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MCR3U 2019-2020 Sem1
Page history
last edited
by Steve Sweeney 3 years, 7 months 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 |
Lesson # |
Topic / Lesson
|
Extra Resources |
Assigned Work:
Nelson Functions 11 (2007)
|
| |
|
|
Course Review |
- Quadratics
- Functions
- Rational Functions
- Exponential Functions
- Trigonometry
- Periodic Functions
- 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 |
|
63 |
Ordinary Annuities - Present Value
|
|
p.520 # 3ac, 4, 9, 14 |
| J14 |
|
62 |
Ordinary Annuities - Future Value
|
|
p.511 # 5ad, 6b, 9, 14 |
| J13 |
|
61 |
Simple & Compound Interest
|
|
p.482 # 5ace, 6, 7
p.490 # 4ace, 6, 8, 15
p.498 # 3ac, 7, 8, 10
|
| J10 |
|
60 |
Pascal's Triangle
|
|
p.466 # 1, 2b, 3ac, 4d, 5cd, 8, 9, 13 |
| J09 |
|
59 |
Geometric Series
|
|
p.459 # 2, (3-6)(even), 7, 12, 15, 16
|
| J08 |
|
58 |
Arithmetic Series
|
|
p.452 # 1-3, (4-7)(even), 10-12, 15
|
| J07 |
|
57 |
Recursive Sequences
|
|
no homework |
| J06 |
|
56 |
Arithmetic & Geometric Sequences
|
|
p.424 # 5, 6, 8odd, 10, 12, 13odd, 15
p.430 # 6odd, 7, 8, 11, 14 |
| D19 |
|
55 |
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
|
|
53 |
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
|
|
52 |
Fundamental Trigonometric Identities
|
|
p.310 # 1-3, 4, 5, 6, 7, 8, 11 ,12, 14
|
|
D10
|
|
51 |
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 |
|
50 |
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
|
|
49 |
Graphing Sinusoidal by Key Properties
|
|
p.383 # 2, 5, 6, 9, 10, 13
p.372 # (10, 11, 12)(bcd)
|
| D03 |
|
48 |
Graphing by Transformations
|
|
complete worksheet
p.383 # 1, 3, 4, 7, 11, 12
|
D02
|
|
47 |
The Unit Circle
|
Interactive Applet - Explore the Unit Circle |
p.363 # 2, 3, 4, 7, 9, 11, 12, 13 |
| N27 |
|
46 |
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
|
|
45 |
3D Word Problems in Trigonometry
|
|
- day1: p.332 # 3acd, 4, 6, 7, 9, 10, 15
- day2: handout
|
N22
|
|
44 |
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
|
|
43 |
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
|
|
42 |
Trigonometry of Obtuse Angles
|
|
Handout (from MHR text, p.281)
# 1, 2odd (express in terms of RAA first)
# 3odd, 5, 6, 9, 12*
|
N18
|
|
41 |
Angles in the Cartesian Plane
|
extra handout 2 and 3 (with answers)
|
handout (with answers) |
| N14 |
|
40 |
Ambiguous Case of Sine Law
|
Geogebra Demo: Ambiguous Case
|
p.318 # 3, 5, 6, 7, 8, 10, 11
|
| N13 |
|
39 |
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 |
|
38 |
Special Triangles & Exact Values
|
VT - KA: Trig with Exact Values |
p.286 # 3, 4, 5, 7, 8, 9, 11, 12, 13 |
| N11 |
|
37 |
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
|
|
|
| N05 |
|
36 |
Half-Life & Doubling Period
|
|
Handout # 1-9 |
| N04 |
|
35 |
Applications of Exponential Functions
|
|
p.261 # 3, 4, 5, 7, 8, 9, 12, 13, 14, 15 |
| N01 |
|
34 |
Solving Exponential Equations
|
|
Handout # (1 - 11, 19, 20) (odd) |
| O31 |
|
|
Experiment: Bouncing Ball |
|
|
|
O31
O30
|
|
33 |
Exponential Equations from Graphs & Points
|
|
|
| O29 |
|
32 |
Summary: Transformations of Exponential Functions
|
|
|
|
O29
O28
|
|
31 |
Transformations of Exponential Functions
|
|
|
O25
|
|
30 |
