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MHF4U

Page history last edited by Steve Sweeney 1 year, 3 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

 

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

note

video lesson

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

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
6

Piecewise Functions

note

video lesson

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

7

Combinations of Functions

(using simple arithmetic operations)

note

video lesson

 

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

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


8

Average & Instantaneous Rates of Change

note

video lesson

 

p.76 # 8, 9

p.85 # 4, 7, 9, 10, 15

9

Graphical Representations of Rate of Change

note

video lesson

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

note

video lesson

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

Characteristics of Polynomials

note

video lesson

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

Characteristics of Factored Form

note

video lesson

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

Transformations of Polynomials

note

video lesson

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

 

Dividing Polynomials

note

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

note

video lesson

KA - Example - Remainder Theorem

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


7

Factoring Cubic Polynomials

note

video lesson
 

WS - Factoring Sum & Difference of Polynomials

(H/W on WS)

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

note

video lesson

  p.204 # 6, 7ad, 10, 13, 16
2

Solving Linear Inequalities

note

video lesson

 

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

3

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]

4

Rates of Change in Polynomials

note

video lesson

  p.235 # 5cde, 6cde, 7, 9, 11 
5

Graphs of Reciprocal Functions

note

video lesson

 

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

# 16 (find equation of reciprocal (shown) and

original function)

6

Rational Functions & Asymptotes

note

video lesson

  p.262 # 1, 2, 3
7

Graphing Rational Functions

note

video lesson

Sample Problem PDF VT

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

worksheet (more complex problems, optional)

8

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)

9

Solving Rational Inequalities

note

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

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 note

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 note

video lesson

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

Transformations of Trig Functions

video 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
5

Graphs of Reciprocal Trig Functions

video note

video lesson

worksheet p.353 # 1, 2, 3, 6, 7
6

Modelling with Trigonometric Function

video note

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

note

video lesson

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

Graphs & Transformations of Log Functions

note

 

p.456 # 1-3 (basics), 4, 5, 8, 9, 11


3

Evaluating Logarithms

note

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

note

video lesson

 

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

5

Solving Exp & Log Equations

note

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

Solving Exp & Log Problems

note

video lesson

Worksheet - Word Problems
p.499 # 1, 2, 3, 5a, 6a, 11, 13, 15
8

Rates of Change in Log Functions

note

 

p.507 # 4, 7acd, 11abc

Note: 7b equation y=0.0017(1.7698)^x

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

note

video lesson

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

Multiplying Functions

note

video lesson

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

Dividing Functions

note

video lesson

 

p.542 # 1, 2, 3

p.544 # 3, 4, 6

5

Composition of Functions

note

video lesson

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

Solving Equations & Inequalities

note

  p.560 # 1, 3, 4, 5ef, 6ace, 9bdf
8
Review - Combinations of Functions   p.576 # 2, 4, 5, 6bcd, 7cd, 8, 9, 11, 12d
8 Evaluation    

 

Review & Final Exam

 

Review

exam review suggestions 

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

 

p.103 # 3, 5, 9, 10

p.111 # 2, 10, 13

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