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
Date | Topic / Lesson |
Extra Resources |
Assigned Work |
Fri J27 |
Final Exam | Carleton Exam Prep Tutoring | |
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 |
||
Test: Combinations of Functions |
|||
J10 |
Review - Combinations of Functions | extra review solutions |
p.576 # 2, 4, 5, 6bcd, 7cd, 8, 9, 11, 12d |
D22 |
Solving Equations & Inequalities |
p.560 # 1, 3, 4, 5ef, 6ace, 9bdf | |
D21 |
Composition of Functions |
p.552 # 1, 2abf, 3, 5aef, 6def, 7cf, 10, 13 | |
D20 |
Dividing Functions |
p.542 # 1, 2, 3 p.544 # 3, 4, 6 |
|
D19 |
Multiplying Functions |
p.537 # 1ae, 3, 4bef, 5bef, 8ad, 11, 12 | |
D14 |
Adding & Subtracting Functions |
p.528 # 1ace, 2, 3, 5, 7, 9acef, 10, 11, 13 | |
D13 | Exploring Combinations of Functions | p.520 # 1, 2 | |
D16 | Test: Logarithmic Functions | ||
D15 | Review | Questions from Other Texts |
*** look at all notes & homework *** p.510 # 1, 2, 3, 6a, 7, 8, 10, 11bc, 13, 14ac, 15bd, 17, 19, 22, 23 |
D12 |
Rates of Change no video lesson |
||
D09 |
Solving Exp & Log Problems |
p.499 # 1, 2, 3, 5a, 6a, 11, 13, 15 |
|
D08 | work period | ||
D07 |
Solving Exp & Log Equations |
p.485 # 2, 8, 10, 17 p.491 # 4, 5, 7, 12 |
|
D06 |
Laws of Logarithms |
p.475 # 5, 6, 7, 9ace, 10ace, 11bde, 17 |
|
D05 |
Evaluating Logarithms |
VT - Changing Base of Logs |
.466 # 3 (using rule 1 or 2),
# 5 (using 1 or 2), 8 (using 4), 6, 9, 12, 17 |
D02 |
Graphs & Transformations of Log Functions video lesson |
p.456 # 1-3 (basics), 4, 5, 8, 9, 11 | |
N28 |
Introduction to Logarithmic Functions |
Handout - Graphs of Exp & Log Functions |
p.451 # 4 - 9 |
Unit 6: Exponential & Logarithmic Functions |
|||
D01 |
Test - Trigonometric Identities & Equations | ||
N30 |
Review | p.440 # 1, 2, 3ac, 4, 5, 6, 7, 8, 9, 10, 11b, 12bcd, 13 | |
N29 | Work Period | focus on solving quadratics, then general review |
|
N25
|
Solving Quadratic Trig Equations |
p.436 # 1, 3, 6ac, 7bd, 8ad, 9ac, 11, 14, 18
|
|
N24 |
Solving Linear Trig Equations |
Sample Quiz Solutions - Compound & Double Angles (potential test questions) |
p.426 # 1bdf, 2bdf, 5, 6bdf, 8, 10bef, 11, 18 |
N23 |
Work Period Practice Quiz: Evaluate Trig Ratios (no calculators) |
Worksheet: RAA, CAST, Trig Ratios (practice problems similar to quiz) |
|
N22
|
Trigonometric Identities |
MCR3U: WS 3.3 Trig Identities(solutions) |
p.416 # 5, 8, (9, 10, 11)(odd), 17 |
N21 |
Double Angle Formulas |
p.407 # 1-3, 5, 6, 8, 9 (see p.406), 13 | |
N17 | work period | ||
N16 |
Compound Angle Formulas (Addition & Subtraction Identities) |
p.400 # 1-4, 5acf, 6cde, 8, 9ade, 10, 13 | |
N07 |
Equivalent Trigonometric Functions |
p.392 # 1, 2a, 3acd, 4a, 5abc |
|
Unit 5: Trig Identities & Equations |
|||
N10 | Midterm Exam | ||
N09 N08 |
Review - Midterm | ||
N15 | Test - Trigonometry Pt1 | ||
N14 |
Review - Trigonometric Functions | p.376 # 1-4, 6, 7, 10, 11bd, 12, 14-17, 19 | |
N04 | Activity - Model Periodic Data | ||
N03 |
Homework / Work Period | ||
N02 |
Modelling with Trigonometric Function |
|
p.360 # 1-3, 5, 6, 7, 9, 11 |
N01 |
Work Period: Graphs of Trigonometric Functions |
worksheet (solutions) |
|
O31 |
Graphs of Reciprocal Trig Functions |
worksheet | p.353 # 1, 2, 3, 6, 7 |
O28 |
Transformations of Trig Functions |
p.343 # 1bd, 3, 4, 5, 8ade, 9, 11, 12, 14 | |
O27 |
Graphs of Trig Functions (focus on tangent function) |
Video: Sine Graph from Circular Motion |
p.336 # 2c, 3, 5 |
O26 |
Radian Angles in the Cartesian Plane |
p.330 # 1-4, 5ace, 6ace, 7ace, 8ace, 9, 11, 13 | |
O21 |
Radian Measure |
p.320 # 1 - 4, 6 - 10, 15 |
|
Unit 4: Trigonometric Functions | |||
O25 | Test - Equations & Inequalities | ||
O24 |
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 |
|
O20 |
Rates of Change in Rational Functions no video lesson |
p.303 # 1, 2, 4, 6bc, 10, 13 | |
O19 |
Solving Rational Inequalities |
p.295 # 1, 4acf, 5ace, 7, 9, 13 | |
O18 |
Solving Rational Equations |
