonometric Functions

note

video lesson


Trig Identities Sheet

WS: RAA & Cast Rule

p.392 # 1, 2a, 3acd, 4a, 5abc
 

Unit 5:

Trig Identities & Equations

   
N10 Midterm Exam    

N09

N08

Review - Midterm    
N15 Test - Trigonometry Pt1    
N14
Review - Trigonometric Functions   p.376 # 1-4, 6, 7, 10, 11bd, 12, 14-17, 19
N04 Activity - Model Periodic Data    
N03
Homework / Work Period

worksheet w/ extra problems

Solutions: 1 2 3 4 5 6 7 8 9 10

 
N02

Modelling with Trigonometric Function

note

video lesson

 
p.360 # 1­-3, 5, 6, 7, 9, 11
N01

Work Period:

Graphs of Trigonometric Functions

  worksheet (solutions)
O31

Graphs of Reciprocal Trig Functions

note

video lesson

worksheet p.353 # 1, 2, 3, 6, 7
O28

Transformations of Trig Functions

note

video lesson

VT (SS) - Graphing Sinusoidal by Transformations

VT (SS) - Determining Sinusoidal Equations from Graphs

p.343 # 1bd, 3, 4, 5, 8ade, 9, 11, 12, 14
O27

Graphs of Trig Functions

(focus on tangent function)

note

video lesson

Video: Sine Graph from Circular Motion
p.336 # 2c, 3, 5
O26

Radian Angles in the Cartesian Plane

note

video lesson

Worksheet - RAA & CAST Rule (w/ Answers)

MCR3U: CAST Rule

VT (SS) - Exercises w/ CAST & Trig Ratios (TOO LOUD!)

p.330 # 1-­4, 5ace, 6ace, 7ace, 8ace, 9, 11, 13 
O21

Radian Measure

note

video lesson

  p.320 # 1 -­ 4, 6 -­ 10, 15
 
  Unit 4: Trigonometric Functions    
O25 Test - Equations & Inequalities    
O24
Review - Polynomial & Rational Functions  

p.240 # 1ac, 2, 3, 4, 6ad, 7ad, 8bd, 10a, 11, 14c, 15, 16

p.308 # 1, 2, 3bd, 5bd, 7bc, 8, 9, 10cd, 11, 12, 13

O20

Rates of Change in Rational Functions

note

no video lesson

  p.303 # 1, 2, 4, 6bc, 10, 13 
O19

Solving Rational Inequalities

note

video lesson

  p.295 # 1, 4acf, 5ace, 7, 9, 13
O18

Solving Rational Equations

note

video lesson

3U Simplify Rationals Lesson VT

3U Multiply/Divide Lesson VT

3U Add/Subtract Lesson VT1 VT2 

p.286 # 5ace, 6bcf, 10, 12, 13

(see p.278 for help on 10, 13)

O17

Graphing Rational Functions

note

video lesson

Sample Problem PDF Video

p.272 # 1, 3, 5bcd, 6bd, 14

worksheet (more complex problems)

O14

Rational Functions & Asymptotes

note

video lesson

  p.262 # 1, 2, 3
O13

Graphs of Reciprocal Functions

note

video lesson

 

p.254 # 1, 2def, 6bcd, 8bdf, 9bc, 11,

# 16 (find equation of reciprocal (shown) and

original function)

O12

Rates of Change in Polynomials

note

video lesson

Quiz - Solving Inequalities

  p.235 # 5cde, 6cde, 7, 9, 11 
O11

Solving Nonlinear Inequalities Algebraically

note

video lesson

 

p.225 # [1bd, 2, 3] fundamentals

5, 6bdf, 7bdf (no graph or use tech), 8, 10, 11, 15

18 [not taking up]

O04

Solving Linear Inequalities

note

video lesson

 

p.213 # 5bdf, 6be, 7bdf, 8, 9, 11, 15, 19

O03

Solving Polynomial Equations

note

video lesson

  p.204 # 6, 7ad, 10, 13, 16
  Unit 3: Solving Equations & Inequalities    
O06
Test - Polynomials
   
O05
Review - Polynomials  

p.161 # 3 - 9

p.184 # 1-3, 7, 9bdf, 10bd, 11ac, 12b, 14ad, 15bd, 16ac, 17bd

S30

Transformations of Polynomials

note

video lesson

  p.155 # 2, 3, 4bde, 5, 6bde, 7, 8, 9, 10ace, 11, 14 
S29

Factoring Cubic Polynomials

note

video lesson
 

WS - Factoring Sum & Difference of Polynomials

(H/W on WS)

