# MHF4U 2016-2017 Semester 1

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:

1. Functions, Grade 11, University Preparation; or
2. Mathematics for College Technology, Grade 12, College Preparation

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 video lesson Khan Academy - What is a Function? (there are several videos in series) Interval Notation p.11 # 1, 2, 3, 4, 6, 8, 11, 12, 14 2 Absolute Value Function video lesson p.16 # 3-10 3 Properties of Graphs video lesson 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 video lesson handout p.36 # 4, 5, 6, 7, 9, 10, 15, 16ab 5 Function Inverses video lesson KA - Function Inverses KA - Restricting Domain for Inverse Functions KA - Determine Inverse Algebraically Ex1 Ex2 Ex3 p.44 # 4, 5, 6bd, 7, 9, 11, 12c, 13, 17 6 Piecewise Functions video lesson KA - Piecewise Example p.51 # 3, 4, 5cd, 6, 8, 9, 11, 13 6 Combinations of Functions (using simple arithmetic operations) video lesson Try to complete Ex.2 & Ex.3 on your own p.57 # 2, 3, 4, 5, 6 7 Average & Instantaneous Rates of Change video lesson p.76 # 8, 9 p.85 # 4, 5, 7 8 Graphical Representations of Rate of Change video lesson p.103 # 3, 5, 9, 10p.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 video lesson [VT - Pascal's Triangle & Binomial Expansion] p.127 # 1 - 5 2 Characteristics of Polynomials video lesson p.136 # 5, 7, 8, 9, 12, 14, 15, 16 3 Characteristics of Factored Form video lesson p.146 # 1, 2, 4, 6, 9, 10, 12, 13, 14 5 Dividing Polynomials video lesson KA - Synthetic Division p.168 # 1, 4, 5ace, 6ace, 7ac, 8d, 9ac, 10ace, 11, 12, 14 6 Factoring Polynomials video lesson 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 video lesson 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 video lesson p.204 # 6, 7ad, 10, 13, 16 2 Solving Linear Inequalities video lesson p.213 # 5bdf, 6be, 7bdf, 8, 9, 11, 15, 19 3 Solving Nonlinear Inequalities Algebraically video lesson 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 video lesson Quiz - Solving Inequalities p.235 # 5cde, 6cde, 7, 9, 11 5 Graphs of Reciprocal Functions video lesson p.254 # 1, 2def, 6bcd, 8bdf, 9bc, 11, # 16 (find equation of reciprocal (shown) and original function) 6 Rational Functions & Asymptotes video lesson p.262 # 1, 2, 3 7 Graphing Rational Functions video lesson Sample Problem PDF VT p.272 # 1, 3, 5bcd, 6bd, 14 8 Solving Rational Equations video lesson 3U Simplify Rationals Lesson VT 3U Multiply/Divide Lesson VT 3U Add/Subtract Lesson VT1 VT2 p.286 # 5ace, 6bcf, 10, 12, 13 (see p.278 for help on 10, 13) 9 Solving Rational Inequalities video lesson 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 video lesson p.320 # 1 -­ 4, 6 -­ 10, 15 2 Radian Angles in the Cartesian Plane video lesson 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 lesson Video: Sine Graph from Circular Motion p.336 # 2c, 3, 5 4 Transformations of Trig Functions video lesson VT (SS) - Graphing Sinusoidal by Transformations VT (SS) - Determining Sinusoidal Equations from Graphs p.343 # 1bd, 3, 4, 5, 8ade, 9, 11, 12, 14 5 Graphs of Reciprocal Trig Functions video lesson 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 worksheet w/ extra problems Solutions: 1 2 3 4 5 6 7 8 9 10 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 video lesson Trig Identities Sheet p.392 # 1, 2a, 3acd, 4a, 5abc 2 Compound Angle Formulas video lesson (Addition & Subtraction Identities) Worksheet - RAA & CAST Rule (w/ Answers) p.400 # 1-­4, 5acf, 6cde, 8, 9ade, 10, 13 3 Double Angle Formulas video lesson p.407 # 1­-3, 5, 6, 8, 9 (see p.406), 13 4 5 Trigonometric Identities video lesson MCR3U: WS 3.3 Trig Identities(solutions) p.416 # 5, 8, (9, 10, 11)(odd), 17 6 Solving Linear Trig Equations video lesson Quiz Solutions - Compound & Double Angles p.426 # 1bdf, 2bdf, 5, 6bdf, 8, 10bef, 11,  18 7 Solving Quadratic Trig Equations video lesson p.436 # 1, 3, 6ac, 7bd, 8ad, 9ac, 11, 14, 18 work period next class before, complete: 1, 3, 6a, 7b, 8a, 9a ­day of, complete: 6c, 7d, 8d, 9c, 11, 14 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 video lesson 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 video lesson 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 video lesson p.475 # 5, 6, 7, 9ace, 10ace, 11bde, 17 5 Solving Exp & Log Equations video lesson 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 video lesson 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 Handout Video - Sound of Adding Sine Waves p.520 # 1, 2 2 Adding & Subtracting Functions video lesson p.528 # 1ace, 2, 3, 5, 7, 9acef, 10, 11, 13 3 Multiplying Functions video lesson p.537 # 1ae, 3, 4bef, 5bef, 8ad, 11, 12 4 Dividing Functions video lesson p.542 # 1, 2, 3 p.544 # 3, 4, 6 5 Composition of Functions video lesson 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

p.103 # 3, 5, 9, 10

p.111 # 2, 10, 13