MCV4UW2013

Grade 12, University Preparation, [|Online Textbook Link], - Get WinRAR to unpack manual
 * MCV4U - Calculus & Vectors**
 * Important Reminders:
 * Exam - Monday, June 24th @ 9 A.M. ||

|| **Assigned Work** || J17 J14 || Exam Review || || p.267 #1bd, 2b, 3, 5b, 6, 7, 8, 9b,10, 11, 14c,17, 18, 19, 20, 21, 24cd, 25, 27, 28, 29, 30, 31
 * **Date** || **Chapter/Topic or Lesson** || ** Lessons, Handouts & Extra Resources **
 * J18

p.218 #10bc p.268#15c p.575 #9a

p.575 #3, 4, 6

p.578 #2, 3, 4

p.557 #1ab, 3c, 4b, 6, 7, 8, 9, 12, 16a, 17ab, 18, 19a, 20bc, 21, 22, 23b, 24, 26, 31, 32, 33, 35 || Matrices (Intersection of 3 planes || || Intersection 2 planes - p.516 #6, 8 Intersection 3 planes - p. 309 #7, 8a || J03 || Review / Workperiod ||  || Read Ch 8 Summary p.479 Review p.480-­483 (34 questions) Chapter 9.1 (Intersections of L & L/ L & Plane) ||
 * J13 || **Vectors Summative** ||  ||   ||
 * J12 || **Calculus Summative** ||  ||   ||
 * J11 || Calculus Review || [[file:Calculus Review (completed).pdf]] || Review: All tests, Derivs, Curve Sketching ||
 * J10 || Intersection of 3 planes || [[file:L10-Intersections of 3 Planes in 3D (completed).pdf|L10-Intersections of 3 Planes in 3D (completed).pdf]] || p.532 #9,10,13 ||
 * J07 || Intersection of two planes &
 * J06 || **Thinking Task #5 - Planes & Intersections** ||  ||   ||
 * J05 || **Unit 6 Test** ||  ||   ||
 * J04
 * M31 || Intersection of Line & Plane || [[file:L7-Intersections of a Line and a Plane (completed).pdf|L7-Intersections of a Line and a Plane (completed).pdf]] || p.496­-498 # 3, 4, 5, 6, 7, 13 ||
 * M30 || Intersection of Line & Line in R3 & R2 || [[file:L6-Intersection of Lines in R3 (completed).pdf|L6-Intersection of Lines in R3 (completed).pdf]] || p.497-­498 #8, 9, 11, 12 ||
 * M29 || Cartesian Equation of a Plane || [[file:L5-Cartesian Equation of a Plane (completed).pdf|L5-Cartesian Equation of a Plane (completed).pdf]] || p.468­-469 #1, 2, 3, 4b, 6,

