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
Per2 |
Per3 | Topic / Lesson |
Extra Resources |
Assigned Work |
J27 | J28 |
Final Exam | ||
J20 | Summative Part 2 | |||
J15 | Quest (long quiz, short test) | |||
J14 | Review - Combinations of Functions | p.576 # 2, 4, 5, 6bcd, 7cd, 8, 9, 11, 12d | ||
J13 | Solving Equations & Inequalities AM PM | p.560 # 1, 3, 4, 5ef, 6ace, 9bdf | ||
J09 | Composition of Functions AM PM | p.552 # 1, 2abf, 3, 5aef, 6def, 7cf, 10, 13 | ||
J08 | Dividing Functions AM PM |
p.542 # 1, 2, 3 p.544 # 3, 4, 6 |
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J07 | Multiplying Functions AM PM | p.537 # 1ae, 3, 4bef, 5bef, 6ef, 8ad, 11, 12 | ||
J06 | Adding & Subtracting Functions AM PM | p.528 # 1ace, 2, 3, 5, 7, 9acef, 10, 11, 13 | ||
J05 | Exploring Combinations of Functions | p.520 # 1, 2 | ||
Unit 7 - Combinations of Functions |
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D17 | Summative Part 1 | |||
D16 D15 D12 |
Summative Prep | |||
D12 | ||||
D11 | Test - Logarithmic Functions | |||
D10 |
Review |
*** look at all notes & homework *** p.510 # 1, 2, 3, 6a, 7, 8, 10, 11bc, 13, 14ac, 15bd, 17, 19, 22, 23 |
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D08 | D09 |
Solving Exp & Log Problems AM PM |
p.499 # 1, 2, 3, 5a, 6a, 11, 13, 15 |
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D09 | D08 |
Rates of Change in Log Functions AM PM |
p.507 # 4, 7, 11abc |
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D05 | Work Period |
p.485 # 4, 6bc, 7, 11 p.492 # 3, 9 |
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D04 | Solving Exp & Log Equations AM PM |
p.485 # 2, 8, 10, 17 p.491 # 4, 5, 7, 12 |
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D03 | Laws of Logarithms AM PM |
p.475 # 5, 6, 7, 9ace, 10ace, 11bde, 17 |
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D02 |
Evaluating Logarithms AM PM |
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 |
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D01 | Retest - Trigonometric Identities & Equations | |||
N28 | Graphs & Transformations of Log Functions AM PM |
p.456 # 1-3 (basics), 4, 5, 8, 9, 11 |
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N27 |
Introduction to Logarithmic Functions AM PM |
Handout - Graphs of Exp & Log Functions |
p.451 # 4 - 9 |
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Unit 6: Exponential & Logarithmic Functions | ||||
N26 | Test - Trigonometric Identities & Equations | |||
N25 | Review | p.440 # 1, 2, 3ac, 4, 5, 6, 7, 8, 9, 10, 11b, 12bcd, 13 | ||
N24 | Work Period | |||
N20 | Solving Quadratic Trig Equations AM PM |
p.436 # 1, 3, 6ac, 7bd, 8ad, 9ac, 11, 14, 18
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N19 | Solving Linear Trig Equations AM PM | Quiz Solutions - Compound & Double Angles |
p.426 # 1bdf, 2bdf, 5, 6bdf, 8, 10bef, 11, 18 |
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N17 | Trigonometric Identities AM PM | MCR3U: WS 3.3 Trig Identities(solutions) | p.416 # 5, 8, (9, 10, 11)(odd), 17 | |
N14 | Double Angle Formulas AM PM | p.407 # 1-3, 5, 6, 8, 9 (see p.406), 13 | ||
N13 |
(Addition & Subtraction Identities) |
Worksheet - RAA & CAST Rule (w/ Answers) |
p.400 # 1-4, 5acf, 6cde, 8, 9ade, 10, 13 | |
N07 | Equivalent Trigonometric Functions AM PM | Trig Identities Sheet |
p.392 # 1, 2a, 3acd, 4a, 5abc |
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Unit 5: Trigonometric Identities & Equations |
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N12 | Test - Trigonometric Functions | |||
N10 | Review - Trigonometric Functions | p.376 # 1-4, 6, 7, 10, 11bd, 12, 14-17, 19 |
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N06 | Rates of Change in Trigonometric Functions AM PM |
p.369 # 1 - 3, 4bd, 6, 7, 8, 12, 15 |
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N05 | Activity - Model Periodic Data | |||
N04 | Homework / Work Period | |||
N03 | Modelling with Trigonometric Function AM PM | |
p.360 # 1-3, 5, 6, 7, 9, 11 | |
O31 | Graphs of Reciprocal Trig Functions AM PM | worksheet | p.353 # 1, 2, 3, 6, 7 | |
O30 | Transformations of Trig Functions AM PM | Video: Sine Graph from Circular Motion |
p.343 # 1bd, 3, 4, 5, 8ade, 9, 11, 12, 14 | |
O29 | Graph of the Tangent Function AM PM | p.336 # 2c, 3, 5 |
