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MCR3U MHR 11 to Nelson 11

Page history last edited by Steve Sweeney 11 months, 3 weeks ago

MCR3U - Functions (University Preparation)

 

This course introduces the mathematical concept of the function by extending students’ experiences with linear and quadratic relations. Students will investigate properties of discrete and continuous functions, including trigonometric and exponential functions; represent functions numerically, algebraically, and graphically; solve problems involving applications of functions; investigate inverse functions; and develop facility in determining equivalent algebraic expressions. Students will reason mathematically and communicate their thinking as they solve multi-step problems.


Prerequisite: Principles of Mathematics, Grade 10, Academic, recommend at least 70% in MPM2D to move on to MCR3U

 

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.

Returned evaluations with be marked in purple.

 

Date Topic / Lesson
Extra Resources

Assigned Work

Text: McGraw-Hill Ryerson Mathematics 11 (2001)

10.02 Final Exam

Unit Reviews:

  1. Quadratics
  2. Functions
  3. Rational Functions
  4. Exponential Functions
  5. Trigonometry
  6. Periodic Functions
  7. Discrete Functions
 
10.01 Review: Final Exam    
8.99 Test - Discrete & Financial Functions    
8.98 Review - Discrete & Financial Functions  

see worksheet for:

  • textbook problems
  • supplementary problems

8.04

8.05

Ordinary Annuities

 

p.531 # 7, 8, 9, 10

p.541 # 8, 10

8.02

8.03

Present & Future Value

 

p.523 # [2], 6, 7, 9, 10, 15

note:

for #10: answer is $4710.92

for #15: GST = 7%, PST = 8%

8.01

8.02

Simple & Compound Interest

 

p.508 # 2 - 5, 7, 11, 13

7.05

7.06

Arithmetic & Geometric Series

 

p.469 #2ac, 3ac, 4a, 7a, 20

p.476 #1ac, 2ac, 3ac, 4, 12a, 17

7.04

Recursive Sequences

(video from class - Nature by Numbers)

[VT - Pascal's Triangle & Binomial Expansion]

p.461 #[1-5] basics, 8, 9, 10, 12

7.01

7.02

Arithmetic & Geometric Sequences

 

p.441 # [1-4][basics], 5-8(adg), 9, 12, 15, 18

p.452 # [1-4][basics], 5-7(adf), 9, 13, 18

7.03

Patterns & Sequences

  p.433 #1ace, 2ace, 3bdgk, 5a, 8
7.00
Unit 7 - Discrete Functions    
6.99
Test: Periodic Functions    

6.981

6.982

Review

Review Handout (review answers)

Q # 8

 
6.063 work period  
  • complete homework
  • start review
  • summative

6.062

Applications of Periodic Functions

worksheet (extra) + hints

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

Why is Period = Circumference in Q#9?

How Does a Circle Relate to Sinusoidal Graphs?

WS # 1, 2 

p.376 # 13, 17, 18ab 

p.388 # 14, 15, 16

(warning: textbook Q & A in radians)

6.061

Equations from Graphs

VT (SS) - Determining Sinusoidal Equations from Graphs

(PDF of Note Taken During Video Tutorial)

p.375 # 7ab, 8b

worksheet (answers)

9.01 Summative Assignment - Work Period (Room 220)

Approved Art List

LibreOffice (was OpenOffice) - Free Download

LibreOffice Draw Document - Grid - Portrait

LibreOffice Draw Document - Grid - Landscape

VT (SS) - Combining an Image with a Grid in a Document

VT (SS) - Part 2 - Choosing Axes, Finding Linear Equation

  • search (online) for art matching course graphs
  • note title, author/artist, and location
  • email me a link or paste image of your selected art
  • try to save a copy to your P: drive
  • paste image (portrait/landscape) into document 
  • bring grid to front, modify for maximum visibility
  • print copy, sketch out possible functions
6.052