8,10, 11, 13, 14 || of a Line in R2 || || p.433­-434 # 1, 2, 3, 4, 5, 6, 7, 9b, 10 || You Tube Cross Product Video Syracuse University Cross Product Applet || p.407­-408 #1, 2, 3, 4abc, 5, 7, 9a, 13 p. 415 #5b, 6, 7 || M03 || Vectors as Forces || || p.362 #3, 5, 6, 8, 10, 11, 12, 16, 17 || A30 || Review || || Review: p.344-347 #1, 2a, 3, 5, 6a, 7, 8, 11, 12b, 15ab, 16c(also find direction), 19a, 21, 23 || also read examples 335-339 || & Vectors in R2 & R3 || || p. 316­-318 #1, 4, 5, 6, 7ab, 8, 12a, 15 p.306­-307 #3, 7, 8, 10, 11 || (no trig optimization - See Handout TR.5) || A15 || Assembly - Senior Band Concert Optimization of Trig || || This is the lesson for Monday Completed See Handout TR.5 #1,2,4,7-10 Also Textbook p.257 #7-13 & p.260 #6,7 || p.260 #1, 2, 3, 4 || || p.245 #1,2a,3,4,5,6,11,12bc || (omit 5c and 9bc) for 7(use graphing technology) || number (e) || || p. 232­-233 #1, 2aef, 3, 4bc, 5a, 7, 8, 12, 13 || =**of Exponential**= =**Functions, Logarithmic Functions,**= =**and Trigonometric Functions**= || =Chapter 5= ||  || || Review p.156-159 #3, 5, 6, 7ab, 8, 9,14, 15, 17, 19 to 24, 26d || || Complete Handout Problems # 11, 12, 13, 14, 15 || (Day 2) || || Continue with curve sketching review || Algorithm || || p. 212 # 4abcde || Work Sheet || 9, 10,11, 17,18abf p.110-113 #3, 4, 8, 10a, 11a, || || Complete Worksheet #1-19 || || p.105 #4, 5 (dot not rewrite in the form suggested) #15, 16 || || p. 97 #4, 5cd, 6, 7, 8, 9, 13 || || p. 90-91 #1abcde, 5abc, 6, 7, 9 || || p.82 # 2, 3def, 4cef, 8ab, 9bf, 14, 15, 16 || || p.52 #4ace, 5bdf, 6, 11, 13, 14, 16 || || p.45 #4, 7, 8, 9 || || p.38 #5, 6, 7, 10de, 11, 12 || || p.30 # 10 - 14 || || p.20 #9c, 10c, 11ef, 16, 20 || || p.9 #3bdf, 4, 6ef, 7 ||
 * M28 || Vector & Parametric Equations of a Plane || [[file:L4-Vector & Parametric Equations of a Plane (completed).pdf|L4-Vector & Parametric Equations of a Plane (completed).pdf]] || p.459-460 #1, 2, 3, 4, 6, 8a, 9, 10, 11, 12b ||
 * M27 || Vector Parametric & Symmetric Equations in R3 || [[file:L3-Vector Parametric & Symmetric Equations in R3 (completed).pdf|L3-Vector Parametric & Symmetric Equations in R3 (completed).pdf]] || p.449-­450 #1bcd, 2bcd, 4abc (part c good question!), 5bde, 6, 9,10d, 12 ||
 * M24 || Work Period ||  ||   ||
 * M23 || Cartesian Equation of a Line in R2 || [[file:L2-Cartesian Equation of a Line in R2 (completed).pdf|L2-Cartesian Equation of a Line in R2 (completed).pdf]] || p.443-444 # 1, 3cd, 4, 5, 6, 7, 9b, 10acef, 11 ||
 * M22 || Vector & Parametric Equations
 * || =**Unit 6: Lines, Planes, and Intersections**= ||  ||   ||
 * M21 || **Unit 5 Test** ||  ||   ||
 * M17 || Work Period (Review) ||  || Continue with review ||
 * M16 || **Thinking Task #4 -**
 * Vectors in R3** ||  ||   ||
 * M15 || Review ||  || p.418-421 #1cd, 2f, 3, 4, 6, 7, 8b, 9, 10, 11, 14, 15, 16, 18bcd, 20c, 22, 23, 29, 30, 31b ||
 * M14 || Application of Dot & Cross Product || [[file:L7-Applications of Dot & Cross Product(Work & Torque) (completed).pdf|L7-Applications of Dot & Cross Product(Work & Torque) (completed).pdf]] || p.414 #1, 3, 8 ||
 * M13 || Cross Product || [[file:L6-Cross Product & Area of Parallelogram (completed).pdf|L6-Cross Product & Area of Parallelogram (completed).pdf]]
 * M10 || Projections || [[file:L5-Projections (completed).pdf|L5-Projections (completed).pdf]] || p.398-400 #1, 6, 7b, 8, 11, 13 ||
 * M09 || Dot Product of Alg Vectors || [[file:L4-Dot Product of Algeb Vectors (completed).pdf|L4-Dot Product of Algeb Vectors (completed).pdf]] || p.385-387 #2, 4, 6bd, 7b, 9b, 10a,11, 12, 14 Also Read Example 5 on page 384 ||
 * M08 || Dot Product of Geo Vectors || [[file:L3-The Dot Product of Geo Vectors (complete).pdf|L3-The Dot Product of Geo Vectors (complete).pdf]] || p.377 #2, 5, 6abe, 7acd, 9, 11, 12 ||
 * M07 || Velocity as Vectors || [[file:L2-Velocity as a Vector (complete).pdf|L2-Velocity as a Vector (complete).pdf]] || p.369 #1, 2, 3, 5, 6, 7, 9, 10 ||
 * M06
 * M02 || **Unit 5 Test** ||  ||   ||
 * M01
 * A29 || Linear Combinations || [[file:L8-Linear Combinations (complete).pdf|L8-Linear Combinations (complete).pdf]] || p.340 #6, 7b, 8, 10, 11, 13, 14
 * A26 || Operation on Vectors in R3 || [[file:L7-Operations on Vectors in R3 (complete).pdf|L7-Operations on Vectors in R3 (complete).pdf]] || p.332 # 1, 2, 3, 4, 5ac, 6ac, 8, 10, 12 ||
 * A25 || **Thinking Task #3 -**
 * Trig Optimization** ||  ||   ||
 * A24 || Operations with Algebraic Vectors in R2 || [[file:L6-Operations with Algebraic Vectors in R2 (complete).pdf|L6-Operations with Algebraic Vectors in R2 (complete).pdf]] || p.325­-326 #3, 4, 5b, 6ac, 7c, 8c, 9, 10, 11, 12, 13a ||
 * A23 || Properties of Vectors
 * A22 || Multiplication of Vectors by Scalar || [[file:L3-Mult of Vector by Scalar (complete).pdf|L3-Mult of Vector by Scalar (complete).pdf]] || p.299-300 # 2, 4, 5, 6de, 9, 10, 13, 14, 15 ||
 * A19 || Addition & Subtraction of Vectors || [[file:L2 - Vector Addition & Subtraction (complete).pdf|L2 - Vector Addition & Subtraction (complete).pdf]] || P 290 #1­-5, 7,9,11­-13 ||
 * A18 || Introduction to Vectors || [[file:L1-Intro to Vectors.pdf|L1-Intro to Vectors.pdf]] || p.279-280 #1-9 ||