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O24 | Radian Angles in the Cartesian Plane AM PM | MCR3U Trig Lessons | p.330 # 1-4, 5ace, 6ace, 7ace, 8ace, 9, 11, 13 | |
O23 | Radian Measure AM PM | p.320 # 1 - 4, 6 - 10, 15 | ||
Unit 4 - Trigonometric Functions | ||||
O28 | Test - Polynomial & Rational Functions | |||
O27 | 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 |
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O22 | O22 |
Rates of Change in Rational Functions AM PM Quiz - Graphing Rational Functions |
p.303 # 1, 2, 4, 6bc, 10, 13 | |
O21 | O21 | Solving Rational Inequalities AM PM | p.295 # 1, 4acf, 5ace, 7, 9, 13 | |
O20 | O20 | Solving Rational Equations AM PM |
p.286 # 5ace, 6bcf, 10, 12, 13 (see p.278 for help on 10, 13) |
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O16 | O16 | Graphing Rational Functions AM PM | Sample Problem PDF VT |
p.272 # 1, 3, 5bcd, 6bd, 14 |
O15 | O15 | Rational Functions & Asymptotes AM PM | p.262 # 1, 2, 3 | |
O14 | O14 | Graphs of Reciprocal Functions AM PM |
p.254 # 1, 2def, 6bcd, 8bdf, 9bc, 11 # 16 (find equation of reciprocal (shown) and original function) |
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O09 | O09 | Rates of Change in Polynomials AM PM | p.235 # 5cde, 6cde, 7, 9, 11 | |
O08 |
O08 |
Work Period: Nonlinear Inequalities Quiz - Solving Inequalities |
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O07 | O07 | Solving Nonlinear Inequalities Algebraically AM PM |
p.225 # [1bd, 2, 3] fundamentals 5, 6bdf, 7bdf (no graph or use tech), 8, 10, 11, 15 18 [not taking up] |
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O06 | O02 | Solving Linear Inequalities AM PM |
p.213 # 5bdf, 6be, 7bdf, 8, 9, 11, 15, 19 |
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O03 | O01 |
Solving Polynomial Equations AM PM | p.204 # 6, 7ad, 10, 13, 16 |
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Unit 3 - Polynomial/Rational Equations & Inequalities | ||||
O02 | O02 |
Test - Polynomals | ||
S30 | S30 | Review - Polynomials |
p.161 # 3 - 9 p.184 # 1-3, 7, 9bdf, 10bd, 11ac, 12b, 14ad, 15bd, 16ac, 17bd |
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S29 | S29 | Transformations of Polynomials AM PM | p.155 # 2, 3, 4bde, 5, 6bde, 7, 8, 9, 10ace, 11, 14 | |
S26 | S26 |
Factoring Cubic Polynomials |
WS - Factoring Sum & Difference of Polynomials (H/W on WS) |
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S25 | S25 | Factoring Polynomials AM PM | KA - Example - Remainder Theorem |
p.176 # [1-3][basics], 4bf, 5ac, 6abc, 7df, 8, 9, 10, 13, 17 |
S24 S23 |
S24 S23 |
Dividing Polynomials AM PM | p.168 # 1, 4, 5ace, 6ace, 7ac, 8d, 9ac, 10ace, 11, 12, 14 | |
S22 | S22 | Combinations of Functions AM PM |
Try to complete Ex.2 & Ex.3 on your own p.57 # 2, 3, 4, 5, 6 |
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S19 | S19 | Characteristics of Factored Form AM PM | p.146 # 1, 2, 4, 6, 9, 10, 12, 13, 14 | |
S18 | S18 | Characteristics of Polynomials AM PM | p.136 # 5, 7, 8, 9, 12, 14, 15, 16 | |
S17 | S17 | Polynomial Functions AM PM | p.127 # 1 - 5 | |
Unit 2 - Polynomials |
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S16 | S16 | Test - Functions & Rates of Change | ||
S15 | S15 | Review - Functions & Rates of Change |
p.60 # 1-4, 6, 7-9, 10-17 p.116 # 2-7 note: many better questions in homework |
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S11 | S11 | Graphical Representations of RoC | ||
S10 | S10 |
Average & Instantaneous Rates of Change |
p.76 # 8, 9 p.85 # 4, 5, 7 |
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Unit 1b - Rates of Change |
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S09 |
S09 |
Piecewise Functions AM PM | KA - Piecewise Example |
p.51 # 3, 4, 5cd, 6, 8, 9, 11, 13 |
S08 |
S08 |
Function Inverses AM PM |
KA - Restricting Domain for Inverse Functions |
p.44 # 4, 5, 6bd, 7, 9, 11, 12c, 13, 17 |
S05 | S05 |
Review: Transformations of Functions |
p.36 # 4, 5, 6, 7, 9, 10, 15, 16ab | |
S04 | S04 | Properties of Graphs AM PM | Khan A - Even/Odd Functions |
p.23 # 12, 3, 4, 5, 7, 8, 9, 10, 14 use handout for 12, 14 |
S03 | S03 | Absolute Value Function AM PM | p.16 # 3-10 | |
Sep2 |
S02 |
Review - Functions, Domain, Range AM PM |
Khan Academy - What is a Function? (there are several videos in series) |
p.11 # 1, 2, 3, 4, 6, 8, 11, 12, 14 |
Unit 1a - Functions (includes review) |