Graphing Sinusoidal by Key Properties

 

p.374 # 2ace, 12bc

p.387 # 2abdeg, 3bd, 5abc, 6ab, 10ab

6.051

Graphing Sinusoidal by Transformations

VT (SS) - Graphing Sinusoidal by Transformations

Geogebra Applet - Graphing Sine & Cosine in Degrees

complete worksheet

p.374 # 1ad, 3ade, 6abe

p.387 # 1abceh, 3ad

6.00

The Unit Circle

Interactive Applet - Explore the Unit Circle   handout # 2, 3, 4, 7, 9, 11, 12, 13
6.00

Intro to Periodic Functions

handout

p.359 #1, 2, 4, 5, 7, 8, 10

6.00 Unit 6: Periodic Functions    
5.99 Test: Trigonometry    
5.98 Review: Trigonometry   Review Handout (with Answers)
5.90

Solving Non-Linear Trig Equations

VT (SS) - Solving Complex Trig Equation

(PDF note of solution)

p.408 # 3abd, 11, 14ace
5.052

Trigonometric Identities, Pt2

How the 6 Major Trig Functions Relate

10 Secret Trig Functions 

WS Part A

WS 3.3 Trig Identities(solutions)

5.051

Trigonometric Identities, Pt1

  p.398 # 2odd, 4odd, 7odd, 10
5.02

Special Triangles & Exact Values

VT - KA: Trig with Exact Values 

Complete Handout Questions,

p.348 # 3

5.042

Solving Trig Equations using CAST

p.408 # 1ace, 2bce, 5ab, 14agi

5.04

Trigonometry of Any Angle (CAST Rule)

WS - ESPA - Cartesian Plane

(required if you did not get perfect on quiz)

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

WS # 1-4 (answers)

p.348 # 1, 2, 6, 7

note: 2*pi = 360 degrees 

5.062

Ambiguous Case of Sine Law

  Review Ex.1 & 2 from p.303
p.308 # 1ace, 2ae, 3cg, 4, 8, 12, 13
5.03

Trigonometry of Obtuse Angles

  p.281 # 1
# 2odd (express in terms of RAA first)
# 3odd, 5, 6, 9, 12*
5.00

Angles in the Cartesian Plane

extra handout 2 and 3 (with answers)
handout (with answers)

5.06

5.07

Review Sine & Cosine Law

VT (SS) - p.294 # 14 (with PDF note of solution)

WS - Sine & Cosine Law (w/ some answers)

MPM2D: Sine Law video lesson

MPM2D Cosine Law video lesson

p.290 # 1-­3 (only do these if having difficulty)

p.290 # 4de, 5ac, 6, 8, 9, 10, 14

5.00

Word Problems in Trigonometry

VT (SS) - p.275 # 19 (pyramid)

VT - Bearing Problems (author has many tutorials)

p.274 # 11, 12 (previously assigned)

p.274 # 13, 16, 19

5.01

Review Right-Angle Trigonometry

VT - KA: Right-Angle Trigonometry

VT - KA: Using Soh Cah Toa

Interactive Quiz - KA: Solve Right Triangles

VT - KA: Trig with Exact Values

Interactive Quiz - KA: Solve with Exact Values

WS - Right Angle Trig (w/ Answers)

p.272 # (1­-10)(odd), 11, 12
5.00
Unit 5 - Trigonometry  Khan Academy - Basic Trigonometry
 
4.99 Test    

4.981

4.982

Review

Extra - Review - Exponential Functions

Handout - Review - Exponential Functions
4.07

Applications - Half-Life & Doubling Period

 
Handout # 1-9
4.00

Model Exponential Equations from Graphs

  Handout # 1-4
4.00

Solving Exponential Equations Algebraically

  p.23 # (1-11, 19, 20)(odd)
4.00

Equations from Graphs

handout
4.06

Transformations of Exponential Functions

handout with completed notes

finish handout (including WS on last page)

WS - Transformations of Exponentials (w/ answers)

4.00

Exploring Graphs of Exponential Functions

VT - Graphing Exponential Functions
finish handout
4.03

Rational Exponents

VT - Rational Exponents

handout # (1-­6)(odd), 8, 10, 12, 14 

answers to homework handout

4.02

Review Exponent Laws

VT - Exponent Laws

p.9 #(1-9)(odd letters), 12, 16
4.00
Unit 4 - Exponential Functions    
2.99 Test: Rational Functions    
2.981