S28

Factoring Polynomials

note

video lesson

KA - Example - Remainder Theorem

p.176 # [1-3][basics], 4bf, 5ac, 6abc, 7df, 8, 9, 10, 13, 17


S27

 

Dividing Polynomials

note

video lesson

Make-up test: Function & Rate of Change

KA - Polynomial Long Division 

KA - Synthetic Division

p.168 # 1, 4, 5ace, 6ace, 7ac, 8d, 9ac, 10ace, 11, 12, 14
S26

Characteristics of Factored Form

note

video lesson

  p.146 # 1, 2, 4, 6, 9, 10, 12, 13, 14
S23

Characteristics of Polynomials

note

video lesson

  p.136 # 5, 7, 8, 9, 12, 14, 15, 16
S20

Polynomial Functions

note

video lesson

[VT - Pascal's Triangle & Binomial Expansion]
p.127 # 1 - 5
  Unit 2: Polynomial Functions    
S22 Test - Functions & Rate of Change    
S21
Review - Functions & Rates of Change  

p.60 #  1-4, 6, 7-9, 10-17

p.116 # 2-7

note: many better questions in daily homework

S19

Graphical Representations of Rate of Change

note

video lesson
  p.103 # 3, 5, 9, 10
p.111 # 2, 10, 13
S16

Average & Instantaneous Rates of Change

note

video lesson

 

p.76 # 8, 9

p.85 # 4, 5, 7

S15

Combinations of Functions note

(using simple arithmetic operations)

note

video lesson

 

Try to complete Ex.2 & Ex.3 on your own

p.57 # 2, 3, 4, 5, 6


S14

Piecewise Functions note

video lesson

KA - Piecewise Example p.51 # 3, 4, 5cd, 6, 8, 9, 11, 13 
S13

Function Inverses note

video lesson

KA - Function Inverses

KA - Restricting Domain for Inverse Functions

KA - Determine Inverse Algebraically Ex1 Ex2 Ex3

MCR3U - Function Inverses

p.44 # 4, 5, 6bd, 7, 9, 11, 12c, 13, 17
S12

Review: Transformations of Functions

note  video lesson

handout
p.36 # 4, 5, 6, 7, 9, 10, 15, 16ab
S09

Properties of Graphs

note

video lesson

Khan A - Even/Odd Functions

handout answers

p.23 # 12, 3, 4, 5, 7, 8, 9, 10, 14

use handout for 12, 14

S08

Absolute Value Function

note

video lesson

  p.16 # 3-10
S07

Review - Functions Domain Range

note

video lesson

Khan Academy - What is a Function?

(there are several videos in series)

Interval Notation

p.11 # 1, 2, 3, 4, 6, 8, 11, 12, 14
 

Unit 1: Functions & Rates of Change

   
S06
Course Intro
 

"Getting Started" from Ch.1, 2, 3

(hand in tomorrow)

 

Unit 1: Functions & Rates of Change

Day Lesson Resources Assigned Work
1

Review - Functions, Domain, Range

video lesson

Khan Academy - What is a Function?

(there are several videos in series)

Interval Notation

p.11 # 1, 2, 3, 4, 6, 8, 11, 12, 14
2

Absolute Value Function

video lesson

  p.16 # 3-10
3

Properties of Graphs

video lesson

Khan A - Even/Odd Functions

p.23 # 12, 3, 4, 5, 7, 8, 9, 10, 14

use handout for 12, 14

4

Review: Transformations of Functions

video lesson

handout
p.36 # 4, 5, 6, 7, 9, 10, 15, 16ab
5

Function Inverses

video lesson

KA - Function Inverses

KA - Restricting Domain for Inverse Functions

KA - Determine Inverse Algebraically Ex1 Ex2 Ex3

MCR3U - Function Inverses

p.44 # 4, 5, 6bd, 7, 9, 11, 12c, 13, 17
6

Piecewise Functions

video lesson

KA - Piecewise Example p.51 # 3, 4, 5cd, 6, 8, 9, 11, 13 
6

Combinations of Functions

(using simple arithmetic operations)

video lesson

 

Try to complete Ex.2 & Ex.3 on your own

p.57 # 2, 3, 4, 5, 6


7

Average & Instantaneous Rates of Change

video lesson

 

p.76 # 8, 9

p.85 # 4, 5, 7

8

Graphical Representations of Rate of Change

video lesson

  p.103 # 3, 5, 9, 10
p.111 # 2, 10, 13
9 Review - Functions & Rates of Change  

p.60 #  1-4, 6, 7-9, 10-17

p.116 # 2-7

note: many better questions in daily homework

 

