MHF4U

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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:

Functions, Grade 11, University Preparation; or
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 note video lesson	handout	p.36 # 4, 5, 6, 7, 9, 10, 15, 16ab
5	Function Inverses note video lesson	KA - Function Inverses KA - Restricting Domain for Inverse Functions KA - Determine Inverse Algebraically Ex1 Ex2 Ex3 MCR3U - Function Inverses	p.44 # 4, 5, 6bd, 7, 9, 11, 12c, 13, 17
6	Piecewise Functions note video lesson	KA - Piecewise Example	p.51 # 3, 4, 5cd, 6, 8, 9, 11, 13
7	Combinations of Functions (using simple arithmetic operations) note video lesson		Try to complete Ex.2 & Ex.3 on your own p.57 # 2, 3, 4, 5, 6
8	Average & Instantaneous Rates of Change note video lesson		p.76 # 8, 9 p.85 # 4, 7, 9, 10, 15
9	Graphical Representations of Rate of Change note video lesson		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 note video lesson	[VT - Pascal's Triangle & Binomial Expansion]	p.127 # 1 - 5
2	Characteristics of Polynomials note video lesson		p.136 # 5, 7, 8, 9, 12, 14, 15, 16
3	Characteristics of Factored Form note video lesson		p.146 # 1, 2, 4, 6, 9, 10, 12, 13, 14
4	Transformations of Polynomials note video lesson		p.155 # 2, 3, 4bde, 5, 6bde, 7, 8, 9ace, 10, 11, 14
5	Dividing Polynomials note video lesson	KA - Polynomial Long Division KA - Synthetic Division	p.168 # 1, 4, 5ace, 6ace, 7ac, 8d, 9ac, 10ace, 11, 12, 14
6	Factoring Polynomials note video lesson	KA - Example - Remainder Theorem	p.176 # [1-3][basics], 4bf, 5ac, 6abc, 7df, 8, 9, 10, 13, 17
7	Factoring Cubic Polynomials note 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 note video lesson		p.204 # 6, 7ad, 10, 13, 16
2	Solving Linear Inequalities note video lesson		p.213 # 5bdf, 6be, 7bdf, 8, 9, 11, 15, 19
3	Solving Nonlinear Inequalities Algebraically note 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 note video lesson		p.235 # 5cde, 6cde, 7, 9, 11
5	Graphs of Reciprocal Functions note video lesson		p.254 # 1, 2def, 6bcd, 8bdf, 9bc, 11, # 16 (find equation of reciprocal (shown) and original function)
6	Rational Functions & Asymptotes note video lesson		p.262 # 1, 2, 3
7	Graphing Rational Functions note video lesson	Sample Problem PDF VT	p.272 # 1, 3, 5bcd, 6bd, 14 worksheet (more complex problems, optional)
8	Solving Rational Equations note 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) + Word Problems Using Rational Functions w Sols
9	Solving Rational Inequalities note 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

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 note 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 note video lesson	Video: Sine Graph from Circular Motion	p.336 # 2c, 3, 5
4	Transformations of Trig Functions video note 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 note video lesson	worksheet	p.353 # 1, 2, 3, 6, 7
6	Modelling with Trigonometric Function video note 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 class note 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 videoNote video lesson		p.407 # 1-3, 5, 6, 8, 9 (see p.406), 13
4 5	Trigonometric Identities videoNote video lesson	MCR3U: WS 3.3 Trig Identities(solutions)	p.416 # 5, 8, (9, 10, 11)(odd), 17
6	Solving Linear Trig Equations videoNote video lesson	Quiz Solutions - Compound & Double Angles	p.426 # 1bdf, 2bdf, 5, 6bdf, 8, 10bef, 11, 18
7	Solving Quadratic Trig Equations videoNote 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 note video lesson	Handout - Graphs of Exp & Log Functions	p.451 # 4 - 9
2	Graphs & Transformations of Log Functions note		p.456 # 1-3 (basics), 4, 5, 8, 9, 11
3	Evaluating Logarithms note 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 note video lesson		p.475 # 5, 6, 7, 9ace, 10ace, 11bde, 17
5	Solving Exp & Log Equations note 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	Solving Exp & Log Problems note video lesson	Worksheet - Word Problems	p.499 # 1, 2, 3, 5a, 6a, 11, 13, 15
8	Rates of Change in Log Functions note		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	Handout Video - Sound of Adding Sine Waves	p.520 # 1, 2
2	Adding & Subtracting Functions note video lesson		p.528 # 1ace, 2, 3, 5, 7, 9acef, 10, 11, 13
3	Multiplying Functions note video lesson		p.537 # 1ae, 3, 4bef, 5bef, 8ad, 11, 12
4	Dividing Functions note video lesson		p.542 # 1, 2, 3 p.544 # 3, 4, 6
5	Composition of Functions note video lesson		p.552 # 1, 2abf, 3, 5aef, 6def, 7cf, 10, 13
6	work period
7	Solving Equations & Inequalities note		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

exam review suggestions

Review # 1 (w/ answers)

Review # 2

Review # 3 (w/ answers)

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

p.103 # 3, 5, 9, 10

p.111 # 2, 10, 13

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