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MCR3U 2019-2020 Sem1

Page history last edited by Steve Sweeney 1 month ago

MCR3U - Functions (University Preparation)

 

This course introduces the mathematical concept of the function by extending student 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.

Date Text Day Topic / Lesson
Extra Resources

Assigned Work:

Nelson Functions 11 (2007)

      Course Review
    1. Quadratics
    2. Functions
    3. Rational Functions
    4. Exponential Functions
    5. Trigonometry
    6. Periodic Functions
    7. Discrete Functions 
J20
    Test: Discrete Functions & Financial Applications
   
J17     Review  
  • p.468 # 4, 5, 7, 8c, 11, 12, 13, 15cd, 16b, 18ef, 19bd, 22d, 23e
  • p.470 # 6, 8bc
  • p.534 # 2, 6, 7, 8c, 10, 11b, 13, 17, 18
J16    

Ordinary Annuities - Present Value

  p.520 # 3ac, 4, 9, 14 
J14    

Ordinary Annuities - Future Value

  p.511 # 5ad, 6b, 9, 14
J13    

Simple & Compound Interest

 

p.482 # 5ace, 6, 7

p.490 # 4ace, 6, 8, 15

p.498 # 3ac, 7, 8, 10

J10    

Pascal's Triangle

  p.466 # 1, 2b, 3ac, 4d, 5cd, 8, 9, 13
J09    

Geometric Series

 

p.459 # 2, (3­-6)(even), 7, 12, 15, 16

J08    

Arithmetic Series

 

p.452 # 1-­3, (4-­7)(even), 10-­12, 15

J07    

Recursive Sequences

  no homework
J06    

Arithmetic & Geometric Sequences

 
p.424 # 5, 6, 8odd, 10, 12, 13odd, 15
p.430 # 6odd, 7, 8, 11, 14
D19    

Patterns & Sequences

  worksheet 
 
    Unit 7: Discrete Functions & Financial Applications
   
D18     Test: Periodic Functions    

D17

D16

    Review

(Extra) Review Handout (review answers)

Q # 8

p.404 # 3, 4, 6, 7, 8, 9, 10, 12, 13

p.406 # 1, 2, 3, 5

p.339 # 6, 7

p.340 # 4

D13     work period    

D12

   

Reciprocal Trigonometric Identities

How the 6 Major Trig Functions Relate

10 Secret Trig Functions 

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

WS 3.3 Trig Identities  (solutions)

D11
   

Fundamental Trigonometric Identities

  p.310 # 1­-3, 4, 5, 6, 7, 8, 11 ,12, 14

D10

   

Applications of Periodic Functions


 

p.398 # 1-10, 12*, 13

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?

D09    

Equations from Graphs

VT (SS) - Determining Sinusoidal Equations from Graphs

(PDF of Note Taken During Video Tutorial)

p.391 # (1-7)(ac if applicable), 8, 11, 14

worksheet (answers)

D05
   

Graphing Sinusoidal by Key Properties

 
p.383 # 2, 5, 6, 9, 10, 13
p.372 # (10, 11, 12)(bcd)
D03    

Graphing by Transformations

complete worksheet

p.383 # 1, 3, 4, 7, 11, 12

 

D02
   

The Unit Circle

Interactive Applet - Explore the Unit Circle   p.363 # 2, 3, 4, 7, 9, 11, 12, 13
N27    

Introduction to Periodic Functions

classNote

  p.352 # 1-9, 11
 
    Unit 6: Periodic Functions
   
N29     Test: Trigonometry    
N28     Review: Trigonometry  

p.338 # 1-5, 8-13

p.340 # 1-3, 6-8

N26

N25 

   

3D Word Problems in Trigonometry

  • day1: p.332 # 3acd, 4, 6, 7, 9, 10, 15
  • day2: handout
N22
   

Solving Trig Equations using CAST

worksheet (with answers)

# 2, 5ab (linear equations)
# 14cdefgi (linear, challenging)
# 3acef, 5cde, 11 (non­linear, challenging)

N21     work period   worksheet (with answers)

N21

N20

   

Trigonometry of Any Angle (CAST Rule)

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

p.299 # 1, 2, 4, 6, 8, 9, 10, 12
N19
   

Trigonometry of Obtuse Angles

 

Handout (from MHR text, p.281)

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

N18
   

Angles in the Cartesian Plane

extra handout 2 and 3 (with answers)
handout (with answers)
N14    

Ambiguous Case of Sine Law

Geogebra Demo: Ambiguous Case

p.318 # 3, 5, 6, 7, 8, 10, 11

N13     

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

Handout:

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

# 4de, 5a, 6, 8, 9, 10, 14

 
N12    

Special Triangles & Exact Values

VT - KA: Trig with Exact Values  p.286 # 3, 4, 5, 7, 8, 9, 11, 12, 13 
N11     

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.280 # 1, 3 - 9, 13, 18 
      Unit 5: Trigonometry    
N08     Test: Exponential Functions    

N07

N06

   

Review: Exponential Functions

classNote

 
N05     

Half-Life & Doubling Period

 
Handout # 1-9 
N04    

Applications of Exponential Functions

classNote

  p.261 # 3, 4, 5, 7, 8, 9, 12, 13, 14, 15
N01    

Solving Exponential Equations

classNote

  Handout # (1 - 11, 19, 20) (odd)
O31     Experiment: Bouncing Ball    

O31

O30

   