Unit 2: Polynomial Functions

Day Lesson Resources Assigned Work
1

Polynomial Functions

video lesson

[VT - Pascal's Triangle & Binomial Expansion]
p.127 # 1 - 5
2

Characteristics of Polynomials

video lesson

  p.136 # 5, 7, 8, 9, 12, 14, 15, 16
3

Characteristics of Factored Form

video lesson

  p.146 # 1, 2, 4, 6, 9, 10, 12, 13, 14
5

 

Dividing Polynomials

video lesson

KA - Polynomial Long Division 

KA - Synthetic Division

p.168 # 1, 4, 5ace, 6ace, 7ac, 8d, 9ac, 10ace, 11, 12, 14
6

Factoring Polynomials

video lesson

KA - Example - Remainder Theorem

p.176 # [1-3][basics], 4bf, 5ac, 6abc, 7df, 8, 9, 10, 13, 17


7

Factoring Cubic Polynomials

video lesson
 

WS - Factoring Sum & Difference of Polynomials

(H/W on WS)

4

Transformations of Polynomials

video lesson

  p.155 # 2, 3, 4bde, 5, 6bde, 7, 8, 9, 10ace, 11, 14 
8 Review - Polynomials  

p.161 # 3 - 9

p.184 # 1-3, 7, 9bdf, 10bd, 11ac, 12b, 14ad, 15bd, 16ac, 17bd

 

Unit 3: Solving Equations & Inequalities

1

Solving Polynomial Equations

video lesson

  p.204 # 6, 7ad, 10, 13, 16
2

Solving Linear Inequalities

video lesson

 

p.213 # 5bdf, 6be, 7bdf, 8, 9, 11, 15, 19

3

Solving Nonlinear Inequalities Algebraically

video lesson

 

p.225 # [1bd, 2, 3] fundamentals

5, 6bdf, 7bdf (no graph or use tech), 8, 10, 11, 15

18 [not taking up]

4

Rates of Change in Polynomials

video lesson

Quiz - Solving Inequalities

  p.235 # 5cde, 6cde, 7, 9, 11 
5

Graphs of Reciprocal Functions

video lesson

 

p.254 # 1, 2def, 6bcd, 8bdf, 9bc, 11,

# 16 (find equation of reciprocal (shown) and

original function)

6

Rational Functions & Asymptotes

video lesson

  p.262 # 1, 2, 3
7

Graphing Rational Functions

video lesson

Sample Problem PDF VT
p.272 # 1, 3, 5bcd, 6bd, 14
8

Solving Rational Equations

video lesson

3U Simplify Rationals Lesson VT

3U Multiply/Divide Lesson VT

3U Add/Subtract Lesson VT1 VT2 

p.286 # 5ace, 6bcf, 10, 12, 13

(see p.278 for help on 10, 13)

9

Solving Rational Inequalities

video lesson

  p.295 # 1, 4acf, 5ace, 7, 9, 13
10

Rates of Change in Rational Functions

Quiz - Graphing Rational Functions

  p.303 # 1, 2, 4, 6bc, 10, 13 
11
Review - Polynomial & Rational Functions  

p.240 # 1ac, 2, 3, 4, 6ad, 7ad, 8bd, 10a, 11, 14c, 15, 16

p.308 # 1, 2, 3bd, 5bd, 7bc, 8, 9, 10cd, 11, 12, 13

 

Unit 4: Trigonometric Functions

 

  Unit 4 - Trigonometric Functions    
0 MCR3U Materials/Skills

Trigonometry of Any Angle - CAST Rule

VT (SS) - Exercises w/ CAST & Trig Ratios (TOO LOUD!)

VT (SS) - Solving Linear Trig Equation using RAA & CAST Rule

 
1

Radian Measure

video lesson

  p.320 # 1 -­ 4, 6 -­ 10, 15 
2

Radian Angles in the Cartesian Plane

video lesson

Worksheet - RAA & CAST Rule (w/ Answers)