 * || =**Unit 5: Vectors**= || =Chapter 6= ||  ||
 * A17 || **Unit 4 Test** ||  ||   ||
 * A16 || Review ||  || p.263-265 #1-9, 11-16, 23
 * A12,
 * A11 || Work Period ||  || p.263-265 #1-9, 11-16, 23 ||
 * A10 ||  || [[file:L6-Derivatives of Trig Functions (complete).pdf|L6-Derivatives of Trig Functions (complete).pdf]] || p.256 #1, 2, 3, 5
 * A09 || Optimization with e^x & ln(x) || [[file:L5 - Optimization with e^x & lnx.ggb|Geogebra File - L5 - Optimization with e^x & lnx.ggb]]
 * A08 || **Thinking Task #2 - Optimization** ||  ||   ||
 * A05 || Derivative of y=log(x) || [[file:L4-Derivative of y=log(x) (complete).pdf|L4-Derivative of y=log(x) (complete).pdf]] || p.578 #1-5,7,9,11 ||
 * A04 || Derivative of y=ln(x) || [[file:L3-Derivative of y=ln(x) (complete).pdf|L3-Derivative of y=ln(x) (complete).pdf]] || p.575 #3-13
 * A03 || Introducing the Natural Logarithm (ln) || [[file:L2-Derivative of y=b^x (completed).pdf|L2-Derivative of y=b^x (completed).pdf]] || p.240 # 1, 2, 4, 5, 6, 9 ||
 * A02 || Introducing Euler's
 * || =**Unit 4: Derivatives**=
 * M28 || **Unit 3 Test - Optimization** ||  ||   ||
 * M27 || Review || [[file:Review-Optimization (complete).pdf|Review-Optimization (complete).pdf]]
 * M26 || Workperiod ||  || Review p.156-159 #3, 5, 6, 7ab, 8, 9,14, 15, 17, 19 to 24, 26d ||
 * M25 || 3.4 Optimization Problems - Economics & Science || [[file:L6-Optimization in Economics (completed).pdf|L6-Optimization in Economics (completed).pdf]] || p. 152­-153 # 2, 3, 4, 5, 6, 7, 10, 12, 13 ||
 * M22 || 3.3 Optimization problems - Optimizing Time || [|You Tube Video - Optimization]
 * M21 || Workperiod & Quiz || [[file:Workperiod & Quiz (completed).pdf|Workperiod & Quiz (completed).pdf]] ||  ||
 * M20 || 3.3 Optimization Problems - Optimizing Distance || [[file:L4-Optimizing Distance (complete).pdf|L4-Optimizing Distance (complete).pdf]] || p. 147 #15, 16, 20 + Handout #1 to 5, 8, 9 ||
 * M19 || 3.3 Optimization Problems - Perimeter, Area, Volume || [[file:L3-Perimeter Area & Volume (complete).pdf|L3-Perimeter Area & Volume (complete).pdf]] || p.145­-146 #1 to 12 (excluding #2) ||
 * M18 || 3.2 Max & Mins on an interval || [[file:L2-Max&Mins on an Interval (Complete).pdf|L2-Max&Mins on an Interval (Complete).pdf]] || p136-138 # 2ab, 3d, 4ab, 6, 7a, 8, 9 ||
 * M08 || 3.1 Position, Velocity and Acceleration || [[file:L1-Position, Velocity & Acceleration (complete).pdf|L1-Position, Velocity & Acceleration (complete).pdf]] || p.127-129 #4, 5, 6c, 8, 9, 11, 12, 13b (read example 4 on p.124), 16 ||
 * || =**Unit 3: Optimization**= || =Chapter 3= ||  ||
 * M07 || **Unit 2 Test -**
 * Curve Sketching** ||  ||   ||
 * M06 || Review - Curve Sketching
 * M05 || **Thinking Task #1** || No Lesson || Continue with curve sketching review ||
 * M04 || Review - Curve Sketching || [[file:Review (complete).pdf|Review (complete).pdf]] || Review: p. 216 # 1, 2, 3, 4, 5, 8, 10, 19, 20 ||
 * M01 || More Sketching / Review || [[file:L6-Special Case Critical Points (Complete).pdf|L6-Special Case Critical Points (Complete).pdf]] || p. 212 # 4fghij ||
 * F28 || 4.5 - Curve Sketching
 * F27 || 4.4 - 2nd Derivative Test, Concavity, Inflection pts || [[file:L4-Inflection Pts & Concavity & 2nd Deriv Test (complete).pdf|L4-Inflection Pts & Concavity & 2nd Deriv Test (complete).pdf]] || p.205 #2, 3, 5, 13a ||
 * F26 || 4.3 - Vertical and Horizontal Asymptotes || [[file:L3-Limits & Asymptotes (complete).pdf|L3-Limits & Asymptotes (complete).pdf]] || p.193 #3, 4, 5, 7, 9, 10ace, 12 ||
 * F25 || 4.2 - Critical points, local maxima, and minima || [[file:L2-Critical Pts & 1st Deriv Test (complete).pdf|L2-Critical Pts & 1st Deriv Test (complete).pdf]] || p. 178 #3, 4, 5bcd, 7cde ||
 * F22 || 4.1 & 4.2 - Increasing and Decreasing Functions || [[file:L1-Increasing & Decreasing Functions (complete).pdf|L1-Increasing & Decreasing Functions (complete).pdf]] || p.169-171 #1ab, 3, 4abcd(algebraically), 8, 9, 10 +
 * || =**Unit 2: Curve Sketching**= || =**Chapter 4**= ||  ||
 * F21 || **Unit 1 Test - Limits & Derivatives** ||  || Read Chapter 4.1 ||
 * F20 || Review ||  || p.56-59 #2ab (use 1st principles),
 * F19 || 2.6 - Combining All The Rules || [[file:L11-Combining the Rules (complete).pdf|L11-Combining the Rules (complete).pdf]]
 * F14 || 2.5 - The Chain Rule || [|Khan Academy - The Chain Rule]
 * F13 || 2.4 - The Quotient Rule || [|Khan Academy - The Quotient Rule]
 * F12 || 2.3 - The Product Rule || [|Khan Academy - The Product Rule]
 * F11 || 2.2 - The Power Rule || [|Khan Academy - Derivatives Power Rule]
 * F08 || 1.6 Continuity || [|Khan Academy - Limits to Define Continuity]
 * F07 || 1.5 Limits (Part 2) || [|Khan Academy - Limit properties]
 * F06 || 1.4 Limits (Part 1) || [|Khan Academy - Intro to limits]
 * F05 || 1.3 Rates of Change (From first principles) || [|Khan Academy - slope of tangent (first principles) Part 2]
 * F04 || 1.2 First Principles
 * Slope of Secant and Tangent || [|Khan Academy - slope of tangent (first principles) Part 1]
 * F01 || 1.1 Radical Expressions: Rationalizing || [|Khan Academy - rationalizing]
 * || =**Unit 1: Limits and Derivatives**= || =**Chapters 1 & 2**= ||  ||

