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# MCV4U 2017-2018 Semester 2

last edited by 2 years, 4 months ago

MCV4U - Calculus & Vectors (University Preparation)

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.

Prerequisites:

1. Functions, Grade 11, University Preparation
2. Advanced Functions, Grade 12, University Preparation (can be taken concurrently, but generally not recommended)

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.

Returned evaluations with be marked in purple.

Nelson Calculus & Vectors Textbook Answers (Updated) Chapters 1-3 Chapters 4-6 Chapters 7-9

Full course (schedule, video lessons, notes, homework) can be found here.

 Day Topic / Lesson Resources Assigned Work J22 Final Exam , 9am, Room 205 J19 J18 J15 J14 Review: Final Exam Review Questions & Unit Summaries Exam Formula Sheet suggested textbook questions J13 Distances between Points, Lines, and Planes classNote video lesson note VT - Distance Between Point and Line in R3 p.540 # 2a, 3a, 5ac, 6b, 8p.550 # 2a, 3a, 5, 6 J12 Intersection of Three Planes classNote video lesson note p.532 #9, 10, 13 J10 work period J09 Solving Systems of Equations using Matrices classNote video lesson note online matrix solver (check steps/answers) p.588 # 4, 6b, 8b, 10ace p.594 # 1c, 3ace J11 Test - Lines & Planes J08 Partial Review - Lines & Planes p.552 # 1, 3, 4, 6, 12ab, 14, 15a, 19, 24, 26 J05 Intersection of Two Planes classNote video lesson note p.516 # 1, 2, 3, 6, 8, 10 J04 Intersection of Lines & Planes classNote video lesson note p.496 # 3, 4, 5, 6, 7, 13 J01 Intersection of Lines in R3 classNote video lesson note p.497 # 8, 9, 11, 12 M31 Cartesian Equation of a Plane classNote video lesson note p.468 # 1, 2, 3, 4b, 6, 8,10, 11, 13, 14 M30 Vector Equations of Planes classNote video lesson note Geogebra demo p.459 #1, 2, 3, 4, 6, 8a, 9, 10, 11, 12b M29 work period M28 Equations of Lines in R3 classNote video lesson note p.450 #14 Video Solution p.450 #14 Text Only Solution p.449 # 3, 6, 7, 8, 9, 12, 14 M25 Cartesian Equation & Normal Vector video lesson note p.443 # 1, 3cd, 4, 5, 6, 7, 9b, 10acef, 11 M24 Vectors & Parametric Equations of Lines in R2 classNote video lesson note p.433 # 1, 2, 3, 4, 5, 6, 7, 9b, 10 Unit 7 - Lines & Planes M22 Test - Applications of Vectors M18 Review - Applications of Vectors p.418 # 1cd, 2f, 3, 4, 6, 7, 8b,  9, 10, 11, 14, 15, 16, 18bcd, 20c, 22, 23, 24, 25, 26, 29, 30, 31b, 32 M17 mock test M16 M15 Applications of Dot & Cross Product classNote video lesson note Handout - Application Problems p.414 # 1, 3, 5, 6, 8, 10 + handout (optional) M14 Cross Product classNote video lesson note p.407 # 1, 2, 3, 4abc, 5, 7, 9a, 13p.415 # 5b, 7 M11 Scalar & Vector Projections Direction Angles & Direction Cosines classNote video lesson note p.398 # 1, 6, 7b, 8, 11, 13, 15, 17 M10 Dot Product of Algebraic Vectors classNote video lesson note p.385 # 2, 4, 6bd, 7b, 9b, 10a, 11, 12, 14+ Read Example 5 on page 384 M09 Dot Product of Geometric Vectors classNote video lesson note p.377 #2, 5, 6abe, 7acd, 9, 11, 12 M08 Velocity Vectors classNote video lesson note p.369 # 3, 4, 6, 7, 9, 10, 11, 14 M04 Vectors as Forces classNote video lesson video lesson - extra exercises videoNote p.362 # 3, 5, 6, 8, 10, 11, 12, 16, 17 Unit 6: Applications of Vectors M07 Test - Introduction to Vectors M02 Review - Vectors p.344 - 347 # 1, 2a, 3, 5, 6a, 7, 8,                             11, 12b, 15ab,                             16c(also find direction),                            19a, 21, 23 M01 Linear Combinations & Spanning Sets classNote old note video lesson p.340 # 6, 7b, 8, 10, 11, 13, 14 A30 Algebraic Vectors in R3 classNote videoLesson old note p.332 # 1, 2, 3, 4, 5ac, 6bd,, 8, 10, 11, 12, 14, 15 A26 Algebraic Vectors in R2 classNote videoLesson old note p.325 # 3, 4, 5b, 6ac, 7c, 8c, 10, 11, 12, 13a A25 Vectors in R2 and R3 classNoteR2 classNoteR3+homework videoLesson (R2) videoLesson (R3) old note Visualize Vectors in R3 3D graph paper: lines dots p. 316 # 1, 4, 5, 6, 7ab, 8, 12a, 15 A24 Properties of Vectors classNote no video old note p.306 # 5, 7, 8, 10, 11 p.308 # 2, 6, 11, 12, 15 A23 Scaling Vectors (stretch, compress, reflect) classNote videoLesson videoNote p.299 # 1, 5, 7, 12, 14, 15, 19, 21* A20 Addition & Subtraction of Vectors video lesson old note p.290 # 1 to 5, 7, 9, 11, 13, 15 A17 Introduction