Mathematics — Grade 12 University Preparation

📐 MHF4U: Advanced Functions

Polynomial, rational, logarithmic, and trigonometric functions; rates of change

110 hours · 117 video lessons · 8 chapters · Prerequisite: MCR3U Functions (Grade 11)

Ch1: Polynomial Functions Ch2: Polynomial Equations Ch3: Rational Functions Ch4: Trigonometry Ch5: Trigonometric Functi Ch6: Exponential & Logari Ch7: Solving Exp. & Log. Ch8: Combining Functions

Chapter 1: Polynomial Functions

Power functions, characteristics, graphing from factored form, even/odd, rates of change

📚 Strand C: Polynomial & Rational ⏱️ ~20h 📹 20 lessons
1.1 — Power Functions
📹 Video Lessons
📖 MHF4U 1.1a Power Functions 21:29 ▶
📝 MHF4U1 1.1b Power Functions Homework Solutions 1:57 ▶
1.2 — Stating Intervals
📹 Video Lessons
📖 MHF4U 1.2 Stating Intervals 11:50 ▶
1.3 — Characteristics of Polynomial Functions
📹 Video Lessons
📖 MHF4U 1.3a Characteristics of Polynomial Functions 31:01 ▶
📝 MHF4U 1.3b Characteristics of Polynomial Functions Homework 3:23 ▶
1.4 — Finite Differences
📹 Video Lessons
📖 MHF4U 1.4a Finite Differences 10:11 ▶
📝 MHF4U 1.4b Finite Differences Homework Solutions 2:25 ▶
1.5 — Graphing from Factored Form
📹 Video Lessons
📖 MHF4U 1.5a Graphing Polynomial Functions from Factored Form 32:37 ▶
📝 MHF4U 1.5b Equations and Graphs of Polynomial Functions Homework Solutions 7:45 ▶
📝 MHF4U 1.5c Extra Practice with Graphs of Polynomial Functions Homework Solutions 6:46 ▶
1.6 — Even and Odd Functions
📹 Video Lessons
📖 MHF4U 1.6a Even and Odd Functions 20:10 ▶
📝 MHF4U 1.6b Even and Odd Functions Homework Solutions 2:44 ▶
1.7 — Transformations of Power Functions
📹 Video Lessons
📖 MHF4U 1.7a Transformations of Power Functions 37:38 ▶
📝 MHF4U 1.7b Transformations of Power Functions Homework Solutions 3:03 ▶
1.8 — Average Rate of Change
📹 Video Lessons
📖 MHF4U 1.8a Average Rate of Change 13:51 ▶
📝 MHF4U 1.8b Average Rate of Change Homework Solutions 2:13 ▶
1.9 — Instantaneous Rate of Change
📹 Video Lessons
📖 MHF4U 1.9a Instantaneous Rate of Change 13:11 ▶
📝 MHF4U 1.9b Instantaneous Rate of Change Homework Solutions 2:25 ▶
1.10 — Chapter Summary & Review
📹 Video Lessons
📋 MHF4U 1.10a Chapter 1 Summary 7:19 ▶
📝 MHF4U 1.10b Chapter 1 Review Homework Solutions 6:10 ▶
📊 Chapter 1 Assessments
🔄 Practice Quiz (AS) 📋 Diagnostic (FOR) ✅ Unit Test (OF)

Chapter 2: Polynomial Equations & Inequalities

Remainder theorem, factor theorem, solving equations, polynomial inequalities

📚 Strand C: Polynomial & Rational ⏱️ ~15h 📹 16 lessons
2.1 — Remainder Theorem & Synthetic Division
📹 Video Lessons
📖 MHF4U 2.1a Remainder Theorem 23:39 ▶
📖 MHF4U 2.1b Synthetic Division 13:00 ▶
📝 MHF4U 2.1c Remainder Theorem Homework Solutions 5:45 ▶
2.2 — Factor Theorem & Sum/Difference of Cubes
📹 Video Lessons
📖 MHF4U 2.2a Factor Theorem 35:50 ▶
📖 MHF4U 2.2b Sum and Difference of Cubes 9:22 ▶
📝 MHF4U 2.2c Factor Theorem Homework Solutions 7:43 ▶
2.3 — Solving Polynomial Equations
📹 Video Lessons
📖 MHF4U 2.3a Solving Polynomial Equations 35:09 ▶
📝 MHF4U 2.3b Solving Polynomial Equations Homework Solutions 4:43 ▶
📝 MHF4U 2.3c Solving Polynomial Equations (Word Problems) Homework Solutions 10:32 ▶
2.4 — Family of Polynomial Functions
📹 Video Lessons
📖 MHF4U 2.4a Family of Polynomial Functions 11:48 ▶
📝 MHF4U 2.4b Family of Polynomial Functions Homework Solutions 4:58 ▶
2.5 — Polynomial Inequalities
📹 Video Lessons
📖 MHF4U 2.5a Polynomial Inequalities 28:00 ▶
📝 MHF4U 2.5b Solving Factorable Polynomial Inequalities Homework Solutions 9:41 ▶
2.6 — Chapter Summary & Review
📹 Video Lessons
📋 MHF4U 2.6a Chapter 2 Summary 6:06 ▶
📝 MHF4U 2.6b Chapter 2 Review Homework Solutions 6:36 ▶
📝 MHF4U 2.6c Chapter 2 Challenge Problems Homework Solutions 13:37 ▶
📊 Chapter 2 Assessments
🔄 Practice Quiz (AS) 📋 Diagnostic (FOR) ✅ Unit Test (OF)

