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:
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 | suggested textbook questions | |
J13 |
Distances between Points, Lines, and Planes |
p.540 # 2a, 3a, 5ac, 6b, 8 p.550 # 2a, 3a, 5, 6 |
|
J12 |
Intersection of Three Planes |
p.532 #9, 10, 13 | |
J10 | work period | ||
J09 |
Solving Systems of Equations using Matrices |
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 |
p.516 # 1, 2, 3, 6, 8, 10 |
|
J04 |
Intersection of Lines & Planes |
p.496 # 3, 4, 5, 6, 7, 13 | |
J01 |
Intersection of Lines in R3 |
p.497 # 8, 9, 11, 12 | |
M31 |
Cartesian Equation of a Plane |
p.468 # 1, 2, 3, 4b, 6, 8,10, 11, 13, 14 | |
M30 |
Vector Equations of Planes |
p.459 #1, 2, 3, 4, 6, 8a, 9, 10, 11, 12b |
|
M29 | work period | ||
M28 |
Equations of Lines in R3 |
p.449 # 3, 6, 7, 8, 9, 12, 14 | |
M25 |
Cartesian Equation & Normal Vector |
p.443 # 1, 3cd, 4, 5, 6, 7, 9b, 10acef, 11 |
|
M24 |
Vectors & Parametric Equations of Lines in R2 |
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 |
p.414 # 1, 3, 5, 6, 8, 10 + handout (optional) |
|
M14 |
Cross Product |
p.407 # 1, 2, 3, 4abc, 5, 7, 9a, 13 p.415 # 5b, 7 |
|
M11 |
Scalar & Vector Projections Direction Angles & Direction Cosines |
p.398 # 1, 6, 7b, 8, 11, 13, 15, 17 | |
M10 |
Dot Product of Algebraic Vectors |
p.385 # 2, 4, 6bd, 7b, 9b, 10a, 11, 12, 14 + Read Example 5 on page 384 |
|
M09 |
Dot Product of Geometric Vectors |
p.377 #2, 5, 6abe, 7acd, 9, 11, 12 | |
M08 |
Velocity Vectors |
note |
p.369 # 3, 4, 6, 7, 9, 10, 11, 14 |
M04 |
Vectors as Forces |
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 |
p.340 # 6, 7b, 8, 10, 11, 13, 14 | |
A30 |
Algebraic Vectors in R3 |
p.332 # 1, 2, 3, 4, 5ac, 6bd,, 8, 10, 11, 12, 14, 15 | |
A26 |
Algebraic Vectors in R2 |
p.325 # 3, 4, 5b, 6ac, 7c, 8c, 10, 11, 12, 13a |
|
A25 |
Vectors in R2 and R3 |
p. 316 # 1, 4, 5, 6, 7ab, 8, 12a, 15 | |
A24 |
Properties of Vectors |
no video |
p.306 # 5, 7, 8, 10, 11 p.308 # 2, 6, 11, 12, 15 |
A23 |
Scaling Vectors (stretch, compress, reflect) |
p.299 # 1, 5, 7, 12, 14, 15, 19, 21* |
|
A20 |
Addition & Subtraction of Vectors | p.290 # 1 to 5, 7, 9, 11, 13, 15 | |
A17 |
Introduction to Vectors |
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 |
video lesson videoNote |
p.259 # 1-8, 10*, 11* |
A12 |
Derivatives of Sine and Cosine |
p.256 #1, 2, 3, 5, 7, 9, 11, 12 | |
A11 A10 |
Optimization of Exponential Functions
|
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 |
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 |
video lesson videoNote |
p.240 # 1, 2, 4, 5, 6, 9 |
A04 |
Derivatives of Natural Exponential Function |
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 |
p.152 # 5, 6, 8, 10, 12, 15, 17* | ||
M23 |
work period quiz |
WS: Extra Optimization Problems | |
M22 |
Quiz - Optimization of Dimensions |
WS # 11-15 | |
M21 |
more examples |
p.147 # 15, 16, 20 Handout # 15, 8, 9 |
|
M20 |
p.145 # 1, 3-12 | ||
M19 |
p.117 # 7, 8 (interval notation, optional) p.136 # 2ab, 3d, 4ab, 6, 7, 8, 9 |
||
M09 |
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 |
|
p. 216 # 1, 2, 3, 4, 5, 8, 10, 19, 20 |
M05 |
Algorithm for Curve Sketching |
WS - Determining Graphs from Equations recommended questions: Part A # 1-6, Part B # 1, 2, 3, 6 |
|
M02 M01 |
p.205 # 2, 3, 5, 10, 11, 12, 13a | ||
F28 |
Quiz - Inc/Dec, Critical Points, HA/VA |
|
p.193 # 3d, 4d, 5d, 6c, 7, 9d, 10, 14 |
F27 |
|
p.193 # (3, 4, 5)(ignore d) p.193 # 6, 9abc, 11, 12, 13, 15* |
|
F26 | |
p.178 # 3, 4ab, 5bcd, 7cdef | |
F23 |
|
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 |
Worksheet (see video for 2 solutions) |
complete worksheet | |
F14 |
Chain Rule |
[VT - SS - Chain Rule] |
p.105 # 4, 5, 11, 15,16, try 8 |
F13 |
p. 97 # 4, 5cd, 6, 7, 8, 9, 13, 17* | ||
F12 |
p. 90 #1abcde, 5abc, 6, 7, 9, 12 |
||
F09 |
[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 |
[VT Series - KA - Continuity] |
p.52 # 4ace, 5bcdf, 7, 8, 12, 14, 15 | |
F07 |
[VT - KA - Properties of Limits] |
p.45 # 4, 7bce, 8cef, 9, 10ad | |
F06 |
handout: Defining the Limit |
p.38 # 5, 6, 7, 10def, 11bc, 12a | |
F05 |
[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 |
p.19 # 4, 5 (basics) p.20 # 8c, 9ac, 10b, 11ef, 16, 20, 25* |
||
F01 |
|
p.9 # 1, 2 (basics) p.9 # 3bdf, 4, 6ef, 7 |
|
Unit 1 - Limits & Derivatives |