Exponential Equations from Graphs & Points

classNote

 
O29    

Summary: Transformations of Exponentials

classNote

 

O29

O28

   

Transformations of Exponential Functions

  • classNote
O25
   

Exploring Graphs of Exponential Functions

VT - Graphing Exponential Functions
finish handout
O24     

Rational Exponents

p.229 # (1-6)(odd), 8, 10, 12, 14 
O23     

Review Exponent Laws

videoLesson

VT - Exponent Laws

p.221 # (1, 2, 4-9, 11, 13, 16, 18)(odd letters) 
      Unit 4: Exponential Functions    
           
O22     Test: Quadratic Functions    
O21    

Review: Quadratic Functions

classNote

p.202 # 1ab, 2abc, 4 ,5, 9, 11, 12 (exact), 13, 14-18, 20-24
O18
   

Intersections of Parabolas & Lines

classNote

p.198 # 2ac, 3, 4ac, 5, 8, 9, 10, 11
O17
   

Families of Quadratics

classNote

 
O16    

Number of Zeroes in Quadratic Functions

classNote

worksheet (no answers)
p.185 # 1ace, 2abc, 3abc, 4, 6, 9, 13, 14, 17*

O15 

   

Solving Quadratic Equations

classNote

p.177 # 1, 2, 7-10, 13, 16* 

O10

O09 

   

Working with Radicals

classNote

Quiz: Vertex by Multiple Methods

p.167 # 1-7(odd), 9, 10, 12, 15*, 16*

 
O08    

Optimal Value using Symmetry

classNote

Solve by factoring or symmetry

p.153 # 4acd, 5, 8,12,15 + worksheet

O07    

Optimal Value by Completing the Square

classNote

All questions by completing the square, by hand (no tech):

p.153 # 4abcd, 6, 7, 8, 9, 10, 11ac, 14*

 
O04
   

Vertex Form from Standard & Factored Form


worksheet (answers)
      Unit 3: Quadratic Functions    
O03     Test: Rational Functions    
O02    

Review: Rational Functions

handout with answers
O01     Rational Expressions with Multiple Operations    
S30
   

Applications of Rational Functions

   
S30     Quiz: Rational Operations & Simplification    
S27    

Graphing Rational Functions

 

complete handout (solutions)

S26
   

Adding & Subtracting Rational Expressions

Lesson: Adding & Subtracting Rational Expressions
p.128 # 5bd, 6bdf, 7bdf, 8ac, 9ac, 11, 16*
S25
   

Multiplying & Dividing Rational Expressions

Lesson: Multiplying & Dividing Rational Expressions
p.121 # 3, 4ad, 5ad, 6-9, 13*
S24    

Equivalent Expressions & Restrictions

Lesson: Equivalent Expressions & Restrictions

Video Tutorial - Simplifying Rationals & Equivalent Expressions

p.112 # (4-6)(ace), 9, 10, 14a, 17*
S24 2
16 Unit 2 - Rational Functions    

S23

  15

Test: Functions

   
S20   14
Review: Functions   Extra WS - Equations from Graphs (with answers)

S19

 

1.08

13

 

Transformations: Equations from Graphs

 
WS - Equations from Graphs (with solutions)

S18

S17

1.08

12

11

Transformations: Summary & Image Points

p.70 # 4, 6, 10 (describe transformations)
+ p.70 # (7­9)b (sketch/graph using transformations)
+ p.70 # 16­18, 22*
S16 1.07
10

Transformations - Horizontal Reflection & Scaling

Lesson: Horizontal Reflections & Scaling

WS - Horizontal Transformations w/ Answers

 p.59 # 3, 4, 7, 8, 11

S16

S13

1.06

10

9

Transformations of Functions

Lesson: Transformations of Functions
MPM2D: Quadratics & Parabolas

complete handout

p.51 # 1-3

S13 1.03
9

Exploring Properties of Parent Functions

start handout on transformations
S12   8
Quiz: Functions, Function Notation, Domain & Range    

S11

1.05
7

Function Inverses

p.46 # 1, 2abc, 3, 4bc, 6bdf, 10, 12, 16, 17
S10
1.04
6

Domain and Range

p.35 # 2-5, 8, 10, 11, 12cd, 13, 17*
S09
  5

Review - Factoring

  • p.556 # 1 - 3
  • worksheets (do as many, or few, as you need)
S06
 
4

Review - Expand Quadratics

Worksheet:

  • # 1acf, 2ace
  • # 8ac, 9ace, 10ae
  • # 11ace, 12ace, 13ace
S05 1.02 3

Function Notation

Video: Domain Range & Function Notation

 

p.22 # 1 - 3, 4 - 7, 11 - 13, 16, 17, 19*

worksheet: Function Notation

(answers)

S04 1.01 2

Relations and Functions

p.11 # 1 - 3, 4, 6 - 13
S04 1.00
2
Unit 1 - Introduction to Functions Khan Academy: Introduction to Functions  
S03 0.01 1

Review - Linear & Quadratic Relations

classNote

videoLesson

S03 0.00
1
Unit 0 - Review & Quadratics    

 

 

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, 3a

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