Chapter 3: Rational Functions

Reciprocal functions, asymptotes, holes, rational equations and inequalities

📚 Strand C: Polynomial & Rational ⏱️ ~15h 📹 19 lessons
3.1 — Introduction to Rational Functions
📹 Video Lessons
📖 MHF4U 3.1 Introduction to Rational Functions 10:55 ▶
3.2 — Reciprocal of Linear Functions
📹 Video Lessons
📖 MHF4U 3.2a Reciprocal of Linear Functions 26:12 ▶
📝 MHF4U 3.2b Reciprocal of Linear Function Homework Solutions 5:07 ▶
📝 MHF4U 3.2c Graphing Reciprocal of Linear Function Homework Solutions 4:40 ▶
3.3 — Reciprocal of Quadratic Functions
📹 Video Lessons
📖 MHF4U 3.3a Reciprocal of Quadratic Functions 28:43 ▶
📝 MHF4U 3.3b Reciprocal of Quadratic Function Homework Solutions 8:23 ▶
📝 MHF4U 3.3c Graphing Reciprocal of Quadratic Function Homework Solutions 8:23 ▶
3.4 — Linear over Linear Rational Functions
📹 Video Lessons
📖 MHF4U 3.4a Linear over Linear Rational Functions 33:35 ▶
📝 MHF4U 3.4b Linear over Linear Rational Functions Homework Solutions 3:10 ▶
📝 MHF4U 3.4c Graphing Linear over Linear Rational Functions Homework Solutions 1:52 ▶
3.5 — Holes and Oblique Asymptotes
📹 Video Lessons
📖 MHF4U 3.5a Holes in Graphs of Rational Function 4:51 ▶
📖 MHF4U 3.5b Practice Graphing Challenging Rational Functions 19:57 ▶
📖 MHF4U 3.5c Oblique Asymptotes 12:49 ▶
3.6 — Rational Equations and Inequalities
📹 Video Lessons
📖 MHF4U 3.6a Rational Equations and Inequalities 33:54 ▶
📝 MHF4U 3.6b Rational Equations and Inequalities Homework Solutions 4:28 ▶
3.7 — Word Problems with Rational Functions
📹 Video Lessons
📖 MHF4U 3.7a Word Problems with Rational Functions and Rational Equations 22:29 ▶
📝 MHF4U 3.7b Word Problems with Rational Functions and Rational Equations Homework Solutions 9:00 ▶
3.8 — Chapter Summary & Review
📹 Video Lessons
📋 MHF4U 3.8a Chapter 3 Summary 4:40 ▶
📝 MHF4U 3.8b Chapter 3 Review Homework Solutions 3:52 ▶
📊 Chapter 3 Assessments
🔄 Practice Quiz (AS) 📋 Diagnostic (FOR) ✅ Unit Test (OF)

