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MCV4U 2017-2018 Semester 2

Page history last edited by Steve Sweeney 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, 8
p.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, 13
p.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

video lesson videoNote

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.241-244
p. 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

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