Grade 12 Advanced Functions
Welcome to MHF 4U. Below you can find all course information. It is your responsibility to be prepared and take notes during class time. Along with class notes there are both non-tech seatwork responsibilities, and software responsibilities.
Welcome to MHF 4U. Below you can find all course information. It is your responsibility to be prepared and take notes during class time. Along with class notes there are both non-tech seatwork responsibilities, and software responsibilities.
Unit 1 Polynomial Functions_Algebra Seatwork Software Assignments
Free TI83 PLUS Calculator and the ROM file
Note1 Function Notation A p11 #4, (6,8,10-12)eop
Note2 Composition of Functions A p20 #(6,11,13,17,19-23)eop
Note3 Inverse of Functions A p27 #1,3,4,7,9,10
Note4 Transformations of Cubics and Quartics Gizmos Login W.S. (Period C); W.S. Gizmo#1: Translating & Scaling Functions
Note5 Dividing Polynomials_Long Division N p42 #1,(2,3)eol,9-11,14
Note6 Synthetic Division N p43 #4-6,12,13 Gizmo#2: Synthetic
Note7 Remainder Theorem A p58 #(4-6)eop, 7-9
Note8 Factor Theorem _ Quiz Thurs Feb 13 A p64 #4,5,10,12,18,21-23
Note9 Factoring a Sum and Difference of Cubes N p51 #(10,11)c, 12,13
Note10 Review A p38 #(1-9)odds,10ab,11; A p72 #5-11; N p77 #21-23
Unit Test Thursday Feb 20
Unit 2 Polynomials Functions_Geometry Unit 2 Polynomials Functions_Geometry
Note1 Solving Polynomial Equations A p80 #(1,3)oep,(4-7)f; A p96 #(1,3-6)eop
Note2 Graphing Polynomials I W.S.
Note3 Graphing Polynomials II N p26 #12,13,16,19; N p16 #10 Gizmo#1: Graphs of Polynomial Functions
Note4 Graphing Polynomials III & Assignment due Mon March 2 N p15 #6,7,9,22 Gizmo#2: Polynomials and Linear Factors
Note5 Finite Differences N p26 #14,15,18; N p16 #14,15
Note6 Determining Equations of Polynomial Functions N p61 #6,11ab,12-14,18; N p16 #11a,16,17
Note7 Polynomial Inequations N p72 #(5,8)odds, 10,14,18a
Note8 Review N p75 #1-7,9,10,12-16,27-32,36 Inequalities PPT demo extension
Unit Test Friday March 6
Unit 3 Rational Functions Unit 3 Rational Functions
Note1 Vertical Asymptotes W.S. #1-11 Asymptote PPT demo
Note2 Horizontal Asymptotes N p357 #9,11a-c,14a; 2 BBQs
Note3 Oblique Asymptotes N p356 #1-4,11d, 4 BBQs Gizmo#1: General Form of a Rational Funct
Note4 Putting It all Together I N p356 #(5,6)odds,7,14 Gizmo#2: Rational Functions
Note5 Putting It all Together II & Assignment Due April 6 N p357 #(5,6)evens,10odds
Note6 Limits and Continuity N p367 #4,11,12,15; N p375 #5,6,8,13eol
Note7 Rational Function Inequalities W.S. with Answers
Note8 Rational Functions Review. Key Learnings N p419 #1-4,11-15,16odds,17,35
Unit Test
Spring 2020 On Line Learning Begins...Check your email and this website as appropriate. Spring isn't cancelled...
Unit 4 Exponential and Logarithmic Functions Unit 4 Exponential and Logarithmic Functions
Note1 Exponent Laws Review N p84 #(2-7)odds; A p436 #(3,7,8)odds; A p440 #(2,4,7)odds
Note2 Investigating Exponential Functions N p103 #3,8,18; A p456 #1,2 Gizmo#1: Exponential Functions
Note3 The Inverse of the Exponential Function N p118 #5even,6,9odd letters,12c,15 Gizmo#2: Log Functions Translating Scaling
Note4 Evaluating Logs N p117 #(1-4,7) every other letter, W.S. #1,2
Note5 Laws of Logs N p125 #(3-8)odds
Note6 Solving Exponential Equations N p126 #9,10; N p132 #(1-6)even
Note7 Solving Log Equations N p147 #7-9,14,17-20, [Optional: A p493 #4,11,12a-c]
Note8 Exponential Growth and Decay N p110 #2,3,6,7,11-13
Note9 Growth & Decay Story Question and Logarithms N p132 #7-12,20; N p140 #6,7,(9,10)odd letters,11
Note10 Review of Logarithmic and Exponential Functions N p157 #1-5,9,10,(11-15)odds,17-29,31-34,39,45
Wednesday May 6 Unit Test Assignment, Hyperlinked Wed morning
Unit 5 Trigonometric Functions Unit 5 Trigonometric Functions
Note1 Radian Measure A p249 #(1-6)aceg,9,10
Note2 Special Angles A p278 #1every other letter; A p283 #3 every other letter Gizmo#1: Cosine Function
Note3 Trigonometric Equations A p319 #3-6,9
Note4 Translations of Parent Trig Graphs A p331 #3,4,6; p337 #5odds,6,9 [Could use Desmos.com to check.]