Chapter 4: Trigonometry

Radian measure, special angles, compound angle formulas, proving identities

📚 Strand B: Trigonometric Functions ⏱️ ~15h 📹 20 lessons
4.1 — Radian Measure
📹 Video Lessons
📖 MHF4U 4.1a Radian Measure 17:04 ▶
📝 MHF4U 4.1b Radian Measure Homework Solutions 5:24 ▶
4.2 — Special Angles and Trig Ratios
📹 Video Lessons
📖 MHF4U 4.2a Special Angles and Trigonometric Ratios Intro 5:24 ▶
📖 MHF4U 4.2b Special Angles and Trigonometric Ratios 18:49 ▶
📖 MHF4U 4.2c Special Angles and Trigonometric Ratios 13:00 ▶
📝 MHF4U 4.2d Special Triangles Homework 10:09 ▶
📖 MHF4U 4.2e Special Angles Chart 9:33 ▶
4.3 — Equivalent Trig Expressions
📹 Video Lessons
📖 MHF4U 4.3a Equivalent Trig Expressions Intro 7:44 ▶
📖 MHF4U 4.3b Equivalent Trig Expressions 12:54 ▶
📖 MHF4U 4.3c Equivalent Trig Expressions 13:53 ▶
📝 MHF4U 4.3d Equivalent Trig Expressions Homework Solutions 11:27 ▶
4.4 — Compound Angles
📹 Video Lessons
📖 MHF4U 4.4a Compound Angles 36:33 ▶
📖 MHF4U 4.4b Compound Angles 17:40 ▶
📝 MHF4U 4.4c Compound Angle Homework Solutions 10:03 ▶
📝 MHF4U 4.4d Double Angle and Half Angle Homework Solutions 12:08 ▶
4.5 — Proving Trig Identities
📹 Video Lessons
📖 MHF4U 4.5a Trig Identities 17:36 ▶
📝 MHF4U 4.5b Prove Trig Identities Homework Solutions 10:14 ▶
📝 MHF4U 4.5c Keep Proving Identities Homework Solutions 11:59 ▶
4.6 — Chapter Summary & Review
📹 Video Lessons
📋 MHF4U 4.6a Chapter 4 Summary 9:18 ▶
📝 MHF4U 4.6b Chapter 4 Review Homework Solutions 8:53 ▶
📊 Chapter 4 Assessments
🔄 Practice Quiz (AS) 📋 Diagnostic (FOR) ✅ Unit Test (OF)

Chapter 5: Trigonometric Functions

Graphing trig functions, transformations, sinusoidal equations, applications

📚 Strand B: Trigonometric Functions ⏱️ ~12h 📹 13 lessons
5.1 — Graphing 6 Trig Functions
📹 Video Lessons
📖 MHF4U 5.1 Graphing 6 Trig Functions and their Properties 32:45 ▶
5.2 — Transformations of Sinusoidal Functions
📹 Video Lessons
📖 MHF4U 5.2a Graphing Transformed Sine and Cosine Functions 23:48 ▶
📖 MHF4U 5.2b Graphing Transformed Sine and Cosine Functions 15:18 ▶
📝 MHF4U 5.2c Graphing Transformed Sine and Cosine Functions Solutions 9:21 ▶
5.3 — Equations of Sinusoidal Functions
📹 Video Lessons
📖 MHF4U 5.3a Equations of Sinusoidal Functions 27:04 ▶
📝 MHF4U 5.3b Equations of Sinusoidal Functions Homework 6:07 ▶
5.4 — Solving Trig Equations
📹 Video Lessons
📖 MHF4U 5.4a Solving Trigonometric Equations 50:01 ▶
📝 MHF4U 5.4b Solve Trigonometric Equations Solutions 10:07 ▶
📝 MHF4U 5.4c Solve Trigonometric Equations (Challenge) Solutions 13:48 ▶
5.5 — Applications of Trig Functions
📹 Video Lessons
📖 MHF4U 5.5a Application of Trigonometric Functions 25:23 ▶
📝 MHF4U 5.5b Solving Trigonometric Word Problems Solutions 7:44 ▶
5.6 — Chapter Summary & Review
📹 Video Lessons
📋 MHF4U 5.6a Chapter 5 Summary 12:26 ▶
📝 MHF4U 5.6b Chapter 5 Review Homework Solutions 10:52 ▶
📊 Chapter 5 Assessments
🔄 Practice Quiz (AS) 📋 Diagnostic (FOR) ✅ Unit Test (OF)