MCR3U Trig Lessons 

p.330 # 1-­4, 5ace, 6ace, 7ace, 8ace, 9, 11, 13 
3

Graphs of Trig Functions

(focus on tangent function)

video lesson

Video: Sine Graph from Circular Motion
p.336 # 2c, 3, 5
4

Transformations of Trig Functions

video lesson

VT (SS) - Graphing Sinusoidal by Transformations

VT (SS) - Determining Sinusoidal Equations from Graphs

p.343 # 1bd, 3, 4, 5, 8ade, 9, 11, 12, 14
5

Graphs of Reciprocal Trig Functions

video lesson

worksheet p.353 # 1, 2, 3, 6, 7
6 Modelling with Trigonometric Function video lesson  
p.360 # 1­-3, 5, 6, 7, 9, 11
7 Homework / Work Period

worksheet w/ extra problems

Solutions: 1 2 3 4 5 6 7 8 9 10

 
8 Activity - Model Periodic Data    
9 Rates of Change in Trigonometric Functions AM PM
  p.369 # 1 - 3, 4bd, 6, 7, 8, 12, 15
10 Review - Trigonometric Functions   p.376 # 1-4, 6, 7, 10, 11bd, 12, 14-17, 19
11
Test - Trigonometric Functions    

 

Unit 5: Trigonometric Identities & Equations

1

Equivalent Trigonometric Functions

video lesson

Trig Identities Sheet
p.392 # 1, 2a, 3acd, 4a, 5abc
2

Compound Angle Formulas

video lesson

(Addition & Subtraction Identities)

Worksheet - RAA & CAST Rule (w/ Answers)
p.400 # 1-­4, 5acf, 6cde, 8, 9ade, 10, 13
3

Double Angle Formulas

video lesson

  p.407 # 1­-3, 5, 6, 8, 9 (see p.406), 13

4

5

Trigonometric Identities

video lesson

MCR3U: WS 3.3 Trig Identities(solutions) p.416 # 5, 8, (9, 10, 11)(odd), 17
6

Solving Linear Trig Equations

video lesson

Quiz Solutions - Compound & Double Angles

p.426 # 1bdf, 2bdf, 5, 6bdf, 8, 10bef, 11, 

18

7

Solving Quadratic Trig Equations

video lesson

 

p.436 # 1, 3, 6ac, 7bd, 8ad, 9ac, 11, 14, 18

  • work period next class
  • before, complete: 1, 3, 6a, 7b, 8a, 9a
  • ­day of, complete: 6c, 7d, 8d, 9c, 11, 14
8 Work Period    
9 Review   p.440 # 1, 2, 3ac, 4, 5, 6, 7, 8, 9, 10, 11b, 12bcd, 13
10
Test - Trigonometric Identities & Equations    

 

Unit 6: Exponential & Logarithmic Functions

1

Introduction to Logarithmic Functions

video lesson

Handout - Graphs of Exp & Log Functions
p.451 # 4 - 9
2 Graphs & Transformations of Log Functions AM PM
 

p.456 # 1-3 (basics), 4, 5, 8, 9, 11


3

Evaluating Logarithms

video lesson

VT - Changing Base of Logs

p.466 # 3 (using rule 1 or 2),

# 5 (using 1 or 2), 8 (using 4), 6, 9, 12, 17

4

Laws of Logarithms

video lesson

 

p.475 # 5, 6, 7, 9ace, 10ace, 11bde, 17

5

Solving Exp & Log Equations

video lesson

 

p.485 # 2, 8, 10, 17

p.491 # 4, 5, 7, 12

6 Work Period  

p.485 # 4, 6bc, 7, 11

p.492 # 3, 9

7 Rates of Change in Log Functions AM PM
  p.507 # 4, 7, 11abc
8

Solving Exp & Log Problems

video lesson

  p.499 # 1, 2, 3, 5a, 6a, 11, 13, 15

9

Review  

*** look at all notes & homework ***

p.510 # 1, 2, 3, 6a, 7, 8, 10, 11bc, 13,

14ac, 15bd, 17, 19, 22, 23

10
Test - Logarithmic Functions    

 

Unit 7: Combinations of Functions

1 Exploring Combinations of Functions

Handout

Video - Sound of Adding Sine Waves

p.520 # 1, 2
2

Adding & Subtracting Functions

video lesson

  p.528 # 1ace, 2, 3, 5, 7, 9acef, 10, 11, 13
3

Multiplying Functions

video lesson

  p.537 # 1ae, 3, 4bef, 5bef, 8ad, 11, 12
4

Dividing Functions

video lesson

 

p.542 # 1, 2, 3

p.544 # 3, 4, 6

5

Composition of Functions

video lesson

  p.552 # 1, 2abf, 3, 5aef, 6def, 7cf, 10, 13
6 Solving Equations & Inequalities AM PM   p.560 # 1, 3, 4, 5ef, 6ace, 9bdf
7 Review - Combinations of Functions   p.576 # 2, 4, 5, 6bcd, 7cd, 8, 9, 11, 12d
8 Evaluation    

 

p.103 # 3, 5, 9, 10

p.111 # 2, 10, 13

Comments (0)

You don't have permission to comment on this page.