Review

handout with answers

p.87 # 21 – 27

p.248 #11, 12

2.902

2.903

Application Problems

   
2.901

Order of Operations

 

p.68 # 10aceg, 14adf

+ worksheet

2.07

Adding & Subtracting Expressions

 

p.58 # 1c, 4c, 5g, 6ac, 10

p.67 # 5c, 6ace, 8ace

2.061

Multiplying Rational Expressions

Video Tutorial - Multiply & Divide Rational Expressions

p.50 # 5ad, 6adgh, 7ae, 8ab, 18

2.04

Equivalent Expressions & Restrictions

Video Tutorial - Simplifying Rationals & Equivalent Expressions
p.40 # 1 - 3 (odd) (fundamentals - optional)
# 4 - 6 (odd), 8, 13, 15
# 16
2.00
Unit 3 - Rational Functions & Expressions    
1.99
Test - Functions    
1.98 Review - Functions   Review Sheet

1.05

Function Inverses

VT (Khan A): Function Inverses  p.215 # 1, 2, 3abci, 5odd, 8odd, 14(i)(iii)(v), 16(i)(iii)(v)
1.082

Transformations - Equations from Graphs

worksheet
1.081

Transformations - Summary

p.240 # 3, 7, 16ef, 17
+ worksheet from yesterday
+ (optional) worksheet on web page
1.07

Horizontal vs Vertical Scaling & Reflection

WS - Transforming Graphs (with solutions)
worksheet + any previous homework
1.07

Transformations - Horizontal Reflection & Scaling

WS - Horizontal Transformations w/ Answers

p.229 # 2cde, 8, 11cdf

p.240 # 1ef, 2cd, 4dfgh, 5cef, 9cd

1.06

Transformations of Functions

MPM2D: Quadratics & Parabolas

part 1: p.241 # 8a, 9a, 5ab, 4ab

part 2: p.241 # 8b, 9b, 5d, 4ce

1.06

Graphs of Parent Functions

VT: Graphing a Radical Function  
1.04

Domain, Range, & Function Notation

p.178 # 1-3, 5, (6-10)(ad), 12, 15, 18
1.00
Unit 2 - Functions, Domain & Range VT: Introduction to Functions   
3.99 Test: Review & Quadratics    
3.98 Review quadratics quick reference
handout
3.07

Families of Quadratics

classNote

handout+worksheet

worksheet#2

3.08

Intersections of Parabolas & Lines

classNote

worksheet
3.05

Solving Quadratic Equations

classNote

p.128 # 2ace, 3ace, 4ace, 12ac
p.130 # 17, 23, 29
3.04

Radicals

classNote

p.106 # (1 - 4)(odd)

p.139 # (1 - 7)(odd), 9, 10a, 14

3.02

Optimal Value using Symmetry

classNote

videoLesson
p.115 # 2bfhl, 3bcgk, 9, 13, 15, 17
3.00

Completing the Square with Fractions

classNote

p.115 # 1cegik, 2odd, 3odd, 7, 14, 16
3.00

Review - Completing the Square

classNote

p.99 # (7, 8, 9)(odd)
3.00

Review - Factoring

classNote

p.3 # 4odd, 5odd, 6odd
3.00

Review - Solve Linear Equations & Expand Quadratics

classNote

  • p.29 # 1acf, 2ace
  • p.31 # 8ac, 9ace, 10ae
  • p.33 # 11ace, 12ace, 13ace
0.01

Review - Linear & Quadratic Relations

classNote

0.00
Unit 1 - Review & Quadratics    
0.00
 

Previous MCR3U Course Notes:

 

 

2, 3, 4, 6, 9, 11, 12, 14, 15

handout # 2, 3, 4, 7, 9, 11, 12, 13

MCR3U - Functions (University Preparation)

This course introduces the mathematical concept of the function by extending students’ experiences with linear and quadratic relations. Students will investigate properties of discrete and continuous functions, including trigonometric and exponential functions; represent functions numerically, algebraically, and graphically; solve problems involving applications of functions; investigate inverse functions; and develop facility in determining equivalent algebraic expressions. Students will reason mathematically and communicate
their thinking as they solve multi-step problems.


