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:
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
Unit 1: Functions & Rates of Change
| Day | Lesson | Resources | Assigned Work |
| 1 |
Review - Functions, Domain, Range |
Khan Academy - What is a Function? (there are several videos in series) |
p.11 # 1, 2, 3, 4, 6, 8, 11, 12, 14 |
| 2 |
Absolute Value Function |
p.16 # 3-10 | |
| 3 |
Properties of Graphs |
Khan A - Even/Odd Functions |
p.23 # 12, 3, 4, 5, 7, 8, 9, 10, 14 use handout for 12, 14 |
| 4 |
Review: Transformations of Functions |
handout |
p.36 # 4, 5, 6, 7, 9, 10, 15, 16ab |
| 5 |
Function Inverses |
KA - Restricting Domain for Inverse Functions |
p.44 # 4, 5, 6bd, 7, 9, 11, 12c, 13, 17 |
| 6 |
Piecewise Functions |
KA - Piecewise Example | p.51 # 3, 4, 5cd, 6, 8, 9, 11, 13 |
|
7 |
Combinations of Functions (using simple arithmetic operations) |
Try to complete Ex.2 & Ex.3 on your own p.57 # 2, 3, 4, 5, 6 |
|
| 8 |
Average & Instantaneous Rates of Change |
p.76 # 8, 9 p.85 # 4, 7, 9, 10, 15 |
|
| 9 |
Graphical Representations of Rate of Change |
p.103 # 3, 5, 9, 10 p.111 # 2, 10, 13 |
|
| 10 |
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 |
Unit 2: Polynomial Functions
| Day | Lesson | Resources | Assigned Work |
| 1 |
Polynomial Functions |
[VT - Pascal's Triangle & Binomial Expansion] |
p.127 # 1 - 5 |
| 2 |
Characteristics of Polynomials |
p.136 # 5, 7, 8, 9, 12, 14, 15, 16 | |
| 3 |
Characteristics of Factored Form |
p.146 # 1, 2, 4, 6, 9, 10, 12, 13, 14 | |
| 4 |
Transformations of Polynomials |
p.155 # 2, 3, 4bde, 5, 6bde, 7, 8, 9ace, 10, 11, 14 | |
| 5
|
Dividing Polynomials |
p.168 # 1, 4, 5ace, 6ace, 7ac, 8d, 9ac, 10ace, 11, 12, 14 | |
| 6 |
Factoring Polynomials |
KA - Example - Remainder Theorem |
p.176 # [1-3][basics], 4bf, 5ac, 6abc, 7df, 8, 9, 10, 13, 17 |
| 7 |
Factoring Cubic Polynomials video lesson |
WS - Factoring Sum & Difference of Polynomials (H/W on WS) |
|
| 8 | Review - Polynomials | Interactive Review: Polynomials |
p.161 # 3 - 9 p.184 # 1-3, 7, 9bdf, 10bd, 11ac, 12b, 14ad, 15bd, 16ac, 17bd |
Unit 3: Solving Equations & Inequalities
| 1 |
Solving Polynomial Equations |
p.204 # 6, 7ad, 10, 13, 16 | |
| 2 |
Solving Linear Inequalities |
p.213 # 5bdf, 6be, 7bdf, 8, 9, 11, 15, 19 |
|
| 3 |
Solving Nonlinear Inequalities Algebraically |
p.225 # [1bd, 2, 3] fundamentals 5, 6bdf, 7bdf (no graph or use tech), 8, 10, 11, 15 18 [not taking up] |
|
| 4 |
Rates of Change in Polynomials |
p.235 # 5cde, 6cde, 7, 9, 11 | |
| 5 |
Graphs of Reciprocal Functions |
p.254 # 1, 2def, 6bcd, 8bdf, 9bc, 11, # 16 (find equation of reciprocal (shown) and original function) |
|
| 6 |
Rational Functions & Asymptotes |
p.262 # 1, 2, 3 | |
| 7 |
Graphing Rational Functions |
Sample Problem PDF VT |
p.272 # 1, 3, 5bcd, 6bd, 14 |
| 8 |
Solving Rational Equations |
p.286 # 5ace, 6bcf, 10, 12, 13 (see p.278 for help on 10, 13) |
|
| 9 |
Solving Rational Inequalities |
p.295 # 1, 4acf, 5ace, 7, 9, 13 | |
| 10 |
Rates of Change in Rational Functions Quiz - Graphing Rational Functions |
p.303 # 1, 2, 4, 6bc, 10, 13 | |
| 11 |
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 |
Unit 4: Trigonometric Functions
| 0 | 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 |
|
| 1 |
Radian Measure |
p.320 # 1 - 4, 6 - 10, 15 | |
