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.
Returned evaluations with be marked in purple.
Chapter | Lesson | Day | Status | Topic / Lesson |
Extra Resources |
Assigned Work: Nelson Functions 11 (2007) |
Assigned Work: MHR Mathematics 11 (2001) |
0.00 |
0.00 | Unit 0 - Review & Quadratics | |||||
0.01 | 0.01 |
1 |
|
|
|
||
0.02 |
|
||||||
0.03 |
|
|
p.3 # 4odd, 5odd, 6odd |
||||
1.00 |
1.00 | Unit 1 - Introduction to Functions | Khan Academy: Introduction to Functions | ||||
1.01 | 1.01 |
4 |
Relations and Functions | Lesson: Domain Range & Function Notation |
p.11 # 1 - 3, 4, 6 - 13 |
||
1.02 | 1.02 |
5 |
Function Notation | p.22 # 1 - 3, 4 - 7, 11 - 13, 16, 17, 19* |
|
||
1.03 | 1.03 |
8 |
need HW |
Exploring Properties of Parent Functions | |||
1.04 |
1.04 |
6 |
need video |
Domain and Range |
p.35 # 2-5, 8, 10, 11, 12cd, 13, 17* |
p.178 # 1-3, 5, (6-10)(ad), 12, 15, 18 |
|
1.05 |
1.05 |
7 |
rework too long? |
Function Inverses |
p.46 # 1, 2abc, 3, 4bc, 6bdf, 10, 12, 16, 17 | p.215 # 1, 2, 3abci, 5odd, 8odd, 14(i)(iii)(v), 16(i)(iii)(v) | |
1.06 | 1.06 |
9 |
use old HW? |
Transformations of Functions |
MPM2D: Quadratics & Parabolas
|
complete handout p.51 # 1-3 |
part 1: p.241 # 8a, 9a, 5ab, 4ab part 2: p.241 # 8b, 9b, 5d, 4ce |
1.03 |
better H/W? |
Graphs of Parent Functions |
|||||
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 |
||||
1.081 |
Transformations - Summary
|
|
p.70 # 4, 6, 10 (describe transformations) + p.70 # (79)b (sketch/graph using transformations) + p.70 # 1618, 22* |
p.240 # 3, 7, 16ef, 17 + worksheet from yesterday + (optional) worksheet on web page |
|||
1.082 |
Transformations - Equations from Graphs |
worksheet |
|||||
1.98 |
Review - Introduction to Functions |
Review Sheet | |||||
1.99 |
Test - Introduction to Functions |
||||||
2.00 |
Unit 2: Equivalent Algebraic Expressions |
||||||
2.01 | Adding and Subtracting Polynomials | ||||||
2.02 | Multiplying Polynomials | ||||||
2.03 | Factoring Polynomials | ||||||
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 |
||||
2.05 | Exploring Graphs of Rational Functions | ||||||
2.061 |
Multiplying Rational Expressions |
Video Tutorial - Multiply & Divide Rational Expressions |
p.50 # 5ad, 6adgh, 7ae, 8ab, 18 |
||||
2.07 |
Adding & Subtracting Expressions |
|
p.58 # 1c, 4c, 5g, 6ac, 10 p.67 # 5c, 6ace, 8ace |
||||
2.901 |
Order of Operations |
p.68 # 10aceg, 14adf |
|||||
2.902 2.903 |
Application Problems |
||||||
2.981 |
Review: Equivalent Algebraic Expressions |
|
p.87 # 21 – 27 p.248 #11, 12 |
||||
2.99 | Test: Equivalent Algebraic Expressions |
||||||
3.00 |
Unit 3: Quadratic Functions |
||||||
3.00 |
Completing the Square with Fractions |
p.115 # 1cegik, 2odd, 3odd, 7, 14, 16 | |||||
3.00 |
|
p.99 # (7, 8, 9)(odd) |
|||||
3.02 |
Optimal Value using Symmetry |
videoLesson |
p.115 # 2bfhl, 3bcgk, 9, 13, 15, 17 |
||||
3.04 |
Radicals |
p.106 # (1 - 4)(odd) p.139 # (1 - 7)(odd), 9, 10a, 14 |
|||||
3.05 |
Solving Quadratic Equations |
p.177 # 1, 2, 7-10, 13, 16* | p.128 # 2ace, 3ace, 4ace, 12ac p.130 # 17, 23, 29 |
||||
3.07 |
Families of Quadratics |
||||||
3.08 |
Intersections of Parabolas & Lines |
p.198 # 2ac, 3, 4ac, 5, 8, 9, 10, 11 |
worksheet | ||||
3.98 | Review | quadratics quick reference |
handout |
||||
3.99 | Test: Review & Quadratics | ||||||
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 |
|||||
4.00 |
Exploring Graphs of Exponential Functions
|
VT - Graphing Exponential Functions |
finish handout | ||||
4.00 |