Prerequisite: Principles of Mathematics, Grade 10, Academic, recommend at least 70% in MPM2D to move on to MCR3U

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.

Returned evaluations with be marked in purple.

Date     Topic / Lesson     Extra Resources     Assigned Work     
                
D05     Constructing the Unit Circle  AM  PM           handout # 2, 3, 4, 7, 9, 11, 12, 13     
D04     Introduction to Periodic Functions  AM  PM           p.359 # 1, 2, 4, 5, 7, 8, 10     
      Unit 6 - Periodic Functions                 
D03     Test - Trigonometry                 
N30     Review - Trigonometry     Formula Sheet for Test     Handout - Trigonometry Review     
N29     Solving Trigonometric Equations (quadratic)  AM  PM           p.408 # 3abde, 6a, 11     
N28     Solving Trigonometric Equations (linear)  AM  PM           p.408 # 1ace, 2adf, 5ab, 14agi
      
N27     Trigonometric Identities, Part 2  AM  PM     

Video Tutorial (poor form)

Video Tutorial (some extra concepts) (1 of 4)
    

WS A # 2, 3, 4, 6, 9, 11, 12, 14, 15

WS 3.3 Trig Identities (solutions)
    
N26     Trigonometric Identities, Part 1  AM  PM     p.398 # 2odd, 4odd, 7odd, 10     
N23     Special Triangles & Exact Values  AM  PM           Attached to Handout     
N22     Trigonometry of Any Angle - CAST Rule  AM  PM           

WS # 1-4 (answers)

(typo in 1a on handout)
    
N21     Work Period & Catch Up                 
N20     Sine Law - Ambiguous Case  AM  PM     

Geogebra Applet - Ambiguous Case of the Sine Law

Some links to similar resources

Video Tutorial: Ambiguous Case
    p.308 # 1ace, 2ae, 3cg, 4, 8, 12, 13     
N19     Review Sine & Cosine Law  AM  PM           p.290 #[1-­3], 4de, 5ac, 6, 8, 9, 10, 14     
N15     Obtuse Angles in Cartesian Plane  AM  PM           

p.281 # 1, 2odd (express in terms of RAA first), 3odd, 5, 6, 9, 12*
    
N14     Angles in Cartesian (x-y) Plane  AM  PM     Geogebra Applet - Principal & Related Acute Angle      

see Handout

# (3 - 9) (odd letters), 11a
    
N13     2D & 3D Right Angle Problems  AM  PM           p.273 # 11, 12, 13, 16, 19     
N12      Review - Right Angle Trigonometry  AM  PM            p.272 # (1-­10)(odd), 11, 12      
      Unit 5 - Trigonometry                 
N09     Test - Exponential Functions                 

N08

N07
    Review - Exponential Functions  AM  PM           Handout - Review - Exponential Functions     
N07     Applications Part 2  AM  PM           WS # 1 - 9     

N06

N05
    Applications Part 1  AM  PM           

WS # 1 - 4

Supplemental Problems (answers)

start review for test!
    
N02     Solving Exponential Equations  AM  PM           p.23 (1-11, 19, 20)(odd letters, ace...)     

N01

O31
    Equations from Graphs  AM  PM           complete worksheet     
O30     Transformations of Exponential Functions  AM  PM           Worksheet     
                        
O25     Graphing Exponential Functions  AM  PM           complete handout     
O24     Rational Exponents  AM  PM           

handout # (1-­6)(odd), 8, 10, 12, 14

answers to homework handout
    
O23     Exponent Laws for Integer Exponents  AM  PM           p.9 #1‐9(odd), 12, 16     
      Unit 4 - Exponential Functions                 
O22     Test - Rational Functions                 
O19     Review - Rational Expressions           Complete review & submit on test day  (Review + Answers)     
O18     Word Problems Involving Rational Expressions  AM  PM                 
O17     

Order of Operations with Rational Expressions*

AM  PM
          

p. 68  # 10 aceg, 14adf

+ worksheet (w/ answers)
    