to Vectors classNote video lesson old note p.279 # 4 to ­ 7, 9, 11 Unit 5 - Vectors A19 Test - Derivatives of Exponential & Trigonometric Functions A18 A16 Review handout - extra questions p.263 # 1-9, 11-16, 23 A13 Derivatives of Tangent classNote video lesson videoNote p.259 # 1-8, 10*, 11* A12 Derivatives of Sine and Cosine classNote Geogebra Applet - Derivative of Sine p.256 #1, 2, 3, 5, 7, 9, 11, 12 A11 A10 Optimization of Exponential Functions classNote videoLesson videoNote Read examples 1 & 2, p.241-244p. 245 # 3, 4, 5, 6, 8, 9, 12bc A09 work period Quiz - Derivatives of Exponential Functions A06 Derivatives of Logarithmic Functions classNote video lesson videoNote p.575 # 3 ­to 13 (Omit 5c, 9bc) p.578 # 1 to ­ 5, 7, 9, 11 A05 Derivatives of General Exponential Functions classNote video lesson videoNote p.240 # 1, 2, 4, 5, 6, 9 A04 Derivatives of Natural Exponential Function classNote video lesson videoNote p. 232 # 1, 2aef, 3, 4bc, 5a, 7, 8, 12, 13 Unit 4 - Exponential, Logarithmic and Trigonometric Functions M28 Review - Applications & Optimization p.156-159  #3, 5, 6, 7ab, 8, 9, 14, 15, 17, 19 to 24, 26d M27 work period / review M26 Optimization of Economics & Science video lesson note p.152 # 5, 6, 8, 10, 12, 15, 17* M23 work period quiz WS: Extra Optimization Problems M22 Optimization of Time video lesson note Quiz - Optimization of Dimensions WS # 11-15 M21 Optimization of Distance video lesson note more examples p.147 # 15, 16, 20 Handout # 1­5, 8, 9 M20 Optimization video lesson note p.145 # 1, 3-­12 M19 Extreme Values video lesson note p.117 # 7, 8 (interval notation, optional) p.136 # 2ab, 3d, 4ab, 6, 7, 8, 9 M09 Higher-Order Derivatives video lesson note review "Need to Know" on p.126 p.127 #4, 5, 6ac, 8, 9, 10, 11, 12, 13b, 16 M08 Test: Curve Sketching M07 M06 Review - Curve Sketching Example: Graph with Cusp p. 216 # 1, 2, 3, 4, 5, 8, 10, 19, 20 M05 Algorithm for Curve Sketching note WS - Determining Graphs from Equations recommended questions: Part A # 1-6, Part B # 1, 2, 3, 6 Geogebra WS: Compare Graphs & Derivatives Geogebra WS: Construct Derivative Graph M02 M01 Concavity & Points of Inflection note video lesson video tutorial - supplemental supplemental note p.205 # 2, 3, 5, 10, 11, 12, 13a F28 Oblique Asymptotes Quiz - Inc/Dec, Critical Points, HA/VA note video lesson p.193 # 3d, 4d, 5d, 6c, 7, 9d, 10, 14 F27 Vertical & Horizontal Asymptotes note video lesson p.193 # (3, 4, 5)(ignore d) p.193 # 6, 9abc, 11, 12, 13, 15* F26 Critical Points & First Derivatives note video lesson p.178 # 3, 4ab, 5bcd, 7cdef F23 Intervals of Increase & Decrease note video lesson p.169 # 1ab, 3, 4abcd (algebraically), 8, 9, 10, 11 Unit 2 - Curve Sketching F22 Test - Limits & Derivatives Real-world Application of Calculus (not at all, but interesting... to me) F20 Review p.56 # 2ab (use 1st principles), 9, 10,11, 17,18abf   p.110 # 3, 4, 8, 10a, 11a, 16, 17, 19, 21, 24 F15 Combining Rules for Derivatives homework # 10, 14, 17, 19 Worksheet (see video for 2 solutions) [VT - SS - Combination of Rules] complete worksheet F14 Chain Rule note video lesson [VT - SS - Chain Rule] p.105 # 4, 5, 11, 15,16, try 8 F13 Quotient Rule note video lesson p. 97 # 4, 5cd, 6, 7, 8, 9, 13, 17* F12 Product Rule note video lesson p. 90 #1abcde, 5abc, 6, 7, 9, 12 F09 Power Rule note video lesson [VT - SS - Power Rule] summarize table on p.81 into your notes read proofs on p.76, p.77 p.82 # 2, 3def, 4cef, 8ab, 9bf, 14, 15, 16 F08 Continuity of Functions note video lesson [VT Series - KA - Continuity] p.52 # 4ace, 5bcdf, 7, 8, 12, 14, 15 F07 Properties of Limits note video lesson [VT - KA - Properties of Limits] [VT - KA - Example - Taking a Limit] [VT - KA - Example - Cubic Limit & Factoring] p.45 # 4, 7bce, 8cef, 9, 10ad F06 Defining Limits note video lesson handout: Defining the Limit p.38 # 5, 6, 7, 10def, 11bc, 12a F05 Rates of Change note video lesson [VT - Pascal's Triangle & Binomial Expansion] p.30 # 7, 9 (use Ex.1 as template) (basics) p.30 # 10, 11, 12, 13, 16, 21* F02 Slope of a Tangent Line note video lesson p.19 # 4, 5 (basics) p.20 # 8c, 9ac, 10b, 11ef, 16, 20, 25* F01 Rationalizing note video lesson p.9 # 1, 2 (basics) p.9 # 3bdf, 4, 6ef, 7 Unit 1 - Limits & Derivatives

1
 Intervals of Increase & Decrease video lesson p.169 # 1ab, 3, 4abcd (algebraically), 8, 9, 10, 11

p.433 # 1, 2, 3, 4, 5, 6, 7, 9b, 10