Exploring Graphs of Exponential Functions
|
KhanA - Graphing Exponential Functions
|
finish handout |
| O24 |
|
29 |
Rational Exponents
|
|
p.229 # (1-6)(odd), 8, 10, 12, 14 |
| O23 |
|
28 |
Review Exponent Laws
|
KhanA - Exponent Laws
|
p.221 # (1, 2, 4-9, 11, 13, 16, 18)(odd letters) |
| |
|
|
Unit 4: Exponential Functions |
|
|
| |
|
|
|
|
|
| O22 |
|
|
Test: Quadratic Functions |
|
|
| O21 |
|
27 |
Review: Quadratic Functions
classNote
|
|
p.202 # 1ab, 2abc, 4 ,5, 9, 11, 12 (exact), 13, 14-18, 20-24 |
O18
|
|
26 |
Intersections of Parabolas & Lines
classNote
|
|
p.198 # 2ac, 3, 4ac, 5, 8, 9, 10, 11
|
O17
|
|
25 |
Families of Quadratics
classNote
|
|
|
| O16 |
|
24 |
Number of Zeroes in Quadratic Functions
classNote
|
worksheet (no answers)
|
p.185 # 1ace, 2abc, 3abc, 4, 6, 9, 13, 14, 17* |
|
O15
|
|
23 |
Solving Quadratic Equations
classNote
|
|
p.177 # 1, 2, 7-10, 13, 16* |
|
O10
O09
|
|
22 |
Working with Radicals
classNote
Quiz: Vertex by Multiple Methods
|
|
p.167 # 1-7(odd), 9, 10, 12, 15*, 16*
|
| O08 |
|
21 |
Optimal Value using Symmetry
classNote
|
|
Solve by factoring or symmetry
p.153 # 4acd, 5, 8,12,15 + worksheet
|
| O07 |
|
20 |
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
|
|
19 |
Vertex Form from Standard & Factored Form
|
|
worksheet (answers)
|
| |
|
|
Unit 3: Quadratic Functions |
|
|
| O03 |
|
|
Test: Rational Functions |
|
|
| O02 |
|
|
Review: Rational Functions
|
|
handout with answers
|
| O01 |
|
18 |
Rational Expressions with Multiple Operations |
|
|
S30
|
|
17 |
Applications of Rational Functions
|
|
|
| S30 |
|
|
Quiz: Rational Operations & Simplification |
|
|
| S27 |
|
16 |
Graphing Rational Functions
|
videoLesson
|
complete handout (solutions)
|
S26
|
|
15 |
Adding & Subtracting Rational Expressions
|
Lesson: Adding & Subtracting Rational Expressions
|
p.128 # 5bd, 6bdf, 7bdf, 8ac, 9ac, 11, 16*
|
S25
|
|
14 |
Multiplying & Dividing Rational Expressions
|
Lesson: Multiplying & Dividing Rational Expressions
|
p.121 # 3, 4ad, 5ad, 6-9, 13*
|
| S24 |
|
13 |
Equivalent Expressions & Restrictions
|
Lesson: Equivalent Expressions & Restrictions
Video Tutorial - Simplifying Rationals & Equivalent Expressions
|
p.112 # (4-6)(ace), 9, 10, 14a, 17*
|
| S24 |
2
|
|
Unit 2 - Rational Functions |
|
|
|
S23
|
|
|
Test: Functions
|
|
|
| S20 |
|
|
Review: Functions |
|
Extra WS - Equations from Graphs (with answers)
|
|
S19
|
1.08
|
12 |
Transformations: Equations from Graphs
|
|
WS - Equations from Graphs (with solutions)
|
|
S18
S17
|
1.08
|
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
|
9 |
Transformations of Functions
|
Lesson: Transformations of Functions
MPM2D: Quadratics & Parabolas
- stretch, compress, and reflect
- translate up/down/left/right
|
complete handout
p.51 # 1-3
|
| S13 |
1.03
|
8 |
Exploring Properties of Parent Functions
|
|
start handout on transformations
|
| S12 |
|
|
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
|
|
Unit 1 - Introduction to Functions |
Khan Academy: Introduction to Functions |
|
| S03 |
0.01 |
1 |
Review - Linear & Quadratic Relations
classNote
videoLesson
|
|
|
| S03 |
0.00
|
|
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
MCR3U 2019-2020 Sem1
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