Note5 Dilatations of Trig Functions A p342 #2,5ac,10a; p348 #2,3ace
Note6 Multiple Transformations A p355 #1,2,5ac,6bd,8a,9c Gizmo#2: Translating Scaling Sine Cosine
Note7 Setting the Scales of the Axes System A p362 #2,3,6abcefg, 9
Note8 Applications of Trig Functions A p369 #1,3,4ab,6-8 Optional: Check out: Colourful development of the trig curves
Note8.5 Optional: Graphing Reciprocal Trig Functions Optional: A p415 #4,7abef, p362 #(6,7)evens
Note9 Solving Linear Trig Equations with Radians A p320 #(10,11)a,b; W.S. #(1,3)every other letter, #4abd
Note10 Quadratic Trig Equations A p320 #(10,11)def, 14c
Note11 Trig Function Review A p372 #(1-4)every other letter,(6,7)ac,9b,12; W.S.
Monday June 8 Unit Test Assignment
Unit 6 Trig Identities and Trig Equations Unit 6 Trig Identities and Trig Equations
Note1 Proving Trig Identities W.S. #1-23 odd numbers
Note2 Solving Trig Equations using Grade 11 Identity Substitutions W.S. #2,3,4 Gizmo#1: Simplifying Trig Expressions
Note3 Co-functions W.S. #1-5, 7d, 8d
Note4 Addition Identities_Sine and Cosine W.S. Every other letter Gizmo#2: Sum & Difference Identities Sine & Cosine
Note5 Addition Identities_Tangent W.S. Every other letter
Spring 2020 On Line Learning Concludes...Summer isn't cancelled...Enjoy it!
Note6 Double Angle Formulas W.S.
Note7 Proving Trig Identities I W.S.(11-17) every other number, (28-48) even numbers
Note8 Proving Trig Identities II & Quiz N p605 #10 even letters
Note9 Solving Trig Equations Revisited W.S.
Note10 Trig Identities and Equations Review I W.S.; N p604 #1-9
Unit Test
Unit 7 Average and Instantaneous Rates of Change Unit 7 Average and Instantaneous Rates of Change
Note1 Rates Of Change N p178 #1,3,6; W.S. A#1-5 Gizmo#1: Distance Time Graphs
Note2 Tangent to a Curve N p179 #7,8a-c,9,10,13; N p190 #3-6; W.S. A#6-10
Note3 Using a Formula to Find Instantaneous Rates of Change N p213 #2even,5,7f,9,15,18
Note4 Limits of Rational, Radical, and Trig Equations N p383 #1; W.S. B#1-5; BBQ 1a-d.
Note5 Rates of Change, Velocity, & Equation of Tangent lines N p190 #7,9,12,13,15,16,18; N p202 #3-5,18; W.S. B#7-10
Note6 In-class Assignment and Work Period W.S
Note7 Review N p256 #1-6,11-17,19,21eol; N p260 #41,42,44,45; W.S.
Unit Test
Unit 8 Characteristics of Functions Unit 8 Characteristics of Functions
Note1 Solving Radical Equations A p110 #(3,8,9)eol, 10ab, 14
Note2 Addition & Subtraction of Functions N p34 #(1-3,7,8,11)odds, 15b,18
Note3 Piece-Wise Functions N p203 #9b,12,13,17, AACQ
Note4 Multiplying Functions N p34 #1d,4,7d,8d,11b,13,21,24; N p35 #9,10b
Note5 Revisit Composition of Functions N p35 #9,10b,14,20,25; A p 21 #23bdf,24
Note6 Composition of Discrete Functions N p439 #1a,3,8,9b,10acf,12
Note7 Symmetry Properties W.S. Parts A,B
Note8 Equations and Inequations A p106 #(3,4,5)ce, W.S.
Note9 Approximating Zeros & Quiz W.S.
Note10 Review W.S.; N p76 #17-20; N p497 #14,15; A p38 some; A p112 some; A p106 #(3,4,5)ce; A p114 #23,24; N p202 #11,13; N p257 #17
Unit Test
Exam Review Exam Review
W.S. [ Same W.S. in PDF Format: W.S. ]; N p165+; N p427+; N p559-560; N p575-579
W.S. [ Same W.S. in PDF Format: W.S. ]; A p113+; A p424+; A p550+
W.S. [ Same W.S. in PDF Format: W.S. ];
Office Hours:
Final Exam: Block C.......June , 2020.......Room 235 9am to 11am.