Unit 4 - Exponential Functions | ||||||
4.02 |
Review Exponent Laws |
p.9 #(1-9)(odd letters), 12, 16 | |||||
4.03 |
Rational Exponents |
VT - Rational Exponents | |||||
4.06 |
Transformations of Exponential Functions |
handout with completed notes |
finish handout (including WS on last page) |
||||
4.07 |
Applications - Half-Life & Doubling Period |
|
Handout # 1-9 | ||||
4.981 4.982 |
Review | Handout - Review - Exponential Functions |
|||||
4.99 | Test | ||||||
5.00 | extra handout 2 and 3 (with answers) |
handout (with answers) | |||||
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 |
||||
5.00 |
Unit 5 - Trigonometry | Khan Academy - Basic Trigonometry |
|||||
5.01 |
Review Right-Angle Trigonometry |
VT - KA: Right-Angle Trigonometry Interactive Quiz - KA: Solve Right Triangles VT - KA: Trig with Exact Values |
p.272 # (1-10)(odd), 11, 12 |
||||
5.02 |
Special Triangles & Exact Values |
VT - KA: Trig with Exact Values |
Complete Handout Questions, p.348 # 3 |
||||
5.03 |
Trigonometry of Obtuse Angles |
p.281 # 1 # 2odd (express in terms of RAA first) # 3odd, 5, 6, 9, 12* |
|||||
5.04 |
Trigonometry of Any Angle (CAST Rule) |
(required if you did not get perfect on quiz) |
p.348 # 1, 2, 6, 7 note: 2*pi = 360 degrees |
||||
5.042 |
Solving Trig Equations using CAST |
|
p.408 # 1ace, 2bce, 5ab, 14agi |
||||
5.051 |
Trigonometric Identities, Pt1 |
p.398 # 2odd, 4odd, 7odd, 10 | |||||
5.052 |
Trigonometric Identities, Pt2 |
WS Part A |
|||||
5.062 |
Ambiguous Case of Sine Law |
Review Ex.1 & 2 from p.303 p.308 # 1ace, 2ae, 3cg, 4, 8, 12, 13 |
|||||
5.06 5.07 |
Review Sine & Cosine Law |
VT (SS) - p.294 # 14 (with PDF note of solution) |
p.290 # 1-3 (only do these if having difficulty) p.290 # 4de, 5ac, 6, 8, 9, 10, 14 |
||||
5.90 |
Solving Non-Linear Trig Equations
|
p.408 # 3abd, 11, 14ace | |||||
5.98 | Review: Trigonometry | Review Handout (with Answers) |
|||||
5.99 | Test: Trigonometry | ||||||
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 | ||||||
6.051 |
Graphing Sinusoidal by Transformations |
p.374 # 1ad, 3ade, 6abe p.387 # 1abceh, 3ad |
|||||
6.052 |
Graphing Sinusoidal by Key Properties |
|
p.374 # 2ace, 12bc p.387 # 2abdeg, 3bd, 5abc, 6ab, 10ab |
||||
6.061 |
Equations from Graphs |
p.375 # 7ab, 8b |
|||||
6.062 |
Applications of Periodic Functions |
Solutions: 1 2 3 4 5 6 7 8 9 10 |
WS # 1, 2 p.376 # 13, 17, 18ab p.388 # 14, 15, 16 (warning: textbook Q & A in radians) |
||||
6.063 | work period |
|
|||||
6.981 6.982 |
Review | ||||||
6.99 |
Test: Periodic Functions | ||||||
7.00 |
Unit 7 - Discrete Functions | ||||||
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 | |||||
7.04 |
Recursive Sequences
|
(video from class - Nature by Numbers) |
p.461 #[1-5] basics, 8, 9, 10, 12 | ||||
7.05 7.06 |
Arithmetic & Geometric Series |
p.469 #2ac, 3ac, 4a, 7a, 20 p.476 #1ac, 2ac, 3ac, 4, 12a, 17 |
|||||
8.01 8.02 |
Simple & Compound Interest |
p.508 # 2 - 5, 7, 11, 13 |
|||||
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% |
|||||
8.04 8.05 |
Ordinary Annuities |
p.531 # 7, 8, 9, 10 p.541 # 8, 10 |
|||||
8.98 | Review - Discrete & Financial Functions |
see worksheet for:
|
|||||
8.99 | Test - Discrete & Financial Functions | ||||||
9.01 | Summative Assignment - Work Period (Room 220) |
LibreOffice (was OpenOffice) - Free Download LibreOffice Draw Document - Grid - Portrait LibreOffice Draw Document - Grid - Landscape |
|
||||
10.01 | Review: Final Exam | ||||||
10.02 | Final Exam |
Unit Reviews: |