Chapter 6: Exponential & Logarithmic Functions

Logarithms, transformations, log laws, logarithmic scales

📚 Strand A: Exponential & Logarithmic ⏱️ ~14h 📹 13 lessons
6.1 — Inverse of Exponential Functions
📹 Video Lessons
📖 MHF4U 6.1a Inverse of an Exponential Function and their Properties 17:37 ▶
📝 MHF4U 6.1b Inverse of an Exponential Function Homework Solutions 2:50 ▶
6.2 — Introduction to Logarithms
📹 Video Lessons
📖 MHF4U 6.2a Introduction to Logarithms 15:51 ▶
📝 MHF4U 6.2b Logarithms Homework Solutions 4:25 ▶
📝 MHF4U 6.2c Logarithm Exercise Homework Solutions 5:40 ▶
6.3 — Transformations of Log Functions
📹 Video Lessons
📖 MHF4U 6.3a Transformations of Logarithmic Functions 23:28 ▶
📝 MHF4U 6.3b Transformations of Logarithmic Functions Homework Solutions 3:35 ▶
6.4 — Power Law of Logarithms
📹 Video Lessons
📖 MHF4U 6.4a Power Law of Logarithms 16:14 ▶
📝 MHF4U 6.4b Power Law of Logarithms Homework Solutions 4:26 ▶
6.5 — Product and Quotient Laws
📹 Video Lessons
📖 MHF4U 6.5a Product and Quotient Law of Logarithms 21:48 ▶
📝 MHF4U 6.5b Product and Quotient Law of Logarithms Homework Solutions 4:24 ▶
6.6 — Logarithmic Scales
📹 Video Lessons
📖 MHF4U 6.6a Logarithmic Scales in Physical Sciences 25:06 ▶
📝 MHF4U 6.6b Logarithmic Scales in Physical Sciences Homework Solution 6:00 ▶
📖 Exponential Growth, Decay & Compound Interest Formulas — The Organic Chemistry Tutor 23:18 ▶
📖 Compound Interest and e — Khan Academy 7:50 ▶
📖 What is e and ln(x)? — Euler's Number and the Natural Logarithm 9:00 ▶
📊 Chapter 6 Assessments
🔄 Practice Quiz (AS) 📋 Diagnostic (FOR) ✅ Unit Test (OF)

Chapter 7: Solving Exp. & Log. Equations

Techniques for solving exponential and logarithmic equations

📚 Strand A: Exponential & Logarithmic ⏱️ ~10h 📹 8 lessons
7.1 — Solving Exponential Equations
📹 Video Lessons
📖 MHF4U 7.1a Solving Exponential Equations 26:35 ▶
📝 MHF4U 7.1b Equivalent Forms of Exponential Equations Homework Solution 3:42 ▶
📝 MHF4U 7.1c Solving More Exponential Equations Homework Solution 8:44 ▶
7.2 — Solving Logarithmic Equations
📹 Video Lessons
📖 MHF4U 7.2a Solving Logarithmic Equations 22:19 ▶
📝 MHF4U 7.2b Solving Logarithmic Equations Homework Sheet 4:01 ▶
7.3 — Chapters 6-7 Summary & Review
📹 Video Lessons
📋 MHF4U 7.3a Chapter 6 and 7 Summary 5:58 ▶
📝 MHF4U 7.3b Chapter 6 Review Homework Solutions 7:12 ▶
📝 MHF4U 7.3c Chapter 7 Review Homework Solutions 7:18 ▶
📊 Chapter 7 Assessments
🔄 Practice Quiz (AS) 📋 Diagnostic (FOR) ✅ Unit Test (OF)

Chapter 8: Combining Functions

Sums, differences, products, quotients, composite functions, modeling

📚 Strand D: Characteristics of Functions ⏱️ ~10h 📹 8 lessons
8.1 — Sums and Differences of Functions
📹 Video Lessons
📖 MHF4U 8.1a Sums and Differences of Functions 19:14 ▶
📝 MHF4U 8.1b Sums and Differences of Functions Homework Solutions 4:47 ▶
8.2 — Products and Quotients of Functions
📹 Video Lessons
📖 MHF4U 8.2a Product and Quotient of Functions 11:09 ▶
📝 MHF4U 8.2b Product and Quotient of Functions Homework Solutions 3:25 ▶
8.3 — Composite Functions
📹 Video Lessons
📖 MHF4U 8.3a Composite Functions 22:32 ▶
📝 MHF4U 8.3b Composite Functions Homework Solutions 5:28 ▶
8.4 — Modeling with Combined Functions
📹 Video Lessons
📖 MHF4U 8.4 Modeling Combining Functions 20:18 ▶
8.5 — Chapter Summary & Review
📹 Video Lessons
📝 MHF4U 8.5 Chapter 8 Review Homework Solutions 2:07 ▶
📖 Comparing Linear, Polynomial & Exponential Functions 9:24 ▶
📖 Comparing Exponential and Logarithmic Functions — Khan Academy 5:32 ▶
📖 Average vs Instantaneous Rate of Change — Trig, Exp, Log & Rational Functions (Advanced Functions 8.8) 10:08 ▶
📊 Chapter 8 Assessments
🔄 Practice Quiz (AS) 📋 Diagnostic (FOR) ✅ Unit Test (OF)

📋 Course Resources & Final Evaluation

Ministry curriculum overview and the comprehensive final exam (30% of course mark)

📚 Ontario Curriculum 2007 (Revised) 📐 Growing Success (2010)
📋 Curriculum Document
MHF4U Curriculum Overview
Strands A–D, mathematical processes, achievement chart, evaluation policy, and chapter mapping.
🎓 Final Exam (30%)
Comprehensive Final Exam — Ch 1–8
3 hours · 100 marks · 25 marks each in K/U, Thinking, Communication, Application. Full answer key included.