Free TI83 PLUS Calculator and the ROM file
Note1 Function Notation A p11 #4, (6,8,10-12)eop
Note2 Composition of Functions A p20 #(6,11,13,17,19-23)eop
Note3 Inverse of Functions A p27 #1,3,4,7,9,10
Note4 Transformations of Cubics and Quartics Gizmos Login W.S. (Period C); W.S. Gizmo#1: Translating & Scaling Functions
Note5 Dividing Polynomials_Long Division N p42 #1,(2,3)eol,9-11,14
Note6 Synthetic Division N p43 #4-6,12,13 Gizmo#2: Synthetic
Note7 Remainder Theorem A p58 #(4-6)eop, 7-9
Note8 Factor Theorem _ Quiz Thurs Feb 13 A p64 #4,5,10,12,18,21-23
Note9 Factoring a Sum and Difference of Cubes N p51 #(10,11)c, 12,13
Note10 Review A p38 #(1-9)odds,10ab,11; A p72 #5-11; N p77 #21-23
Unit Test Thursday Feb 20
Unit 2 Polynomials Functions_Geometry Unit 2 Polynomials Functions_Geometry
Note1 Solving Polynomial Equations A p80 #(1,3)oep,(4-7)f; A p96 #(1,3-6)eop
Note2 Graphing Polynomials I W.S.
Note3 Graphing Polynomials II N p26 #12,13,16,19; N p16 #10 Gizmo#1: Graphs of Polynomial Functions
Note4 Graphing Polynomials III & Assignment due Mon March 2 N p15 #6,7,9,22 Gizmo#2: Polynomials and Linear Factors
Note5 Finite Differences N p26 #14,15,18; N p16 #14,15
Note6 Determining Equations of Polynomial Functions N p61 #6,11ab,12-14,18; N p16 #11a,16,17
Note7 Polynomial Inequations N p72 #(5,8)odds, 10,14,18a
Note8 Review N p75 #1-7,9,10,12-16,27-32,36 Inequalities PPT demo extension
Unit Test Friday March 6
Unit 3 Rational Functions Unit 3 Rational Functions
Note1 Vertical Asymptotes W.S. #1-11 Asymptote PPT demo
Note2 Horizontal Asymptotes N p357 #9,11a-c,14a; 2 BBQs
Note3 Oblique Asymptotes N p356 #1-4,11d, 4 BBQs Gizmo#1: General Form of a Rational Funct
Note4 Putting It all Together I N p356 #(5,6)odds,7,14 Gizmo#2: Rational Functions
Note5 Putting It all Together II & Assignment Due April 6 N p357 #(5,6)evens,10odds
Note6 Limits and Continuity N p367 #4,11,12,15; N p375 #5,6,8,13eol
Note7 Rational Function Inequalities W.S. with Answers
Note8 Rational Functions Review. Key Learnings N p419 #1-4,11-15,16odds,17,35
Unit Test
Spring 2020 On Line Learning Begins...Check your email and this website as appropriate. Spring isn't cancelled...
Unit 4 Exponential and Logarithmic Functions Unit 4 Exponential and Logarithmic Functions
Note1 Exponent Laws Review N p84 #(2-7)odds; A p436 #(3,7,8)odds; A p440 #(2,4,7)odds
Note2 Investigating Exponential Functions N p103 #3,8,18; A p456 #1,2 Gizmo#1: Exponential Functions
Note3 The Inverse of the Exponential Function N p118 #5even,6,9odd letters,12c,15 Gizmo#2: Log Functions Translating Scaling
Note4 Evaluating Logs N p117 #(1-4,7) every other letter, W.S. #1,2
Note5 Laws of Logs N p125 #(3-8)odds
Note6 Solving Exponential Equations N p126 #9,10; N p132 #(1-6)even
Note7 Solving Log Equations N p147 #7-9,14,17-20, [Optional: A p493 #4,11,12a-c]
Note8 Exponential Growth and Decay N p110 #2,3,6,7,11-13
Note9 Growth & Decay Story Question and Logarithms N p132 #7-12,20; N p140 #6,7,(9,10)odd letters,11
Note10 Review of Logarithmic and Exponential Functions N p157 #1-5,9,10,(11-15)odds,17-29,31-34,39,45
Wednesday May 6 Unit Test Assignment, Hyperlinked Wed morning
Unit 5 Trigonometric Functions Unit 5 Trigonometric Functions
Note1 Radian Measure A p249 #(1-6)aceg,9,10
Note2 Special Angles A p278 #1every other letter; A p283 #3 every other letter Gizmo#1: Cosine Function
Note3 Trigonometric Equations A p319 #3-6,9
Note4 Translations of Parent Trig Graphs A p331 #3,4,6; p337 #5odds,6,9 [Could use Desmos.com to check.]
