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MCV4U 2017-2018 Semester 2
Page history
last edited
by Steve Sweeney 5 years, 9 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:
- Functions, Grade 11, University Preparation
- 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
MCV4U 2017-2018 Semester 2
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