O15      Add & Subtract Rational Expressions  AM  PM     

Video Tutorial - Add & Subtract Rational Expressions

Video Tutorial - Add & Subtract Rational Expressions, #2
    

p.58 # 1c, 4c, 5g, 6ac, 10

p.67 # 5c, 6ace, 8ace
      
O12      Multiply & Divide Rational Expressions  AM  PM     Video Tutorial - Multiply & Divide Rational Expressions     p.50  # 5ad, 6adgh, 7ae, 8ab, 18      
O11     Equivalent Expressions  AM  PM     Video Tutorial - Simplifying Rationals & Equivalent Expressions     p.40 # 1-3(odd), 4-6(odd), 8, 13, 15, 16     
      Unit 3 - Rational Functions                 
O10      Test - Functions                 
O09      Review - Functions                 
O04     Thinking Task - Functions, Transformations, Inverses                 
O03      

Transformations from Graphs

AM PM
          WS - Determine Transformations from Graphs (solutions)     
O01     Equivalent Transformations  AM  PM           WS transformations (solutions)     20
S28     Inverse Functions  AM  PM     Video Tutorial: Function Inverses      p.215 # 1, 2, 3abci, 5odd, 8odd, 14(i)(iii)(v), 16(i)(iii)(v)     19
S27     

Horizontal Reflect & Stretch

AM PM
          

p.229 # 2cde, 8, 11cdf

p.240 # 1ef, 2cd, 4dfgh, 5cef, 9cd
    18
S26     

Transformations  AM  PM

(same as from Gr.10)
                17
S25     Parent Functions  AM  PM     Video Tutorial: Graphing a Radical Function     

p.179 # 12, 21, 25, 26, 32*

+ worksheet (solutions)
    16
S24     Functions, Domain, Range  AM  PM     

Video Tutorial: Is the Relation a Function (given Set)?

Video Tutorial: Is the Relation a Function (given Scatter Plot)?

What is a function? (covers multiple lessons)
    p.178 # 1-3, 5, (6-10)(ad), 15, 18     15
      Unit 2 - Functions                 
S21     Test - Quadratics                 14

S20

S19
    Review - Quadratics                 13
S18     Families of Quadratics  AM  PM           Worksheet     11
S17     Intersection of Quadratics & Lines  AM  PM           Worksheet     10
S14     

Solving Quadratic Equations with Exact Solutions

AM  PM
          p.128 # 2ace, 3ace, 4ace, 12ac, 13ace
p.130 # 17, 23, 29     9
S13     Working with Radicals  AM  PM           p.106 # (1 ­ - 4)(odd)
p.139 # (1 ­ - 6)(odd)     8
S12     Optimal Values by Factoring  AM  PM           p.115 # 2f, 3bcfgk, 9, 13, 15, 18     7
S11     

Completing the Square w/ Fractions & Decimals

AM   PM
          p.115 # 1cegik, 3odd, 7, 14, 16     6
S10     Completing the Square  AM  PM           p.99 # 7odd, 8odd, 9odd     5
S07     

Review - Factoring Quadratic Relations

Edits: AM  PM
    

Factoring Practice

(2 sheets, version A, B,

with solutions)
    p.3 # 4odd, 5odd, 6odd     4
S06     

Review - Solving Linear Systems

Review - Expanding Binomial Expressions

Edits:  AM  PM
          p.29 # 1acf, 2ace
p.31 # 8ac, 9ace, 10ae
p.33 # 11ace, 12ace, 13ace     3
S05     

Review - Linear & Quadratic Relations

Edits:  AM  PM
    Handout - Properties of Linear & Quadratic Relations     

Complete quizzes & check online solutions

Gr.10 Quiz - Linear Systems (w/ Answers)

Gr.10 Quiz - Properties of Quadratics (w/ Solutions)
    2
S04     Introduction to MCR3U (short class)     MPM2D Course Notes -  Fall 2011-2012     Review notes from MPM2D (ha!), focus on quadratics     1
      Unit 1 - Review & Quadratics                 
            

Previous Course Notes:

Winter 2011-2012

Winter 2010-2011
          

2, 3, 4, 6, 9, 11, 12, 14, 15

handout # 2, 3, 4, 7, 9, 11, 12, 13

p.374 # 1ad, 3ade, 6abe
p.387 # 1abceh, 3ad

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