| 2 |
Radian Angles in the Cartesian Plane |
Worksheet - RAA & CAST Rule (w/ Answers) MCR3U Trig Lessons |
p.330 # 1-4, 5ace, 6ace, 7ace, 8ace, 9, 11, 13 |
| 3 |
Graphs of Trig Functions (focus on tangent function) |
Video: Sine Graph from Circular Motion |
p.336 # 2c, 3, 5 |
| 4 |
Transformations of Trig Functions |
p.343 # 1bd, 3, 4, 5, 8ade, 9, 11, 12, 14 | |
| 5 |
Graphs of Reciprocal Trig Functions |
worksheet | p.353 # 1, 2, 3, 6, 7 |
| 6 |
Modelling with Trigonometric Function |
|
p.360 # 1-3, 5, 6, 7, 9, 11 |
| 7 | Homework / Work Period | ||
| 8 | Activity - Model Periodic Data | ||
| 9 | Rates of Change in Trigonometric Functions AM PM |
p.369 # 1 - 3, 4bd, 6, 7, 8, 12, 15 |
|
| 10 | Review - Trigonometric Functions | p.376 # 1-4, 6, 7, 10, 11bd, 12, 14-17, 19 |
|
| 11 |
Test - Trigonometric Functions |
Unit 5: Trigonometric Identities & Equations
| 1 |
Equivalent Trigonometric Functions |
Trig Identities Sheet |
p.392 # 1, 2a, 3acd, 4a, 5abc |
| 2 |
Compound Angle Formulas (Addition & Subtraction Identities) |
Worksheet - RAA & CAST Rule (w/ Answers) |
p.400 # 1-4, 5acf, 6cde, 8, 9ade, 10, 13 |
| 3 |
Double Angle Formulas |
p.407 # 1-3, 5, 6, 8, 9 (see p.406), 13 | |
|
4 5 |
Trigonometric Identities |
MCR3U: WS 3.3 Trig Identities(solutions) | p.416 # 5, 8, (9, 10, 11)(odd), 17 |
| 6 |
Solving Linear Trig Equations |
Quiz Solutions - Compound & Double Angles |
p.426 # 1bdf, 2bdf, 5, 6bdf, 8, 10bef, 11, 18 |
| 7 |
Solving Quadratic Trig Equations |
p.436 # 1, 3, 6ac, 7bd, 8ad, 9ac, 11, 14, 18
|
|
| 8 | Work Period | ||
| 9 | Review | p.440 # 1, 2, 3ac, 4, 5, 6, 7, 8, 9, 10, 11b, 12bcd, 13 | |
| 10 |
Test - Trigonometric Identities & Equations |
Unit 6: Exponential & Logarithmic Functions
| 1 |
Introduction to Logarithmic Functions |
Handout - Graphs of Exp & Log Functions |
p.451 # 4 - 9 |
| 2 |
Graphs & Transformations of Log Functions |
p.456 # 1-3 (basics), 4, 5, 8, 9, 11 |
|
| 3 |
Evaluating Logarithms |
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 |
| 4 |
Laws of Logarithms |
p.475 # 5, 6, 7, 9ace, 10ace, 11bde, 17 |
|
| 5 |
Solving Exp & Log Equations |
p.485 # 2, 8, 10, 17 p.491 # 4, 5, 7, 12 |
|
| 6 | Work Period |
p.485 # 4, 6bc, 7, 11 p.492 # 3, 9 |
|
| 7 |
Solving Exp & Log Problems |
Worksheet - Word Problems |
p.499 # 1, 2, 3, 5a, 6a, 11, 13, 15 |
| 8 |
Rates of Change in Log Functions |
p.507 # 4, 7acd, 11abc Note: 7b equation y=0.0017(1.7698)^x |
|
|
9 |
Review |
*** look at all notes & homework *** p.510 # 1, 2, 3, 6a, 7, 8, 10, 11bc, 13, 14ac, 15bd, 17, 19, 22, 23 |
|
| 10 |
Test - Logarithmic Functions |
Unit 7: Combinations of Functions
| 1 | Exploring Combinations of Functions | p.520 # 1, 2 | |
| 2 |
Adding & Subtracting Functions |
p.528 # 1ace, 2, 3, 5, 7, 9acef, 10, 11, 13 | |
| 3 |
Multiplying Functions |
p.537 # 1ae, 3, 4bef, 5bef, 8ad, 11, 12 | |
| 4 |
Dividing Functions |
p.542 # 1, 2, 3 p.544 # 3, 4, 6 |
|
|
5 |
Composition of Functions |
p.552 # 1, 2abf, 3, 5aef, 6def, 7cf, 10, 13 | |
| 6 | work period | ||
| 7 |
Solving Equations & Inequalities |
p.560 # 1, 3, 4, 5ef, 6ace, 9bdf | |
| 8 |
Review - Combinations of Functions | p.576 # 2, 4, 5, 6bcd, 7cd, 8, 9, 11, 12d | |
| 8 | Evaluation |
Review & Final Exam
| |
Review |
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 |