Note5 Dilatations of Trig Functions A p342 #2,5ac,10a; p348 #2,3ace
Note6 Multiple Transformations A p355 #1,2,5ac,6bd,8a,9c Gizmo#2: Translating Scaling Sine Cosine
Note7 Setting the Scales of the Axes System A p362 #2,3,6abcefg, 9
Note8 Applications of Trig Functions A p369 #1,3,4ab,6-8 Optional: Check out: Colourful development of the trig curves
Note8.5 Optional: Graphing Reciprocal Trig Functions Optional: A p415 #4,7abef, p362 #(6,7)evens
Note9 Solving Linear Trig Equations with Radians A p320 #(10,11)a,b; W.S. #(1,3)every other letter, #4abd
Note10 Quadratic Trig Equations A p320 #(10,11)def, 14c
Note11 Trig Function Review A p372 #(1-4)every other letter,(6,7)ac,9b,12; W.S.
Monday June 8 Unit Test Assignment
Unit 6 Trig Identities and Trig Equations Unit 6 Trig Identities and Trig Equations
Note1 Proving Trig Identities W.S. #1-23 odd numbers
Note2 Solving Trig Equations using Grade 11 Identity Substitutions W.S. #2,3,4 Gizmo#1: Simplifying Trig Expressions
Note3 Co-functions W.S. #1-5, 7d, 8d
Note4 Addition Identities_Sine and Cosine W.S. Every other letter Gizmo#2: Sum & Difference Identities Sine & Cosine
Note5 Addition Identities_Tangent W.S. Every other letter
Spring 2020 On Line Learning Concludes...Summer isn't cancelled...Enjoy it!
Note6 Double Angle Formulas W.S.
Note7 Proving Trig Identities I W.S.(11-17) every other number, (28-48) even numbers
Note8 Proving Trig Identities II & Quiz N p605 #10 even letters
Note9 Solving Trig Equations Revisited W.S.
Note10 Trig Identities and Equations Review I W.S.; N p604 #1-9
Unit Test
Unit 7 Average and Instantaneous Rates of Change Unit 7 Average and Instantaneous Rates of Change
Note1 Rates Of Change N p178 #1,3,6; W.S. A#1-5 Gizmo#1: Distance Time Graphs
Note2 Tangent to a Curve N p179 #7,8a-c,9,10,13; N p190 #3-6; W.S. A#6-10
Note3 Using a Formula to Find Instantaneous Rates of Change N p213 #2even,5,7f,9,15,18
Note4 Limits of Rational, Radical, and Trig Equations N p383 #1; W.S. B#1-5; BBQ 1a-d.
Note5 Rates of Change, Velocity, & Equation of Tangent lines N p190 #7,9,12,13,15,16,18; N p202 #3-5,18; W.S. B#7-10
Note6 In-class Assignment and Work Period W.S
Note7 Review N p256 #1-6,11-17,19,21eol; N p260 #41,42,44,45; W.S.
Unit Test
Unit 8 Characteristics of Functions Unit 8 Characteristics of Functions
Note1 Solving Radical Equations A p110 #(3,8,9)eol, 10ab, 14
Note2 Addition & Subtraction of Functions N p34 #(1-3,7,8,11)odds, 15b,18
Note3 Piece-Wise Functions N p203 #9b,12,13,17, AACQ
Note4 Multiplying Functions N p34 #1d,4,7d,8d,11b,13,21,24; N p35 #9,10b
Note5 Revisit Composition of Functions N p35 #9,10b,14,20,25; A p 21 #23bdf,24
Note6 Composition of Discrete Functions N p439 #1a,3,8,9b,10acf,12
Note7 Symmetry Properties W.S. Parts A,B
Note8 Equations and Inequations A p106 #(3,4,5)ce, W.S.
Note9 Approximating Zeros & Quiz W.S.
Note10 Review W.S.; N p76 #17-20; N p497 #14,15; A p38 some; A p112 some; A p106 #(3,4,5)ce; A p114 #23,24; N p202 #11,13; N p257 #17
Unit Test
Exam Review Exam Review
W.S. [ Same W.S. in PDF Format: W.S. ]; N p165+; N p427+; N p559-560; N p575-579
W.S. [ Same W.S. in PDF Format: W.S. ]; A p113+; A p424+; A p550+
W.S. [ Same W.S. in PDF Format: W.S. ];
Office Hours:
Final Exam: Block C.......June , 2020.......Room 235 9am to 11am.