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MHF4U 2018-2019 Semester 1

Page history last edited by Steve Sweeney 1 year, 10 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

 

Mark Breakdown:

     Unit Tests: 70%

     Final Exam: 30%

 

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

MHF4U Solutions Manual

  

Full Course (all video lessons, completed notes, assigned homework, extra resources)

 

Date  Topic / Lesson

Extra Resources

Assigned Work

J25

Final Exam

Friday, January 25th

Room 205

9am (textbook return 8:45am)

   

J24

J23

J22

J21

J18

J17

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

J16 Test - Combinations of Functions    
J15
Review - Combinations of Functions   p.576 # 2, 4, 5, 6bcd, 7cd, 8, 9, 11, 12d
J14

Solving Equations & Inequalities

class note

note

  p.560 # 1, 3, 4, 5ef, 6ace, 9bdf
J11 work period    
J10 work period    

J09

Composition of Functions

class note

note

video lesson

  p.552 # 1, 2abf, 3, 5aef, 6def, 7cf, 10, 13
J08

Dividing Functions

class note

note

video lesson

 

p.542 # 1, 2, 3

p.544 # 3, 4, 6

J07

Multiplying Functions

class note

note

video lesson

  p.537 # 1ae, 3, 4bef, 5bef, 8ad, 11, 12
D20

Adding & Subtracting Functions

class note

note

video lesson

  p.528 # 1ace, 2, 3, 5, 7, 9acef, 10, 11, 13
D19 Exploring Combinations of Functions

Handout

Video - Sound of Adding Sine Waves

p.520 # 1, 2
 

Unit 7: Combinations of Functions

   
D18
Test - Logarithmic Functions    

D17

 

Review  

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

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

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

D14

Rates of Change in Log Functions

note

 

p.507 # 4, 7acd, 11abc

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

D13 work period    
D12

Solving Exp & Log Problems

class note

note

video lesson

Worksheet - Word Problems
p.499 # 1, 2, 3, 5a, 6a, 11, 13, 15
D11
Work Period  

p.485 # 4, 6bc, 7, 11

p.492 # 3, 9

D10

Solving Exp & Log Equations

class note

note

video lesson

 

p.485 # 2, 8, 10, 17

p.491 # 4, 5, 7, 12

D07

Laws of Logarithms

class note

note

video lesson

 

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

D05

Evaluating Logarithms

class note

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

D04

Graphs & Transformations of Log Functions

class note

note

Worksheet - Transformations

p.456 # 1-3 (basics), 4, 5, 8, 9, 11

N28

Introduction to Logarithmic Functions

class note

video note

video lesson

Handout - Graphs of Exp & Log Functions
p.451 # 4 - 9
  Unit 6: Exponential & Logarithmic Functions    
D03
Test: Trig Identities & Equations    

N30

N29

Review   p.440 # 1, 2, 3ac, 4, 5, 6, 7, 8, 9, 10, 11b, 12bcd, 13
N27 work period    
N26

Solving Quadratic Trig Equations

class notes

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
N23 PD Day    
N22 assembly    
N21

Solving Linear Trig Equations

video lesson

Quiz Solutions - Compound & Double Angles

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

18

N20 work period    

N19

Trigonometric Identities

class note

video lesson

MCR3U: WS 3.3 Trig Identities(solutions)

MHF4U: WS Trig Identities (solutions)

p.416 # 5, 8, (9, 10, 11)(odd), 17
N16

Double Angle Formulas

class note

video lesson

  p.407 # 1­-3, 5, 6, 8, 9 (see p.406), 13
N15

Compound Angle Formulas

class note

video lesson

(Addition & Subtraction Identities)

Worksheet - RAA & CAST Rule (w/ Answers)
p.400 # 1-­4, 5acf, 6cde, 8, 9ade, 10, 13
N14

Equivalent Trigonometric Functions

class note

video lesson

Trig Identities Sheet
p.392 # 1, 2a, 3acd, 4a, 5abc
  Unit 5: Trigonometric Identities & Equations    
N13 Test: Trigonometric Functions    

N12

N09

Review: Trigonometric Functions   p.376 # 1-4, 6, 7, 10, 11bd, 12, 14-17, 19
N08 Activity: Model Periodic Data    
N07