This course builds on students’ previous experience with functions and their developing understanding of rates of change. Students will solve problems involving geometric and algebraic representations of vectors and representations of lines and planes in three-dimensional space; broaden their understanding of rates of change to include the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions; and apply these concepts and skills to the modelling of real-world relationships. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended for students who choose to pursue careers in fields such as science, engineering, economics, and some areas of business, including those students who will be required to take a university-level calculus, linear algebra, or physics course.
 * Overall Course Description **

In this course, students will:
 * Develop, select, apply, compare, and adapt a variety of problem-solving strategies as they pose and solve problems and conduct investigations, to help deepen their mathematical understanding;
 * Develop and apply reasoning skills (e.g., use of inductive reasoning, deductive reasoning, and counter-examples; construction of proofs) to make mathematical conjectures, assess conjectures, and justify conclusions, and plan and construct organized mathematical arguments;
 * Demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by assessing the effectiveness of strategies and processes used, by proposing alternative approaches, by judging the reasonableness of results, by verifying solutions);
 * Select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems;
 * Make connections among mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, current events, art and culture, sports);
 * Create a variety of representations of mathematical ideas (e.g., numeric, geometric, algebraic, graphical, pictorial representations; onscreen dynamic representations), connect and compare them, and select and apply the appropriate representations to solve problems;
 * Communicate mathematical thinking orally, visually, and in writing, using precise mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions.

** Prerequisites **
Advanced Functions course (MHF4U) must be taken prior to or concurrently with Calculus and Vectors (MCV4U).

Resources

 * Course Texts: **
 * Donato, Malinowski, Murray et al., "**Calculus and Vectors**", Nelson Education, 2009.
 * Other:**


 * Additional Resources**:
 * eLearningOntario - []
 * The Ontario Curriculum, Grades 11 and 12 Mathematics - []
 * Ministry of Education website - []
 * Sir Robert Borden mathematics video website - []