p.286 # 5ace, 6bcf, 10, 12, 13 (see p.278 for help on 10, 13) |
|
O17 |
Graphing Rational Functions |
Sample Problem PDF Video |
p.272 # 1, 3, 5bcd, 6bd, 14 |
O14 |
Rational Functions & Asymptotes |
p.262 # 1, 2, 3 | |
O13 |
Graphs of Reciprocal Functions |
p.254 # 1, 2def, 6bcd, 8bdf, 9bc, 11, # 16 (find equation of reciprocal (shown) and original function) |
|
O12 |
Rates of Change in Polynomials Quiz - Solving Inequalities |
p.235 # 5cde, 6cde, 7, 9, 11 | |
O11 |
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] |
|
O04 |
Solving Linear Inequalities |
p.213 # 5bdf, 6be, 7bdf, 8, 9, 11, 15, 19 |
|
O03 |
Solving Polynomial Equations |
p.204 # 6, 7ad, 10, 13, 16 | |
Unit 3: Solving Equations & Inequalities | |||
O06 |
Test - Polynomials |
||
O05 |
Review - Polynomials |
p.161 # 3 - 9 p.184 # 1-3, 7, 9bdf, 10bd, 11ac, 12b, 14ad, 15bd, 16ac, 17bd |
|
S30 |
Transformations of Polynomials |
p.155 # 2, 3, 4bde, 5, 6bde, 7, 8, 9, 10ace, 11, 14 | |
S29 |
Factoring Cubic Polynomials video lesson |
WS - Factoring Sum & Difference of Polynomials (H/W on WS) |
|
S28 |
Factoring Polynomials |
KA - Example - Remainder Theorem |
p.176 # [1-3][basics], 4bf, 5ac, 6abc, 7df, 8, 9, 10, 13, 17 |
S27
|
Dividing Polynomials Make-up test: Function & Rate of Change |
p.168 # 1, 4, 5ace, 6ace, 7ac, 8d, 9ac, 10ace, 11, 12, 14 | |
S26 |
Characteristics of Factored Form |
p.146 # 1, 2, 4, 6, 9, 10, 12, 13, 14 | |
S23 |
Characteristics of Polynomials |
p.136 # 5, 7, 8, 9, 12, 14, 15, 16 | |
S20 |
Polynomial Functions |
[VT - Pascal's Triangle & Binomial Expansion] |
p.127 # 1 - 5 |
Unit 2: Polynomial Functions | |||
S22 | Test - Functions & Rate of Change | ||
S21 |
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 |
|
S19 |
Graphical Representations of Rate of Change video lesson |
p.103 # 3, 5, 9, 10 p.111 # 2, 10, 13 |
|
S16 |
Average & Instantaneous Rates of Change |
p.76 # 8, 9 p.85 # 4, 5, 7 |
|
S15 |
Combinations of Functions note (using simple arithmetic operations) |
Try to complete Ex.2 & Ex.3 on your own p.57 # 2, 3, 4, 5, 6 |
|
S14 |
Piecewise Functions note |
KA - Piecewise Example | p.51 # 3, 4, 5cd, 6, 8, 9, 11, 13 |
S13 |
Function Inverses note |
KA - Restricting Domain for Inverse Functions |
p.44 # 4, 5, 6bd, 7, 9, 11, 12c, 13, 17 |
S12 |
Review: Transformations of Functions |
handout |
p.36 # 4, 5, 6, 7, 9, 10, 15, 16ab |
S09 |
Properties of Graphs |
p.23 # 12, 3, 4, 5, 7, 8, 9, 10, 14 use handout for 12, 14 |
|
S08 | p.16 # 3-10 | ||
S07 |
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 |
Unit 1: Functions & Rates of Change |
|||
S06 |
Course Intro |
"Getting Started" from Ch.1, 2, 3 (hand in tomorrow) |
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 |
6 |
Combinations of Functions (using simple arithmetic operations) |
Try to complete Ex.2 & Ex.3 on your own p.57 # 2, 3, 4, 5, 6 |
|
7 |
Average & Instantaneous Rates of Change |
p.76 # 8, 9 p.85 # 4, 5, 7 |
|
8 |
Graphical Representations of Rate of Change |
p.103 # 3, 5, 9, 10 p.111 # 2, 10, 13 |
|
9 | 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 | |
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) |
|
4 |
Transformations of Polynomials |
p.155 # 2, 3, 4bde, 5, 6bde, 7, 8, 9, 10ace, 11, 14 | |
8 | 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 Quiz - Solving Inequalities |
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
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 video lesson | |
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 AM PM |
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 | Rates of Change in Log Functions AM PM |
p.507 # 4, 7, 11abc |
|
8 |
Solving Exp & Log Problems |
p.499 # 1, 2, 3, 5a, 6a, 11, 13, 15 |
|
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 | Solving Equations & Inequalities AM PM | p.560 # 1, 3, 4, 5ef, 6ace, 9bdf | |
7 | Review - Combinations of Functions | p.576 # 2, 4, 5, 6bcd, 7cd, 8, 9, 11, 12d | |
8 | Evaluation |