Rates of Change in Trigonometric Functions

no video lesson

note

  p.369 # 1 - 3, 4bd, 6, 7, 8, 12, 15

N06

N05

Modelling with Trigonometric Function

video note

video lesson

worksheet w/ extra problems

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


p.360 # 1­-3, 5, 6, 7, 9, 11
N02

Graphs of Reciprocal Trig Functions

video note

video lesson

worksheet p.353 # 1, 2, 3, 6, 7
N01

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
O31

Graphs of Trig Functions

(focus on tangent function)

video note

video lesson

Video: Sine Graph from Circular Motion
p.336 # 2c, 3, 5
O30

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 
O29

Radian Measure

video lesson

  p.320 # 1 -­ 4, 6 -­ 10, 15 
 
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

 
  Unit 4: Trigonometric Functions
   
O26 Test: Polynomial & Rational Inequalities    

O25

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

O23

Rates of Change in Rational Functions

no video lesson

  p.303 # 1, 2, 4, 6bc, 10, 13 
O22

Solving Rational Inequalities

note

video lesson

  p.295 # 1, 4acf, 5ace, 7, 9, 13
O19

Solving Rational Equations

class note

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)

O18

Graphing Rational Functions

class note

note

video lesson

Sample Problem PDF VT

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

worksheet (more complex problems, optional)

O17

Rational Functions & Asymptotes

class note

note

video lesson

  p.262 # 1, 2, 3
O16

Graphs of Reciprocal Functions

class note

note

video lesson

 

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

# 16 (find equation of reciprocal (shown) and

original function)

O15

Rates of Change in Polynomials

note

video lesson

  p.235 # 5cde, 6cde, 7, 9, 11 
O12

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]

O11

Solving Linear Inequalities

class note

note

video lesson

 

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

O04

Solving Polynomial Equations

class note

note

video lesson

  p.204 # 6, 7ad, 10, 13, 16
  Unit 3: Equations & Inequalities    
O10 Test: Polynomials    
O09
Review - Polynomials  

p.161 # 3 - 9

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

O03

Factoring Cubic Polynomials

class note

note

video lesson
 

WS - Factoring Sum & Difference of Polynomials

(H/W on WS)

O02

O01

Factoring Polynomials

class note

note

video lesson

KA - Example - Remainder Theorem

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

S28

Dividing Polynomials

class note

note

video lesson

KA - Polynomial Long Division 

KA - Synthetic Division

p.168 # 1, 4, 5ace, 6ace, 7ac, 8d, 9ac, 10ace, 11, 12, 14
S27

Transformations of Polynomials

class note

video note

video lesson

  p.155 # 2, 3, 4bde, 5, 6bde, 7, 8, 9ace, 10, 11, 14 
S26

Characteristics of Factored Form

class note

note

video lesson

  p.146 # 1, 2, 4, 6, 9, 10, 12, 13, 14
S25

Characteristics of Polynomials

note

video lesson

  p.136 # 5, 7, 8, 9, 12, 14, 15, 16
S21

Polynomial Functions

note

video lesson

[VT - Pascal's Triangle & Binomial Expansion]
p.127 # 1 - 5
  Unit 2: Polynomial Functions    
S20 Test: Functions & Rate of Change    
S19
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

S18

Graphical Representations of Rate of Change

note

video lesson

  p.103 # 3, 5, 9, 10
p.111 # 2, 10, 13
S17 work period    
S14

Average & Instantaneous Rates of Change

note

video lesson

 

p.76 # 8, 9

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


S13

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

S12

Piecewise Functions

note

video lesson

KA - Piecewise Example p.51 # 3, 4, 5cd, 6, 8, 9, 11, 13 
S11

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
S10

Review: Transformations of Functions

note

video lesson

handout
p.36 # 4, 5, 6, 7, 9, 10, 15, 16ab
S07

Properties of Graphs

video lesson

Khan A - Even/Odd Functions

Interval Notation

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

use handout for 12, 14

S06

Absolute Value Function

video lesson

  p.16 # 3-10
S05

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
 

Unit 1: Functions & Rates of Change

   
S04
Course Intro
 

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

(hand in tomorrow)

 

Full Course (all video lessons, completed notes, assigned homework, extra resources)

 

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